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DESIGN STUDY FOR A HIGH RELIABILITYFIVE-YEAR SPACECRAFT TAPE TRANSPORT

Final ReportIITRI Project No. E6179Contract No. NAS5-21556

Goddard Space Flight CenterGreenbelt, Maryland

Prepared by

G.S.L. BennDr. R.L Eshleman

IIT Research Institute10 West 35th StreetChicago, Illinois 60616

November 1971

C

lIT RESEARCH INSTITUTE

N O T I C E

THIS DOCUMENT HAS BEEN REPRODUCED FROM THE

BEST COPY FURNISHED US BY THE SPONSORING

AGENCY. ALTHOUGH IT IS RECOGNIZED THAT CER-

TAIN PORTIONS ARE ILLEGIBLE, IT IS BEING RE-

LEASED IN THE INTEREST OF MAKING AVAILABLE

AS MUCH INFORMATION AS POSSIBLE.

:CrECDiNG PAGE BLANK NOT FIL ME

FOREWORD

This is the Final Report on IIT Research InstituteProject No. E6179 entitled, "Design Study for a HighReliability Five-Year Spacecraft Tape Recorder." Thework was performed for the National Aeronautics and SpaceAdministration, Goddard Space Flight Center, under ContractNo. NAS5-21556.

The work, completed over a nine month period, was moni-tored by Mr. Carl Powell of GSFC. IITRI personnel contri-buting to the technical content of this report includeDr. R.L. Eshleman, Dr. E.E. Hahn, W.J. Courtney, E. Swider,D.W. Hanify, R.J. Owen and G.S.L. Benn. Special acknowledge-ment is due to T.M. Scopelite, Manager, Mechanical Systemsfor his assistance and direction throughout the program.

Respectfully submitted,

IIT RESEARCH INSTITUTE

G.S.L. BennResearch Engineer

Approved:

.T. JacobiAssistant DirectorElectronics Research


iii .. .....

Preceding page blank

ABSTRACT

The main objective of this design study was the develop-ment of a design for a spacecraft tape transport which in-herently possessed high reliability and was capable of un-attended operation at 100% duty cycle over a period of fiveyears. The initial establishment of a philosophy of approachthat life should predominate and that the design should notbe constrained by imposed specifications, differed from thatnormally followed in the design of a magnetic tape transportfor unattended use in space. This philosophy generated a setof reliability guidelines and program goals that were appliedto a transport configuration study from which a coplanar reelto reel concept with independently motor driven reels and cap-stans was considered to be the most desirable candidate fora high reliability five-year tape transport.

Following the establishment of the overall transport con-cept a detailed study of all of the life limiting constraintsassociated with the transport were carefully analyzed usingmodeling techniques. These design techniques included a res-ponse analysis from which the performance of the transportcould be determined under operating conditions for a varietyof conceptual variations both in a new and aged condition; ananalysis of a double cone guidance technique which yielded anoptimum design for maximum guidance with minimum tape degrada-tion; an analysis of the tape pack design to eliminate spokingcaused by negative tangential stress within the pack; a detailedevaluation of the stress levels experienced by the magnetictape throughout the system; a general review of the bearingand lubrication technology as applied to satellite recordersand hence the recommendation for using standard load carryingantifriction ball bearings coupled with a lubricant replenish-ment system; and finally, a detailed kinetic analysis to deter-mine the change in kinetic properties of the transport duringoperation.

The results of these various analyses were then applied toa conceptual layout of the tape transport, which is functionallydescribed in modular form, and from this, a system performanceanalysis was conducted which indicated that the transport per-formance compared favorably with existing satellite recorders.Finally, a testing technique to assure long life was established.This technique does not rely upon accelerated test procedures orthe unrealistic requirement of life testing for the full term.It does, however, make it possible to establish theusable lifeof the transport with a high level of confidence and hence maybe applied to confirm the design practices developed duringthis design study.


iv

The design of a spacecraft tape transport resulting fromthis study, clearly illustrates that the survivability ofmechanical devices for-unattended operation over a five yearperiod is within the capability of the state of the art.Although the proposed system is similar to those used in groundbased transports, its application to the space environmentis unique. This represents a major redirection of engineeringtechniques for the design of magnetic tape transports, whereall of the design criteria have been selectively directed to-wards maximizing the operational life of the machine.


V

TABLE OF CONTENTS

Page

1. INTRODUCTION . ....... ........................... 1

1.1 Program Objectives . . . . ....................... 1

1.2 Report Organization . ......................... 4

2. TECHNICAL DISCUSSION .............................. 5

2.1 General Philosophy . .......................... 5

2.1.1 Modularization ....................... 9

2.1.2 Analytical Modeling ................. 10

2.2 Configuration Study ......................... 12

2.2.1 Tape Managem ent ...................... 12

2.2.2 Reliability Criteria .................. 14

2.2.2.1 Mechanical Complexity ........ 14

2,2.2.2 Interacting Functions ........ 15

2,2.2e3 Component Selection .......... 15

2.2.2.4 Component Acquisition ...... 16

2.2.2.5 Modularization . .............. 16

2.2°2.6 Tape Handling . ............... 16

2.2.3 Transport Comparison .................. 17

2.3 The Five Year Tape Transport ................. 25

2.3.1 Functional Layout ..................... 25

2.3.1.1 Reel Assembly . ............... 31

2.3.1.2 Idler Assembly .......... 31

2.3.1.3 Capstans Assemblies .......... 32

2.3.1.4 Recording Heads .............. 32


vi

TABLE OF CONTENTS (CONT'D)

Page

2.3.2 Critical Areas ........................ 36

2.3.2.1 Bearings and LubricationSystems ...................... 36

2.3.2.2 Tape Stress .................. 41

2.3e3 System Performance .................... 49

2.3.3,1 General Analysis ............. 50

2.3.3.2 Guidance .. ................... 51

2.3.3.3 Local Dynamic Analysis ...... 55

2.3.3.4 System Natural Frequency ..... 56

2.3.3.5 Response ..................... 64

2.4 Testing Techniques for Five Year Life ..... 73

2.4.1 General ......... .................... 73

2.4.2 Sample Models for Life ................ 74

2.4.3 Engineering Strategy .................. 76

2.4.3.1 Performance Function ...... 77

2.4.3°2 Wear Function ................ 78

2.4.3.3 Life Function... ............ 80

2.4.4 Implementation .. ..................... 81

2.4.4.1 Partial Model ................ 82

2.4.4.2 Full Model....... ........... 82

2.4.4.3 Evaluation ................... 83

3. DESIGN TECHNIQUES AND RESULTS . .................... 87

3.1 Response Analysis ......................... 87

3.1.1 Modeling .......................... 87


vii


Page

3.1.1.1 Reel Model .................. . 92

3.1.1.2 Tape Model ................. 94

3.1.1.3 Capstan Model ................ 95

3.1.1.4 Idler Model .............. 96

3.1.1.5 Head Model ................... 96

3.1.2 Mathematical Solution ................. 97

3.1.2.1 Natural Frequency ........ 97

3.1.2.2 Steady State VibrationResponse................... 102

3.1.2.3 System Response.............. 104

3.1.3 Computation Program Documentation .... 106

3.2 Double Cone Guide Roller Transient Analysis.. 135

3.2.1 Modeling ................. .......... 138

3.2.2 Analysis .............................. 139

3.2.3 Computational Procedure ............... 148

3.2.3.1 Computer Program Use ........ 149

3.3 Tape Pack Design Analysis ................ 161

3.3.1 Modeling . ... ................... 161

3.3.2 Computation Procedure................. 161

3.4 Tape Stress Over a Double Cone Guide Roller.. 169

3.4.1 Modeling............................ 169

3.4.2 Computational Procedure ............... 175

3.5 Bearings and Lubrication ..................... 185

3.5.1 Bearing Contact Stresses ........... 187


viii


Page

3.5.1.1 General ........; ........... 187

3.5.1.2 Combined Axial and RadialLoads ..................... 188

3.5.1.3 Preload Effects ......... 189

3.5.1.4 Shaft Misalignment ......... 192

3.5.2 Bearing Torque ..................... 192

3.5.3 Bearing Life Prediction ............. 194

3.5.4 Materials ................. 197

3.5.5 Lubrication and Environment....... 199

3.6 Kinetic Analysis ............................ 205

3.6.1 Modeling ........................... 205

3.6.1.1 Rotational Velocities ....... 205

3.6.1.2 Reel Inertia ................ 205

3.6.1.3 Torque Determination ........ 208

3.6.1.4 Angular Momentum . ........... 208

3.6.1.5 Rotational Energy ........... 209

3.6.1.6 Rotational Power .,.......... 209

3.6.2 Computational Procedure .............. 209

3.7 Alternative Speed Reducer .... . ............. 217

REFERENCES .................................. 221


ix

LIST OF FIGURES

Figure Page

1 Basic Reel Configuration Concepts ............. 22

2 Coplanar Tape Transport Concept ................ 27

3 Flow Diagram of Applied Design Techniques ...... 29

4 Bearing Lubrication System ... .............. 39

5 Dynamic Tape Tension Profile ................... 42

6 Allowable Tape Pack Stress Distribution ....... 44

7 Actual Tape Pack Stress Distribution ........... 45

8 Tape Stress Passing Over Capstans (Oxide Out).. 46

9 Tape Stress Passing Over Capstans (Oxide In)... 47

10 Tape Stress Passing Over Double Coned Idler .... 48

11 Kinetic Properties During Operation ............ 52

12 Double Coned Idler............................. 54

13 Schematic Diagram of Five Year Transport ....... 58

14 Model of Any Tape Transport Component.......... 60

15 High Frequency Model ........................... 62

16 Comparison of Natural Frequencies andExcitation Frequencies ........................ 66

17 Relationship Between Eccentricity andChange in Tape Length .......................... 67

18 Evaluatory Positions of Signal and DataIntegrity .. .... ................................ 75

19 Signal and Data Integrity. ...................... 77

20 Performance Function Curve .................... 78

21 Wear Function Curve ........................... 78

22 Life Function Curve........................... 81


X

LIST OF FIGURES (CONT'D)

Figure Page

23 Partial Model ................................. 82

24 Full Model .........................0.......... 83

25 Modified Performance Function ................. 84

26 Modified Life Function ....................... 84

27 Model Elements ... 0...... ............ 0... 0 88

28 Simulation Model .............................. 89

29 Separately Excited Shunt Motor................. 90

30 Reel Model ................................... 92

31 Tape Model................................... 94

32 Capstan Model ..................................00000000 95

33 Head Model .... ...... ...........0........... 96

34 Natural Frequency Model .,................ .... 99

35 Solution of System Natural Frequencies ......... 101

36 Computer Program Flow Diagram ................. 109

37 TTDSM Computer Program ...... ............ .· .... 111

38 TTDSM Input Data Cards ........................ 119

39 Natural Frequency Output Data.......... .......... 127

40 Vibration Response Output Data (Amplitudeand Phase)..,0............................... 133

41 Vibration Response Output Data (rms Velocities) 134

42 Double Cone Guide Roller System............... 135

43 Tape Torsional Restraint....................... 138

44 Roller Geometry ............................ 139

45 Beam Model of Tape ... ,..,.. ........... 143


xi

LIST OF FIGURES (CONT'D)

Figure Page

46 Double Cone Transient Analysis ComputerFlow Diagram .............. ............. 153

47 Double Cone Transient Analysis ComputerProgram .......... .......................... 155

48 Double Cone Transient Analysis Input Data Card. 156

49 Double Cone Transient Analysis Input/OutputData.. .00. 0000......o.......................... 157

50 Double Cone Roller Guidance Performance........ 1 5 9

51 Tape Pack Analysis Computer Flow Diagram ...... 164

52 Tape Pack Analysis Computer Program ............ 1 6 5

53 Minimum Tape Pack Stress at Various WindingTensions ................0.................... 167

54 Tape Roller System ........................... 170

55 Equivalent Cross Sections .................... 173

56 Tape Stresses Over Double Cone RollerInput Data .......0..0...........0............ 170 ,

57 Computer Program for Stress Analysis........... 176

58 Principal Stresses in Tape Passing Over aDouble Cone Idler...........................oo 179

59 Curvature Values for Standard and InstrumentBearings ................... .................... 186

60 Contact Stress R4B Size Bearings ............... 191

61 Schematic of Lubricant Replenishment Concept... 202

62 Kinetic Analysis Input Data................... 210

63 Kinetic Analysis Computer Program ............. 211

64 Kinetic Analysis Output Data................... 213

65 Alternate Motor Speed Reducer ................. 219


xii

LIST OF TABLES

Table Page

1 Concept Comparison ........................ 18

2 Transport Configuration Design Evaluation ..... 23

3 Bearings for Long Life Transport .............. 38

4 Torque and Mechanical Power Requirements ..... 53

5 Motor Sizes ................................... 53

6 Dynamic Description of Five Year Transport.... 59

7 System Natural Frequencies .................... 61

8 High System Natural Frequencies ........... 63

9 Tape Vibration Response at Head ............... 69

10 Computed Values of Jitter.................... 72

11 Guide Roller Transient Analysis Nomenclature.. 136

12 Tape Pack Design Analysis Nomenclature ....... 162

13 Kinetic Analysis Nomenclature ................. 206


xiii

DESIGN STUDY FOR A HIGH RELIABILITY FIVE-YEAR

SPACECRAFT TAPE TRANSPORT

1. INTRODUCTION

1.1 Program Objectives

The purpose of a tape recorder is to store and retrieve

data without significantly degrading the information content.

Although tape recorders may be used to either expand or com-

press data in time, the principal reason for their widespread

use in satellite systems is the large storage capacity pro-

vided. In comparison with other techniques for achieving

large memories, tape recorders have proven to be efficient on

a size, weight, and cost basis. In order to provide access

to the data stored, it is necessary for the tape transport to

move tape past the read and/or write head and to provide

intimate contact between the tape and heads. Historically,

satellite transports have experienced difficulty in fulfilling

these requirements.

Traditionally, space transport systems have been designed

to satisfy the requirements of the signal processing system

as well as being contained by severe weight, volume, and

power limitations. The broad goal of this study was to pro-

vide the maximum engineering latitude in the development of

a design which would lead to a transport with a five year

mission life. Clearly, to achieve this goal, it was necessary

to adopt a general approach of reducing mechanical complexity

and operational constraints and, where possible, to shift the

demand of high critical performance from the mechanical sub-

system to the electronics subsystem.


1

The objective of this program was, therefore, to develop

a design for a tape transport which inherently possessed high

reliability and was capable of unattended operation over a

five-year period at a data storage capacity commensurate with

future mission requirements. In order to fulfill this require-

ment it was necessary at the commencement of this study to

specify a philosophy of approach and establish certain goals,

which would lead to a logical derivation of a design which

possessed the required reliability as prescribed in the Goddard

Space Flight Center specification No. S-731-P-105. These

goals included:

· The identification of a transport configurationin which all considerations were made on thebasis of long life.

* The identification of a set of specificationsthat were compatible with satellite operation,but were not life limiting and, therefore,were not self defeating. This implied identi-fication of life limiting constraints.

· The identification of a course of actionwhich would maximize life and, if the needbe, a series of alternatives.

In order to achieve these goals of this design study, it was

necessary to formulate a set of guidelines. These guidelines

together with the engineering strategy involved in the ful-

fillment of the program objectives are outlined in more detail

in a later section.

The tape transport configuration selected during this pro-

gram is discussed in greater detail in Section 2 of this report.

It is, however, necessary to establish at this point that al-

though the selected configuration has been chosen on the basis

of careful engineering judgement, the choice of configuration

is only a small but important part of the prime objective. Of


2

equal significance, and yet not so obvious, are such factors

as the choice, installation, and lubrication of the bearings;

the minimization of stress levels in the magnetic tape; the

concept and advantages of modularization techniques; overall

fabrication methods; the relative size and position of the

various transport elements; and the selection of critical

subelements. Also of importance is the understanding that

the term'five year life'used throughout this report is meant

to represent continuous operation at 100% duty cycle. An

arbitrary value of 10,000 tape passes per year has been assigned

which is typical of the earth orbital requirements. The major

significance is that the long life requirement of the transport

may be defined as the ability to record and reproduce data

successfully for 50,000 full tape passes.

This study program has resulted in a tape transport design

where all considerations of its design were made on the basis

of maximizing life. It will be seen that the transport con-

figuration is not in itself unique, however, all criteria lead-

ing to its formulation have been arrived at by maximizing all

of the analytical techniques currently available and insuring

that the imposed reliability guidelines were adhered to through-

out the program. This represents a major redirection of

engineering techniques for the design of magnetic tape trans-

ports, where all of the design criteria have been selectively

directed towards maximizing the operational life of the machine.


3

1.2 Report Organization

The technical discussion in Section 2 of this report is

divided into four parts. The first describes the general philo-

sophy and method of approach that was used throughout theDesign Study. This section also describes the major goals of

the program and outlines a set of guidelines that were esta-blished in order to successfully achieve these goals. This is

followed by a definition of the proposed modularization tech-

nique and a description of the analytical modeling of the

mechanical system. The second part outlines the various methods

of approach that were undertaken in the prior selection of thetransport configuration, various trade off studies are explained,

and reasons for the final choice of configuration are stated.

The third part describes in detail the high reliability five-

year tape transport that resulted from this Design Study. The

functional layout is described, followed by a description of

the major critical areas of bearings and tape stresses through-

out the system. This is followed by a description of the over-

all system performance and a proposed testing technique for

five-year life.

Section 3 of this report, entitled Design Techniques

and Results, contains the indepth analytical work that was

undertaken in a variety of subject areas. Included in this

section are the formulation of the mathematical models derived

during the program, the computer programs used, and the analy-

tical results that were obtained and later applied to the over-

all design study.


4

2. TECHNICAL DISCUSSION

2.1 General Philosophy

In order to achieve the main objective of this design

study an overall philosophy was established together with a

set of program goals which differed from those normally fol-

lowed in the design of a magnetic tape transport for unattended

use in space.

In the past, satellite receivers have by necessity been

designed to conform to a set of stringent specifications.

These specifications not only established performance criteria

but contained fundamental specification values for power,

weight, and volume. Such values were obviously necessary in

terms of payload and limited available power, but it implied

that the system mechanics were slave to unusually tight limita-

tions. Many such recorders were produced and it is a tribute

to engineering ingenuity that these transports fulfilled these

stringent specifications. Recently, however, greater emphasis

has been placed on extending the operational life of such

systems and it is here that failures have occurred. It is not

unreasonable to conclude that the heavy burden placed on the

mechanical system in achieving the unusual specifications

resulted in the life limitations that have been experienced.

Mechanical failures have been observed, the weakest link

generally failing first such as the magnetic tape, belts,

bearings, etc. Certain failures are not always catastrophic

such as an increase in tape flutter or deterioration in guid-

ance, but even these can be related to failures in the mechan-

ical system.

It was for this reason that the underlying philosophy

of approach established during this study was that the trans-

port design should be directed towards maximizing life without


5

the constraints of imposed specifications. Obviously, for

operation in space, tape recorders must conform to an envelope

of general specifications but these should not be imposed.

Implied in this is that the design study would identify a set

of specifications that were compatible with life but were not

life limiting. This would, therefore, allow the mechanical

system to operate in a regime where it can exist for five years.

Operational regime implies dimensional as well as performance

areas in which the mechanics can operate in a realm of reason-

able capability.

Coupled with the identification of a set of specifications

was the need to identify a transport configuration where all

consideration was made on the basis of long life. In the past,

the need to conform to specific geometric form factors and

limited power availability have generated a family of satellite

recorders which include novel configurations, such as the

negator spring coaxial reel type. Long operating life was

not, however, a primary consideration and although much effort

has subsequently been expended in extending the operational

life of these and other transport designs so that now one year

operation is possible and two probable, life beyond two years

is considered unproven and probably unobtainable.

It was mandatory, therefore, in considering a high relia-

bility five-year transport design to identify a transport

configuration which was in no way influenced by an factor other

than those related to maximizing life. Realistically, trade

offs between life and even the broad envelope of specifications

were bound to occur and infact did.

The philosophy that life shall predominate over all other

requirements led to a set of program goals necessary to achieve

the prime objective. These goals were:


6

* The identification of a set of specificationswithin a broad envelope that were compatiblewith satellite operation, and were not lifelimiting.

* The identification of a transport configurationin which all considerations were made on thebasis of long life.

* The identification of life limiting aspectsof the transport as a whole.

* The identification of a design procedureusing analytical modeling tomaximize life.

In order to achieve these goals and objectives it was

necessary to establish a set of rules or guidelines, the use

of which would allow trade off decision-criteria to be consis-

tent throughout the program. These Machine System Reliability

Guidelines were:

* To recognize the limitations of applyingtraditional reliability analysis to satellitetape recorders.

* To maximize all of the analytical capabil-ities relevent to the overall system.

* Ensure adaptability to modularization.

* To adhere to minimum mechanical complexity,but to temper this with minimum interactivemechanical functions.

* To select a system and components wellwithin historically proven performanceregimes.

* To acquire components from the largestproduction population possible, thereforeattempting to obtain not a unique samplebut a statistically average sample.

* To recognize the need to establish real-istic life testing techniques throughoutthe system.


7

Many of these guidelines are self explanatory, but one or

two require a brief explanation. There is a drawback to

applying traditional reliability analysis to satellite tape

recorders, this is primarily one of limited knowledge. There

is only a small amount of failure rate information available

and little or no knowledge on the prognosis relative to life

of a running system. A failure in orbit may be due to a

multiplicity of causes but the exact cause usually remains

unknown or uncertain. Clearly the construction of models for

failure when information is so sparce is difficult. The lack

of relevant information with regards to failure can be attri-

buted to two main reasons. First, the difficulty and therefore

the expense of testing and evaluating mechanical systems is

prohibitive. This is coupled with the inexactitude in mechan-

ical systems to successfully duplicate accelerated life tests

in real time. Second and more important is that the accuracy

of correlating test data with prediction is questionable. The

reliability of mechanical components is related not only to

fabrication of the element but to the installation of that

element into the system. The success of a mechanical element

such as a belt or bearing in achieving many mission lifetimes

on a life test model appears to have little relationship to

the failure of an identical element installed in another sys-

tem, and therefore the ability to generalize test data is very

difficult. What is needed to overcome this severe limitation

in mechanical systems for long term unattended use is a radi-

cally new approach both in the analytical design stage and in

the subsequent life testing, so that a mechanical element can

be selected on the basis of its own behavior rather than on

the premise that an identical element behaved well in life

tests. To realize this approach requires modularization of

the transport.


8

2.1.1 Modularization

Modularization was the key design strategy selected to

overcome the insufficiency of failure information connected

with products of extremely limited number such as satellite

tape recorders.

Modularization in this context implies unitizing a

functional subsystem. Storage of the tape is one example of

a function; its related subsystem is not the reel alone, it

is the reel, the bearings, the bearing supports, and the drive

system. All of these are designed to form a module which can

then be inserted as a unit into the principal tape transport.

The advantages to such a system are many but the prime

advantage is associated with a new approach to pre-flight

testing to ensure long life.. Modularization of a transport,

to be effective,requires fabrication of several modules of the

same function. Let us say, for example, that six or eight

reel assemblies are fabricated. Each one is then subjected as

a subsystem to a burn in period of 10% of the total operational

life required, in this case six months. Burn in periods are

used in electronics but not well established in mechanical

systems. This is the way that long life mechanisms should

be evaluated to eliminate short term failures. During this

burn in period all the modules are continually evaluated so

that a running signature of performance is established for each

over a five to six month period. At the end of this multi-

month evaluation period, one or two modules are then selected

on the basis of performance, i.e., drag, torque, acoustic

signature, etc. In this way there is some evidence that a

module will continue without a major change or serious degrad-

ation which would indicate that an early failure is likely

to occur.

The set of modules selected would then be assembled into

the transport as a whole and qualification testing would begin.


9

While this transport is being qualified as a complete mechan-

ical system, the remainder of the modularized subsystems would

continue to be tested as individual units. In this way, at

the end of the qualification period all modules would still

have an equal life evaluation time and any component degrada-

tion may be observed. If component failure occurred during

qualification in the assembled transport, 'then only the module

responsible for the failure need be replaced by an equivalent

module that is still performing satisfactorily.

2.1.2 Analytical Modeling

To overcome the severe limitations of a mechanical system

for long term unattended use, emphasis was placed on analytical

modeling of mechanical systems. The analytical model of the

tape transport is an integral portion of the design approach.

The model allows the maximization of the conceptual design by

variation of model parameters. In this way a design can be

obtained that requires minimum hardware development.

The design procedure using the analytical model begins

with the selection of a concept. This concept was selected

on the basis of minimizing the number of critical elements

in the system. The analytical model of this concept is used

to select dimensions, materials, and components based on long

life and performance. The stresses in the various components

are compared to their strengths, the performance of the system

is,with typical error sources,compared to that of normal

transports. In addition, the degraded (with respect to wear)

transport performance is compared to that of the new trans-

port. In this way the performance of the transport after a

finite time interval can be assessed.

During the study, as the mechanical system was function-

ally described, each of the main subsystems were analytically

designed to maximize the systems mission life reliability.


10

In this context, reliability is meant to encompass:

· Structural integrity in withstanding theshock, vibration, and thermal environment.

* The maintenance of system performancewithin acceptable bounds, e.g., the tapemotion irregularities such as time base errorand skew must not exceed a specified limitdue to the effects of operational aging.

* The design against catastrophic fatiguefailure of elements such as belts and bearings.

Relative to the reliability analyses, the first step in-

volved is defining the function of each component in the tape

transport system, parameter limits for satisfactory operation,

and functional relationships and interaction with other compon-

ents. The second step consisted of an analysis of all possible

failure and degradation modes which would be applicable to

individual system components or combinations of components,

and an evaluation of design and application factors which could

contribute to specific failure modes. Complete analysis of

failure modes require a quantative, or at least a qualitative,

evaluation of likelihood of occurrence. The information neces-

sary to conduct such an analysis came from engineering design

and stress analysis, published reliability handbook data, com-

ponent and equipment manufacturer data, and specific although

limited information on failures in present tape transport

systems. Further failure mode evaluation was obtained by means

of criticality analysis, where probability of each failure was

combined with some measure of its effect on system operation

to rank each possible failure according to a criticality index.

Comparison of various subsystems in terms of reliability

characteristics was made on the basis of a number of possible

failure modes for each system, comparison of effects on per-

formance, and a comparison of failure criticalities of each

element. This evaluation also gave an indication of points

where redesign, derating, improved quality control and

lIT RESEARCH -INSTITUTE

11

inspection would be most effective in improving reliability.

For portions of the tape transport system where varying amounts

of failure rate data were available, evaluations and comparisons

were made on the basis of subsystem reliability analyses based

on such data, utilizing standard reliability modeling, and

prediction techniques.

In evaluating the long term operating performance, it was

essential to simulate the design in dynamic terms and then to

study the influence of error source generators, such as bearings

and eccentricity in film guiding surfaces, as well as predict

the implications of aging effects due to wear and lubricant

viscosity variations. To this end, use was made of fundamental

analytical techniques , developed at IITRI for the computer

simulation of a transport system as affected by error and sys-

tem parameter variations. This analysis, was effective in

portraying how certain performance parameters degrade with

operational life; and more particularly focused the design on

those areas to which system performance was most sensitive.

Thus an approach selected to meet the prime requirement,

a five-year life expectancy, emerged in a program of design

of modules with adequate margins against all stresses to mini-

mize all possible failure modes.

2.2 Configuration Study

2.2.1 Tape Management

Inevitably, the initial design of a high reliability tape

transport system focused upon the resolution of three main

design areas; namely, tape storage, tape tensioning, and tape

metering. For higher storage capacities, the technique success-

ful to date has been the reel-to-reel system. Other approaches,

such as cartridges and bin storage, produce exceptionally large

and random tension pulsations; and in general violate the axiom

of stringent control of tape tension and tape velocity through-

out the systems operational history. The objective in designingIIT RESEARCH INSTITUTE

12

a reel system is to provide sufficient structural integrity

to the reel itself and its support so that precise motion can

be achieved. This point cannot be over-emphasized, since the

main dynamic errors of any transport result from poor reeling

and inadequate tensioning.

Two basic reel positions have been traditionally utilized

in previous satellite transports; coaxial and coplanar. The

choice between these configurations, strongly influences the

final tape path. The principal differences between these two

main configurations are the change in tape elevation (as

required in coaxial systems), and the complexity of the tape

tensioning and guiding system. Variations on these two basic

types together with several other configurations were the

basis of the initial configuration study.

The singular objective of the configuration study was to

identify a transport whose potential for achieving an unatten-

ded five-year mission life was established through historical

performance, and where possible, through engineering analytics.

In this study, the central trade-off decision focused on

performance reliability; that is, when given a choice between

several functionally acceptable alternatives, the selection

was made on the basis of the component, module, or system which

had the greatest chance of achieving a five-year life. At the

onset of this effort, it was recognized that to identify a

system whose life would be unquestionably the maximum among

all possible choices could not be absolutely ascertained either

theoretically or experimentally. But, by utilizing the relia-

bility criteria, the system selected at least represented the

best first approximation based on good engineering judgements

and practices.

To initiate this task, several basic transport configu-

rations were described in the terms of the following:


13

* Reel configuration, e.g., co-planar orcoaxial;

· reel drive technique, e.g., electric motors,spring motor, or peripheral belt;

* tape path trajectory;

· tape metering technique

Further, these configurations were selected from those systems

that had been, or were in the process of being, used in satel-

lite applications. The basic transports considered were:

1. Co-Planar, Reel-to-Reel. Tape meteringachieved by servo controlled reel speeds.

2. Co-Planar, Reel-to-Reel, with capstan meteringsystems, i.e., single capstan, dual capstan,a differential capstan. Further, reel drivesand tape pack tensioning achieved by springmotors or individual reel motors.

3. Co-Axial Reel-to-Reel, with capstan and reeldrives similar to (2).

4. Co-Planar Reel-to-Reel with tape metering andreel drive achieved with a peripheral belt.

5. Newell Drive, with a single capstan drivingboth tape and reels.

To delineate a high reliability five-year design from

either one or a combination of the above concepts, the follow-

ing elements of "designed-in" mechanical reliability were

established as a means for evaluating the intrinsic reliability

of a particular configuration.

2.2.2 Reliability Criteria

2.2. 2.1 Minimum Mechanical Complexity

For the function required, e.g., for multiple speeds, it

is essential to transform speed changing functions to motor

and electric controls and away from belt drive-complex mechan-

ical transmissions.


14

2.2.2.2 Minimum Interacting Mechanical Functions

This criteria emphasizes the need for assuring against

serially adding functions, that is, each component is inde-

pendent from an adjacent failure probability. For example:

* Using a capstan to drive the tape;

* the tape to drive the reel;

* the reels to drive a tachometer;

* the tachometer to drive a motor controller; and

* the motor controller to control the motor speed.

Failure anywhere in this serial loop results in failure of the

total system. Further, there is no possibility for filtering

or impeding incipient failures or their impact in the system.

Therefore, minimum interacting mechanical functions were

deemed crucial to successfully achieving a sound uncomplicated

mechanical design.

2.2.2.3 Select and Design System Components WellWithin Historically Proven Applicationsand Performance Regimes

This factor focuses upon specific elements within a trans-

port to assure the proper application of mechanical components

from the points of view of function and life. In this study,

this implied that use could not be made of a mechanical system

that had neither performance experience nor manufacturing

quality control history behind it. It was, therefore, essen-

tial that the mechanical system have some historical evidence

of successful operation in the multi-year area. When components

are not chosen in this regime then the effective prediction of

life is difficult and there is no operational justification

or experimental evidence whatsoever to substantiate long life.


15

2.2.2.4 Component Acquisition from LargestPopulation Possible

It is essential that a specific configuration does not

require exotic or limited available components, since these

elements have little or no performance history from which to

judge life. Selection from a large population insures that

not a unique sample by a statistically average sample is

obtained that has a record of proven performance.

2.2.2.5 Adaptability to Modularization

To bring a five-year life design through the development

and system qualification phases, it was essential to the devel-

opment scheme to separately test and evaluate subsystems such

as capstan modules and reel-to-reel drive subassemblies. This

approach became particularly cogent when it was recognized

that component run in and evaluation might require 10% of the

mission life. Hence, it was anticipated that the testing and

qualification cycle would entail the simultaneous testing of

several identical models of all transport subsystems. Subse-

quent testing of the total system could progress into the

qualification phase. When a subsystem fails in this critical

period, it is impossible, because of time limitations, to

recycle the whole transport. Thus, the modularization strategy

permits the failed module to be removed and replaced by a

qualified substitute, thereby permitting the transport quali=

fication to progress without a major setback or delay.

2.2.2.6 Minimum Tape Handling Stress

For a transport that is expected to produce at least

50,000 tape passes, a critical limitation of the system is in

the tape handling area. To minimize tape oriented problems,

it is important to reduce to an absolute minimum, the mechani-

cally induced stresses. There are two main areas in which

high stress levels occur in the magnetic tape system; namely,


16

the tape pack itself and that associated with the tape handling

and guidance. This is an extremely critical area which has

been somewhat neglected throughout the industry in the past.

Therefore, all of the configurations were carefully

examined during this study and compared for their ability to

handle the tape in a manner which minimizes the tape stresses

thoughout the system. There is little doubt that when the

magnetic tape experiences severe stress levels while being

handled, premature degradation often follows. To meet the

prime objective of a five-year operational life high stress

levels had to be eliminated throughout the tape pack system.

2.2.3 Transport Comparisons

The first step in the choice of a configuration for

a high reliability five-year tape transport was a general

comparison of the five basic reel configuration concepts

shown in Figure 1. This entailed listing all of the advan-

tages and disadvantages of each system and examining the var-

ious implications with regard to the reliability criteria and

guidelines that had been established. As an example, a short

form concept comparison is shown in Table 1, indicating the

major advantages and disadvantages of the five concepts.

The next step was a comparison of alternative reel drive

systems. Reel drives for the five basic concepts may be cate-

gorized into four basic types:

Type 1 Spring Devices

Type 2 Servo Controlled Motors

Type 3 Newell System

Type 4 Peripheral Belt


17

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1. SpringDevice

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Motors

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Use of this essential component division then allowed

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below.

REEL DRIVE COMPARISON

a. Spring Comparison

Advantages

1. Low power require-ment.

Disadvantages

1. Poor history of negatorspring.

2. Mechanical complexity.

3. Gear or linkage pertubations.

4. Uneven tension profile.

5. Intricate assembly.


20

2 Motors

b. Two Variable Speed Motors

Advantages

1. Constructionalsimplicity.

2. Ease of modulari-zation.

3. Electro/mechanicalemphasis.

4. Large population.

Disadvantages

1. Increased power.

2. Increased weight.

3. Increased volume.

4. Small population withoutbrushes.

5. Electronic control required.

6. Tension sensing problems.

7. Tape speed ratio require highratio for direct drive motor.

8. Alignment of reels to motorshaft.

c. P-Belt with Constant Speed Motor

Advantages

1. Low power require-ment.

2. Reel simplicity.

Disadvantages

1. P-belt must be guided.

2. Uneven tension profile.

3. High stress in p-belt.

4. Many bearings.

5. Frictional coupling.

6. Small population (motors).

7. Difficult to inspect belt.

8. Belt installation problems.

9. Difficult to control tension.

Obviously it was difficult to include every detail of the

complex evaluation in this report, a great deal of which relied

upon experience and engineering judgement, but the overall

results are summarized in Table 2 where the transport configu-

rations (1) through (5) are evaluated with respect to the long

life mechanical characteristics previously described. This

evaluation is reported in the form of numerical ratings 0

through 10 with ten indicating best compliance with the goals

of the program. Numerical values are included to simplify


21

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interpretation of comparative rank. The table illustrates the

design team's collective judgement on the relative importance of

various characteristics, such as reel configuration and drive

techniques and their influence on the total system's reliability

rating. No attempt was made to weight the relative significance

between the elements of the design criteria. In designing a

system to survive five times longer than previous transport

life, a relaxation in any of the design goals could lead to

failure. If a weighting factor were to be applied, clearly

tape handling would represent the critical factor for long

mission periods.

By including additional evaluation points, such as geometric

form and power consumption, Table 2 demonstrates the reason

spring driven co-axial reel systems have been selected for

missions where limited volume, low power, and moderate tape

life were required. For extended mission durations, mechanical

component reliability and tape integrity must be maintained.

In this application, the system with the greatest "designed-in"

reliability should be selected. Therefore, system No. 2a, which

consists of individually servo motor controlled, co-planar reels

and capstans was selected as the candidate transport configura-

tion.

In summary, five basic transport configurations were

identified and described in terms of their reel configuration,

reel drive technique, tape path trajectory, and tape metering

technique. By establishing a set of reliability criteria to-

gether with the overall program guidelines, the five con-

cepts were then compared for their "intrinsic reliability".

This comparison resulted in a choice of concept No. 2a, that

is, a reel-to-reel coplanar configuration with independently

motor driven reels and capstans as the most desirable candidate

for a high reliability five-year tape transport.


24

2.3 Five Year Tape Transport

2.3.1 Functional Layout

Following the choice of the most desirable concept

as a reel-to-reel coplanar configuration with independently

motor driven reels and capstans, the next stage in the design

study was a conceptual layout of such a configuration. Consid-

eration was given to obtain maximum reliability for required

performance, and as such, all assemblies were designed for

mechanical simplicity, minimum constructional error and for

ease of fabrication and assembly. In order to satisfy the

guideline of minimum mechanical complexity, and also to reduce

inherent error and failure sources, the minimum number of

rotating elements were chosen that were compatible with meeting

the performance specifications of guidance and tape speed

irregularities. The IITRI coplanar tape transport concept is

shown in Figure 2 and contains the following modules:

* reels for tape storage

* ': double cone idlers for tape guidance

· capstans for filtering and tape metering

· head for recording and reproduction

Although the functional layout of the transport as con-

ceived is readily adaptable to a variety of tape widths and

tape lengths. Specific dimensions were assumed in order to

allow the system performance and response analysis to be under-

taken. The tape dimensions used for illustration throughout

for this report are therefore:

Width 0.5 inches

Thickness 0.001 inches

Length 1200 feet

These dimensions, although not directly aimed at a specific


25

mission requirement, are adequate enough to be applicable to a

generalized earth orbiting mission. Although pertinent, the

head/tape interface and the magnetic tape were not directly

studied during this effort. Use was made of the recent Head/

Tape Interface Study2 conducted for Goddard Space Flight Center,

and the Magnetic Tape for Five-Year Life3 is currently being

studied for Goddard in a separate program.

It can be seen that this conceptual layout requires mini-

mum space consistent with high reliability and acceptable per-

formance. The exact size and arrangement of the subsystems

within the tape deck were established by applying the results

obtained from the various detailed designed studies in Section 3

of this report. These included both system and individual

component analyses as well as stress analyses on the tape and

bearings to show reliability of critical components. This

technique is shown diagrammatically in Figure 3.

The initial step in the engineering development of this

five-year transport was the selection of a tape handling system

that has the following characteristics:

e Satisfies basic transport requirementsof tape storage, tracking, and metering

* Excludes the main failure modes commonto many satellite recorders, e.g., gearsbelts, and clutches

* Meets or exceeds the head/tape interfaceguidelines established under NASA/GSFCContract No. NAS5-11622

* Meets or exceeds the tape handlingguidelines of Contract No. NAS5-11622

* Has provisions in the tape loop toisolate and filter from the head area,errors resulting from wear out andother aging effects that can be antici-pated after 50,000 hours of operation

· Exhibits high probability of survivalagainst catastrophic component failure


26

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DESIGN TECHNIQUES

Figure 3

FLOW DIAGRAM OF APPLIED DESIGN TECHNIQUES

29

Figure 2 illustrates the basic transport configuration

that satisifies the above goals. This system has coplanar

motor driven reels that straddle the tape handling area.

Tracking is accomplished by the incorporation of two double

coned idlers. Also, the head is isolated from the reels and

idlers by a set of individually driven dual capstans. To sat-

isfy the tape handling and head/tape interface guidelines,

independently driven reels are employed to assure tape pack

integrity and to effect constant tape tensions in the regime

of 8 ounces per inch width. Double coned idlers are utilized

to minimize tracking errors resulting from the reels and from

within the tape loop. The technique of individually driven

dual capstans provides a method for precisely metering the tape

past the head as well as providing the means for fine tuning

the head/tape contact pressure. Further, the dual capstans

straddling the head are the primary means of filtering from

the head regime, dynamics disturbances emanating from the

reel and idler assemblies. These disturbances are anticipated

to be originally the result of bearing torque pulsations and

component machining variations; but in the latter stages of

life, major errors will result from aging and wear out.

From the computer simulation models (Section 3.3) the reel-

tape system was designed to assure tape pack integrity, i.e.,

that no clinching occurs. Also to effect the precision tracking

required at the head, the IITRI tracking model was utilized

to size the free tape lengths and idler geometry. The tape

path geometry and tension profile was selected so that tape

stresses will be under 3500 psi throughout the transport.

As a means for further insuring against catastrophic

component failure, all bearings are lubricated with both a

grease (Andoc C) and periodically, a liquid lubricant, that

will replenish the bearing lubricant supply. Specific details

on lubricant techniques and bearing selection are discussed

in depth in Section 3.5. It is sufficient to note that all


30

mechanical elements have been derated so that the total mechanical

failure rate will not diminish the transport reliability to less

that 99.9% for the mission life.

2.3.1.1 Reel Assembly

Storage of the magnetic tape is provided by the reel

assembly shown in Figure 2. The reel assembly is an independent

module that includes the reel, a reel support structure and

bearings, lubricant seals and re-supply lines, and a D-C drive

motor. This compact configuration is obtained by directly

attaching the D-C motor armature to the reel. The D-C motor

field housing is an integral part of the module's support

housing. Substantial bearings of the Precision Class 7 type

are preloaded to a 1/2 to 1 lb level by using the calibrated

preload spring technique. Preloadings is employed to assure

effective bearing performance as well as to minimize the run-out

effects resulting from internal bearing clearances. Reel shaft

run-out errors are directly translated into gross tape tracking

errors. To minimize the reel generated tracking errors and

hence to negate the necessity for severe tracking idler configu-

rations, pre-loading and precision mechanical assembly procedures

are employed to control reel hub run-out to less than + .001

inch.

2.3.1.2 Idler Assembly

Tape guidance (control of vertical tracking error) is

performed by the double cone idler assembly modified by crown-

ing the apex shown in Figure 2. The double cone roller is

mounted on an inner roller to provide vertical adjustment to

the dynamic center of the roller. A locking ring maintains

the relative position of the two rollers. A support post to

the tape deck provides bearing mounting facility, direct

bearing lubrication and bearing preload support. Two anti-

friction ball bearings preload by a bolt and spring washer are

used to mount the idler. The integral mounting post assure

a tape path parallel to the deck.IIT RESEARCH INSTITUTE

31

2.3.1.3 Capstan Assemblies

Capstan assemblies are provided for low and high speed

tape metering. Both assemblies utilize direct drive DC motors

to control the tension of the tape in the vicinity of the head

and to mechanically filter tape propagated disturbances. The

DC motors induce damping from the electrical field and help

to control tensions through drive or drag (back emf).

The fast capstan is driven directly by a direct driven

DC motor with the motor armature mounted directly on the cap-

stan shaft. This shaft also contains a tachometer mounting

position. The driven shaft is mounted to the structure that

attaches to the tape deck through two ball bearings. In

addition, the motor field is an integral part of this structure

which provides bearing lubrication access.

Alternate means are available for obtaining slow cap-

stan speeds, but these are mechanically complex (Section 3.7).

Mechanical simplicity is achieved with the use of a low

speed DC motor in the fast capstan assembly. The low speed

motor must be governed by a tachometer in a control system

that achieves acceptable slow speed performance. This mode

of operation fulfills one of the objectives of this program,

i.e., the replacement of low reliability mechanical components

with electrical components.

2.3.1.4 Recording Heads

The location of the recording head between the two capstan

assemblies is shown in Figure 2. A single head stack is indi-

cated over that of a multiple head stack arrangement in order

to conform with the guidelines for head selection and operational

constraints2 established under Contract No. NAS5-11622. The

guidelines applicable to the recording head are as follows:


32

* The core and block materials used in the frontface of the head in the contact area shouldfall in the category of "hard" materials,i.e., greater than 100 Rockwell B; brassshould be avoided.

* Voids or gaps between laminations or other dis-continuities on the front face should be lessthan 50 microinches in width.

* There should be no scratch in the directionof tape motion on the contact surface of thehead that is deeper than 12 microinches. Also,there should be no scratches perpendicular tothe direction of tape motion.

· A break-in period of 200 passes is advisable.Following this break-in the head should meetthe surface finish guidelines above. Observa-tion of a deep scratch, indicating repeateddamage by debris in the same area, should because for replacing the tape and relapping thehead.

* The maximum tape tension should be defined bythe tape path and tape pack stress considera-tions.

* The required normal force at the gap line shouldbe defined by maximizing the reproduce outputsignal of the shortest wavelength being repro-duced.

* Tape wrap angle should be minimized.

* The minimum head radius consistent with thepacking density of the information being storedshould be utilized.

· The number of heads should be minimized. Eraseheads should be out of contact when possible.

These guidelines'were established in order to negate the

frictional drag and debris problems that occur at the head

tape interface and hence improve the probability of success-

ful operation of satellite recorder systems operating for a

period of one year or 10,000 tape passes.


33

Many of these guidelines were confirmed in a separate

study4 where a safe operating area for the head tape inter-

face was postulated. This operating area was defined by the

maximumtorque capabilityof the transport, the minimum tension

required for guidance and reproduce signal response, the maxi-

mum tape stress throughout the tape path and the change in the

physical parameters between the head and tape. It is essential

therefore, that when considering a recording head for use over

a period of five years or 50,000 tape passes, that all of these

guidelines by strictly adhered to and that a safe operating

area is defined during the early stages of the transport design.

Another major consideration with regard to the recording

headfor use in a five year transport is that of wear. Wear

is directly related to the quantity of tape passing over head,

which for a five year mission may approach 60 million feet of

tape. Rates of wear of various head materials in general use

are difficult to establish exactly,because of the variety of

conditions that influence the wear rate. However, a typical

rate of wear for hard core materials, such as Alfesil, isin the order of 50 x 10-6 inches for the first million feet

of tape. Although this rate of wear may decrease for each

successive million feet of tape, use of this initial wear

rate allows a maximum expected head wear to be established.

For five year continuous operation where 60 x 106 feet of

tape will pass over the head surface, a maximum expected wear

of 0.003 inches would be anticipated. Such total wear may

not be serious for low packing density systems, however if

high linear packing densities are encountered such a wear

rate may be a high proportion of the available interface depth.

As such, changes in the electrical and performance specifica-

tions of the head must be anticipated and the drive and repro-

duce electronics designed to accomodate such changes. Equally

essential is that any wear experienced on the front face of


34

the recording head in no way interferes with the tracking

requirement of the magnetic tape. Anticlastic curvature of

the tape generally leads to increased wear at the tape edges.

Tracking abnormalities may be avoided by removing the head

material in this region of high wear.

Another form of wear which strongly influences the re-

liability of a recording head is gap smear. Gap smear, or

loss of gap integrity, is caused by the movement of the core

material across the working gap of the head until a condition

is reached where it shorts out the effective gap length re-

sulting in a serious reduction in the head efficiency. In

order to negate this wear phenomena it is essential that the

head chosen for unattended operation for a period of five years

has a core material that is the least susceptable to smearing

(such as the hard materials) and that the gap length specified

for data reproduction be no smaller than 50 microinches.


35

2.3.2 Critical Areas

2.3.2.1 Bearings and Lubrication System

Bearings are one of the principal sources of transport

system failure, either by degradation of performanceor cata-

strophic failure. Therefore, special emphasis has been placed

on long life bearing design with proper lubrication. The

following considerations discussed in detail in Section 3.5,

govern long life bearing design.

* bearing contact stresses

* preload effects

* shaft misalignment

e bearing torque

· bearing life

* materials

* lubrication and environment

These considerations were observed in the selection,

mounting, and preloading of the bearings detailed in Table 3

and used in the long life transport concept. The considerations

of misalignment, ball and retainer materials and lubricant

are discussed in Section 3.5. Recommendations are listed

below.

Shaft Misalignment Less than 0.3 milliradians or

3 x 10 4 inches off center peraxial inch of shaft center.

Ball Material 440C stainless steel (highhumidity)

52100 Steel (low humidity)

Retainer Material Bronze


36

The bearing lubrication system for the five year tape

transport is schematically shown in Figure 4. It consists

of storage reservoirs, dispensers, and lubricant feeder lines

which provide periodic, incremental lubrication of the tape

transport oearings. Periodic lubrication will insure bearing

performance after long period of inactivity and long life.

The reservoir and dispenser are basically constructed the

same way. The large reservoirs pistons maintain a constant

spring load on the oil while the small reservoirs pistons are

pulled back by solenoids and forced forward by springs during

an oiling sequence.

The reservoirs body are made of plastic and are used to

separate the inert gas of the environment from the oil. These

diaphragms are commercially available. Proper fabric and

elastomeric sealant will be selected to be compatible with the

environmental gas and fluids used. This will provide a non-

porous membrane or wall between the two substances.

The feeder lines (stainless steel hypodermic tubing)

insure proper oil delivery. When not in use the solenoid is

de-energized with the small rolling diaphragm keeping the oil

contained in the large reservoir due to the forward position

of the piston with its diaphragm sealing off the intake part

until the oiling sequence.

To oil the bearings, the solenoid is energized and the

piston pulls back allowing the oil from the large reservoir to

fill the small reservoir and loading a spring. At the same

time the upper check valve (see drawings) opens to allow the

oil to flow between the two reservoirs, while the lower valve

closes to prevent sucking the oil back from the feeder lines.

When the solenoid is de-energized the spring pushes the

plunger forward, forcing the oil into the feeder lines and

thereby lubricating the bearings. This time, however, the


37

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upper valve closes to prevent any flow between reservoirs

while the lower valve opens to allow the oil to flow in the

feeder lines. When the small plunger reaches the forward

position the oiling cycle is completed.

2.3.2.2 Tape Stress

The second major long life reliability constraining item

is the tape. Unfortunately, the fatigue data needed to

realistically assess tape life is not available at this time.

In view of this fact, the mechanical components involved in

tape storage, handling, and tensioning were designed to mini-

mize tape degradation. Material constants for presently avail-

able tapes were used in the analysis of the design concept.

Double cone idlers were designed to minimize tape stress

(static considerations) yet achieve acceptable guidance.- This

involves a trade off between guidance and reliability because

increased tape tension and cone angle yields increased guidance

and decreased life. In addition increased tape tension

increases bearing radial loads lowering bearing life. Capstan

roller diameters were selected to minimize tape stress. The

tape packs were designed to enable storage of 1200 feet of

tape without spoking or cinching. Stresses in the tape pack

were found in the design analysis.

Tape tension profiles shown in Figure 5 were selected

to achieve adequate handling and control of the tape. Four

ounces of tension is maintained by the reel motors to achieve

good tape packing without spoking. In addition the reel motors

maintain four ounces around the idlers which insures the

required guidance performance. Five to six ounces of tape

tension are maintained at the head by the capstans to achieve

control and metering during record and reproduce.


41

"0a)0NT

o

Hz

L

n H

a) z

PL4 P4H

-

42

The tape tension profile shown in Figure 5 was used to

design the:

* tape packs to minimize stress and avoid spoking

* capstans to minimize tape stress

· idlers to achieve guidance with minimum tape stress

Tape pack design was based on the analysis reported in

Section 3.3. The computer program in Section 3.3 determines

tape pack stresses for varied hub diameter, hub thickness, hub

material, tape width, tape material, tape length, and tape

tension. A parameter variation was run to obtain the design

data shown in Section 3.3. Tape pack spoking is avoided by

maintaining a positive tangential stress throughout the tape

pack. Figure 6 illustrates allowable and nonallowable tape

pack stress distributions. From the design data shown in

Section 3.3 the following tape pack parameters were selected:

Hub diameter - 4.0 inches

Hub thickness - 0.5 inches

Hub material - Aluminum

Tape tension - Four ounces

Figure 7 shows the stress distribution in the aforementioned

tape pack.

The capstan outside diameters were selected on the basis

of the tape stress induced by six ounces of tension. The

results of Figures 8 and 9 were obtained from a computer

program developed in a recent Head/Tape Interface Study2. Tape

stresses over cylindrical rollers with 1 inch and 1-1/2 inch

diameter were obtained for varied -tape tensions. Since the

oxide faces the capstan in one instance, these results are also

shown on Figure 9 . A 1.25 inch diameter capstan resulted in

the following maximum stresses in the Mylar and oxide materials

of the tape.


43

CircumferentialStress (a)

Tape Pack

AllowableStress

NotAllowableStress

: [I iReelRadius(R)

\-- Comr/ession Region*

*Compression Regionmay lead to localizedtape buckling andtape spoking

Figure 6

ALLOWABLE TAPE PACK STRESS DISTRIBUTIONS

44

Winding Tension = 4.0 oz

Tape Pack

Reel Radius (in)

Figure 7

ACTUAL TAPE PACK STRESS DISTRIBUTION

45

500

' -I

b

4)

U$"-

cd

C,

400

300

200

100

-A A A- Mylar

---C--o- ---- Oxide

1.0 in.dia.

1.25 in.dia.

1.0 in.dia.

0-- ( 1.25 in.dia.

I I I I I I I I I 1 2 3 4 5 6 7 8 9 10

Tape Tension (oz)

Figure 8

TAPE STRESS PASSING OVER CAPSTAN, MYLAR ON CAPSTAN SURFACE

46

20

18

16

14

.,w0u

Co

Cn0)54-

. 4

Ux

12

10

8

6

4

0

0I

I

I

A - ~ A- A Mylar

--------o o-- Oxide

1.0 in.dia.

1.25 in.dia.

1.25 in.dia.

I I I I 1 1,1 0 lin.dia.1 2 3

l I l7 8 9 10

6

Tape Tension (oz)

Figure 9

TAPE STRESS PASSING OVER CAPSTANS, OXIDE FACING CAPSTAN SURFACE

47

20

18

16

.,4

04

!i

.,Q)

14

12

10

8

6

4

2

0

2 4 5

I

I

I

_-

I

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=\ O

30

2° -A-'

[ylar

)xide

Mylar

Oxide

3 °

-I- I , I I III ---J - --- L - - 1 2 - -A - - I -- I - I !

1 2 3 4 5 6 7 8 9 10

Tape Tension (oz)

Figure 10

TAPE STRESS PASSING OVER DOUBLE CONED IDLER

48

8

7

6

5

4

.,

to

r-4

a)M

9

z2

1

n

1

3 -

7

i

I

I

_

_

_

Mylar Oxide

Oxide Facing Capstan 1350 psi 25 psi

Mylar Facing Capstan 1325 225

The double cone idlers induce tape stress due to the cone

angle, diameter, and apex radius. See Section 3.4 for details.

The values of tape tension, 4 oz.; of the cone angle, 2°;

and of the idler major diameter, 1-1/2 in.; were selected to

achieve adequate guidance. The computer program in Section 3.4

was used to calculate stress values shown in Figure 10. The

effect of tape tension on tape stress and for an apex radius

of 1 inch for a cone angle of 2° and 3° is plotted. The

stresses in the tape are 3400 psi in the Mylar, and 568 psi in

the oxide for the selected idler. Therefore, the balance

between tape stress and proper guidance has been achieved.

2.3.3 System Performance

Reliability and long life have been the major concerns

in the design of the five year tape transport. Within the

framework of the highly reliable design, some minimum mechanical

system performance must be achieved. This section is devoted

to the analysis of the transport to determine its performance

as a function of its life. The analysis of the transport con-

sisted of:

· Determination of the transport inertia,power requirements, and momentum

* Examination of the tape guidance for statedperformance and probably error disturbance

* Calculation of transport system naturalfrequencies and comparison of these frequenciesto system excitation frequencies

-Calculation of system response (specificallythe tape at the head) for varied input distur-bances including bearing pertubations, motorcogging and part rotational eccentricities.


49

These analyses are used to show where trade offs could be

made to maintain performance and to determine the effect of

possible component failures on performance. The following

physical quantities provide a measure of the transport perfor-

mance.

Jitter is the time displacement between succes-sive bits of information

Flutter is the (rms) vibration velocity of thetape (low frequency range 0-50 Hz, high frequencyrange - above 50 Hz)

Lateral Tracking Error is the vertical alignmenterror between tape and head due to tracking per-turbations.

2.3.3.1 General Analysis

The gross kinetic properties of the transport were cal-

culated as a function of time using the computer programs

given in Section 3.6. The following transport operational

characteristics were determined.

* Reel inertia as a function of quantity oftape storage.

* Motor torque requirements to meter and storetape. (Friction losses estimated in a sepa-rate calculation).

* Reel angular momentum.

e Rotational kinetic energy.

e Power.

The results of the computer calculations of the kinetic

properties for the given transport using a tape speed of 32

ips are shown below:

· Power (in-lb/sec) 0.5 x 10- 3

· Torque (in-lb) 0.53 x 104

* Momentum (in-lb-sec) 0.884 x 10- 1


50

* Energy (in-lb)

· Inertia (in-lb-sec2 ) 0.82 x 10-2

It is of interest to note in Figure 11 that these proper-

ties remain relatively constant during the operation of the

transport. For more detail of these results, see Section 3.6.

The additional torque and power required due to friction

and tensioning is given in Table 4.

The total mechanical power requirements for the mechanical

operation of the transport is 3.5 watts. The torque available

is compared to the calculated required torque in Table 5.

This table shows that adequate motor torque is available to

operate all transport components.

2.3.3.2 Guidance

Tape transport lateral error is introduced by errors in

reel and capstan runout due to machining and assembly tolerances.

These errors can never be completely eliminated but they can

be minimized. The function of the guidance element (double

cone roller) is to attenuate these errors and to minimize them

at the head. Good guidance depends on the inlet tape length

(to the idler), the tape elastic properties, the tape geometry,

the double cone idler geometry, and tape tension. The idlers

were designed through the use of the computer program given

in Section 3.2. The parameters noted above were varied to

obtain a design that would give the required guidance for anti-

cipated input errors at the reels. Figure 12 shows the double

cone idler with the appropriate dimensions. Error attenuation

must be achieved with a minimum of 4 ounces of tape tension.

The minimum inlet tape length to the idlers is 3 inches and

standard 1 mil 1/2 inch magnetic tape was used.


51

0.476

Rotational Power (Left Reel)

Torque Potential (Left Reel)

Angular Momentum (Left Reel)Angular Momentum (Left Reel)

__ --- dRotational Energy (LefP_-A----

A .- A

t Reel)

Moment of Inertia (Left Reel)

I I I I i II100 200 300 400

Time (sec)

Figure 11

KINETIC PROPERTIES DURING OPERATION

52

--I l

,n X-

.- I

5

4

3 L

5.4 1-

,aL - 5.2O

*H Xv 5.0

4.8

8

6

lIU ^-

tW Io

Xx1_/

0.H

A -.

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,aXx- '*H ._~

41

3

8

n IO

X

6_-

4

. ..0 _A2 __ j

0 500I I I I I I ill I I i I

Table 4

TORQUE AND MECHANICAL POWER REQUIREMENTS OF FIVE YEARTAPE TRANSPORT DUE TO FRICTION AND TENSIONING AT 32 IPS

Component/Purpose

Reel/Packing

Reel/Bearings

Capstan/Tensioning

Capstan/Bearings

Idler/Bearings

Head/Drag

Torque (in-oz)Load (oz)

10 in-oz

36 x 10-3 in-oz

8 oz

22 x 10-3 in-oz

22 x 10 -3 in-oz

1 oz

Other

Milliwatts

.900

6.5

1792

11.2

13.4

224

500

Total for Transport - 3.5 watts

Table 5

MOTOR SIZES

MotorPowerWatts

TorqueAvailable Required

60 in-oz

15 in-oz

10 in-oz

2.5 in-oz

53

Reel

Capstan

1.66

1.73

-I -

C1l H

w

;

O1- 0

54

The important dimensionless handling parameters given in

Section 3.2 are:

P atL = 182DI

Q = L E- = 0.52 (2)

where

a = 2° = cone angle

t = .001 in = tape thickness

L = 3 in = head/tape length

D = 1.5 in = major roller diameter

E = 8 x 105 lb/in2 tape modulus of elasticity

I = tw3 = 1.04 x 10 5 in4 tape moment of inertia

T = 4 oz = tape tension

The dimensionless handling parameters were obtained from

the tracking model developed in Section 3.2. The tracking

model uses the geometry of a rigid double-coned roller with a

length of flexible tape leading into the roller to determine

how the double cone stabilizes the tape lateral motion. Using

the displacement response of the tape with the rigid tracking

of the roller, the effectiveness of the roller can be assessed.

Guidance analysis of these handling parameters P and Q

yields an idler output response of .0005 inches for an input

error of .005 inches. Hence, the double cone idler provides

a 90% attenuation of the input error.

2.3.3.3 Local Dynamic Analysis

Tape flutter and jitter at the head are caused by mechan-

ical and electrical system errors such as bearing torque


55

perturbations, component eccentricities, and motor cogging.

Flutter and jitter magnitudes are determined by the simulation

model described in Section 3.1 for the newly constructed recor-

der and for recorders degraded through usage. In addition to

response calculation, the local dynamic analysis includes system

natural frequency analysis. The process of moving the tape from

reel to reel produces the tape excitation. Therefore, flutter

and jitter are tape velocity sensitive.

Figure 13 shows the schematic diagram of the five year

tape transport. The physical description of the transport is

given in Table 6 . The general element used to simulate each

component of the simulation model is shown in Figure 14.

Inertia, damping to ground, damping across the tape, tape elas-

ticity, and general excitation are allowed for each element.

The transport dynamic behavior is then simulated by a model

composed of as many of these elements as are required to achieve

the desired simulation. The detail of the response obtained

from the simulation model increases with the number of compon-

ents utilized; however, the computer time required also

increases.

2.3.3.4 System Natural Frequency

System natural frequencies were calculated and compared

to mechanical excitation frequencies to avoid difficulties in

performance because the coincidence of the two generates reso-

nance. Resonance can deteriorate system performance and/or

cause mechanical failures. The system natural frequencies

were calculated using the dynamic simulation model described

in Section 3.1. Table 7 shows the first five system natural

frequencies of the tape transport concept.- These results

show little change in natural frequency when the tape distri-

bution on the reels is varied, the higher natural frequencies

are associated with the tape mass. These frequencies can be

calculated from the model shown in Figure 15. Since the


56

ratio of the mass of the tape to the mass of its constraining

elements is less than .01, the longitudinal vibration of a

fixed bar simulates the higher vibration modes of the tape.

The mass of a four inch length of tape is:

Wt

mt= g (3)

where Wt = tape weight

g = gravitational constant

.05 x .001 x .5 x 4t 386

mt= 2.59 x 10 7 lb sec2

in

The equivalent mass of the idler supporting the tape is

M J .853 x 10-

4 lb sec2 in (4)eq r- (.75)2 in2

where J = idler inertia

r = idler radius

M = 1.54 x 10-4

eq

The ratio of the tape mass to its end connected mass

2.59 x 10-7

M= 4 = 0016 (5)1.54 x 10

is an order of magnitude less than the allowable mass ratio

established through sensitivity analysis of mass-spring5

systems

IiT RESEARCH INSTITUTE

57

a)r4a)a

.l rl o

u (

asa

oW 'n

0 )

a)(1)

: 0 -

0 0

010bD

Clul91 u

coz

4 '1

O

oala

(1

Q

58

d)a)

0ptH4-I

H,-1

COa)

H.I 0HU

Table 6

DYNAMIC DESCRIPTION OF FIVE YEARHIGH RELIABILITY TAPE TRANSPORT

Damping TapeComponent Radius Inertia Constant Length

(in) (in lb sec2) (in lb sec) (in)

Reel 2.53 0.81 x 10 2 0.18 x 10-3 3.375

Idler 0.75 0.853 x 10- 4 0.33 x 104 4.0

Capstan 0.625 0.91 x 10- 4 0.27 x 10

-4 1.6

Head 1.0* 0.2 x 10 6 0.002 1.6

Capstan 0.625 0.277 x 10 - 3 0.27 x 10 - 4 4.0

Idler 0.75 0.853 x 10O 4 0.33 x 10 4 3.375

Reel 2.53 0.81 x 102 0.18 x 10 3

*Equivalent Radius

59

Where

k

Cg

k = tape stiffness

Cr = tape damping

J = reel, idler, or capstan inertia

r = reel, idler, or capstan radius

Cg = external damping

Ts,Tc,w = external disturbance description

Figure 14

MODEL OF ANY TAPE TRANSPORT COMPONENT

60

Table 7

FIVE YEAR TAPE TRANSPORT SYSTEM NATURAL FREQUENCIES (Hz)

(NO TAPE MASS INCLUDED)

% Tape on Reel No. 1Natural

Frequencies 100 75 50

1 25.18 25.83 26.02

2 50.05 52.25 52.3

3 100.77 100.65 100.58

4 177.44 178.96 179.90

5 186.16 182.5 -

61

1 -

o-IOt

Un

uw Z5

XHX

rI r-0

62

.,lIc) !!)i-It ox0oII

I-)

The formula for the natural frequencies of a fixed rod

is:

fn = E (6)

where fn = the nth natural frequency (Hz)

n = 1, 2, 3, ............

= unsupported tape length

E = tape modulus of elasticity

p = tape density

Using a tape modulus of 8 x 105 lb/in2 and a specific

weight of .05 lb/in3, the following formula for natural fre-

quencies is obtained.

f = 19600 n (7)

This formula is written in this form because of changing

tape lengths (at the reels) during operation and differing

tape lengths between components. Table 8 shows the range of

natural frequencies obtained from the five year transport con-

cept.

Table 8

HIGH SYSTEM NATURAL FREQUENCIES

Tape Length Natural Frequency (Hz)

4 4900n

3.125 6250n

2-7/8 to 4 4900n to 6800n

It is obvious that short tape spans raise the natural fre-

quencies. From an operational point of view, it is important

to minimize the number of natural frequencies. Therefore,


63

equal unchanging tape lengths between components is the optimum

design solution because only one set of natural frequencies (fn)

need be avoided by proper selection of the system excitations

(tape velocity). Changing lengths (i.e., between the reels

and idlers) cause changing frequencies and the liklihood of

excitation. Different spacing of components yields a set of

natural frequencies for each different spacing.

Figure 16 shows a plot of the natural frequencies and

excitation frequencies (above 10 Hz) for the five year tape

transport concept.

2.3.3.5 Response

The response calculation gives a quantitative analysis of

the performance of the tape transport which is preferable to

the qualitative measure of the natural frequency calculation.

Using the computer program discussed in Section 3.1, the trans-

port tape response for inherent system excitations was com-

puted. Three types of excitations were applied to the dynamic

model of the transport.

® Component once-per-revolution bearing torqueperturbation excitations

* Component once-per-revolution eccentricities

* Motor twice-per-revolution perturbationexcitations

* motor 2000-per-revolution perturbationtachometer excitations

The torque excitations are directly entered in the simu-

lation program while the displacement (eccentricities) must be

related to torque through the tape constants. Figure 17 is a

free body diagram showing the relationship between eccentricity,

£, and related tape length, A6. The change in torque as a

result of tape lengths A and B due to the eccentricity are:


64

AA (TA + EA 6) (R + AR) - TA R (8)

AB (T+ EA ) (R - AR) - T R (9)a6B (- AR) -T B

with

At = ATA - ATB , and (10)

combining equations and dropping second order terms, AT becomes

A = EAA6 R ( ) + (TA + TB) AR (11)6A B B )

A6 = f(e,e) = £ sin wt

AR = f(£,e) = - sin ct

therefore

At = EA £ R (6- 6B)sin owt + (TA + TB) j sin wt (12)

The torque perturbation for the following idler configu-

ration with an .0001 eccentricity becomes0.25 x 10-2 in-lb.

E = 8 x 105 lb-in

A = .0005 in2

£ = .0001 in

TA

TB = 4 oz

R = 0.75 in

6A = 3.0 in

6B = 4. 0 in


65

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ua)

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z=

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zwC-I olw14

O

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C( U

34-

Ocu

Up,r-4

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FI~olI

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*Ha

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WC

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(U

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Pcd w

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66

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67

Table 9 shows tape vibration response due to bearing

torque perturbations, component eccentricities, and motor cog-

ging for tape speeds of 1-1/2 and 32 ips. The response is shown

in terms of instantaneous absolute displacement and flutter

(rms velocity). These responses were calculated for a newly

constructed transport.

In order to determine the jitter from the vibration res-

ponse data, the relative tape displacement between bits is

obtained from the following relationship:

n

Jitter = Xi (t + T) - Xi(T) (13)i= 1

where

Xi(t + T) = tape displacement at time = t + T due toi th disturbance

Ir = bit spacing in seconds

Xi (t) = instantaneous tape displacement due toi th disturbance

For a given disturbance, the tape displacement is harmonic

and, therefore

Xi = aisin (cit - 0i ) (14)

where

ai = disturbances amplitude

0i = disturbance phase angle

xi = disturbance frequency

Then the jitter for thei th disturbance is

Ti = a [sin (t+ 'r) - i] - a sin [cWit - 0i] (15)


68

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Expanding the transcendental functions and making small

angle assumptions the jitter is

Zi = ai xi T cos (wit - 0i) (16)

with a maximum value of

Itil max = aiti X (17)

and

V= n

B

B = in/Bit

V = tape speed

ri = disturbing component radius

ni = disturbance order of tape speed

then

a.n.

ITil max ri B (18)

For a conservative answer, the random addition is

bounded by:

Itj max 1 r.B (19)i= 1


71

,

Table 10 shows values of jitter computed from results

of Table 9 for a 3000 bit/in spacing at 1l-1/2 and 32 ips tape

speed. The first column shows results for a newly constructed

recorder while the second column shows the jitter for a recorder

subject to extensive wear. Thus the local dynamic model pro-

vides a measure of the tape recorder performance as a function

of its life.

Table 10

COMPUTED VALUES OF JITTER

Jitter(microinches)

The results of Table 10 for the non-degraded state cor-

relate with the analytical predictions of other investigations6

as well as with published performance ratings of existing

satellite recorders. The degraded performance is a factor

of four increase in the jitter level, but still only represents

a 1% variation in this bit cell spacing. This variation is

clearly acceptable from a data processing standpoint.

.IIT RESEARCH INSTITUTE

72

Degraded(.0005 in Flutter

Tape Speed Time (sec) New Tolerances) (in/sec) (new)

1-1/2 ips .000222 .75 2.9 .0018 in/sec

32 ips .0000104 .45 2.0 .027 in/sec

2.4 Testing Techniques for Five Year Life

2.4.1 General

In attempting to establish the required testing techniquesto assure long life for an unattended period of five years,

two specific problems are encountered. The first relates to

the unrealistic requirement of life testing for the full time

period of five years. Even attempting to life test for asignificant proportion of the total life period is clearly

impractical. The second problem arises from the inability toaccelerate the life test in a way which would allow correlation

between accelerated and real time. Although accelerated life

tests are well documented in certain fields, the applicationof these techniques to rotating mechanisms such as antifriction

ball bearings is not applicable. Life accelerating in thiscase means rotational acceleration, and hence an overall changein the required mode of operation with a corresponding changein all known wear and degradation mechanisms.

The need for establishing a life assurance testing tech-nique is essential in attempting to verify many of the designprocedures developed in this study. As both actual life and

accelerated life testing cannot be directly applied, it has beennecessary to develop a strategy which could be adopted at somelater date to verify the overall design concept. This sectionoutlines such a strategy and indicates how it may be implementedby the combination of a wear model, which relates disturbanceerrors to time; and a performance model, which relates systemperformance to disturbance errors; so that an overall life modelmay be generated so relating the performance of a system totime.

73

2.4.2 Simple Model for Life

Although the prime requisite of long life has been the

major goal of this design study, it is necessary at this point

in time to define this statement in terms of system performance.

End of life should therefore be related to the inability of

the total system to adequately recover data in a form which

would allow meaningful interpretation. End of life may, there-

fore, be defined in relationship to the ability of the machine

to record or reproduce, or the degradation of the bit error

rate of the signal output, or an increase in the time base error

of the system which would influence the recovery of the recorded

data. It is not necessary to absolutely define end of life in

these terms at this time, what is essential, however, is to

acknowledge that a transport that is successfully recording and

reproducing data after 50,000 tape passes (i.e., 10,000 passes

per year, 100% duty cycle) fulfills the prime objective of the

program irrespective of its actual mechanical condition.

The successful recovery of the data, termed data integrity,

is therefore related to end of life

End of Life = f (Data Integrity)

This statement, however, is of little or no value in assessing

the condition of the transport with regards to time. Data

integrity is effectively a digital condition, that is, there

are only two possible levels. The data is either recoverable

(e.g., a one level) or it is not (e.g., a zero level). There

is not a condition between these two levels which has an iden-

tifiable value that can be used to interpret the condition of

the overall transport. The reason for this is obviously assoc-

iated with the data processing electronics such as squaring and

buffering circuits, which are used to manipulate and mold the

reproduced output signal into the required form for data

collection.

74

In order to assess the condition of the transport and

hence interpret the degradation of life, an analog condition

as opposed to a digital condition is required. Such an

analog condition is available at a point in the reproduce

electronics prior to any form of signal processing. The

recovery of a signal at this point is termed signal integrity

and its analog nature is meant to represent a gradual change

with respect to time. The position of observing signal inte-

grity and data integrity and their respective relationship

with time is diagrammatically shown in Figure 18.

Signal Integrity Data Integrity

S.I. < D.I.

Time TimeSignal Integrity Data Integrity

d{ * Signal |

Processing

Tape

Figure 18

EVALUATORY POSITIONS OF SIGNAL AND DATA INTEGRITY

The measurement of signal integrity by observing a variety

of reproduce parameters such as flutter, time displacement

error, wavelength response, signal to noise level, etc., allows

the performance of the transport to be monitored and hence

its short term degradation to be assessed even though the

reduced performance level of signal integrity in no way influ-

ences the data integrity measured after suitable signal

processing.

Signal integrity, therefore, relates to a change in

75

overall performance of the machine and hence to a change

in life, as life is the relationship between performance and

time. This may be represented as:

A Life = f(Signal Integrity)

Although end of life is related to the data integrity, the

change in life is not directly related,

A Life # f(Data Integrity)

It is for this reason that use should be made of the

signal integrity as opposed to the data integrity in any test-

ing technique to predict or confirm the life of a transport

system. It is interesting to note that the signal integrity

of a system can be easily correlated to both the head/tape

interface as well as to tape motion control and hence is a

parameter that can be continually monitored and related to

other aspects of the transport design.

2.4.3 Engineering Strategy

We have already shown that the end of life of a transport

system may be related to the data integrity and that a change

in life is observed only by evaluating the change in signal

integrity of the system prior to any processing electronics.

These two relationships may be superimposed as shown inFigure 19. With the ability to predict the rate of change

of signal integrity (h-) and knowing the level below which

compensation is not possible, then it is feasible to determine

the point at which data integrity is lost and hence end of

life. However, the rate of change of signal integrity is

not itself constant and is more probably exponentionally

related to time. Therefore, it is essential to define a

76

Data Integrity

e' I~ ~ ~ %J', Signal Integrity

0 4 Level Below which Compensationa) - 5 - ~is not Possible

Time

End of LifeFigure 19

SIGNAL AND DATA INTEGRITY

strategy which will allow the relationship between signal

integrity (e.g., performance) and time to be predicted.

Such a strategy requires the establishment of two speci-

fic relationships, namely, the change in the systems perform-

ance against induced system errors and the change in the

errors of the system with time. The former will be called the

performance function and the latter the wear function of the

system. A combination of these two functions allows a pre-

dictable relation to be established between performance and

time, that is, a life function.

2.4.3.1 Performance Function

This relates to the transports performance to a change

in errors of the system and is illustrated in Figure 20.This relationship simply states that as the magnitude of the

errors in the system increase, a corresponding decrease in

performance can be expected. It is possible to theoretically

predict this relationship using the dynamic model of the trans-

port developed during this design study, however, as important

is the fact that this relationship can be evaluated in the

laboratory. This is achieved by artificially inducing errors

77

into the system and measuring their influence on the overall

signal integrity of the system.

a)

0

p44a)

[System Errors]

Figure 20

PERFORMANCE FUNCTION CURVE

2.4.3.2 Wear Function

This function relates the rate of change of system errors

with time, and is illustrated in Figure 21.

Time

Figure 21

WEAR FUNCTION CURVE

78

It is effectively a wear life diagram which shows that

the rate of wear within the system, once past a point where

catastrophic failure may occur, will follow a well defined

path which is dependent upon the operating conditions of the

system. Wear life diagrams for certain mechanisms are well

documented7 . They show that after an initial run in period

a constant wear rate is maintained until a point where accel-erated wear takes over owing to some external influence

such as lubricant breakdown in the case of antifriction

ball bearings.

As this wear function is related to real time it is

impossible to construct a precise curve without long term

life testing. However, there are several criteria which

afford us the ability to predict such a curve with a reason-

able degree of confidence. First the concept of modularization

coupled with module burn in periods, allows the initial vari-

ation owing to the run in period to be overcome, hence

establishing the magnitude of the linear portion of the wear

function curve. Second, the overall philosophy of design

which has been implement throughout this design study together

with the removal and or control of all critical elements

negates the probability of sudden catastrophic failure occur-

ring during the early life period of the transport. What

remains is the need to predict the length of the linear portion

of the curve and the establishment of the point in time when

accelerated wear occurs. Again, the overall design approach

is predicated upon insuring that accelerated wear will not

take place during the proposed lifetime. It is for this reason

that, throughout the design study, emphasis has been placed

on minimizing stresses and loads throughout the system especi-

ally those that influence life as in the magnetic tape androtational components. The need for including a continual

79

feed lubrication system is one example where the added com-plexity required to implement pulsed lubrication throughoutlife was considered to be acceptable in order to insure thatthe bearing system did not experience accelerated wear owingto lack of adequate lubrication.

Given these design criteria together with a wealth ofdocumented material in the literature for specific components;it is possible to construct, with a-certain high value ofconfidence, a wear function curve for the overall transport.Such a curve combined with an evaluated version of the per-formance function allows the life function curve to be predic-ted.

2.4.3.3 Life Function

This function relates the rate of change of the trans-ports performance with time. As described earlier, theperformance value is meant to represent the signal integrityof the system prior to any electronic compensation, and henceis a parameter than can be evaluated.

The combination of the performance function whichrelates measured system performance with induced errors andthe wear function which indicates the rate of change of actualerrors with time allows the life function curve to be con-structed

nlep X Me = t AP (20)

Such a curve may be represented as shown in Figure 22. Thislife function is still a predicted relationship but its valueis of paramount importance for two specific reasons. First,it allows the above parameters to be more accurately definedwith a certain degree of realism and as important, it forms afirm base which, with additional inputs from evaluatory pro-cedures, allows the function to be continually modified torepresent a more exacting relationship of performance with time.

80

S I \

v

p

o

I 1% - - p cPt

hS~~~~~~~ l : ~Timemv,~~~ ~t s t(max)

Figure 22

LIFE FUNCTION CURVE

where the following parameters may be defined:

P0 = performance envelope at t = 0

Ps = specified performance without compensation

Psc = specified performance with compensation

t(max) = maximum life span of data integrity

ts

= specified life span for design

This modification is explained in greater detail in the fol-

lowing section on implementation and evaluation.

2.4.4 Implementation

It is possible to implement the engineering test strat-

egy by using either partial or full models of the proposed

transport. Both are described briefly in this section,

however use of a full model has certain advantages and is

recommended for a more precise evaluation of the total system.

81

2.4.4.1 Partial Model

A partial model is meant to represent the division of

the overall transport into subelements which may or may not

have been modularized. These subelements are then constructed

and tested individually as opposed to collectively, to assess

their contribution to the overall performance of the machine

in terms of signal integrity. As an example the effect of

errors in a reel assembly module may be examined theoretically

and then experimentally verified by inducing errors into a

fabricated reel assembly and measuring the change in response

at the recording head (Figure 23).

Induced Errors lei

MI(t) Reel

TapeK

1

Measured-esponse AP

Figure 23

PARTIAL MODEL

More detailed explanation of these models can be found in

Section 3.1.1 of this report.

2.4.4.2 Full Model

A full model is meant to represent a complete mechanical

version of the transport design. This approach to evaluation

82

and hence determination of the life function curve is recom-

mended as it combines all elements of the transport in a com-

posite form (Figure 24).

M1 (t)

Reel

(___ T ape

Guide

Head

AC apstan

Figure 24

FULL MODEL

2.4.4.3 Evaluation

The evaluation of a full model of the transport allows

the predicted life function curve to be continuously up-dated

as the evaluation period progresses. The original life

function curve combines the predicted wear function with a

performance function curve generated from the mathematical

model of the tape transport. This performance curve is

then adjusted according to the results obtained from actually

inducing errors into the system and measuring the effect onthe signal integrity of the system (Figure 25). This

measured curve is then used to adjust the original life

function curve as shown in Figure 26 to obtain a first degree

modification.

83

Theoretical

MeasuredN

Errors

Figure 25

MODIFIED PERFORMANCE FUNCTION

Modification

2ndModification

- P

Figure 26

MODIFIED LIFE FUNCTION CURVE

84

a,0q4

w

'he %

Po

sc

This modified life function curve allows more represen-

tative values of the maximum life span and probable specified

life span to be determined. The next adjustment results from

updatingthe wear function curve. Such updating can only occur

with time, however, an accurate determination of the slope of

the linear portion of the curve should be possible over a time

period of a few months and, hence, a second and more accurate

modification of the life function curve will result.

Using these procedures it will be possible to establish,

with a high level of confidence, the usable life of the trans-

port and, hence, confirm the design practices and manufacturing

procedures developed during this design study.

85

T)') VNI PAGElR IINATK NGfT rTIlA

3. DESIGN TECHNIQUES AND RESULTS

3.1 Response Analysis

This task was concerned with the performance of the tape

transport concept under operating conditions. Wow and flutter

characteristics of the transport were determined for system con-

ceptual variations. Forces, torques, and tensions obtained from

this task were utilized in the critical component analysis to

assess the reliability.

The design information on the dynamic performance of the

mechanical system components were obtained from a digital simula-

tion model. The model used in this task consists of an arrange-

ment of lumped springs, mass and dashpots that can be used tosimulate the physical behavior (response) of the transport to

internal and external disturbances. Mathematical relationships

are written between the lumped elements that are arranged to com-

pose the transport. This modular techynique allows a concept

change by rearranging lumped elements representing the model.The mathematical relationships (equations of motion) that simulate

the models dynamic behavior are programmed for solution on the

digital computer. The effect of design parameter changes on the:

performance and reliability can be determined from the numerical

solution of these equations of motion.

3.1.1 Modeling

The modeling process is very important in the simulation of

the total transport system because the mathematical solution will

represent the physical behavior to the degree that the model

duplicates the physical features of the transport. The important

mechanical characteristics of this system are its mass, elasticity

and damping. Lumped elements (non-elastic masses, non-massive


87 Preceding page blank 7

springs and non-elastic massive dashpots are used to represent

this system. The mathematical descriptions of these lumped

elements are shown in Figure 27. In addition, mathematical

models are made of the internal and external disturbances such

as friction and drag, ball bearing excitation and motor speed

fluctions.

(a) Mass Element

(a) Mass Element

k

,~X·

d2xk(y - x) = F

k(y - x) = Fs

(21)

(22)

(b) Spring Element

c

Po 3 dx = Fdcd(t dt F ddxHE (23)

(c) Damping Element

Figure 27

MODEL ELEMENTS


88

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vrX

a)a)P4a)-i0 0,.-I

,-

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'0

000

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H

C,,QHHr-4a)

a) 30P4

4-.U

89

4u

-1-

o"'S

AC

4J

cn I

2 X

X 4

The transport concept shown in Figure 13 is now modeled

for dynamic analysis. Figure 28 shows a conceptual model of

the transport with each subsystem component identified with

its appropriate lumped parameter. The subsystems modeled are:

* Reels

· Capstans

· Heads

* Idler Rollers

* Tape

A separately excited DC shunt motor has been modeled for

the present analysis. If other type motors are used, they will

be modeled as needed. This is an illustration of the integra-

tion of the electrical actuation components into the mechanical

systems model. Figure 29 shows a schematic diagram of a

separately excited shunt motor.

I-- -P Va

Figure 29

SEPARATELY EXCITED SHUNT MOTOR


90

*The sum of the voltage changes in the armature circuit

yields the following equation.

dI

=Vg + a = Vg + IaR a + L a (24)

-where

Va = Armature voltage

Vg = Induced voltage

Ia = Armature current

Ra = Armature resistance

La = Armature inductance

t = Time

The back emf is related to the motor speed through the following

relationship.

Vg = KD 9 ~ (25)

where

KD = proportionality constant

p= flux

w = angular velocity

The motor torque, T is related to the armature current Ia

through the following relationship

T = KD Ia (26)-

These three equations are combined to obtain the following

equation relating the torque, speed and armature voltage.


91

R LV, = K' a a dT

Va = KD + T + D dt

Where

Kb = KDX

dTThe term t-E shows that transient responses are obtained.

(27)'

3.1.1.1 Reel Model

Figure 30 shows a schematic view of a reel with stored tape.

The equation of motion for the reel subassembly is:

doJY = - fo + T0 sin nrt - rFT + T (28)"

e

To sin n at

S

/111y17/

T

Figure 30

REEL MODEL


92

Wheref = friction coefficient

T = motor torque

FT = tape tension

r = tape pack radius

To = disturbing torque (bearings)

= - reel speed

JR = reel and tape pack moment of inertia

t = time

n = disturbance frequency multiples

The tape pack radius, tape transport length and moment ofinertia are functions of time or length of tape transferred,

and are described by

r = ro + Au (tape addition) (29)

r - rM - du (tape removal) (30)

dr =+ UW (31)

S re (32)

S= r·e + r (tape speed) (33)

w(4 4JR = b [r4(t) - r4 ] + JH(34)

Where

e = angular coordinate of reel

S = tape transport length

ro

= inner tape pack diameter

u = tape thickness

rM = maximum tape pack diameter

b = tape width

lIT RESEARCH' INSTITUTE

93

p = tape density

JH = hub moment of inertiaJR = hub and tape pack moment of inertia

= reel speed

t = time

3.1.1.2 Tape Model

The tape (Figure 31) is modeled as a massless spring

with a stiffness,

k = EAt

where

k = tape spring constant

E = tape modulus of elasticity

Z = tape length

A = tape cross-sectional area

A = bu

F "I,T

FT

Figure 31 TAPE MODEL


94

(35)

3.1.1.3 Capstan Model

The capstan model is shown in Figure.32. It has a fixed

moment of inertia, JR and a fixed radius, rc . The equation of

motion for the capstan including motor torque, friction and

bearing excitation is Equation 13.

Fic

F0

T sin n wt

Figure 32

CAPSTAN MODEL

doc

cc o c C c c (36)

Where

ec = angular displacement

Tc = disturbance torque

J = capstan moment of inertiacfc = capstan friction coefficient

Wc = capstan speedrc = capstan radius

Fo = output tape tension

Fi= input tape tension

n = disturbance frequency as speed multiple


95

3.1.1.4 Idler Model

The idler roll model is identical to the capstan except

no motor torque is included. Therefore, the idler model is

obtained by setting T = 0 in Equation 36.

3.1.1.5 Head Model

The final element in the dynamic model is the head, Fig-

ure 33, which exerts a drag on the tape. The equation of

motion for the head-tape force balance as shown in Figure 33

is given below.

Fi + fo - fl(SH) = Fo(37)

where

F, = input tension

F = output tension

f = static friction forceo

fln = dynamic friction coefficients

SH = tape velocity at head

HFi | __,F°

Fi F

FH et 0

Figure 33

HEAD MODEL

IIT RESEARCH INSTITUT'E

96

3.1.2 Mathematical Solution

The equations of motion derived in the preceding sectionswere used to solve the dynamic system response to input distur-bances and to determine the transport natural frequencies.Input disturbances due to torque perturbations (bearing error),geometry variations (machining error such as eccentricities,out of roundness etc.) and electrical phenomena such as coggingcan be applied to the simulation model. The tape behavior ateach component in the transport is calculated as a function ofthe input disturbances. The analysis was conducted in threeparts:

* Natural frequency

* Steady state vibration response

* System response

These analyses are described individually. In each casethe equations of motion were derived for the long-life transportconcept, then generalized for use in the analysis of any othertransport. The natural frequency analysis and steady statevibration response have been programmed for the digital computer.These problem-oriented computer programs are operational. Eachanalysis is described herein along with some results and ausers guide.

3.1.2.1 Natural Frequency

Undamped system natural frequencies are useful in systemdesign to avoid difficulties in the system dynamic performance.The coincidence of disturbance frequencies to natural frequenciesyields a potential source of operational difficulties. Eitherthe performance of the transport will be degraded or the tapelife could be shortened. Therefore the natural frequencyanalysis is an indicator of dynamic compatibility of thecomponents in the transport system.

llT RESEARCH INSTITUTE

97

Figure34 shows the dynamic model for the five-year trans-

port. The equations of motion (38 through 43) are given in

terms of

* Tape stiffness k. = EWt

0

0

a

. $i

capstan, idler, reel inertia Ji

capstan, idler, reel radius r.

capstan, idler, reel displacement Si

where

= tape Modulus of

= tape width

= tape thickness

= tape length

= time

Elasticity

d 2 S1

+ kl (S - S2) = 0dt - -

d2S

+ k1dtI

(S2 - S1) + k2 (S2 - S3) = 0

d2S3

3+ k2 (S3 - S2) + k3 (S3 - S4) = O

d2 S47 + k3 (S4 - S3 ) + k4 (S4 - S5) = O0


98

E

W

t

ti

t

J1

l1(38)

J1

J3

r3

J4

r 4

(39)

(40)

(41)

7

C I

cro~

c.,.

1

mC

WD

o4

zCo

o

w vdW

4)

f C

4

-I

477

99

J d 2 SJ5 d25 + k

4(S5 - S

4) + k5 (S5 - S ) = (42)r5 dt

J6 d2S6J- d S + k5 (S6 - S5) = O (43)r6

The Holzer method was used to solve these equations of

motion for the system natural frequencies. This method uses

an assumed frequency to determine whether the resulting mode

shape* satisfies the boundary conditions. (In this case the

torque on the reels is zero.) If the trial frequency does not

satisfy the boundary conditions, then a new trial frequency is

selected. This selection process is made in an orderly manner

on the basis of the residual calculated as a result of non-

conformance of the mode shape to the boundary condition.

Since the mode shape depends on a relative arrangement of the

system components, the initial reel displacement is always

assumed to be unity. The general recurrence relationship

Equation 44, based on a steady state vibratory motion, is used

to determine the mode shape as a function of trial frequencyJ.

cu and system component inertia -2 and tape elasticity ki.

r.1

n - 1

2 z u, i(44)Sn Sn 1 (44)

i=l

Each system natural frequency has an associated mode shapethat defines the relative positions of the components in thesystem while it is vibrating at the natural frequency.


100

where

Sn - nth Reel, Idler, Capstan displacement

The indicator which determines whether or not a trial frequencyis a natural frequency is the residual function (Equation 45)

n

J 2R= j S 2 (45)

i - 1

Natural frequencies are determined in an orderly manner byplotting residual, R, as a function of trial frequency, cn, Fig-ure 35. The intersections of the curve yield the system naturalfrequencies. It is easy to grasp the amount of calculationnecessary to determine each natural frequency. For this reasonthe natural frequency calculation is performed on the digital

Residual -4- Natural FrequenciesFunction (R)

(,)Trial

Frequency

Figure 35

SOLUTION OF SYSTEM NATURAL FREQUENCIES (HOLZER METHOD)

computer. The flow diagram and computer program for the com-putation are shown in Figures 36 and 37. The computer programis problem oriented and therefore the relevant tape transportis simulated by using alternate input cards for a componentand a tape length. The computer program use is describedunder computer documentation (Section 3.1.3).

IIT RESEARCH INSTITUTE101

3.1.2.2 Steady State Vibration Response

The mathematical model of the tape transport was used tosimulate the steady state vibration response (displacements and

velocities) of the tape at the transport components. Vibration

disturbances generating this response are geometry errors in

components size, bearing perturbational torques and any other

disturbing forces or displacements. The vibration simulation

model is problem oriented and therefore can be used to evaluate

varied tape transport concepts, The concept is simulated on

the computer by stacking the input cards in the order of concept

arrangement.

Components such as reels, idlers and capstans are simulatedas masses, the tape can have mass, damping and elasticity and

damping is allowed between the components and ground. A general

equation of motion (Equation 46) for any transport element was

written.

2Jn d2Sn 1 dSnn )dt + rn (Sn - Sn-1)kn-1 (46)

+ r .( - S + l)k + r { n _ n + = T sin N Vtn n n /n Ydt dt C ns n rn

+ Tn cos Nnn n rn

where:

Sn = displacement of nth component, in

t = time

rn = radius of nth component, in

Jn = polar moment of inertia of nth component, in-lb-sec2


102

Nn

kn

Cn

fn

= disturbance frequency

= Spring constant of tape length between, lb/inn and n + 1 component

= damping constant of tape between, lb-secn and n + 1 component. in

= damping constant from nth component and groundin-lb-sec.

radKTKn

Bn = R = electric motor constants, in-lb-secrad

KT = Torque sensitivity, lb-in/amp

KB = Back cmf, volts secrad

Tns = Perturbational torque, in-lb

Tnc

R = armature resistance, ohms

V = tape velocity

Harmonic motion (Equations 47-49) is assumed and a set of

2n algebraic equations that yield Sn as a function of the dis-

turbance parameter result,

Sn = Ansin cn t + BnCos crnt (47)

dSn - wn(Ancos cot = B sin uot)

dt n n n n n

d2Sn 2

tn

(48)

(49)

*where

VNn

On rndisturbance frequency


103

The algebraic equations are obtained by substitutingEquations 47-49 in the equations of motion and equating sineand cosine terms. A representative set of these equationsfollow. Equation 50 comes from the sine terms and Equation 51from the cosine terms.

j M 2

rnkn An-l + rn(knn (50kn) )n

n n n) + nCnn Bn rnknAn+ + rC Bl = T-n~n

-rnk n-Bn-l+ rnCnn - r (fn + ) An (51)n

+ r (kn1 + kn) n r k =n n-l n rn n n n+1 n+l

The set of simultaneous equations are formed on the computeraccording to the input data and solved on the computer for eachinput disturbance (frequency). The results (velocity at the headand other components) for each input disturbance are superimposed

to obtain the total wow and flutter. Use of the computer programis described in the section on computation.

3.1.2.3 System Response

The mathematical simulation of the dynamics of the tapetransport as it operates has been formulated for computer cal-culation. The equations of motion for each component as shownin the previous section are generalized in terms of the springs,masses, dampers, and motor constants that make up the transport.The motor voltages and torque perturbations are entered asinput functions.


104

Jn dg~ + (52)Jnr dg + 1 f g + r (S - S n)knn n

Vt+ rn(Sn - Sn+l)kn + r(gn - gn+l)Cn = Tnssin 4n r

Vt+ TncC O S An r + Tn

n

Ln dTn R n T + K r Vn (53)K-n Tn n

dSdSn (54)dt gn

where

gn = tape velocity at components

T = component torquen

Vn = armature voltage

L = armature inductance

Jn = ( - 4Pn b (r4 (t) -r° ) + J

For idlers and heads equation 53 is not used and the torque

term (Tn) in equation 52 is zero. The computer code (not com-

plete at this time) for this dynamic simulation forms the conceptthrough stacking of the cards. A set of n first order differ-

ential equations are obtained and solved with a Runge Kutta

numerical integration routine.


105

3.1.3 Computation Program Documentation

Natural frequencies and vibration response of tape trans-

port mechanical components (heads, idler, capstan, reel, and

tape) are calculated on this tape transport dynamic simulation

model (TTDSM). Natural frequency calculations are performed

using the Holzer Method of calculation and the steady state

vibration response is obtained through the use of a standard

simultaneous equation solver.

The flow diagram for the complete computer program is

shown in Figure 36. The computer program itself is shown in

Figure 37 on pages 111 to 118. The simulation of a specific

model transport is formed by proper sequencing of the data

cards as shown in Figure 38. This is followed by the necessary

documentation for the cards contained in such a data deck.

The use of this computer program is illustrated as an

example for one specific problem on the five year high relia-

bility tape transport. The first example is the derivation

of the natural frequencies of the system. The input data for

the natural frequency calculation is shown on page 123. The

natural frequencies are obtained through a searching technque

and therefore, the initial step size (delta) should be larger

than 5.0 rad sec"1 and the starting frequency must be greater

than zero. The searching technique ends either after the set

number of frequencies or on the maximum frequency, while the

error criterion is used to determine the natural frequency

accuracy span. It should be noted that in these examples the

tape mass is included and modeled in terms of an equivalent low

inertia idler in the center of each system element. The resul-

ting output data is shown in Figure 39 on page127 where the

natural frequency is given in hertz and the mode shape (theta)

in radians.


, I 106

The second illustrated example is that of the steady

state vibrational response. The input data for this calcula-

tion is given on page12 9 to 131. Here the forcing frequency

(a single frequency forcing function is allowed per data set)

is shown as ST.FREQ., the damping constant on each mechanical

component as DRAG COEF, and the forcing function amplitudes

(sine and cosine components to obtain proper phasing if required

as PERT TORQ. Again the tape mass is modeled in terms of a

equivalent low inertia idler in the center of each system ele-

ment. The output data shown in Figures 40 and 41 on page 133

andl34 tabulates the response (i.e., displacement) at each

component in the transport in terms of amplitude and phase

angle and also shows the rms vibration velocity of each element

of the transport.


1070)

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hli ~11~

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Preceding page blank PTAPE TRANSPORT DYNAMIC SfM1;UIMION AiUDEL U,.`

'1, tDVF)'T.FNSION A(25,25 ,B3(25),C(?5) ,D(25),TL(25) ,r3(25), CN(25) R(22* 15).BK(25,25),AJ(25),AK(25), F(25)tCC(25), X(25), 1R(25),JC(253* 2),X0(25,25)4 :iA = 15* : , 4 I:1l25,!A* ;s bO,j 4 Jd):1,25,17* 4 XD( I,JI ) : 0.08* 5 "nO 761 T:1,25 ,19* CO 760 JI=1,25,.

ll.4 760i 1*( ,d ): 0.012' ;(.I) n,13* B3(I) = OC14* C(I): ) .015* CC(I) = 0.016* ) :17* IR(I ) 'l 1P JC(I) = C,21Qa FF(I) = 0,0 20 * CN(U) = 0.0

;s'~* c(I) = OI.. (.

A JI) 0 . O~3· A JT(! ) = 0,024* X( I ) = ,25* 761 AK(I) := 0.2."* REl. MfO')ET27* kr\ AD ( -, i) D T, T i AX ,AMT , EC SF ! N , i< I I SCi S2,$ r, FL2P* Ci F r': Q A- ( t.I 0 .5. 413, I 1 0. ) , .3)29* Fi ,k-, (5,20) U)ENIS', ! TNEI',THKT,WITHT,V

?# F(Rc'AT ( 5-10.5 )31' WiTrk (6.30) DELTTlilAXAMT,ECSF,N,KIISCIPIS2 C2,FSFL32* 3n F"cR"¼AT ( 19H1C0NTR OL l'!PUT. DATA//7HA DELT4:=E105I5X6HT MIAX=F'10.5,533* . .X'AM T.TAPE:E1O5,5iX12HERRRO CR'.IT=E1iO .5 ,SXS lHST, FF ' :E1i,.5/9 H NO,F34f 2i,'-:;;: I 3 lX:8hNOU. SETS:13 t , X4 SC 1-1 3, :7X4i4SC2= I, 324XlnhF REG. I !T. =E1O34* ;5 /15T MAX ,. F .REt-tE LCY: = E ,31)36* t, l TTE ( 6 4) D 'IST iM O E T K T , I TT HT37* 40 FORMAT ( 16H TAPE INPUT DATA/ gH DENSITY ElO5,5, Y9 4MOF. LST:F 1,53A ,II 5X9HTHK1TAPE:EIO. S,5X94WTH,TAP.:F-lO.5,5X9HTAPE VFL=E10.5/)39* W,'IT T (6,50)4q* 50 Cs {RMAT ( C 26;Hi TAPE TRA'\iSPORT I liPUT ,[ATA /)41, IF ( ISCi - 2 ) 55, 40,5 146642* 5 = 143 J 1

4 F J - ) 7, 7, 1:l

Figure 37

TTDSM COMPUTER PROGRAM

111

46* 70 READ (5,80) J,AJHUjRHURFDRAGTS,TCAKDRA,VAMNA47* RO FORMAT (i1,RE9.4,11,I3)4S* kWRITE (6,90) JAJiUI3,RHUL3B,FIDRAGTSTCAKDRApVAMQNA494* 90 FORMAT(11H REEL,COn)E:I1,2X10HHINE.RT,HUBE9,4',2X6H R, HWU3=E9,42X1 OQADR5u* 1AG COEF=E9.4,2X13HPFRT,TORQ(S ) E9,4,2X3HPERT, TOR (C):E9 . 4/6X5HFLU51* 2X=E9.4,2X7HRESIST:E9.4 ?X6HVOLTSE9 .4,2X6PT ,CD = I ,2X3HNA: 13//)52* 100 IF ( J - 3) 140, 110. 1405:3* 110 N-AD (5,120) J,AJH4LI,RHUB,FDRAG,TS,TC,AKDRA,VAA MJNA54* 120 F-ORMAT (I1,RE9.4I1,II3)55* W;PITE (6,130) JAJHUBRHUBt,FDRAGTSTCAKO,RAVA,MNA.56* 130 FORMAT (14H CAPSTAN,CODE :I 2X10HINERTHU-E9g.4, 2X6HRH 3UB=Eg9.4,2X57* 1CH[DRAG COEF':E9.4,2X13HPERTTORO(S)=E9.4t2Xl3HPERT,TORG(C) E9. 4/654 ?F LYl:F9 . 4 ,2X 7HRF.S I ST E9.4 ,2XHVMTS:E9. 4 ,2Xi PT, o r) , 2X .J! , a =T 3/

60* I ( J - 7 ) 14, /1, 14061* 71 REA'D (5,72) JBJHUH,GR62r, 72 FO'1,qAT ( ]1,2E9.4 )63* WR IT (6.73) JtJHU3,GR64* 73 FM A ( 2H2, CAPSTAN REDUCERPCODE:l lio. J IlNEHTIA:E9,4,1.3H GFAR R65* 1ATIO:F9.4//)6h* 1,40 IF ( J - 4) 18,, 150a 18067* 150 READ (5,160) JAJH0B .RHHUBFDRAGwTSiTCAKODRAVAMN,'A68 * 1 6 0 FORMAT ( I1BiE9 .4.113))69* W'!ITE (6,170) J,AJ4UfiRHUB3,FDRAGTS,TC,sMC N

-7!1, 170 FORMAT (12H ICLFR,cr. lDEI1,2Xl()iNERT,IJ:!:-E§ 4 ,42 yGR.H'it:E9.42X,:?lz71b lD''H''lr', COEF'-t;93.4,X13H PERT.TO~(,..5):Eg.4,2X$3!. E.,lTOR:-,(C):EO.4r/2XAc;p72* 2T .C:] =11,2XHNA=I3/i)73* 180 IF ( J - 5 ) 220, 190, 22074* 190 REaD (5,200) JFO,Fl,CNNM75* 200 F(RMAT ( I1,5EY.4,I1 )7A* W '! Tt (6 r10) JFO, F ',* CN* ¢

77* 210 F9Rt'4T ( 1I I HEAC, C.0r)E: I 2XH. STA T, F9RI CT:9. 4 2XI Y , FRiCT:F:9. 4,7R* 1) 4 y14HDYN,F', I CT, N ) E 9,4,2X6HPT CO 11./ )79* JCC : 480. 1A = TL(I-1)81* 220 IF ( J - 6 ) 260, 230, 260b2* 23) RF-A[) (5,240) J,TLL.,Ml83* 240 FOR:i'AT- ( I1,E9.4,I )64* WRTTE (6,25) J,TL.L,M65* 250 FORMAT (11H TAPE,CODE:11,2XOHITAPE LGTH:E9,4,2X6,PT.CD=Ii//)86* TL(I ) = TLL67* IF' (JCC - 4 ) 260, 255, 260,38R* 255 TL(I-1):TL(l)+s3A89t AAK (I-1 ) : ( MODET-;14K r*lTHT ) f TL (-1.90* GO TO 6091,* 260 AJ(I ) = AJHUB + ( 3JHtlJ*(GR*:*2,))9?.2* BJHUB3 = 0.093* Gn 0 ,09G;, R( ! ) = -RHU'di')... I F ( J- 1 ) 262,262, 26196-> 261 AK( I) : ( t O1L)EF *THKTT*WVI4T ) / 'I) L I 9.7* 262 AJ(I) : AJ(I) / ( R( I )*2,0) 9* AL I99* 1I:+ 1

10,.q~> i) IF ( J - 1 ) 270, 2'70, 601"1* 270 OMFG = SF

l.'3. 280 G = 1.0104* DELOMG = DELT1.0_5' I__ P = 1

r -Trl--~ -- -1-RRF5. mr*----A -t

112

106* 290 FA= 0.01077 S = 1.0108* DELTS : 0.0109* I : 1110* 300 S -S - DELTS111* IF ( IP - 2 ) 360, 310' 310112* 310 IF ( I - 1 ) 340, 320, 340113* 320 WPITE (68330)114. 330 FORMAT ( 30H NATURAL FREtGUENCY CALCULATION// 9H $TAT I ONS10HrL' E T

115* 1A(RAD),5X13HTORPUE(IN!-LR)//)116i 340 THE = S / H( )117* WaITE (6,350) IJ,TH,FA1.AR* ]350 FP0MAT ( 7H 12,5XE10.4,#XE10.4 )

119* 360 FA= FA+ AJ(I)*(OMFV**2,0)*S120* IF ( I - L ) 370, 38+r, 380121* 370 DELTS FA/ AK( I)122* 1 = I + 1123* GO TO 300124* 380 IF ( IP - 2 ) 390, 470, 470

125* 390 IF ( F-O,.Q) 400, 430, 410126* 400 IF ( r- - 1.l ) 410. 420, 410127* 410 AA : FG A128' IF ( AA -. n0) 450, 420, 420129* 420 OMEG OMEG + UELO MG ?eP a'130* F A131.* G,( TO 29Q132* 430 A(0!FC : OMEG / 6,2631R133* WR I TE (6,440) NlAQOMEG134* 440 FORMAT ( 22HlNATURAL FREQUENCY NOI13,2H =E10,5,3H H7//)

135* IP = 3136* GO TO 290137. 450 iF ( DELOMG - EC ) 430, 460, 46n1.38 460 COEG = OMEG - ELO0IG139* DELOMG =.DELOMG / 16.0140* OMEG = OMFG + DELOIG141i GO TO 290142* 470 IF ( MNf - NJ ) 4A0O,481* 481

143* 4800 IF ( OM G - FL ) 460, 481, 481144* 480 OMEG = OMEG + FS145* NN : MN - 1146* GO TO 280147* 481 IF ( KA - K ) 482, 10000, 10000148* 482 KA = KA + 1149* GO TO 51504 486 I: 151" 490 IF ( I - 1 ) 495, 495, 500152* 495 J = 2153* GO TO 505154* 500 AAK = AK(I-2)155* 505 IF ( J - 2 ) 54n, 510, 540156* 510 READ (5,520)J,AJHLJB,RHUB,FDRAG,TS,TC,AKDRAVA,M,NjA157* 520 FORMAT (I1,8E9.4,I,13)158* WRITE ( 6,530)JAJHUBRHIJB, FDRAG.TS TC AKODRA VA M NA

159* 530 FORMAT(1iH REELCODE=I1,2X10HINERTHUB=E9F,42X6HR,HLIB:E9,4,2X1D0 DR

160* lAG COEF=E9.4#2X13HPERT.TOR(;(S)=9,4,2X13HPERAI, TOR(C):=E9.4/6XS5HFLU

161. 2?X=E9.4,2X7HRES lSTE9 4 2X6HVOLTS IE 9.4,2X6HPT- .Ci I, 1, 2?X3'l1A= 1 3// )

162* IF (I - 1 ) 780, 660, 780163Q 540 IF ( J - 3) 580, 550, 580164* 550 READ (5,560)J,AJHUB,RHUBFFDRAG,TSTC,AKD,R.AVAM,NA165* 560 FORMAT (11,8E9.4,11,I3)

-gU-11~3T-Co-t -)

113

16*6 WRITE (6,57 ) J. AJHU RHUB, FORAG, TS, TC, A<D, RAVA, M, NA1674s 570 FORMAT (14H CAPSTAN,CODE=!1,2XtOHINERT.HUB:E9.4,2X6HR.,UB:E9.4,2Y

16* 1lOHDRAG COEF:E9.4,2X13HPERT,TORH (S):E9. 4,2X3HPERT,TORC(G)CE)9.4/1X169* 25HFLUX=E9.4,2X7HRESIST=E9,4,2X 6HVOLTS=E9,4,2X6HPT,CO.:1,2X3HNA:13/170* 3/)171* GO TO 670172* 5B0 IF ( J - 4 ) 630, 590, 630173- 590 RFAD (5,600)J.AJHU3IRHUB,FDRAG,TS,TC,AKD,'A,VA M. .' 4174. 600 FORMAT ( I1.8E9.4,11.13)175* WRITE (6,610)J, AJHURRHUBFDRAGTS,TC,M, NA176* 610 FORMAT (12H IDLER,CODE:I 1, 2XIOHINERT .HUBF.E9 .42X6HR.HUJ:E9. 4, 2XI177* 1DRAG COFF=E9. 4,2X1)HPE RT. TOR ( S) :E9,4,2X13HPERT TOR ( C ) =E9,4/SX6HP178* 2T.CD:I1,2X3HNA=I3//)179* GO TO 6701a80 630] ,REA (5,640) J,FO,F1,CijN, M181* 640 FORMAT ( !1,.3E94, I1)182* WRITE (6,650) J,FOF1,CNN,M183* 650 FORMAT (11H HEAD,CODE:11,2XX11HSTATFRICT:E9,4,2XlOHOYN.FRICT:E9,4,184* 2x.l,4lWYN, FR[CT. (N):F,4 4, 2X6HPT. COI 1//)185*' 17 = 3lb6 .6* TO 70D187* 660 IZ = 21 8M* GO TO 700189. 670 17 : 1

790 RE AD (5,730) J,TLL,M,1l 91 710 FORMAT ( I1,E9.4,I1 )192. WrTh. (6 ,72C) ,J,-TLL,M193 7?20 FORMAT (11H TAPEC0DE=II2X1OHlAPE LGTHE9:,4,2X6HPT.CO:]E//)194* TL( I TLL195 lF (C IZ - 2 ) 730, 750, 7401956' 730 AK (I)=((MOOFT * THKTT* WTHT) / lt(I ))197* A(T,I+) 1.0;19Q d(f+l,-A2) : (( AK)*( RHUB**2.0)) / hJuJR199* 4(I+1,!) : (-1.0)*t( RHLIB**2,0)/ AJHUB)* ( pAK + AK(I))200* A4(+1,1+1) =((-to)/AJHUR) * ( FDRAG + ((AKD**2,0) /RA ))201*i 4(!+1,I+2) = ((RHU3**2.O)/,AJHUB )*AK(I)202-, LUC [) = (T$* NHdUP)/ AJHiUR.0.3 '! . .. ( " : A, ,^ !.!

20 4' GO TO 770205* 740 AK(I)=((MO3FT *THKT* WTHT) / TL(I))206* A (I, -2) = AAK / Fl27* A( ! I ) (K( I )-AAK ) / F12 '3 a A( A ,I+ ) = -AK(I) / F j9: tiPI ) P -I) / 1

O21'* CN(I ) CNN211.!. * AKK( )21.2 I1 + 1213' GO TO 505214* 750 I = 1215* T = o.0216* 4K( )= ( M1FT * THT WT4T) / TL( I ) )217* A(1,2) 1,0218* 4(2,1) : (-1. )* ( HHUB**2, ) / AjH Ij)* AK(t)219* 4(2,2) (-1, / AJHUB)* ( FORAG + (( AKD**2,0 ) / PA))220* A(2,3) (-1,0)* A(2,!)221* B?(2) ( TS* RHUE3) / AJHUB222*; C(2) ( 'I4A* V ) / RHUB223* 770 I : I +2224* GO TO 490?25 __ 7O_ ,+ ) A 1I0 Figure 37(Cont.)

114

226* A(I+1, 1-2) ( AAK* (RHUB4*2,0)) / AJHUB

227* A I+1 I) = (-1,0)* ((RHUB**2,0') / AJHUB ). * AAK228* A(I +1,I+1) - -10O/AJHUB) * ( FDRAG + (( AKD**2,0) / RA ))

229* B(I) : ( TS* RHUB) / AJHUB230* D(I) =( NA * V ) / RHUB231* KK e I +1232* WRITE (6,7B5)233* 785 FORMAT ( 23H1FORCEDL RESPONSE OUTPUT//)

234* 790 I = 1235* 795 DO 810 JJ=1,KKt1236* IF ( Bb(JJ) - 0.0 ) 796) 7988, 796237* 796 IF ( R(JJ) - 0,0 ) 798, 7989, 7988238* 7989 A3BB 0.0239* GO TO 799240* 798 $ 5B = -1,o*RB(JJ )241* GO TO 799242* 7988 AB8 : B3(JJ)243* 799 D0 800 JJJ=1,KK,1244* 8nU R(.,(IJ) = R(JJ) + A(jIJ,JjJ)*CC(JJJ)

74N, Y(JJ) = R(JJ) + B(JJ)*( SIN( C(JU)*T)) + ABii

246* 810 CYn TI4IUE247* DO 820 JJ:1,KK,1248* BK(I,JJ) = DELT * R(JJ)249* 820 CONTINUE259*p IF' ( I - 1 ) 830, '130, R60251 * 83i} T = T + ( [)ELT / 2,0 )252* 840 UO ' 5I JJ=1O,KK,?53* 850 CC(JJ) = CC(JJ) + ( BK(I,JJ) / 2,0 )254* GO TO 890255* 860 IF- ( I - 3 ) 84C0,8/0900256* 870 T = 'T + ( OFLT / 2.0 )257* CC(JJ) = 'CC(JJ) + BK(I,.4J)25R* 890 1 = l + 1259* GO TO) 705260* 900 DO 940 JJ=iKKI261 I I1262* 910 C(JJ) = C(JJ) + (1.0 /6.0)*( dK(I,JJ) +(2.,O*K(I+I.JJ))+(2.,O*K(!263* 1+?,JJd) + +K(I+3,JJ))264* IF ( IJ- 1 ) 9209 920, 931265* 920 WRITL (6,930) r,C(JJ)266* 930 FORMAT ( 6H TIME=EIO.4,5X9HRESPONSE=EIO.4//)267* GO TO 9406R* 93 1WRITE (6,932) JJ,C(JJ)

269* 932 FORMAT ( 4H JJ=I3,2X6HC(JJ)=E10 .4)270* 940 CONTI |UE271* IF ( T - TMAX ) 790, 790, 1000

272* 1000 IF ( KA - i ) 1010o 10000, 10000

273* 1010 K = KA + 1274* GO TO 5275* 14R6 I = 1276* 1490 IF ( I - I ) 1495, 1495, 1500

277* 1495 J = 2278* GO TO 1505279* 1500 AAK 2 AK(I-2)280* CCH : CH281* 1505 IF ( J - 2 ) 1540, 1510, 1540?82* 1.510 READ (5,1520)JAJHUB,RHIJB ,F[DRAGTS,TC,AKDO , ,VA ,M,NA283* 1520 FORMAT (I1,8E9,4tI1,13)284* WRITE (6p1530)J.AJHUB, RHUB, FORAGTS,TC, AKD,RAVA,M,t!A

285* i 5_ 3FOR MAT(llH REE ODE:1,2 X 1 INE RT ,HU:E9.4,2X6H._lHU:X.42 OR

286* lAG COEF=E9.4,2Xl3HPERT TOR( S) E9,4,2Xl3HPERT TOR( C )E9.4/6X5H'LU-287. !X=E9.4,2X7AHRESlST=E9,4,2X6HVOLTS=E9,442X6HPTCD i1,2X3HNA=I3 //)28'* IF ( - 1 ) 1780' 1660' 1780289* 1540 IF ( J - 3) 1580, 1550. 1580290* 1550 READ (5,1560)JwAJHUB, RHUB,FDRAG, TSTCAK0,RAVAMINA291* 1560 FORMAT (I1,8E9,4,l'1i3)292* TE (6,1570)J, AJkHRJ.iHUBpFDRAGTS,TC, AKDRA VA ,M NA.293* 1:570 FC0RMAT (14H CAPSTAN,CODE: 1,2Xl.OHINERT.HUB:E9 ,4,2X6HR,HUs=F9.4,2 X294* 1.iHDRAG CoEF:E9.4,2X13HPERT,TORO(S):E9,4p2X15HPERTr,'OR(C):F9.4/2954 25HPFLUX:E9.4,2X7HRES ISTE9,4,2X6HVOLTS=E9.4,2X6PT.C !;1, 2X3HNA ! 3/296* 3/)297* IF ( J - 7 ) 1670. 1571t 1670298* 1571 9RAD (5,1572) J,B,J.'iBGRBFDRAG,BAKD,PRA299* '1572 FORMAT ( !1.5E9.4 )300. WRITEt (6,1573) JBJHiUB,GRBFDRAGpAkD,oBRA.301* 1573 FORMAT ( 22H CAPSTAN REDUCER,CODE=I1,lOH INERTIA=E9,4,13H GEAR R302* lAT!O0:E9.4,12H DRAG C0EF:E9,4,N? FLUX=E,9.4,13H RESISTANCE:E9.4//303* 2 )

304* Rs : 'jF * GR305* Go : 0.0306* GO TO 1670307* 1580 IF ( J - 4 ) 1630, 1590, 163030A* 1590 READ (5,1600)JtAJHUB,RRHUB,FDRAGTSTGAKDRAVA,#M#NA309* 1600 FORMAT ( I1,8E9.4,*11I3)37i* WqRITL (6,l161)J,AJH(iJH, RHURFDRACwTS,TC, M,NIA311* 1_610 F9ORMAT (12H IDi FR*C;oL :!,12XlD ICERT42XE94,312L 1DPAG COLF:-E9,4, X 1 3tPERT.TORQG(S ) E9.4,2X13HPErRT ,TRO(C ) :E9, 4 /5X6HP3.13* 2T. CD: 11,2X3HNA: 1 3//)314* GO TO 1670315. 1630 READ (5,1640)J,FO,FlCNN,M

164G0 F)R'AT ( 2 ,3E9 4,J1)7.017- WPRITL (6,1.650)J,F(O,F1,CNN,M

_1~ . .1 65J FORMAT (I.H 1 HEADOCODDE=IlX1I.HSTAT.FRICT:E9,.42X<lOrD4yNtl ,FRICT:E9 .4,319. 12X14rDYN FRiICT ( N ) E9. 42X6PT. C= I 1//)32* I 7 3321' GO TO 1700322, 1660 IZ : 2323* GO TO 17Q037;24,a 1670 17 = 1325* 1700 READ (5,1710)JTLLMCH326 1710 FOPMAT ( IlE9,4,I:,E9.4)327* WRITE (6,1720)J ,TLLMCH32; 1720 FOr)lRMT (.1H TAPE:,CQfE=11,2Xl0OT PpE LGTH=E9.4,2X6CNPT,.CrD= ,21. 1H;;LA7529-? ];DW COEF,:E9,4//)

533* IF ( J - 5 ) 1725, 1721,, 1725331-' 1 72_1 TTL = TLL

53:: C-"GO TO 16303:53, t.*725 TLL rLL + TTL334* TT : 0.Q

<3c I5* ;'- ( Z - 2 ) 1730, 1750, 1730336* 1750 A'(I) 7 (( MODET* THKT* WTHT) / TLL)337* A(1,1) RHUB*AK(I))-((AJHUB* ( SF**2,0)) /RHUB)338* BET (( AKD**2.) / RA)339* A(i,2) : ((-SF/RHUB) * ( FDRAG+bETA ))-( RHL3B*CH* SF)340* A(],3) = (-AK(I)* RHYB)34l* A(2,1) = -A(1,2)342* A(2,2) = (1,,i)343* A(2,4) = A(1,3)344* B(.) = TS345* B(2) :ITC

3_i1ur16 37 (Cent116

346* A(1,4) = ( rHUB*CH* SF)347* A(2,3) = -A(1,4)34* i =: I + 2349* GO TO 149075n* %730 AK(I) ( MODET*THKT* WTHT) / TLL)

351* I .(I) := HUB*(AAK+AK(I))-(( AJHUB*(SF**2.0)) / RHUB)-((BJNUB*(RSF352* .2 Q) ) /RHU )353" F I U B = 0.0354* A(Il,I+) A( ,I )355* A(!,I-2) : -RHU~9*AAK356* A( I , 1-1) HB*CCH*S357* B.TA -(( AKD**2.O) / RA)

358* B£..rFTA (( BAKU**?2O) / BRA)359* A( I, I+1): (-1.0 )( ( (/RU)*( FDRAG+RETA ) +( RHUjB ( CH+CC I)*SF )

_3,,.* 1(( ( SF*4*2.0) / H HUL) ( RFDRAG + BRETA))

361J* BSF = Q.03624 HAKO O n363* BRA : 0.0364* F:T4 = .,

3h6* a( , I+2) : -RHH*tAK(I)367* A( I,+3) = RHUB*CH*SF369* A(c+1,I ) : -A( + 1 )3697 A( 1+,-2) . -A( I * I3)

37 t A(I+ + , 2) - (I,I +3)\72?' A(IA 1+1, [+3) = A( 1, 1+?)373* R( I ) TS374 * B(+i) TC375* I I + 2376* G 0 TO ,14gn377* : 780 A( 1,-2) -H¢* A iK37* A ! 1-1 ) = RFlJHUJ*oCC N*HSF379* A([,I : (4HUB*A4AK) - ((AJHUB* (SF*,2.0)) / RHUB)

38,n BETA = (( AKD**?.O) / RA)

381* A( ,I+1) = (-1.,)*((( FDRAG + BETA) /RHIJB) +CCH)*SF

3d2* AII+ . 1-2) -A(I,I'-i)

385 * IC +,I+ 1 = -1 ( )-2

3846* ( I-T ) = TS3,7' .1) : TC387* + = ' + 1T

39* - l : 1,0

391* N - KK392* PO 1971 JJ=IKK,I-93 S 1971 A(jJ,KK+1 ) - B(J)

j94::a CA L L SiM E- ( (ANM4X Ir ,,,JCN ESP1 ,XERR )79'~* r "'*TE (6,1975) KA'.596. 1P7: ~ kr-i l:T ( 3 H1SEl' NO .I3,16H RFSPOCiS OUTPIT //)

397* -)0 181.0 JJ=I,KK,2398* APF$ = (C X(JJ)**2,0) + ( X(JJ+I)**2.0))**O,5

399* AA : ATAN( X(JJ) / X(JJ+1))40n, w i T (6t1..800) dJX(JJ)401,* 18 90 L 'r. %.VAT ( 12H ELF MENT NO.I 1 3,X 5(9HPRESPO)NSE E1 5,1 S X61 ,Ch. )402* JZ : JJ+L

403* W, 1TE (6,1801) JZ,X(JZ),ARES,PHA404* 1801 FORMAT ( 12H ELEMENT NO.I3,5X9HRESPONSE=E10,5,1X6HINCHEIS,Xt9Hq:,ESP40.. .......... _'S APLITlDE=ElO,5t, 1X6HINCHES,5X6HPHdSE:9F9.4, 4lX4HRAD //)

Figure 37 (Cont.)

117

X[(KA,JJ) = SF * ARES51.0 CONT I JE

IF ( KA - K ) 1220* 1830, 18301A20 KA : KA + 1

GO TO 51850 WRITE (6j1831),.31 FORI'AT ( 29H1TOTAL FORCED RESPONSE OUTPUT //)

DO 1860 JJ:=1,KK,2DO 1850 KA=w!Kl

1850 AVEL - AVEL + XD(KAJJ)**2.0VEL = ( AVEL**0.5)JZ = JJ+1WITtE (6,1.851) JJ,.JZVEL

:851 FO)<MAT ( 9H ELEMFNT(I2,1H-I2,12 ),9Xg Hv9FLOCITY=ElQ.5,9 H IN./SFC./)

AVEL = )rfVEL = 0. 0

8I 60 (Oh!T I NLi.E100l O0 E!ND

ENi nF uLCC, 11trf FORTPAN V COMPILAlTION. 0 *,IACGOSTlC* MIESSAGF($)

Figure 37 (Cont.)

118

4 . 4

41J.411.412*

414*415*41 7*

421

422*423*

TTDSM: Tape Transport Dynamic Simulation Model

Capstan Card

Tape Card

Head Card

Tape Card

Capstan Card

Tape Card

Idler Card

Tape Card

Reel Card

I/

R

Tape Co)nstants Card

Control Card

Figure 38

TTDSM INPUT DATA

119

/

I/ Reel Card /

I _1___-I-

I

CONTROL CARD

Nomenclature

Frequency Step Size

Blank

Blank

Error Criterion

Starting Frequency

Number of Frequency

Number of Data Sets

Switch 1

Blank

Frequency Interval

Maximum Frequency

Field

1-10

11-20

21-30

31-40

41-50

51-53

54-56

57-59

60-62

63-72

73-80

Format

E10.5

E10.5

E10.5

I3

I3

I3

E10.5

E8.3

Units

Rad/sec

Feet

Rad/sec

Rad/sec

Note 1

Rad/sec

Rad/sec

Note 1: ISC1 = 1 for natural frequency calculationISC1 = 3 for linear forced response calculation

TAPE CONSTANTS CARD

Nomenclature

Tape Density

Modulus of Elasticity

Thickness

Width

Tape Velocity

Field

1-10

11-20

21-30

31-40

41-50

Format

E10.5

E10.5

E10.5

E10.5

E10.5

Units

lb/in

lb/in

in

in

in/sec


120

Code

DELT

EC

SF

N

K

ISC1

FS

FL

Code

DENST

MODET

THKT

WTHT

V

REEL, CAPSTAN, AND IDLER CARDS

Code Nomenclature Field Format Units

J Next Element* 1 Il

AJHUB Inertia 2-10 E9.4 lb/in/sec

RHUB Radius 11-19 E9.4 in

FDRAG Drag Coefficient 20-28 E9.4 lb/in/sec

TS Torque Perturbation 29-37 E9.4 in/lb(sine)

TC Torque Perturbation 38-46 E9.4 in/lb(cosine)

AKD** Flux 47-55 E9.4

RA**v Resistance 56-64 E9.4 Ohms

VA** Voltage 65-73 E9.4 Volts

M Linear Subroutine Code 74 I1

NA Perturbation Ratio 75-77 I3

*Next Element Code. Each of the following inputcards requires a "next element" code to informthe computer of what type of data is to be readfrom the following card. The following integersare entered in the first data field column "J".

Enter J=1 to end reading

Enter J=2 if next element is a reel

Enter J=3 if next element is a capstan

Enter J=4 if next element is an idler

Enter J=5 if next element is a head

Enter J=6 if next element is a tape

Enter J=7 if next element is a reducer

The program assumes that the first card after thecontrol and tape constant cards will be a reel.

**Equal to +0.0000 + 00 for idlers

Flux= KTKB

where: K = torque senstivity in-oz

back E volts-sec)


121

TAPE CARD

Nomenclature

Next Element

Tape Length

Linear SubroutineCode

Head Constant

Field Format

1 11

2-10 E9.4

11 11

12-20 E9.4

Units

in

lb/sec/in

HEAD CARD

Nomenclature

Next Element

Static Friction

Dynamic Friction

Dynamic Friction (vt)

Linear SubroutineCode

Field

1

2-10

11-19

20-28

29

Format

Il

E9.4

E9.4

E9.4

Il

Units

lb

lb/sec/in

LOW SPEED CAPSTAN REDUCER

Nomenclature

Next Element

Inertia

Gear Ratio

Drag Coefficient

Flux

Resistance

Field Format

1 Il

2-10 E9.4

11-19 E9.4

20-28 E9.4

29-37 E9.4

38-46 E9.4

Units

lb/in/sec

C:l

in/lb/sec

Ohms


122

Code

J

TLL

M

CH

Code

J

FO

Fl

CNN

M

Code

J

BJHUB

GR

BFDRAG

BKD

BRA

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Preceding page blank NATURAL FREQUENCY NO, 1 = .24669+02 HZ

NATURAL FREQUENCY CALCULATION

STATION THETA(RAD)

I ,3949-002 ,8415-003 .9108-004 .4800-005 .4430-t0 6 .1067+007 -,1014+00A -.9544-019 - 1700-00

10 - 1521-00 11 - .6979-01

NAI URAL F tEOUFJNCY NO. 2

TORQUE(IN-LR)

, 0000,3051+02.3051+02.3300+02,3300+02, 3456+02, 3456+02

520 6 +0.5205+01,4 741+01.474 !+ :1

.30339+U? H4


STATION THETA(RAD)

1 .*3949-n02 .7603-003 ,6942-004 .2190-i-005 -- 1323-r0

-,- 3205-f07 -,8934-00-1 . 1551.+01v , 4.79+01.

10 ,5335+0111 ,2768R+nl

NATURAL FREOUENCY NO. 3

TOR0UE( IN-L)

, 4614+024615+02

, 4902+02,4902*02.4d32+02

4832+cU2- 3427+03- 342 7+03

- 322b+03- . 3225+03

*11633+j] s Z

NATURAL FREQUENCY CALCUILATION

THETA(RAD)

, 3949 -00-,2524+01-,.8061+01

- ,7205+01- 1337+02- . 4136+01

1399-0 - .1722-00- ,5756-00-,4690-00-,1999-0O0

TORQUE(IN-LR)

, 6 84+03,6781+03.1683+03*1873+03

-, 8575+03-, 8579403

*,4219+02.4216+02.7191+01.7136+01

Figure 39

NATURAL FREQUENCY OUTPUT DATA

127

STATION

123456789

1011

N4TURAL FREQUENCY NO. 4 = .17537+03 HZ

NATURAL FREQUENCY CA.CULATION

STATION THETA(RAD)

1 .3949-002 -,7008+013 -.2001+024 -,7480+015 .,9541-016 .:6008+017 .1912+N28 -,1701+049 -,454A+04

10 -. ,592+0411 .9031 +n02

NATURAL FREQUENCY NO. 5 =

TORQUE( IN-LB)

.00001542+04.1540+04

",1223+04-. 1225+04- . 1206+04- .,1207+04

,2784+06- 277 +06

- 3501+06- .3506+06

.19322+03 HZ


STATION THETA(RAD)

1 ,3949-n02 -,8721+ll3 -,2457+024 -,4581+0145 4,.1484+0?

5 .44612+D1.7 -,9254-019 ..4214+019 . 130+02

10 , 2233+nl11 - .1585+nl

NATt!RAL FEOUtLNCY NC . 6

TORQUE(IN-LB)

. )00 0

.1872+04,1869+04

- , 2250+04-,2252+04,9472+03,9487+03

- .6942+03- . 926+03

.1202+04, 1203+ 0 4

.56391+34 iH/

NATURAL FREOUENCY CALCULATION

THETA(RAD)

. 3949-00-,8279+04-, 6366+045593+07

. 1653+03- 4325+n7-, 4966+074620+12

- 5332+09,4671+10.1224+10

TORQUE(IN-LB)

.0000,1594+07

-, 6 746+06- ,9097+09

. 0 89+o+ .8 7 85+ 0 9

-, 2481+O9-, 7508+14,7515+14

-. 9764+12.3026 + 1 ?

Figure 39 (Cont.)

NATURAL FREQUENCY OUTPUT DATA

128

STATION

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rTOrAL FONCED RESPONSE OIJTPUT

LLEMENT( 1- 2)

ELEMENT( 3- 4)

ELEMENI( 5- 6)

ELEM E! 1( 7- 8)

ELE EN' I 9-1Q)

EL, E.' T ( 11-12)

ELEMEN (13-14)

ELEMEl( 15-16)

ELEMENT 17-1iB

ELEMENT(19-2U)

ELEMENT (21-22)

vELOCI TY

vELOCITY=

VELOCITY=

vELOCITY=

VELOCITY=

vELOC ITY=

VELOCITY=

ELOC I TY=

!ELOCITY=

vEELOCITY=

VELOCITY:

.19276-02

19242-02

. 19221--02

,18727-02

i,8399-02

,17939-02

t 17785-02

, 17864-02

,* 1106-02

,1l114-02

,1 3 134-02

DATA CARDS ENCOUNTERED BY SYSTEM - IGNORED

E NO

Figure 41

VIBRATION RESPONSE OUTPUT DATA (RMS VELOCITIES)

134

IN, /SEC,

IN. /SEC,

I N ,/Si- ,

IN./SEC.

IN./S&.C,

!N. /SEC.

IN,/SEC.

IN./SEC,I N . / SEC ,

I N. /SEC,

IN./SEC,I \, StC.ec

3.2 Double Cone Guide Roller Transient Analysis

The guiding action of a crowned roller, was studied by

determining the tape response to a given input disturbance as

it passes over the roller. The position of a tape on a double

cone guide roller for a harmonic off center position at the

input roller (Figure 42) is investigated. This non-linear

analysis provides design data on the attenuation of input

disturbances, ei, to the tape. The calculated transfer function

yields the tape response, eoo Table 11 gives the nomenclature

for the analysis and problem description.

Double ConeCenterline

C

I_ _ _ _ _ _ _ _ L I

iT

TapeCenterline

Figure 42 T

DOUBLE CONE GUIDE ROLLER SYSTEMIIT RESEARCH INSTITUTE

135

ei,

1

t---

Table 11

GUIDE ROLLER TRANSIENT ANALYSIS NOMENCLATURE

C constant

d diameter of cylinder roller

D maximum diameter of double cone roller

eo distance tape is off-center at double cone roller

ei

distance tape is off-center on cylindrical roller

E modulus of elasticity of tape

K torsional spring stiffness at junction of tape anddouble cone roller

L length between rollers

M moment in tape

P dimensionless geometry factor

Q dimensionless tension

R dimensionless moment

r tape reaction

s arc length

so

original tape length

S dimensionless torsional spring stiffness

t tape thickness

T tape tension

U dimensionless output eccentricity

V dimensionless input eccentricity

W tape width

Wc Tape Contact width

y coordinate to point along width of tape measured fromdouble cone roller center

y' slope of tape at cone roller

Z dimensionless tape width

a cone angle for roller

e strain in tape

sc strain in tape due to cone

0o strain constant


136

Table 11

GUIDE ROLLER TRANSIENT ANALYSIS NOMENCLATURE

Poisson's ratio for tape

stress in tape

system response


137

wC

3.2.1 Modeling

It is assumed that the tape can be modeled as a beam

fixed at the point where the tape leaves the cylindricalroller and pinned at its junction with the double cone-

roller. The effects of local slippage between the tape andthe roller are modeled with a torsion spring, (Figure 43).

However, it is assumed that the frictional forces between theroller and the tape are sufficient to prevent any gross

relative motion.

k

Figure 43

TAPE TORSIONAL RESTRAINT

A torsion spring, k, also provides a simulation of the resist-ance to tape rotation as it enters the double cone roller. Theloading on the beam is given by the stress distribution acrossthe tape at its junction with the double cone roller. This

loading was determined from the tape tension in its free stateand the strain distribution in the tape as it passes aroundthe double cone roller.


138

3.2.2 Analysis

The strain distribution across the tape due to roller

geometry and global tape tension is given by the following

expressions

£ = go + C lYI (55)

Where so represents the tape tension and C lyl represents thestrain to roller geometry.

For some wrap angle around the cone, Ae, the arc length at

position Y is

s = (D/2- lYI acL) (56)

where the cone angle, a is assumed to be small. Figure 44' shows

the geometry of the roller. The original length of the tape

along this arc is approximately

so= (D/2) Ad (57)

D

- ay

FIl IYga

Figure 44

ROLLER GEOMETRY


139

The strain due to the cone is

Eo = (S - SO)/S = -2 IYI a/DFrom this expression the constant C becomes

C = -2a/D

(58)

(59)

Therefore

£ = o - 2 ca IYl /D (60)

Using Hooket s law, the stress in the tape is proportional to

the strain a, therefore

a = Ee = E ( o - 2Ca IYI /D) (61)

The total tension in the tape when it is displaced an amount,

e, off the center of the coned roller will be

W W2 + eo + eo

T =f tdy = E ( - 2 a jy /D) tdy

(W- e )2 e°

o e

E -°o - 2a (-y)/D] tdy + E(sO - 2ca y/D) tdy

2 - eo o


140

I

/-(2 - o)2 0o

= Et E y + ay. /D]

2 eo)

W+ e

+Et y-ay /

0

= Et o( - eO) - a( - eo) 2/ D + -o(2- + eoe) - ( + e)2/D

Collecting terms yields,

T = Et (sW - aW 2 /2D -2ae 2 /D)0 0

(62)

In the evaluation of the integral of the absolute value of y

it was assumed that e0 < W/2. Thus it can be seen that the

tension, T, in the tape at its entry to the roller is a function

of: a constant strain So; the roller geometry a and D; the

tape geometry W and t; the tape physical property E; and the

tape output exit position eO.

The tape stress distribution also results in a moment

about the center line of the tape given by

W2

M=

J (W2

+ 0 e

(y - eo) ctdy = ( (y

= eo) - e )

eo ) E (es - 2 alyI /D) tdy

o 2+0 e o

(y - eo) E 0 - 2 a (-y) /D] tdy + (y-eo)E(EO-2ay/D) tdy

W2 a eo) 0


141

0

Et [(- eo) o) + y( (o - 2eoa/D) + y 2(2a/D) dy

+ e

M = Et [ (e £ y) (y)+ (y2 /2) (s - 2eo/D + y3/3) (2a/D

1(

[(~~~~~._eo )o

(w+ +

o 0 0 0+ Et [-eoo ) (y) + (y 2/2) (Eo + 2eoa/D + (y3/3) (-2a/D)

= Et {(-eooo) (W- _- eeo) + -2 e) /2] (o - 2eoa/D)

+ L, 2 - %/ , ,.,-~,.,/ ,~3 /3] /o /n'~ 4- (-eoao) (W 4 eo)

+ + eo)2 /21 (o + 2eoaD) + (W + eo)3 /3 (-2ca/D}

Finally, collecting terms yields

= (Ee tc/6D) (4eW2 _ 3W2 )

(63)

Again in the development of this equation, it was assumed that

eo

< W/2. The moment, M, is then a function of: the tape

modulus of elasticity E; the tape geometry t and W the roller


142

geometry a and D; and the roller exit displacement eo. There,

fore, both the tension and the tape moment are nonlinear func-

tions of the tape exit displacement.

Figure 45shows the beam used to simulate the behavior of

the tape between rollers. K is a local torsional spring used

to simulate local slippage at the point where the tape initially

contacts the roller.

L

Figure 45

BEAM MODEL OF TAPE

The total moments MT, at any position in this beam is given by

MT = EIy"' - r (L - x) - M - T (eo - y) - Kyo (64)

or

Ely" - Ty = r (L - x) - M + Ky'

(65)EIy" - Ty = r (L - x) - M - T eo - Kyo


143

!

The solution to this differential equation yields the displace-ment of the tape at any position as a function of its propertiesand end conditions.

y = C1 cosh ( T/EI x) + C2 sinh (7/ I x)+ (L - x)

M + T e + KyT (66)

Taking derivatives

Y' = C1 -T7 sinh ( -T/E x) + C2 T/I cosh

Y" = C1 (T/EI cosh (~-/f x) + C2(T/EI) sinh

At x = 0, y = ei, therefore

rL M + T e + Ky°eI = +T T 0

At x = 0, y' = yi, therefore

Yi = C2 TE - T

At x = L, y = eo, therefore

T(/-VEi x) -r(67)

(-J/-Ti x)(68)

(69)

e = C1 cosh (T/EI L) + C2 sinh (IT/E L) -

At x = L, y' = yo is given by

M+Teo+ Ky'

°

T

(71)

Y O 1

C T/EI sinh ( T/EI L) + C2 T/I cosh (TEI L) -T

(72)


144

(70)

Equations 69 through 72 can be rewritten

C1 [1] + C2 [01 + r + Y 0 [- K = ei + eo + M (73)

C1 [01 + C2 [ E]+ r [- ] + y' [0 = i (74)

o 7

C1 L =sinh ( L)]+C2 [ ecosh (+y'0 L-~]=O (76)

Solving the above set of simultaneous equations for thecoefficient C1 and C2, yields the following slope equation

Y = (( T L)2 (2 L +M ) Msinh (- L) +( E L)2 (i

+ + L) [l-cosh ( L) + Y'i L

- sinh (- L)]) (( L)2 T sinh ( L)

- 2 L L K l-cosh ( 4 L) + L cosh ( L)

- sinh (E L)} (77)


145

The following nondimensional parameters are defined to simplify

the calculation procedure.

P = atL4DI

Q = L

MLEI

S = KLEI

U = L

e iV = L

Z = -L

ratio of roller geometry to tape geometry

(78)

ratio of tape tension to tape lateralstiffness (79)

ratio of roller movement to tape lateralstiffness (80)

ratio of roller torsional stiffness totape lateral stiffness (81)

ratio of response to free tape length (82)

ratio of input disturbance to free tapelength (

ratio of tape width to free tape length

Substituting these relationships into equation 77 yields

y R 2Ry=Q = (2U +- ) sinh (Q) + Q(V + 3U + 2)

[1 - cosh (Q)] + y'i [Q- sinh (Q)])

- (S sin- cosh (QQ) + Q cosh (Q)

- sinh (Q)4

(83)

(84)

(85)


146

(

Substituting equation 63 into 80

EeotaL (4eo2

_ 3W2 ) tL

4e

6 DEI - 6DI L(4eo2 _-3W2 )

L

R = -P (4U2 - 3Z2 )

Since the full width of the tape may not be in contact with the

double cone roller, this width (and thus Z) must be computed.

The tape will be in contact as long as its stress, a, is posi-

tive. For this to be true the total strain zero or equation 61

becomes

WEo 2a (- + eo)

D = 0

Then

W= - 2 a e )

o 2oDD

where W = tape contract widthc

Substituting this into equation

width Wc is obtained.

_t W

T Et 2aW (C - eo)T= D

62, the tension for a contact

aWc2

2D

2ae2 1

D

TL2 2 etL4 FW2 2Wce 2eo2TL 2 atL c co 0EI- = =EI L2L2 +L 2 °= L LJ

Q2 P 24zu 4u2)


147

(86)

(87)

(88)

(89)

Solving this equation for Zc

2

Z = V L6U2 ~ 4 1- 4728 _ 2

Zc=-2U + 8U2 +2 2 (90)

P

Here the positive sign for the radical was chosen since Zc is

the width to length ratio.

3.2.3 Computational Procedure

Equations 85 , 86 , and 90 are used to obtain the response

of the system for given values of the dimensionless geometry

factory P, the dimensionless tape width, the dimensionless

tension Q, the dimensionless torsional spring stiffness and

given values for the input eccentricity V. The input eccent-

ricity is given by

V = Vm sin (B A) (91)

Where Vm is the dimensionless amplitude of the input disturbance,

B is the dimensionless frequency (2vL/\), the dimensionless

tape position parameter A is the length of tape passing around

input roller divided by L and A is the wave length of the

input disturbance.

Then

Y'i = B Vm cos (B A) (92)

Figure 46 is a flow diagram for a computer program to

carry out the calculations described above. The program is

designed to compute response for the continuous sinusoidal input

of equation 91 or for a single sinusoidal pulse (one-half wave).


148

The program described first reads in the relevant data and

prints the data out along with a heading. A and U are set to

their initial values of zero. Then the dimensionless width is

checked for full contact using equation 90. If full contact

does not exist the value for full contact is used instead of

the actual width in succeeding calculations. The dimensionless

movement R is then calculated according to equation 86. The

input tape eccentricity and slope are calculated in accordance

with the continuous or pulse input depending on the sign of

the input magnitude (equations 91 and 92 ). Then equation 85

is used to calculate the output slope Y' . After printing out

A, V, U, and Z (displacement, input eccentricity, output

eccentricity, and contact width) a length of tape DA is passed

over the rollers by incrementing A by an amount DA. As the

tape rolls into the coned roller U, the dimensionless response,

is reduced by an amount Y'O DA,since no slippage on the rollers

is assumed. The program then checks A to determine if the

length desired has passed over the rollers. If it has, the cal-

culations are complete; if not, the contact width is again

calculated and the program proceeds from that point as des-

cribed before.

The computer flow diagram and computer program follow

as Figures 46 and 47, respectively.

3.2.3.1 Computer Program Use

The computer program for the transient analysis of the

double cone guide roller can be used to evaluated specific

guidance designs or it can be used to generate general design

data. The use of this computer program involves selection of

pertinent input data. To illustrate its use, a preliminary

analysis of the guidance system used in the functional layout,

Figure 2, of the five year recorder was made.


149

Double coned roller Diameter, D = 1.5 in.

Double coned roller Angle,

Tape thickness,

Distance between rollers,

Tape tension,

Tape modulus,

Tape width,

Input disturbance,

Torsional stiffness ratio,

Disturbance wave length,

Length of tape handled,

X = 1.75 deg.

t = .001 in.

L = 4.675 in.

T = 6 oz.

E = 800,000 psi

W = .5 in.

ei = 0.14 in.

S = KL/EI = 10

A= 18.85 in./cycle

t = 1500 in.

The dimensionless variables are now formed.

P = DtL4 = 1000DI

Q = L = 1.0

S = KL 3.0E1

e.VM = = .003

Z = W = .107L

The calculation step size, D, is selected and appears on the

computer input/out data. The constant, C, is equal to 2w/A.

The computer input data is shown in Figure 48 as it appears on

the data card. Figure 49 shows the input/output data for the

selected tape handling analysis. The input data is given to

the computer and is printed out prior to the output data. The


150

four output data columns are

X = vt

e.V =

L

eOU = o

L

WZ =o

L

length of tape passing over thedouble-coned roller as a functionof tape velocity and elapsed time.

dimensionless input disturbanceas a function of x.

dimensionless output response asa function of x.

dimensionless tape contact widthas' function of x.

The guidance system performance is assessed by computing

the percentage disturbance transmission past the double coned

roller.

Disturbance Transmission (DT) = peak output response x 100%peak input disturbanceproblem,

For the foregoing problem,

.= 0074DT = .003 X 100% = 24.3% (93)

Finally,

Figure 50 shows a plot of the input/output data generated on

this computer program. It indicates the response attenuation

of the input disturbance with a phase lag of about 90 degrees.

Iit RESEARCH INSTITUTE

151

H

0~

~

H0

--

--- -

z\4 Hn X

00

Preceding page blank | :

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INP

L,* 1U! D.)TA//3H P=e3I3.4 5X2HZ=E13 4 ,5X 2HGz= EI34,5X 2HSEEi3.4/3H V=E13,4

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7* 3X1r\/V,12X1 , 12XlHZ/)*" X=-( .

9* 4 -'.U+U+F 4 r 22. U+3SOPT(b.6*U *U+2.Q*Q/(P?)

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14' (".( TO 7144 6 Z ~Tj. 5* 7 q - f "' :h i/6 t )* ( 4 . *L*U- 3 , *Z Z )

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23* 9 iF (C*X-3.1415927) 10,11,1124 lI V=-V ' i*F I N8 X)2r5* y =-CVCVM*COfS(CX )26* GC TO 1?27* 11 V=On2R* Y I= O.29* 12 YP=(ti*4(2.*U+R/Q**2)*SH+Q*(V+3,*U++2*R/Q**2)*(1,-CH)+Yl*(GI-SH))/(30* iS*SH- ( 2, *:/ S/* ( 1, -O H) +Q*CH-SH )3!* i9QTT (6,13) X,V,UZ32* 13 FORMAT (4E13.4)33* U=U-YP*DX34' X)X+!Dx35* IF (X-XI ) 4,4 136* E '

ENO 9OF UCC 11i08 F2RTRAN V COMPIL4 TION, 0 *DIAGNOSTIC* MESSAGE(S)

Figure 47

DOUBLE CONE TRANSIENT ANALYSIS COMPUTER PROGRAM

155

P Z Q S VM C D L

"!" ~', . . 1 : C ,'F

o00-l 0 DOIoo o' 0oo o0a0 ooooo Ooo o Ioo0oooo', 0000000 100 00000 0000000000000aA~ 1 2 3 4 5 6 7 8 9 s 11 121314 S I1i I7 1920 0O 221324 2522 n 2829230 1323334353637363940414243444546474849505162 53545556s75859606166364 650%1686910 In 1 131475171n 1is39

11. 1111111! 111111 1 111111 11111111 1111111111111111, 111111 111111111 11111111111111

2222222222 22 2222222 2 2222 222222222222 2 2 222222222222222222222222222222222222222 2

,3 3 3 333 L 31 3 3 3 ! 33 i 333 3 3 31 , i i', 3 3 333 3 33 3 3 33 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 w

4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 7_4 4i _ 4 !44, 444444_4444 o

F SSi S'5SiS 5ji5 5-l5!,j......... 55i 5555555555555555555555555

89 3 n 3 ii 9 t 5 ° i 6 S iI 94999 99 888 89 8 8 8 8 8 8 98 8 8 8 8 8 8 8 8 8 8 8 8 8 8

~..'i 99I 9 9 9', 9 9999 9 99 9 999 q9 999999999999999999 99999999999 9 999999999 99999999 9991 2 3 4 5 6 7 6 5 1S 10 2 1 4 I 1 I' 14 15 1 i 22 2 24 2 621 26 28 23 3 2 31 3 34 35 36 37 30 3940 41 42 444 4546 4 7 48 49 50 51 5253 54 5556 57 58 59 6 162 63 64 656 67 68 63 70 712i 73 I ' 756 7 1 30

Figure 48

DOUBLE CONE TRANSIENT ANALYSIS INPUT DATA CARD

156

DOUBLE CONE GUIDE ROLLER TRANSIENT ANALYSIS

INxPUT OATA

p= - .2 720+03V-= . 1660-02

OUJTPUT DATA

Z= ,1660-00C: .3330-00

X

000002500-00

.5000-00

.7500-Ot0

1i250+01,1500+Ol,,1750+01

250U+01.2750+01.300n+01,3250+01.3500+o0123750+013 7 f 4 i34 j

,40( 1+ 01.4250+(1

45nO+01,4750+01.500C (+i15250(+01

.5 750+ 01,6 Q0U0+016250+01

6750+01

7250+i1-7500r4C775T'+0i

.91100+01

.9 t5 (3 + Q I

.n25*02.1905+32,1375+02

1 125 .+ 3 2, t1,Y' ,

.,OOCO,13S0-03* 2751-03.41,03-035426-036712 - 0.3

.7951 - 0 3

.91.35-031026-021. 131 -021228-02

,1316-02.1396-02.1466-02.1526 -02.1575-02.161 .3-02.16h4[-021656-021660-021653-021634 - 02

. 160C4-02.1563-02.1511-02.144 -02,1376-02

2 1294-02.1203-02.1104-02.996R8-03* 8 30-03.7630-03.6378-03

.3750-03

.2392-03

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-. 4454-03-. 5769-0J-. 7 ,43-03-. 626R-03-. 9437-03

.0000o1002-05

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.1466-03

.1540-03

.1610-03

. 1675-03

.1/36-03

.1790 03,1639-Q3,1882-03, 1918-03.1947-03,1968-03.1.98J-03,199g-03,1989-031981-03

,1965-03.1942-03.1911-03,1873-03,129-03.1'/77-03.1719-03,1655-03

.4459-01,4459-01.4458-01.4458-01.4457-01.4457-01.4456-01.4455-01.4453-01.4452-01,4451-01.4449-01.4448-01,4446-01,4445-01.4443-01,4441-01,4440-01,4438-01,4436-01,4435-01.4433-01.4431-01.4430-01,4428-03..4427-01.4426-01.4425-01.4423-01.4422-01,4422-01,4421-01..4420-01.4420-01.442?0-01.4420-01.4420-01. 4420-01.4420-01,4420-01.4421-0D1.4422-01,4423-01.'4424-01.4425-01.4426-01

Figure 49

DOUBLE CONE TRANSIENT ANALYSIS-EXAMPLE OF INPUT/OUTPUT DATA

157

Q=DX=

,5200-00.2500-00

SCXM:

,3000+nl,3!)00+o03

z

W <

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3.3 Tape Pack Design Analysis

3.3.1 Modeling

The major cause of damage in a tape pack arises from

spoking. It can be eliminated through the design of tape

packs without negative tangential stressed tape loops. The

stress distribution in a roll of magnetic tape which has been

wound at constant tension on a thickwalled cylindrical reel is

computed with the aid of a digital computer. The computational

procedure is outlined below.

1. Start with one layer of tape on the reel.

2. Compute the stress in this layer due to the'tension.

3. Add another layer of tape.

4. Compute the stress in this layer due'to the tension.

5. Compute the stresses in the tape layers belowthis outer layer due to the pressure from theouter layer.

6. Add these computed stresses to the previousstresses in the various layers to obtain theirtotal stresses.

7. Return to 3 and repeat until the total numberof layers desired are taken into account.

The stress equations for a thick walled cylinder were utilized·

in this analysis. This assumption was used in an earlier

analysis by G.K.I. The tape geometry, tape physical proper-

ties, the geometry of the tape pack, the hub geometry, and

the hub material properties can be varied in this procedure.

3.3.2 Computation Procedure

The nomenclature and formulas necessary for this analysis

are given on the following page. Flow diagrams (Figures 51 and 52)

for a computer program and a computer program to carry out the

procedure also are given. The input to the program is explained

in the nomenclature while the output is self-explanatory.

- -Preceding------ ]IIT RESEARCH INSTITUTE

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1* DIMENSION S(5000)2* 1 REAO (5,2) TR,WR,ERHR,TT,WT.ETPT,T,IT,IIRP3* 2 FORMAT (2F5,OF1o0,F .3F5,0,FlO.02F5,.,215,F5,O)4. RR=RR/2.54 WRITE (6,3) TRWRERRR,RP$TTWTETPToT6* 3 FORMAT (19H1TAPE PACK STRESSES///6X2HTR,lOX2HWR,lOX2HER4lOX2NRR,107* 1X2'4RP/5E2, 4//6X2HTT, iOX2HWT, IOX2HET#,OX2HPT,lOX1HT/5E12 4/)8. 1=19. IQ:II+110* H: RR11* A=RRi2" 3=RR13* DO 4 J-1,000014. 4 S(J):T/(WT*TT)15* TL=,52359878*B16* WRITE (h,5) I*R,S(l)17* 5 FORMAT (/ 6 H WRAPS,4X6HRADIUS,6X6HSTRESS/I6,?Ei2.4//6N WRAPS,4X6HRA18* 1DIUS,6X6HSTRESS)19* 6 !=i+l20* B=B+TT21, TL=TL+.*52359878B22* IF (I-IT) 7./e123. 7 P=r/(WTY6)24* PR=(P/ET)*(2,.eBB/(B*B-A*A))/((WT/(WR*ER))*((2,.*A*(ATR)+TR#TR)/(T25* 1R*(2,.A-rK) )+RP)+(BOB+A*A)/(ET*(3*B.A*A))+PT/ETi26. J=127* 8 AJzJZSH* N=RR+AJ*Tl29 DOSJ:=(PRA*A/(R*R))*(B*B+H*R)/(B*8"A*A)-(p*BE3/(R.R) )(A.A+R*R)/(B*3D. 1B6-AA)31* S(J)=S(J)+DSJ52* IF (I-O) 11,9,954* 9 WRITE (6,10) JR,S(J)34* 10 FORMAT (16,2E12.4)j5. 11 JOJ+II56o IF (J-1) 8#122i237* 12 IF (I'IO) 6,13,13,38* 13 Q:=!Q+IIJ9e WRITE (6,14) I,TL40* 14 FORMAT (//1H I16,1HO WRAPS OR *F5,0 49H FEET OF TAPE WERE USED FOR41 1 THE PRECEDING RESULTS//6H WRAPS,4X6HRADIUS,6X6HSTRESS)42* GO TO 643* E, Q

ENr OF OCC 11)8 FORTHAN V COMPZIATIUN, 0 *OlAGNOSTICa

MESSAGE(S)

Figure 52

TAPE PACK ANALYSIS COMPUTER PROGRAM

165

Figure 53 shows the minimum tape pack stress for a varied

amount of tape as a function of winding tension for a 1/2 in.

thick, 2 in. dia. aluminum hub.


166

cI4

I I

0I

o 0II0

C']

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Lfl

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Id r

Ir01

o~

u~

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IZ

F;' I

/I

I _

O

OI

H,

I-4

I o

o.j

E

z H

· ,.~ ,.~ I

I t

W

Z H

0H

0

0b

O

H*,1

0 I

0 I I

0 u

Z -

C'4

00

I .t

00

) O

/ I

H

4

I SIN

U

C

\o000II

E -

/ /

_o

t /

/

0

o o oo

o o

(1g d)

0a ~

o z

dw

nm~u

167

apn-vma~'T phn rl IrtTP }rm Trt a:6 .3.4 Tape Stress in a Double Coned Roller

3.4.1 Modeling

This analysis is performed to determine the stress in a

magnetic tape as it passes over a double coned roller with a

cone angle, a, a major radius, tD and a total wrap angle, 0.

As the tape passes around the roller, longitudinal fibers near

the center of the tape are elongated more than those near the

edge. For the purposes of practical tape transports, the tape

is assumed to pass around a straight roller to a double coned

roller and onto a second straight roller, (Figure 54). The

straight rollers are assumed to be at equal distances, L, from

the double cone roller. The tape system is symmetric about

the verticle through the double cone roller and therefore the

analysis is simplified by/ investigating half of the total

system. The roller radius for small values of a at any

position y, Figure 54 is given by

r = D - ya (94)

The length of tape in contact with the roller at any position y

is given by

LT = Or= ( D ya )0 (95)

At the outside edge of the tape

LTE = (2 -2 ) (96)

where

W is the tape width


Preceding page blank 169

! -- D

yi I

T- Po "'

0 22

LL

I/

Double Clne Roller

Straighti Roller

StraightRoller

Figure 54

TAPE ROLLER SYSTEM


170

The difference in the tape length at any position y is

6 = LT - LTE = 8 - y) (97)

If a first order approximation is used (no Poisson effect)

the strain distribution is

M -2Ea(y _ y) (98)LTET E D - Wa

The stress distribution is

= EE 2Ea(- y) (99)OL =

D - WA

For Layer 1

a = 2Ela(- - y) (100)D - Wa

For Layer 2

2E2CY(W2 - ) (101)L2 = -D- Wc

The local tension associated with a specific contact width

is determined by equating the summation of stresses across the

tape to the tape tension.

W

TR = 2 ((Lltl + cL2 t2) dy (102)

where Wo

is the total tape width in contact.


171

This relationship becomes

aEltl + E2t2) 2TR = DEt 2 t2 (103)

or an explicit relationship for W°

is

W° 1 4 - 1 + -El tl (104)oW Elt + E2 t2 (104)

or approximately

DTR 1 (105)o a a Elt1 + E2t2

The stress, due to excess tension, after total tape width

contact is achieved is given by

a1 [T W ] tlE 1 + t2 E2 (106)

02 rW T Eltl + E2t2

Tc is the tension for full tape width contact, W

The stresses along the tape length due to bending around the

roller are

E Y

°BA = 1 ( 1 PO) (108)

wherePo = radius of curvature of roller apex

= centroid of the equivalent cross-section

l1 = Poisson's ratio inside tape layer

42 = Poisson's ratio outside tape layerlIT RESEARCH INSTITUTE

172

and

- 2 E2 2][tl + E2 t22 +2 E2 ti t

E2(tl + t2 )

A

w > I I

E

t2 I I

E I1

Original Section Equivalent Section

Figure 55

EQUIVALENT CROSS-SECTIONS

0 BB = E 1 2al-2 ( 1

1J - 1)OBC = E2 2+D~ \D )

aBD E2 D


173

(109)

(110)

(111)

II-I .

e 1 tE0 - I Y

IJ _

E,,W I Y

The stress in the direction of the tape width due to bending

around the roller are

=WB = 2.WAEl | 1 + I2c'WB -~ -1 2 22 2

OWD =E (Y - tl) 1+ 22

2

aWD = E2(i - t1 t2 )

1 - P2

1 + 2 2P 0 D|

The total stress in the direction of tape motion are:

aLA = CL1 + C1 + CBA

aLB =L1 l + G1 + aBB

aLC = aL2 + '2 + 'BC

OLD a= L2 + a2 + °BD


174

(112)

(113)

(114)

(115)

(116)

(117)

(118)

(119)

3.4.2 Computational Procedure

The preceding tape stresses and their respective contact

widths were programmed for analysis on the digital computer.

A description of the computer input data is shown in Figure

56 and the computer program in Figure 57. A sample of the

output data generated from this analysis is shown in Figure 58

where principal stresses are given for both the oxide layer

and mylar layer at each of two parts, that is, on the outer

surface and on the inner surface. The direction of the prin-

cipal stresses are also specified as along the length, width,

and thickness. As is usual, positive stresses are tensile and

negative stresses are compressive. The actual width of tape

in contact with the roller is also printed out as contact

width.

Code

I

D

TT

W

R

ALP

TO

TM

EO

EM

PO

PM

Nomenclature Field

Orientation 1 = oxide out - 10 = oxide in

Roller major diameter 2-10

Total tape tension 11-20

Tape width 21-30

Roller apex curvature 31-40

Cone tape angle 41-50

Oxide thickness 1-10

Mylar thickness 11-20

Elastic modulus of oxide" 21-30

Elastic modulus of Mylar 31-40

Poisson's ratio, oxide 41-50

Poisson's ratio, Mylar 51-60

Format

I1

F9.0

F10.0

F10.0

F10.0

F10.0

F10.0

F10.0

F10.0

F10.0

F10.0

F10.0

Units

in

oz

in

in

rad

in

in

psi

psi

Figure 56

TAPE STRESSES OVER DOUBLE CONE ROLLER INPUT DATA

lIT RE'SEARCH - IN'STITUTE,

175

14 1 READ(5,2) I,DTT,W,R,ALP2, 2 FORMAT (It,F9.0$,15F1 0 )

3* READ (5,3) TO,TM,EO,EM sPOPM4e 3 FORMAT (6F10,0)5* iF(I) 4,4,56* 4 EI=EO7* E2=EM89 P-=PO

p2:PM9* p2=p1g* Tl=TO11* T2=TM124 TW=TT/W13* GO TO 6140 5 EL=EmI15' E2-E0OI.h6 P.=PM17* P2:PO1* TI:TIHl19 T2=TO20* TW=TT/W21* 6 CONTINUE22* CW:W23* Tlt.=T124* T2L=T225* EL:E2*(I,-Pl*P l)/( EI*(1.-P2PP2))

26* TE:T1L*E1+T2L*E2 \27* Y=:(TiL*T1L+EL*f2L*T2L+2.9EL*TIL*T2L)/(2*( T1L+EL*T2L))28* SBA:=(El*Y/(l.-Pl*P1))*(2,/D+PI/R)29* SPRH(El*Y-.TL)/(1,-PI*P1))*(2,/D+P1/R)30* SBC=(E2*(Y"T1L)/(1.-P2*P2))*(2,/D+P2/R)31* SDt=(E2*(YTL-T2L,)/(1.-P2*P2))*(2./D+P2/R)32* RHO=:/2.33. AR3C=(RHO-CW*ALP)34* Ql=(E1*ALP*CW)/(ABC)35' Q2=(E2*ALP*Cw)/(AbC)36* TR=((ALP/2.)*TE*CW*CW)/(RHO-CW*ALP)37* TWL=TW/16.-TR/CW38* IF (TWL) 30,31,3139* 30 CW:(TrT/TE)*(-,+(1,+(2.*RHO*TE )/(TT*ALp))**,5)40* ARC:(RHO-CW*ALP)41* Ql=(EI*ALP*CW)/(AbC)420 QG2 ( 2*ALP*CW)/(ABC)43* 31 SI=TWL*E1/TE44* S2:TWL*E2/TE45* SLA=SB3A+G+S146* SLBSS f3SBB++S147* SLC:SBC+G2+524g, SLD:SRU+Q +S249* SWa=(El*y/(1,-IPZlP))*(,l/R+2.*pz/o)50* SWU=(E1*(Y-T1L)/(1.-P I*Pl) )(1./R+2,P/1/D)

Figure 57

COMPUTER PROGRAM FOR STRESS ANALYSIS(DOUBLE CONE ROLLER)

176

'5i* SWC=(E2*(Y-TIL)/(1.-P2*P2))#(1, ./R+2,*P2/D)52* SWC=(E2*(Y-TL-T2L)/(1.-P2*P2))*(1,/R+2.*P2/D)

STd:U.O543F ST:=0.0n55' , TC=0.56* ST)=0.. '57* T=TW*W58* T'zTRT*16,59* IF (I) 7!7,860* 7 SOSL = SLA61* SOST = STA62* SOSW SWA63* SOCL = SLI64* SOCT = STR65* SOCW = SW 66* SMSL = SLn67* SMST = STD6R* . SMSW = SWO69* S tCL = SLC70* SMC T = ST

!/* SMCW = SWC72* ,;O TO 2073* 8 SOSL = SL=74* ST = STO754 SOSW = SwD76* SOCL LC '-77* SOCT = STC78* SOCW = SWC79* SMSL = SLA80* S MST = STA8J SMSW = SWA

2~ SMCL = SL38 3 SMCT = STR84* SMCW = SWBt5* 20 CO.T I NlE86* WRITE (6h9)87* 90F'ORMAT (CIHlOX, 54HPRINCIPAL STRESSES IN TAPE PASSING OVER DB-CNEa* 1iD ROLLER ////)89* WRTTL (6 ,10)90* 10 FORMAT (5X,19HPHYSICAL PARAMETERS //)91* WRITE (6#14)rT,W,DR,CW92* 140FORMAT ( 8X,30HTAPE TENSION ,F10,2,2X,3HOZ,o/93* 1 !X,30HTAPt WIDTH ,Fl10,32X,3HIN,,/94* 2 8X,30HROLLER DIAMETER ,Fl0,3,2X,3HIN,,/95 3 8X,30HCHOWN RADIUS ,FIO.2,2X,3HIN,,/96* 4 8X,30hCONTACT WIDTH $FlO,2,2X*3HIN,//)97* WRITE (6,11)98* 11 FORMAT (5X.15HIAPE PROPERTIES //)99* WRITE ( 6 ,.15)TO,TM,LOEMP OPM

100* 150FORMAT ( RX,'30HOXIUE THICKNESS ,F10,5,2X,3HIN,,/

Figure 57 (Cont.)


177

1 8X,0SOHMYLAR THICKNESS eF10s5,2X,3HIN,/ /

2 X,3*OHOXIL)E ELASTIC MODULUS ,F10O,O2X,3HPSTI/3 8X,3OHMYLAR ELASTIC MODULUS ,F100O,2X,3HPS!I/4 8X,30HPOISSON'S RATIO (OXIDE) ,Fl0O2,2X,3H w/5 3X,30HPOISSON'S RATIO (MYLAR) ,F10i2,2X,3H //)

1F (I) 25,25, ; 625 wRITL (6h12)12 FORMAT(5X,43HOXIDE STRESSESIPSI (OXIDE AWAY FROM ROLLER)//)

GO TO 2326 W1TE. (6,22)22 FORMAT (5X,41HOXIDE STRESSESPSI (OXIDE AGAINST ROLLER)//)23 CONTINUE

WR!TE (6,16) SOSL,SOST,SOSW,SOCLSOCT,sOCW160nORMAT ( X,J0OHSURFACE,LtENGTH OIRECTION

1. RX,0HsUQFACE, THICKNESS DIRECTION2 8XOHSURAC-EWIn0TH DIRECTION3 8X, 30HCEN1ER.,LENGTH DIRECTION4 . X,30HCENTER, ICKNES5 DIRECTION

h X,30HCE.!FTR, WI)DTH DIRECTION

WIt TL ( 6,15)13 FORMAT (5X,18HlIYLAH STRESSLS,PSI //)

wRITE (6, 17) SMSL.SMST,SMSWSMCL*SMCT.SMCW! 10/F RMAT ( X,3JOhSURF ACE L.tNGTH !DIRECTION

1 RX,0JhSUR ACE TH ICKNESS DIRECTION2 lX, JOFhSURFACE iWIDH DIRECTION3 8,30OHCLNTER, LENGTH DIRECTION4 RX,O0HCENTER, THICKNESS DIRECTION; A~X, JOHCENIERH,, WIDTH DIRECTIONGO TO 1F ND)

Figure 57

,Flo,0,2X,3HPSI,/,Fl0,02X,3HPSI,/#F1I0,,2X,3HPS ,/,FlOIO,2Xv3HPSl /,F10,O,2X3HPSI ./,FlO,0#2X, 3HPSI,//)

,FlO,0,2X,3HPSI /,FI00,02X,3HPSI,/,F100,o2X,3HPSI,/,F1,0.2X,3HPSI ,/,F10,O,2X,3HPSI /)sFI0l1,2XX3HPSI,//)

0 *DIAGNOSTIC* MESSAGE(S)

(Cont.)


178

1. U2

103*104*105"106 *1 ) 7 *108*109 :11 0'

113*1.14 115*116h117 *18*

12n0'121*122?123"124*125*1. 26 *127*

129*1. 3n*

,On (IF, 'IC ii f!P, FLPRAN V COM!IL .A I. ITON.

PRINCIPAL STRESSeS IN TAPE PASSING OVER OB-CNEO ROLLER 20

, . ,

PHySICAL, PARAMETERS -" ' ' -

T'P ENSION 4.00 .Z,TAPE W(iTH ,500 tN,R OUlLER ,DIAMETER ZtO0 IN. UCROWN RAD I US. '........ ........... , :.: ...-.- ,..--CONTACT WIDTH ...... ,1. I.N.

TAPE PROPERTIES

OXIUL THICKNESS 000.0C02G -. IN.,MYLAR .rI' t CNFS . ............ , 0.. .K..0..9 IN,. ... ..........OXI't; ELASTIC IQUQ,'U S .O0OCO PS! IMYLAR ELASTIC MODJL.'JS 65000', :PS'POI'S50N-5 RATIO (OXDe) ,40-POISS,0O'fS RA-TO (MYL.;-AR'5).-- .. ..:-' . .... 40' ' "

0XIDL ',TRE SESPSI' (OXI)DE AWAY F-QM RQLLER) . - ::

SURFACE LENGTH -D I.E('T I 0OS ...... .. ... ! . ...SU rFACE, 'rH I OTKPS 0. CTi- OIC ....... LC'I, PSI ...sLJ!*FAOE, ',g [ D'I'H O 4IRLC I:..I 4". . .......... P D l 1j .... P.[SCE:NTERjLENGT H. DIR;,CT TI? N 52:7 P$l!CENTERTHICKNESS DIRFEClON- . , PSCENTLR",,WIDTH DIRECTION .. .,' PS I

,iYLAR 5 S H Ei,$.P5. I

SURFACEP,[ENGTH DIFHECTION 4~, P$s:SURFRACE, TICK NESSS- .--JIRCECIIONN- - .. ... ..... , .. $, ....... SURFACE .W I!Th D.I r.El.I )ON ..- ................... 567, PSICEN T L.- ENRTI .FNT-D I'Pk;CT I ON)- - .4234 , PS- ....CENTLH, rHICKNESS UtREGfTION, n. CENTERoWTDTH DIRECTION 54, .PS!

Figure 58

PRINCIPAL STRESSES IN TAPE PASSINGOVER DOUBLE CONE ROLLER

179

PRINCIPAL STRESSES IN TAPE PASSING OVER DUBCNEO ROLLER -30

PHYSICAL PARAMETERS

TAPE TENSIONTAPE WIDTHROLLER DIAMETERCROWN RADIUSCONTACT WIDTH

4,QQ OZ,.500 IN.

1.,500 IN,- - -100 -IN,

- - --,1-5 IN.

TAPE PROPERTIES

OXIDE THICKNESSMYLAK THICKNESSOXILD ELASTIC MODULUSmYLAH EL4STIC MODULUSPOISSON'S RATIO (OXIDE)POISSON'S RATIO (MYLAR)

. 00020.0009200000o,

650000,.40,40

IN,IN,PSIPSI

OXIDt 5TRESSESPSI (OXIDE. AWAY FROM RQI..ER)

SURFACELENGTH DIRECTION 665. PSISURFACE,THICKNESS DIRECT I ON -.. PSI .SLHFACE.WIDTH DIRECTION 117, PSICENTLRLENGTH DIRECTION 624, PSICENTERsTHICKNESS DIRECTION O, PSICr.NTERWIDTH DIRECTION 81, PSI

MYLAR STRESSES, PSI .

SURFACE,LENGTH DIRECTION 2820, PSISURFACETHICKNESS DIRECTION ---.. - .- --- O, -PSISURFACE,WIDTH DIRECTION - -- - - -567, PSICENTERtLENGTH. DIRECTION - - -- 4.054, PSICENTtRTHICKNESS DIRECTION O, PSICENTER, WIDTH DIRECTION 524. PS!

Figure 58 (Cont.)

-PRINCIPAL STRESSES IN TAPE PASSINGOVER DOUBLE CONE ROLLER

180

pRINCIPAL STRESSES IN TAPE PASSING OVER DB-CNED ROLLER 30

PHYSICAL PARAMETERS

TAPE TENSIONTAPE WIDTHROLLER DIAMETERCROWN RADIUSCrNTlACT WiiDTH .

.6.O Z,.,500 IN,

I ,500 IN,1.0 . .IN,

. .19 IN.,

TAPE PROPERTIES

OXIDE THICKNESSMYLAR THI!CKNESSOXIDE ELASTIC MODULUSMYLAR ELASTIC MODULUSPQISSON'S RATIO (QXIDE)POIS50N'q RATIO -(MYLAR)

.. -.-..-. 00020- I IN,t· .00092 I.N,.

--' 1000Q0, PSI650000, PSI

,40· - ,4-0

OXIDE STRFSSES,PSI (QXICE AWAY FROM ROQLER,)

SURFACE:LENGTH DIRECTION -'785, -PS!SURFACE,THICKNESS -- I RECTION - -. - - - -O.- - -PS-ISURliFCE,WIDTH DIRECTION --- 117-, PSICENThRLENGTH DIRECTION 744. PSICENTERTHICKNESS DIRECTION 0, PSICENTER,WIDTH PIRECTION Bi,' PSI

MYLAR STRESSES,PSI

SURFACE,LENGTH D IRECTION 36Q1, PSISURF ACGETHICKNESS DI?-RECTI-ON - o , PS ISURFACEWIDTH I RECT-I ON - -- --- - - ------567, PSICENTER, LENGTH DIRECTION - 4835, PS!CENTERTHICKNESS PIRECTION O, PSICENTERWIDTH DIRECTION 524, PSI

Figure 58 (Cont.)


181

PHINCIPAL STRESSES IN TAPE PASSING OVER OB-CNED ROLLER 30

P-YS!CAL pARAMETERS

InPE. TESION '3.,00 OL,TA4P WIUTH ,500 IN,()OLLER D!AMETER 1,500 IN,

CROwN Ai[ I i!S 1.00 IN.C:iu raC r 'IiT" .21 IN,

TAPE PWQoPE~rI'IES

!OXI E THICKr K NS S .00020 I N,'YLLR THTICKNES- .00092 IN,OXIltE ELAST1C 'IODULJS 100000, PSIPiYL. A ELASTIC MODULUS 650000. PSIPcISSON'S RATIO (OXIDE) ,40mOIbSON'S RATIO (MYLAR} ,40

X'i-L STRESSES,PSI (UXirD. AWAY FPOf R0OLLER)

SLURFACELENGTH DIRFCTION 886, PSI: ! ,AF P C,F rF I C<K NE ;S [rC'D r ION Q. PS!' ;F ACE i. IDTH-4 D!RECT WI[) 117, PSI:-\ T'E LENGTH cDLT'CTLT!Cr 4845, PSICENTERTHICKNESS UIRECTION 0, PS!CE'J:NTRWIDTH DIRECTION 81. PS!

YLA, $ &THESSES,PS!

SURfACE,LENGTH DIRECTION 4259. PSIiURAC.ETHTCKKNESS DIRECTION 0. PSI

S 'F IACE, I[T DIREICTION -567, P!ICE'NER,LENGTH DIREC'IION 5493. PSICENT'ri THICKNESS Ul.RECTION 0O PSICENTe R.,WIDTH DIRECTION 524, PSI

Figure 58 (Cont.)


182

PKINCIP4L STRESSES IN TAPE PASSING OVER DB-CNED ROLLER 30

~~~~·.- . .- ^-...~j.lL,.PHYSICAL PARAMETERS ............ :...

TAPE TENSION O,0NO OZ.TAPE WIDTH , IN,ROLLER DIAMETER ;,0 INCROWN RADIUS.........................._ .. ... ......... ....... ..................COfN4TACT WI0THi .24 I N. CONTAG~r w I OT~'4 .2 .- .... -.. IN~.- -. . -... .... -....-....... ..: :... ..... ...... .. ... .. .---

TAPE PROPERTIES

OXIDE THICKNEFSS .0...00020 .I N,."NYLAR T C i(KN:LS:.S .. .......... O .00g 2 -...I-N, OXIDE ELASTIC MOQLUL.s L Q0 00, PSIMYLAR ELASTIC MODULUS 650000, PSPOIS' 01 N'S RATIO '(XIDE) ,40POIS50N'S PATI'O (-MiYLAR) .............. 4 . ....

QXIDE STRESSESPSI (OXiUO AWAY FROM ROLLER)

SUtRF rC.E,.NGTH O4 IREC4T-I.ON.--. . . ..... ... . . ...... g.~6 ., .4... .I...... ........ ....O1%EC T-L-UIQ. ....... .. 0, ....PSI

..SUiF A6,,/I.- g- I . ..............D ............P.....17, PSCEN T/gR L4ENGTH 0E-1 93, PS" ~,,, Ct-N......, .,4- PSI ... :.CENTER THICKNESS UIREQTION 0, P5SCENTERW!DTH DIRECTION '81 PSI

A'Y LAP .STRiESSESPSI .

SURFACELENGTH DIRECTION 4840, PSISURF .eCE, 't'H !O C--E$,q t~}E-?- t--O;N .....-.......................bJRFACE, W I DT4 DWiCT4In -,567 . PSIC-E N".R.LENGrH Ot. R U% rE ICTt)--f 60..........--.. .-- -0.74, PSICL N l' THk t C K.IE S t O lECT;10N O, PSICENTE.RWDTH PIRECTION 5 P4, PS!

Figure 58 (Cont.)


183

3.5 Bearings and Lubrication

A general review of bearing technology has identified the

anti-friction ball bearing as an excellent candidate for the

five-year transport. Utilizing conservative design procedures,

for both the bearing and its lubricant system, will produce a

highly reliable bearing system, if meticulous cleanliness

procedures and cautious assembly practice are followed during

the fabrication and check-out phases. The application of rol-

ling bearings to the five-year transport is further enhanced

over other bearing techniques, e.g., the aerostatic bearing,

because it is easily incorporated into the transport structure

with only minimal penalties in power consumption,. Relative

to this latter point, the ball bearing requires an order of

magnitude (a factor of 20) less power than its equivalent

aerostatic (pressurized air) bearing.

Traditionally, instrument ball bearings have been used in

satellite recorders because they require the lowest power

levels. Instrument ball bearings differ from the standard

contact type ball bearing in that the curvature between balls

and races is greater. Standard load carrying bearings have a

curvature ratio of approximately 52% while instrument bearings

are about 57%. The larger degree of curvature, see Figure 59,

(increasing percentage) leads to higher contact stress, but

also to lower torque resistance. For the goals of the five-

year transport, this type of trade away from reliability cannot

be made so automatically. To achieve the reliability levels

required here, major design areas dominating the use of ball

bearings are:


185


INSTRUMENT BEARING

RCurvature Ratio ( = 57%

"- D

Contact Area ---

-6- D

STANDARD LOAD BEARING

CurvatR,

ture Ratio (~2) = 52% Ball - Race

LARGER Contact Areahence lower stress levelsbut higher torque resistance

Figure 59

CURVATURE RATIOS FOR STANDARD AND INSTRUMENT BEARINGS

186

Race

; 11-- "`-.

* Designing for installation, that is,specifying installation practices whichdo not contribute excessive installationloads and hence only bearing failure.

* Use under a limiting contact stress forboth short term loads, e.g., high "g"shock loads, and the operating loadsresulting from pre-loads and tape tensions.

* Lubricant system design for long termeffectiveness.

* Final bearing selection after bearing testing.

Relative to the above, the following sections elaborate on the

basic technology and specify a recommended design and testing

procedure for the total bearing system, i.e., bearing and

lubricant.

3.5.1 Bearing Contact St~resses

3.5.1.1 General

Loads between balls and races produce large stresses

because of the resulting small contact areas. Due to the

effects of surface curvature, the inner race will generally

experience larger stress levels than the outer race. To

quantitize these stress levels, investigations have utilized

Hertzian contact stress theory that specifies the contact area

as a portion of the surface of an ellipsoid of revolution.

From this type of analysis, stress levels of 200,000 to

500,000 psi can be rationalized, previous use of point loads

did not yield direct insight into the mechanics within the

ball to race contact region. Because of the analytical com-

plexity associated with the elasticity analysis of ball bearings,

a vast assemblage of analytical and experimental data has been

developed to predict the stress distributions throughout the

bearing set. Most of this experimental data focuses on deter=

mining the magnitude of the contact region for a range of

bearing parameters, and also on developing approximate stress

and load formulae. To these results, the following sections

are addressed,


187

3.5.1.2 Contact Stresses Under CombinedRadial and Axial Loads

For the applications to the five-year transport, bearingassemblies will be subjected to both radial and axial loads.Normal transport loads result from tape tensions (radial forces)and pre-load forces (axial forces). During launch, shock andvibration can produce stress levels several times greater thanthose ordinarily encountered. Hence, its imperative that stressesbe evaluated for the launch as well as the orbiting modes. Forthe short term loads, industry practice recommends contact stressesno more than 300,000 psi; whereas, for the long term operatingconditions, maximum stresses of about 200,000 psi are recommended.To calculate these stresses, the following equations are provided:

Fr Fa

(120)JQ JZcos a JaZ sin a (120)

whereQ = max contact load

Fr = applied radial load

Fa = applied axial load

Z = number of balls

a contact angle during load

Jr = radial bearing parameter

Ja = axial bearing parameter9

The dimensionless bearing parameters Jr, Ja are tabulated for

various values of F tan a.a

188

Using Q from equation 120 the following relationship from

Hertzian contact stress theory is employed to determine the

maximum stress, e.g.:

-2Ff 72 =(121)

wherea = maximum compressive stress, psi

a,b = contact area parameters for various balland race curvatures and Q. These parametersare also tabulated in Harris7

Thus, by determining the applied loads for normal operation as

well as during launch, the resulting stresses can be calculated

and then compared to the following criteria for long life:

a < 200,000 psi normal loads - both radialand pre-load

(122)

o < 300,000 psi normal transport loads plusshock and vibration loads

3.5.1.3 Preload Effects

The techniques of pre-loading bearings have been employed

in transport technology as a basic method for removing radial and

axial play, and thereby assuring greater rotational accuracy of

the rotating shaft. Originally, stringent wow and flutter require-ments dominated the design to the point where substantial emphasiswas placed upon achieving a high degree of mechanical accuracy.By selecting Precision Class 7 or 9 instrument bearings and thenutilizing pre-loading and precise machining practices, the

requirements for dimensional accuracy were largely attained. Pre-loading produces further advantages by developing a smootherrunning bearing. Reduced torque pulsations result because theball-race geometrical relationships remain essentially constant

189

under varying loads; and further, self-excited oscillations

between balls and races are diminished.

In the development of a five-year transport, extremely finerunning bearings are not nearly as important as assuring a highprobability of survival for the mission life. Hence, the balancebetween wow and flutter performance and reliability must beestablished. For this case, a direct link exists between lifeand pre-loading. Figure 60 illustrates the maximum contact stressresulting pre-loading a R4B ball bearing. It is seen that forrelatively small axial loads, rather appreciable stresses(a > 200,000 psi) occur. For maximum life, minimization of amust also be considered in balance with the necessity for elimi-nating self-excited oscillations. These oscillations contributeto the reduction of operational life by increasing the number ofapplied load cycles. To obtain smooth operation, a rule of thumbis to apply an axial pre-load of not more than 10% of the bearingsdynamic load capacity. This load level is essentially a limitationon loading because of the effects on fatigue life. In recorderapplications, it has been generally found that 1% of the dynamiccapacity is sufficient, but this load should be verified experi-mentally for each case.

The two methods of preloading, that is, shimming (mechanicalinterference) and spring loading, require thorough analysis priorto their adaptation to the transport system. If shock and vibrationisolation between the transport and space vehicle is not possible,shim pre-loading is essential as resonance of the spring loadingwould result. Resonance must be circumvented because unacceptablylarge contact stresses will be produced. In general, where largethermal gradiants are encountered, spring pre-loading is mandatoryto accommodate differential expansion. Thus, the mission environ-ment from launch through orbital operation dictates the bearingconfiguration; and further, it must be recognized that conflictingrequirements will lead to trades and modifications of the originalgoals. As an example, if thermal gradiants of 60°C are possible,

190

8-

\) F

c4) U

C

l)

0

Q/0

~~

0U

0~3

o ,~

\N

o

w*

r-4c

0 -

EH

.) q

90 0

,sd '(xH

ssaI

S iu

oo

u a

191

it will be necessary to use spring pre-loading and thus shock

and vibration isolation techniques must be implemented to main-

tain the shock and vibration disturbances to low amplitude and

frequency levels.

3.5.1.4 Shaft Misalignment

A recent paper in "Wear".l illustrates quite graphically

the deliterious effects of bearing misalignment. At approximately

5 milli-radians of misalignment the stress on the cage pockets

increases rapidly. The article recommends the maintenance of less

than 2 milli-radians misalignment which amounts to 2 x 10 3 inches

in off axis center. The bearing used for the experimental study

reported on in the paper had a one-inch bore and thus could accom-

modate greater misalignment than the instrument sized bearings

which would be used in a recorder. The bearing alignment should

be accomplished by through boring the bearing housing. In any

case the greatest misalignment that could be accepted is less 0.3

milli-radians or 3 x 10- 4 inches off center per axial inch length

of shaft.

3.5.2 Bearing Torque

The torque resistant of a bearing - assuming adequate

lubrication - can be determined from:

M fl FBdm (123)

whereM = bearing torque

fl = coefficient of friction (empirically basedcalculation)

FB = combined bearing load

dm = ball pitch diameter

192

and

fl = dssY (Ref. 11) (124)

where

Fs = bearing static equivalent load

Cs = bearing static capacity

z and y are functions of the bearing design andare related to the bearing type andbearing construction.

The value of z for ball bearings ranges from 0.003 to

0.0013 and y ranges from 0.33 to 0.4 thus the coefficient of

friction, fl, could range from 1o2 x 10-4 to 6 x 10-4 for

Fs= 0.1. The lower coefficient of friction applies to a self-

C5

aligning bearing a = 10° , and the higher coefficient of friction

applies to a deep groove bearing where a = 0°,. These represent

two distinct bearing types.

The bearing equivalent load for bearing friction resistance

torque evaluation is:

FB = 0.9 FA cot a - 0.1 Fr (Ref. 12 ) (125)

or

FB = Fr (126)

where the one yielding the larger value of FB is used.

As an illustrative example the R4B bearing is selected,

Basic parameters of this bearing type are:

a = 16° Fs 3.2 lb.

dm = .434 in. Cs = 70 lb.

Fr

= 3 lb. Z - 0.0005 } Table 14.1

Fr = 16 oz. = 1 lb. Y 0.36

Then from equations 124 and 125

FB = 8.4 lb.

and

fl = 0.00047


193

from equation 123

M= fl FB dm

= 1.72 x 10 lb.in.

= 27.5 x 10 oz.in.

The power required for the bearing friction resistance oper-ating at a shaft speed of 2,000 rpm (cu = 209 rad/s) is:

P = cMor (127)

P = 40.8 x 10-3 watts/bearing

Obviously if the radial load (Fr

in equation 125) is themajor component of the loading then any perturbation of the tape

tension will be reflected directly in the bearing friction torque.

If, on the other hand, the radial load is a fraction of the axialload then any tape tension perturbation would have a very weak

effect on the bearing friction resistance. The bearing frictionalresistance due to the windage effect of the lubricant oil is

approximately one order of magnitude less than resistance due tothe bearing loadings.

3.5.3 Bearing Life Prediction

Bearing life prediction is based on the experimental datadeveloped by the bearing manufacturers. All of the bearing manu-

facturer's catalogue data is based on the L1 0life. The L1 0 life

is the life that 90% of the bearing would exhibit if loaded andcycled in an identical manner, i.e., speed, load, lubricant, andtemperature.

The basic dynamic capacity for both the outer and inner raceof a ball bearing is given by:

2fc A0.41 0.3 1.8 -0.33 (Ref. 13QC = A 2.K 1cOS (D) (z) lbs. (128)

194

whereA - material constant

f 5 curvature (r/D)

r = raceway groove radius

D = ball diameter

D cos a7a - dm

dm-= pitch diameter

a = contact angle

Z = number of balls

K(I- )1.39K = ( 0

3 3 3for inner race contact

(1 + )

K( 1 + ).39K (1 + ) 0 3 3 3 for outer race contact

The smallest value of Qc is that value of the contact load

for which 90% of the bearing will withstand one million (106)

revolutions without failure. The value of A is dependent on the

type bearing and the type and hardness of the bearing steel. For

single row ball bearings the value of A was determined to be 745014

from the statistical data, however, Palmgren recommends that a

value of 7080 should be used to account for manufacturing inaccurac-

ies.

Once the maximum contact load is determined from equation 120

the life (L) in revolutions for the desired bearing load can be

determined from:

L = Q, 13 (129)

195

This life (L) in revolutions is the L1 0 life, i.e., the

probability of survival for L revolutions is 90% since it is

based on L10 life studies and analysis of the Weiball statisticallife plots. Note that this life is, for the case considered,either inner or outer race contact. The life of the bearingis based on the probability of failure for both races. The life

(L) in revolutions for both inner and outer race is:

-L = L 1.111 -0.9 (130

whereLi = L10 life of inner race

Lo = L10 life of outer race

Estimates must be made for a life rating beyond the L10 life.15There are a number of methods that can be used The method which

will be used is that presented by McCool . If a survival probab-ility of S is desired then the life (Ls) in revolutions is:

Ls

= A1 A2 A3 (Q ) (13;1)

wherek = 3 for ball bearings

A1 = reliability factor

A2 = environment factor

A3 = material factor

The reliability factor Al is the factor that pushes the

extrapolation of the 90% experimental data supporting L1 0bearing

life. McCool1 6 lists the desired probability of survival, s, inpercent from 90 to 99 versus the A1 factor as:

S% 90 95 96 97 98 99

Al 1.0 .62 .53 .44 .33 .21

196

and gives the following equation which can be used to determine

Al for 0.90 < S < .999 as1

A1 = 1 (n 1).5 (132)

where K = 0.10536 for ball bearings.

Since the bearings will be fabricated from first class vacuum

degassed special melts the use of A3 = 1 is conservative. Actually

the standard material 52100 produced by special process can result

in an L10 life in excess of the L10 life predicted by the bearing

standards. Such examples have been reported where L10 life has

been extended by a factor of 20.

The environment factor A2 is equal to unity under standard

conditions and is predominantly effected by the lubricant. If a

full lubricant film can be maintained, then A2 = 1 is conservative.

One can object to the use of the A1, A2, and A3 factors (see16

discussion reference , however until a considerable body of

data for 99% probability of survival is developed one must extra-

polate and this method separates out the important factors. The

environmental factor A2 is of particular interest for instrument

bearings as it illustrates the importance of the lubricant.

3.5.4 Materials

For fatigue resistance, the best bearing steel is vacuumed

processed 52100 steel. The steel is vacuum processed to take

fullest advantage of the available technology. Essentially what

is being paid for by vacuum processing is less dispersion on a

Weibull life plot, which is the basis for the life estimate. The

52100 series steel is chosen in the absence of a corrosive atmosphere

because of the greater technical background in the production of

this alloy, and because its machinability characteristics are

slightly superior to the other material candidate, 440C stainless

steel.

197

Both 440C and 52100 steels are well within their preferredoperating temperature range since the recorder has a range from-5° to +600 C. However, the recorder tape may have to operate inan environment of relatively high humidity. In this event the440C stainless steel should be specified because of its greaterresistance to corrosion.

For the five year life requirement, most of the common retainermaterials such as brass and steel are immediately eliminated.Although these retainer materials can operate successfully overa wide temperature range they suffer from inherent wear pattern prob-lems'and a lack of retection of the oil source. The optimum retainermaterial choice within the temperature region of -5° to +60°C is atpresent a porous phenolic impregnated with the same oil as that usedfor lubrication. A possible challenger could be porous bronze,which is currently used for high speed, high temperature applications.

The ball retainer must also be chosen to enhance the overallbearing reliability. The advantages and disadvantages of porousphenolic and porous bronze retainers indicates that experimentalvalidation is in order. With adequate lubrication, a phenolicretainer will exhibit minimal wear. The manner in which it wearsis to smear the plastic from ball to raceway and finally seizethe bearing because of reduced radial play. With a bronze retainer,the wear consists of small metallic particles which can be thrownout of the bearing. In any case, they do not exhibit the stickingthat is shown by plastics. Thus, the bearing can continue rollingafter a somewhat greater degree of wear takes place. Bronze alsowears at a lower rate than does a phenolic. If one was attemptingto extract the most life after an adequate lubricant replenishmentwas completely depleted, an oil filled porous bronze is a challengingcandidate.

198

3.5.5 Lubrication and Environment

The weakest link in the life chain of an instrument bearing

is lubrication. Typically, instrument bearings are lubricated

and are on their way to a predictable end at an unpredictable

time. Usually lubrication starvation does not cause the failure.

Air borne contamination, improper cleaning procedures, and

maintenance initiated deterioration are more likely to be the

root of the problem.

If the design life objective was 1000 hours or less, then

satisfactory lubrication could be obtained with a one-shot instal-

lation. However with a life requirement in the tens of thousands

of hours, possibly operating continuously, lubricant replenishment

must be incorporated into the recorder bearing design. Two

schemes of lubricant replenishment are available; a reservoir of

lubricant at each bearing and wick feed, or a central lubricant

reservoir from which lubricant could be periodically pumped through

capillary tubes to each bearing.

Andok C lubricating grease with a phenolic retainer has long

been a standby in instrument bearing lubrication. Review of the

differences between grease and "oil only lubrication" shows that

the major difference is the mixture of small soap spheroids1 7

in

with the oil. The effect of the soap breakdown is to raise the

apparent viscosity of the lubricating oil, thus increasing the

minimum oil thickness separating the ball to race contact. As an

example, the rolling speed of a 3/16 ball in a typical recorder

application would range from 1 to 15 in./sec. With a G1 lithium

hydroxysterate soap grease, the minimum film thickness would range

from h , 3 x 10 in. to 12 x 10-6 in. while the base oil alone

-6would generate a thickness range from h 2 x 10 in. to

8 x 106 in. for the same load and speed conditions.

199

Considerations of oil film thickness -- particularly between

the balls and the races -- is crucial to the success of the

bearing system. Tallian9 -clearly illustrates the impact of film

thickness on L10 life. He reports on the statistical evidence

that a ratio of film thickness composite surface roughness, ~o,

of less than a factor of two (2) results in major life reduction,

e.g., a change in ~ from 2 to 1 produces a L10 reduction from100% to 50%. Hence, a main design specification for the lubri-

cant is that for the transport's bearing range of speeds, loads,

and temperature, ~ should be maximized, i.e.,

Minimum Film Thickness(h) (133)= Composite Surface Roughness (R

t > 2 (preferably: e = 4, L1 0

increased 200%) (134)

Numerically, this ratio represents a film thickness criteria of:

h - 40 x 10-6 in.

since, for precision bearing, the surface roughness factor (R)

is approximately

R = 10 x 10=6 in.

17In the work by Dyson and Wilson 7 bearing failures have been

attributed to oil starvation. In one case, starvation occurred

after 45 minutes of operation at a rather high rolling speed of

80 in./sec. The important parameters which effect film starvation

are the oil viscosity and surface tension. Starvation does not

recessarily imply a lack of oil in the general sense but more

specifically the problem of oil supply at the inlet position of

the ball. The correct amount of oil is more important than an

excess of oil since an excess of oil can lead to churning, thus

heating the oil, decreasing the viscosity, and wastefully absorbing

power. At relatively slow ball speeds ( a few in./sec.) expected

in a recorder, it is unlikely that film oil starvation would be

encountered. However, loss of oil may be experienced owing to the

200

zero gravity effect. In such a case, minute amounts of oil maysplash away from the ball, and not return to the bottom of therace. This "lost" oil must be minimized and replaced.

Oil loss can be minimized by presenting non-wetting surfacesin areas adjacent to the bearing (Fig. 61). Where oil is at ajunction of a non-wetting surface and the bearing,the surfacetension of the oil can be used to prevent further oil exit motion.

20A low surface energy layer such as Nye Bar is commerciallyavailable and can be easily applied to surfaces adjacent to abearing. A Teflon liner would also serve the same purpose.

Continuing the exploration of methods to ensure sufficientlubrication, one can consider the combination of zero gravity andwetting surfaces. Any splashed off oil from the bearings, willnot have zero velocity. It will at least drift in the shafthousing until it hits the shaft housing or the shaft. If it hitsthe shaft it will experience a velocity change. Ultimately anydrifting oil must contact the shaft housing wall. The shafthousing wall should have an oil wetting surface. Any oil thatcontacts such a surface would spread. The surface tension effectcould then be used to return the "lost" oil to a central storagefrom where it could by recycled. In theory this scheme would workif the ancillary flow control problems do not produce a reliabilitypenalty on the recycling of the lubricating oil.

The oil chosen as the lubricant must have a relatively flatviscosity curve with respect to temperature between -50C and 600C.It must be highly refined so that any varnish forming impuritiesare removed. It must not contain any oxidation preventive additives;since the complete recorder should be in an inert gas environment.The soap which carries the oil must be a non-caking type andinvestigation should be made into the effects of long term shelflife on any candidates; since, that is probably the closest testto setting in a bearing for long periods that can be made.

201

Oil Barrier

Oil Reservoir

'Bearing Housing

Non WettingBarrier Film

b) Oil Reservoir - Wick Feed Lubricant Replenishment

Barrier

Oil Inlet Port

Non WettingBarrier Film

a) Pulsed Lubricant - Replenishment

Figure 61

SCHEMATIC OF LUBRICANT REPLENISHMENT CONCEPTS

202

1

II

The necessary gas environment to maximize reliability is

therefore a low humidity, inert gas. An acceptable candidate

is nitrogen with a trace of helium for leak checking. The

consideration of over-riding importance is to insure the absence

of oxygen. Essentially all lubricants are oxidized at a rate

that is an exponential function of temperature. The operating

temperature of the recorder is not severe, but the greatest

environmental damage to lubricants is the development of the

so called "brown sugar"; a result of lubricant oxidation. Con-

tinuing the discussion of the gas environment, it-would be

preferable to reduce the water content to zero. A conflicting

requirement is the required humidity level of the tape. If the

water level cannot be reduced to minimal levels -- say 5%

relative humidity -- then the use of 52100 steel should be

reevaluated and 440C stainless steel becomes preferable bearing

material.


203

mT-rTh;qT1T 1 qT,, NT7 i"TOT F:ThThS

3.6 Kinetic Analysis

3.6.1 Modeling

The function of this analysis is to determine the

changes in kinetic properties as magnetic tape is transferred

from one tape reel (assumed to be on the right) to another

tape reel (on the left) ignoring the effects of system friction

and tape tension drag. The nomenclature is given in Table 13.

3.6.1.1 Rotational Velocities of the Tape Reels

The change in radius of the reel hubs plus tape over

time is given by the expression:

1

rL = (rH 2 + VT62 (135)

1

rR ( r HO2= &(L-VT),(r 2 + -VT (136)R ('HO VPt

The rotational velocities of the reels are:

XL V (137)~L -rL

CI>R rR (138)C'R rR

3.6.1.2 Reel Inertia

TpHW(rHO4 - rHi )Iu = (139)

ILT =pTW (rL

4- rHO

4 )

4 4WVPTW(rL _ rHO )

2


205Preceding page blank

(140)

Table 13

KINETIC ANALYSIS NOMENCLATURE

= outside radius of the left reel including tape

= outside radius of the right reel including tape

= outside radius of the tape reel hub

= inside radius of the tape reel hub

= tape velocity

= time since analysis began

= thickness of tape

= packing factor for tape

= total length of tape

= rotational velocity of left reel

= rotational velocity of right reel

= moment of inertia of the reel hubs

= moment of inertia of the tape on the:left reel

= moment of inertia of the tape on the right reel

= density of the hub material/g

= density of the tape/g

= width of the tape

= moment of inertia of the left hub and tape (reel)

= moment of inertia of the right hub and tape (reel)

= angular acceleration of the left reel

= angular acceleration of the right reel


206

rL

rR

rHO

rHI

V

T

6

PT

L

LDL

R

IH

ILT

IRT

PH

PT

W

IL

IR

aL

aR

Table 13 (Cont.)

KINETIC ANALYSIS NOMENCLATURE

= torque potential of left reel

= torque potential of right reel

= rotational energy of the left reel

= rotational energy of the right reel

= rotational power of the left reel

= rotational power of the right reel


207

TL

TR

EL

ER

PL

PR

IRT =

VpTW(rR rH04 )

2

IL = IH + ILT

IR = IH + IRT

3.6.1.3 Torque Determination

.L2 -wL1aL = XL - T2 - T1

e R2 - R1aR = R - R2 - R1

zL = ILaL

rR = IRR

3.6.1.4 Angular Momentum

ML = ILWL

MR = IRWR


208

(141)

(142)

(143)

(144)

(145)

(146)

(147)

(148)

(149)

3.6.1.5 Rotational Energy

2E ILL (150)

L 2

E IR2R (151)R 2

3.6.1.6 Rotational Power

PL = EL 2 T (152)

ER2 -ER1 (153)PR = ER = T- T1

3.6.2 Computation and Documentation

The preceding formulas were programmed on the digital

computer in order of their appearance. The required input

data is shown in Figure 62, and the computer program in

Figure 63. The input/output data is shown in Figure 64

where the results can be read directly from the computer

printout. The example shown illustrates the change of the

various kinetic properties in five second time increments at

a tape speed of 32.0 inches per.second.


209

FormatNomenclature

Inside Hub Radius

Outside Hub Radius

Hub Density

Tape Length

Tape Width

Tape Thickness

Packing Factor

Tape Velocity

Time Increment

Tape Density

1-7

8-14

15-21

22-28

29-35

36-42

43-49

50-56

57-63

64-70

10F7.0

10F7 .0

10F7.0

10F7.0

10F7.0

10F7.0

10F7.0

10F7.0

10F7.0

10F7.0

ins

ins

lb in

ft

ins

ins

-1in sec

sec

lb in

Figure 62

KINETIC ANALYSIS INPUT DATA

210

RH

RHO

DH

D

W

DE

PT

V

DT

UnitsFieldCode

1* RtAD 20,RHRHO,DH , tW,DEPTV T#DT

2* 20 FORMAT ( tOF7.0 )

' "t -PY 3.141.59 Figure 6344 5 = O* 1.2.0'

;A 1 -r.. KINETIC ANALYSIS COMPUTER PROGRAM

7'-' UO = f!,n7~', O = OR

9* E0 0= 0.0

1 ;' -((RUY))2. + ((T py) ) )*O511* C' (_ f; HCO)$"2 2.O +( ((B*DitE) / (PT/*PY)))**O*5 ) /

13* C RL + Rq14* ... - V/RL15* R' ; - V/R

6'i , '-* ;; ( PY-V*D4*OW* ((RHO**4.0) - (RH**4.0 ))) /(2,0* 386,0887T = ( l-',)Y*"Ii*(( RL*4.0 ) -( FRHQO 40 )3*PT) /(2.r> 33 .]dr8

81P 8* ;' : I:f - ",F'T"-W* ((RtR*4.U) - (RH*'*4,0))TPT) /(2,0* 3P, 6.08R1 9i A,!L : hH + AiTL2 )~ A tpi = ATM4-i + I F'R.4 :.. ' + L.r

2.:2 0.' = ......L .7)Ct'. r -:/* (

1 ''.'1' - A *t r't

4 * 0'=_ -'! EG , iA,E~St AL.A! L =il, : !- 70!t".iL / i'

.1 .- Li I *.-:i = I Cl i ,Lt : . / 2

37' 3lri* = - A !..Pt L2

3tr* i'" = TIR !i!G31'i EL= (/I -. (( 'iGL*f2 )) / 2T39*- C' i; = ( ;,!' * (O'IE!GN:2,0)) / 2., .3'-4 : ;r 2 2_ + L ....34

37* t:: : _ rl

3R* P.;RqL = nE!._ / T3'J* Fr',:, = DE / T,l, , ~ ~ r -.... 4, _ 2kC:, 24 , 24Q

41 e ;2 ;:T I ''!42'; 23t i ~3 ;, '; 1t; 3'3H TI!r I; L:tNGTH RADL RAD.R CTR.D Cr"FGA L Oi'EGA R INpERT L,43* I"FRf R '!r'F. E L iQFiEG R ERG L FRG R ERG T TORrGUE L TORQUJE R POWLP4 . l. r , . i< )

45; FRtl'f '~546* 2335 F: 'rM I 13J..2-H SFC;. INCHES IN . IN. IN. iRAD/SEC R;iD/SEC i[i!LB6C247* .t I N, 2 IiNLLBSECG INLUBSEC IN.LB lLB INL L IN.LB , ,LBS I LBS. INLFR/S48r 2tEC I I.U/$ C / )

49: AA = 5.05 * 240 PRINf 250,C(A,B,RL,RR,C,OP1EGL,OMEGR,AIL ,AIR ,OMEGIL,OMEG1P,E LLR,51. . 4ET, TQRK'L, TORgR, PWRLI PWRR )52* 250 FORMAT ( F5.0,F7.C,3F6. 3,E 3,3F6.3,4E9 .4 )

.n O ¢ tA A + TF ( r - ) 4 0 270, 270

58,:, ?270 P rINTr 28056, 2120 Fc:RMA'\r ( 102H JR HlUB OR HUB DENS.HUB LGT,TAPE WDT.TAPE I' -57 1].KTAPE PK FCTR rAPE VEL TIME INCR DENS.TAPE /)

P R I'N 2 8528D5 k- Fi,!·/'F ( 1.it-! IN(;CHES INCHES Li' W// I 3 F3 E T ! 'CH.S i

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211

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3.7 Alternate Motor Speed Reducer

The requirement of providing different tape speeds for the

record and reproduce mode of an operable transport has histori-

cally been accomplished by using either gear or belt pulley

assemblies. Such speed reducers coupled with capstan diameters

in the order of 0.5 inches or less have allowed reasonably high

rotational motor speeds to be used.

The use of this type of speed reducer was eliminated with

the decision to minimize all possible critical components within

the transport including gears and belts. A direct drive strat-

egy was adopted where the capstan became an integral part of

the drive motor in a modularized form.

A further requirement of minimizing stress levels within

the tape demanded a substantial increase in the diameter of the

drive capstans up to a minimum of 1.0 inch diameter. These two

requirements coupled with an assumed low tape speed in the

order of 1.5 inches per second result in a low motor speed of

approximately 20 rpm.

Although the use of such a low motor speed is not con-

sidered to be detrimental to the overall life of the transport

at this time, a design was conceived for an alternate slow

speed capstan in which a six to one reducer allows a motor

speed of approximately 120 rpm to be maintained for a tape

speed of 1.5 inches per second.

The mechanical reducer illustrated in Figure 65 is an

integral part of the capstan/motor assembly and situated between

them. Three disks (steel rim mounted on an elastomer support)

are driven by the motor shaft through friction, enough force

is obtained between the disks and the drive shaft to insure

rolling and hence no slippage. Gear or belt pulsations are,

of course, eliminated in this transmission, as the outer dia-

meter of the disks drive the capstan from the inside. A unique

feature of this drive is the method for decoupling the reducer


217

during the high speed mode. During playback at high speed,the slow speed capstan would drive the slow motor at a 24:1

increase in its normal speed. To circumvent this condition,

the cage that couples the planetary disks is unlocked duringthe high speed mode. This unlocking of the cage permits the

planetary disks to freely rotate and hence allows the drive

to operate at a speed ratio of 1:1.

It is obvious from the underlying philosophy adoptedthroughout this design study that the concept of direct drive

even at low motor speeds is desirable owing to the complexity

of this arrangement. In the event, however, that the required

motor characteristics are not obtainable at extremely lowrotational speeds, this assembly is considered to be the mostdesirable alternative to obtaining reliable operation at low

tape speeds.


218

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Preceding page blankREFERENCES

1. Scopelite, ToMo, Error Analysis of Tape TransportSystems, IIT Research Institute, Project Noo K1039,September 1967.

2. Owen, R.J., Magnetic Head/Tape Interface Study forSatellite Tape Recorders, Contract No. NAS5-11622,IIT Research Institute, Project E6134, February1971.

3. Owen, R.J., Five Year Magnetic Tape for UnattendedSatellite Tape Recorders, Contract No. NAS5-21623,IIT Research Institute, Project E6205, to be pub-lished,

4, Benn. GoSLo., Mariner Mars-71 Head/Tape Stick-SlipStudy, JoPoLo Contract No. 952832, IIT ResearchInstitute, Project E6169, February 1971.

5. Eshleman, R.Lo and Rao, P.N., "The Response ofMechanical Shock Isolation Elements to High RateInput Loading," Shock and Vibration Bulletin,No. 40, p. 5, December 1969, ppo 217-234.

6. Davies, GoLo, "Magnetic Tape Instrumentation,"McGraw-Hill, New York, 1961,

7. Eschman, P,, "Roller Bearing Wear Life," ASME,1967.

8. Magnetic Tape Study, ASTM Report Noo AD 238 884L,January 31, 1960.

9. Harris, To.A, "Roller Bearing Analysis," 1st Edition1966 - J. Wiley and Son, New York, p, 171.

10. Crawford, T.S., "The Experimental Determination ofBall Bearing Cage Stress," Wear (16), 1970, ppo 43-52.

11. Harris, opo cit,, p. 446.

12. Ibid., p. 477,

13. Ibid., p. 350.

14. Palmgren, A., "Ball and Roller Bearing Engineering,"3rd Edition, Burbank, 1959.

15. Harris, op. cit., ppo 412-415.


221

REFERENCES (CONT'D)

16. McCool, J.L., "Load Ratings and Fatigue Life Predictionfor Ball and Roller Bearings," ASME Trans., J. LubeTech., January 1970.

17. Dyson, A., Wilson, A.R., Film Thickness in Elastohydro-dynamic Lubrication of Rollers by Grease, Inst. ofMech. Eng. Symposium on the Use of Grease as an Engineer-ing Component, London, February 19-20, 1970.

18. Wedeven, L.D., et al,"Optical Analysis of Ball BearingStarvation," ASME, 70-LUB-19.

19. Tallian, ToE., "On Computing Concept Modes in RollingContact," ASLE Trans., V. 10, 1967, pp. 418-439.

20. William F. Nye, Inc., Bedford, Massachusetts.


222

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