AGMA 918-A93

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    AGMA 918-A93

    /

    c= Reproduced By GLOBAL

    a ENGINEERINGDOCUMENTS

    B z With The Permission Of AGM

    -7 Under Royalty Agreement

    AMERICAN GEAR MANUFACTURERS ASSOCIATIOiV

    A Summary of Numerical Examples

    Demonstrating the Procedures or

    Calculating Geometry Factors for

    Spur and Helical Gears

    AGMA INFORMATION SHEE

    (This InformationSheet s NOT an AGMA Standard)

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    918-A93, A Summary of Numerical Examples Demonstrating the Procedures for

    Calculating Geometry Factors for Spur and Helical Gears

    CAUTION NOTICE: AGMA standards are subject to constant improvement, revision, or withdrawal as

    dictated by experience. Any person who refers to any AGMA Technical Publication should be sure that the

    publication is the latest available from the Associat ion on the subject matter.

    [Tables or other self-supporting sections may be quoted or extracted in their entirety. Credit line should read:

    Extracted from AGMA 918-A93, A Summary of Numerical Examples Demonstrating the Procedures for

    Calculathg Geometry Factors for Spur and Helical Gears, with the permission of the publisher, the American

    Gear Manufacturers Association, 1500 King Street, Suite 201, Alexandria, Virginia 22314.1

    ABSTRACT

    This information sheet provides numeri cal examples for calculating the pitting resistance geometry factor, I,

    and bending strength geometry factor,J, for typical gearsetsthat are generated by rack-type tools hobs, rack

    cutters or generating grinding wheels) or piniowtype tools disk-type shaper cutters). The numerical

    examples are shown in tabular form and provide thevaluesforall variables as calculated using the procedures

    and equations in AGMA 908-B89. A flow chart, intended to assist in the development of a computer program

    for these variables, is also included.

    Copyright 0,1993 by American Gear Manufacturers Association

    Published by

    American Gear Manufacturers Association

    1500 King Street, Suite 201, Alexandria, Virginia 22314

    January, 1993

    ISBN: 1-5558~17-0

    ii

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    Table of Contents

    Page

    Foreword . . . . . . . . . . . . . . . .

    . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

    V

    1 Scope

    .........................................................................

    1

    1.1

    Numericalexamples

    .............................................................

    1

    1.2 Flow chart ...................................................................... 1

    1.3

    Exceptions

    .....................................................................

    1

    2

    Definitions and symbols

    ..........................................................

    1

    2.1

    Definitions

    ......................................................................

    1

    2.2

    Symbols

    .......................................................................

    1

    3 Numericalexamples

    .............................................................

    4

    3.1

    Examples

    ......................................................................

    4

    3.2

    Tabulation of examples

    ..........................................................

    5

    4 Flow chart

    ...................................................................

    28

    5 Cutting tool geometry

    ...........................................................

    37

    5.1

    Rack type cutting tools

    ..........................................................

    37

    5.2 Pinion type cutting tools ......................................................... 37

    5.3

    Cutting tool drawings

    ...........................................................

    37

    Tables

    I Symbols used in equations

    ....................................................... 2

    2A Accurate spur gears, example 3.1 .l

    ...............................................

    6

    2B Accurate spur gears, example 3.1 l

    ...............................................

    7

    3A Inaccurate spur gears, example 3.1.2

    ..............................................

    8

    3B Inaccurate spur gears, example 3.1.2

    ..............................................

    9

    4A Conventional helical gears, example 3.1.3

    ..............

    :

    ..........................

    10

    4B Conventional helical gears, example 3.1.3

    ......................................... 11

    5A Low axial contact ratio LACR) helical gears, example 3.1.4

    .........................

    12

    5B Low axial contact ratio LACR) helical gears, example 3.1.4 ......................... 13

    6A Conventional helical gears, different tools, example 3.15

    ............................ 14

    6B Conventional heli cal gears, different tools, example 3.1.5

    ............................

    15

    7A Spur sun and planet gear, example 3.1.6

    ..........................................

    16

    7B Spur sun and planet gear, example 3.1.6

    ..........................................

    17

    8A Spur planet and ring gear, example 3.1.7

    ..........................................

    18

    8B Spur planet and ring gear, example 3.1.7

    ..........................................

    19

    9A Helical sun and planet gear, example 3.1.8

    ........................................

    20

    9B Helical sun and planet gear, example 3.1.8

    ........................................

    21

    10A Helical planet and ring gear, example 3.1.9

    ........................................

    22

    1OB Helical planet and ring gear, example 3.1.9

    ........................................

    23

    11A Conventional double helical gears, example 3.1 .I 0 .................................

    24

    11B Conventional double helical gears, example 3.1

    l 0

    .................................

    25

    12.r Herringbone gears, example 3.1.11

    ...............................................

    26

    12B Herringbone gears, example 3.1 .ll

    ...............................................

    27

    Figures

    1 Flow chart for Z and .Zsubroutines for AGlvlA 908-B89

    ... ...........................

    28

    2 Hobfor examples3.1.1 and3.1.2

    ................................................

    37

    3

    Hobforexamples3.1.3and3.1.4

    ................................................

    38

    .

    III

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    Table of Contents cant)

    4

    5

    6

    7

    8

    9

    10

    11

    12

    Page

    Hobfor example3.1.5

    ..........................................................

    38

    Helical pinion type shaper cutter for example 3.1.5

    .................................

    39

    Hobforexamples3.1.6and3.1.7

    ................................................

    39

    Spur pinion type shaper cutter for example 3.1.7 ................................... 40

    Hob for example 3.1.8

    ..........................................................

    40

    Helical pinion type shaper cutter for examples 3.1.8 and 3.1.9

    .......................

    41

    Helical pinion type shaper cutter for example 3.1.9

    .................................

    41

    Hobforexample3.1.10

    .........................................................

    42

    Helical pinion type shaper cutter for example 3.1 .ll

    ................................

    42

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    [The foreword, footnotes, and annexes, if any, in this document are provided for informational purposes only

    and are not to be construed to be part of AGMA 918A93,

    A Summary of Numerical Examples Demonstrating

    the Procedures for Calculating Geometry Factors for Spur and Helical Gears.]

    This AGMA information sheet and related publications are based on typical or average data, conditions, or

    application.

    This information sheet, AGMA 918-A93, was prepared o assist designers in the proper use and interpretation

    of AGMA 908B89 and to assist in the development of computer programs when calculating geometry factors

    for pitting resistance, I, and bending strength, J. A flow chart provides a step by step procedure for the

    calculation of these factors, either manually or by computer program. Several examples are provided to

    demonstrate the calculation procedure for the various characteristics of geometry as described in AGMA

    908-B89.

    These include accurateand inaccurate spur gears, conventional and LACR helical gears, internal and external

    gears, double helical and her ringbone Sykes) gears, and addendum modifications. The calculation of J-fac-

    tor for internal gears is not defined in AGMA 908B89 and, therefore, is not covered in this information sheet. A

    tabulation of all calculated variab les is provided for each example based on its design criieria.

    This provides

    the designer with known results to check against when calculating or programming these factors.

    Suggestions for the improvement of this information sheet will be welcome. They should be sent to the

    American Gear Manufacturers Association, 1500 King Street, Suite 201, Alexandria, Virginia, 22314.

    V

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    PERSONNEL of the AGMA Commit tee for Helical Gear Rating

    Chairman: D. McCarthy (Dorris Company)

    Vice Chairman: N. Hulse (General Electric)

    ACTIVE MEMBERS

    K. E. Acheson .......

    The Gear Works-Seattle

    M. Antosiewicz

    ...... Falk

    J. Bentley ........... Peerless-Winsmith

    E. S. Bemdt .........

    C M of Indiana

    J. D. Black

    ..........

    GM/Allison Div.

    E. J. Bodensieck

    .....

    Bodensieck Engineering

    N. K. Burrel l .........

    Metal Improvement Co.

    M. F. Dalton .........

    General Electric

    G. DeLange .........

    Emerson Power Trans.

    J. Ft. DeMarai s

    .......

    Bison Gear

    R. J. Drago ..........

    Boeing

    R. L. Errichello .......

    Academic Member

    H. Hagan ............

    Cincinnati Gear

    H. Ft. Johnson .......

    Lufkin Industries

    0. LaBath ........... Cincinnati Gear

    ASSOCIATE MEMBERS

    G. Lian ..............

    L. Lloyd .............

    D. R. McViiie ........

    A. Milbum ...........

    C. Moyer ............

    R. Nay ..............

    M. W. Neesley

    .......

    W. P. Pizzichil ........

    J. W. Polder

    .........

    E. R. Sewal l .........

    J. Tellman ...........

    T. Tumbull ...........

    W. Wagner ..........

    C. C. Wang ..........

    R. Wasilewski ........

    J. Adamson .........

    R. G. Allenby ........

    J. Amendola .........

    K. Beckman .........

    D. L. Borden .........

    E. R. Braun ..........

    G. Buziuk ...........

    A. Cardou ...........

    M. R. Chaplin ........

    J. Cianc i ............

    A. S. Cohen .........

    J. T. Cook

    ...........

    R. DiRusso ..........

    D. W. Dudiey ........

    K. A. Evans ..........

    R. Geary ............

    R. Giuff ra ...........

    L. L. Haas ...........

    F. M. Hager ..........

    TIW Systems

    Hamilton Gear

    MAAGlArtec

    Lufkin Industries

    Gear Research Institute

    Eaton

    Brad-Foote

    Universite Lava1

    Contour Hardening Inc.

    General Electric

    Engranes y Maquinaria

    Power-Tech

    Kaman

    Honorary Member

    GM-Saginaw Div.

    Terre11 ear Drives

    ABS

    SPECO Corporation

    Cummins Engine

    A. C. Hayes .........

    DACA

    W. H. Heller .........

    Peerless-Winsmith

    G. Henriot ........... Engrenages et Reducteurs

    M. Hirt ..............

    Renk Tacke GmbH

    D. R. Houser ........ Academic Member

    . lrey ...............

    New Angle Gear

    T. W. Jessup

    ......... Lucas Western Inc./ATD

    T. Kameyama

    ........

    SeikiiKogyosho

    M. Lawrenz

    ..........

    Metal Improvement

    J. Liesicki

    ...........

    Falk Corporation

    J. Maddock

    ..........

    Consultant

    D. Mairet

    ...........

    Falk Corporation

    T. J. Maiuri ..........

    P. C. McAvoy ........

    B. W. McCoy ........

    F. Myers ............

    D. Moser ............

    B. L. Mumford

    .......

    W. Nagel i ...........

    B. C. Newcomb

    ......

    H. C. A. Nielsen

    ......

    J. Nyerup ...........

    . Okamoto ..........

    G. E. Olson ..........

    J. A. Pennell .........

    A. E. Phillips .........

    B. D. Pyeatt .........

    V. Z. Rychlinski

    ......

    E. Sandberg .........

    Amarillo Gear Co.

    Lufkin Industries

    Gear Engineers, Inc.

    Milbum Engineering

    The Timken Co.

    Pratt Whitney

    WesTech Gear

    Philadelphia Gear

    Academic Member

    Sewall Gear

    Reliance Electric/Reeves

    Mobile Pulley Machine

    Sewall Gear

    3E Software Engrg.

    Arrow Gear

    Gleason Works

    Cummins Engine

    Marathon Letourneau

    Horsburgh Scott

    Nuttall Gear

    Alten-Foundry

    MAAG

    Chicago Gear-D-O-James

    F. L. Smith

    F. L. Smith

    Nippon Gear

    Cleveland Gear

    Academic Member

    Reliance Electric

    Amarillo Gear

    Brad Foote

    Det Norske Veritas

    W. F. Schierrenbeck . . Xtek Incorporated

    A. Seireg ............

    Academic Member

    E. E. Shipley ......... Mechanica l Technology

    D. A. Sylvester

    ....... Flender Corporat ion

    D. Set for. ..........

    Precision Gear

    L. J. Smith ........... Invincible Gear

    . A. Thoma .........

    Honorary Member

    W. J. Toner ..........

    IMO Delaval, Inc.

    H. J. Trapp ..........

    Klingelnberg

    F. C. Uherek .........

    Flender Corporation

    T. Urabe ............

    Tsubakimoto Chain

    D. A. Wagner ........

    General Motors/AGT

    H. Winter ............

    Academic Member

    vi

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    AGMA919-493

    A Summary of Numerical

    Examples Demonstrating

    the Procedures for Calculat-

    ing Geometry Factors for

    Spur and Helical Gears

    1 Scope

    This information sheet provides a set of numerical

    examples which calculate the geometry factor for

    pitting resistance, I, and bending strength, J, for a

    variety of gearsets selected to demonstrate thevari-

    ous gear geometries analyzed in AGMA 908-l389,

    Geometry Factors for Determining the Pitting Resis-

    tance and Bending Strength of Spur, Helical and

    Herringbone Gear Teeth. A flow chart is also in-

    cluded to formalize the calculation procedures for

    the numerical examples and to assist in the practical

    application of AGMA 908-889.

    1 .l

    Numerical examples

    Numerical examples wer e selected to demonstrate

    the following conditions: accurate and inaccurate

    spur gears, conventional and LACR low axial con-

    tact ratio) helical gears, internal and external gears,

    double helical and herringbone Sykes) gears and

    addendum modification. For simplification pur-

    poses and for demonstrating the effect on resulting

    geometry factors, similar examples were selected

    with different load locations example 3.1 lvs3.12)

    and face widths example 3.1.3 vs 3.1.4)

    The results are presented in tabular form by provid-

    ing the numerical results for each equation as pre-

    sented in AGMA 908-689 and appropriate to that

    gear geometry. Gear cutter data is presented for

    each component in each numerical example. All

    gearsets a re functional and do not violate any of the

    exceptions stated n the scope of AGMA 908-B89.

    The examples used are for demonstration purposes

    only and are not intended to be recommendations

    for gearset design.

    12 Flow chart

    The flow chart provides a step by step procedure for

    calculating geometry factors, I and J, using the

    equations and instructions from AGMA 908-B89.

    The numerical value tables are formatted to coin-

    cide with the flow chart procedures.

    1.3 Exceptions

    A procedure for the calculation of bending strength

    geometry factor,

    J,

    for internal gears has not been

    established by AGMA. For this reason, numerical

    examples and flow chart procedures for such a cal-

    culation are not included.

    2 Definitions and symbols

    2.1 Definitions

    The terms used, wherever applicable, conform to

    the following standards:

    ANSI Y10.3-1968, Letter Symbols for Quantities

    Used in Mechanics of Solids,

    AGMA 904-B89, Metric Usage;

    AGMA 1012-F90, Gear Nomenclature, Definitions

    of Terms with, Symbols.

    2.2 Symbols

    The symbols used in the geometry factor formulas

    are shown in table 1.

    NOTE - The symbols, definitions and terminology

    used in this information heet may differ from other

    AGMA documents. The user should not assume that

    familiar symbols can be used without a careful study of

    these definitions.

    Units of measure are not shown in table 1 because

    the equationsare in terms of unity normal module or

    unity normal diimetral pitch.

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    AGMA 919-A93

    Symbols

    C&,...C(j

    Gzl, cm+ cnt

    ch

    cr

    cv

    Di

    d

    F

    fi

    F2

    H

    &lo

    hF

    Z

    J

    Kf

    Kv

    L

    L

    min

    M

    mF

    mG

    “N

    mn

    mP

    II

    n0

    5 n2

    *a

    Plld

    pb

    PN

    PX

    R19R2

    Rbl’ Rb2

    Rbc

    Table 1 - Symbols used in equations

    Terms

    distances along line of action (See figure 3-I of AGMA 9084389)

    distances along line of action of virtual spur gear

    helical factor

    operating center distance

    helical overlap factor

    inside diameter of internal gear

    pinion operating pitch diameter

    effective face width

    gear type code

    spur gear load sharing code

    parameter for stress correction factor

    nominal tool addendum

    height of Lewis parabola

    pitting resistance geo metry factor

    bending strength geometry factor

    stress correction factor

    helix angle factor

    parameter for stress correction factor

    minimum length of contact lines

    parameter for stress correction factor

    axial contact ratio

    gear ratio

    load sharing ratio

    normal module

    transverse contact ratio

    virtual tooth number

    virtual tooth number of tool

    tooth numb er, pinion and gear

    fractional part of

    mF

    tool tooth number

    fractional part of

    mp

    normal diametral pitch

    transverse base pitch

    normal base pitch

    axial pitch

    standard pitch radii, pinion and gear

    base radii, pinion and gear

    base radius of tool

    continued

    2

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    AGMA 919-A93

    Table 1 (continued)

    Symbols

    Rc

    Rrnl

    ROL Ro2

    R

    oc

    ‘m rn2

    I,

    ‘n

    rm

    II

    5lo

    rs

    no

    ‘ha 9?&a2

    rid, hb2

    ‘?lbO

    rnL

    SF

    S,

    Snl, Sn2

    l

    STlO

    sns

    Tl

    To1

    us

    x

    X17X2

    xtz

    X0

    XgbXg2

    Y

    Y

    Y'

    z

    O1n

    ani

    Pn

    4

    60

    6

    a0

    qnF

    Terms

    standard pitch radius of tool

    mean radius of pinion

    addendum radii, pinion and gear, internal and external

    outside radius of tool

    reference pitch radii of virtual spur gear

    generating pitch radius of virtual spur gear

    reference pitch radius of virtual tool

    generating pitch radius of virtual tool

    radius to center “9” of tool tip radius

    virtual outside radii

    virtual base radii

    virtual base radii of tool

    virtual load radius

    tooth thickness at criiical section

    reference normal circular tooth thickness

    reference no rmal circular tooth thickness, pinion and gear

    tooth thickness at outside diameter

    reference normal circular tooth thickness of tool

    standard tooth thickness, thinned for backlash

    temporary variable

    temporary variable

    stock allowance per side of tooth, for finishing

    addendum modification coefficient at zero backlash

    addendum modification coefficient, pinion and gear

    generating rack shift coefficient

    addendum modification coefficient of tool

    generating rack shii coefficient, pinion and gear

    tooth form factor

    iteration function

    derivative of iteration function

    active length of line of action

    angle of surface, normal

    iteration ang le

    angle between tangent to fillet and tooth center line

    amount gear tooth is thinned for backlash

    amount of p rotuberance, tool

    amount of effective protuberance, tool

    ordinate of criiical point “F

    continued

    3

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    AGMA 91 &A93

    Table

    1 (concluded)

    Symbols

    en

    em

    KFKS

    hns

    z

    Pla P2

    bzl~ brl2

    Pa0

    PF

    cp

    bt

    4::

    4);

    L

    - blpo

    r

    4hs

    hlW

    +r

    w

    vb

    yr

    co

    0 tool

    1 pinion

    2 gear

    Terms

    angular displacement of gear

    angular displacement of tool

    distance from pitch point to points “F’ and “S’

    angle to center “S” of tool tip radius

    auxiliary angle locating point “s”

    abscissa of criiical point “F

    radii of curvature of profiles at point of contact stress calculation

    radii of curvature of profile at mean radius

    tool tip radius

    minimum radius of curvature of fillet curve

    standard transverse pressure angle

    standard normal pressure angle

    generating pressure angle

    iteration value for generating pressure angle

    load angle

    pressure angle at radius where tool tooth is pointed

    operating normal pressure angle

    pressure angle at point “s” on tool

    pressure angle at load application point

    operating transverse pressure angle

    standard helix angle

    base helix angle

    operating helix angle

    angle of inclination of helical contact line

    Subscripts

    n normal or virtual spur gear

    r

    0

    El

    erating or running

    sence

    of a subscript indicates transverse

    3 Numerical examples

    Eleven numerical examples, based on actual gear-

    sets, are presented to demonstrate the calculation

    of both geometry factors, I and

    J,

    using the proce-

    dures outlined in AGMA 908-B89.

    3.1 l Accurate spur gears

    This example demonstrates a spur gearset which

    meets the criteria of table 5-l in AGMA 908-B89 for

    load sharing and is therefore considered loaded at

    the highest point of single tooth contact.

    3.12 Inaccurate spur gears

    3.1 Examples

    The following examples were selected to illustrate

    the various types of gearing

    and geometry eatures

    found in most of today’s gearing.

    This example, which uses the same geometry as

    3.1 l, does not meet the criteria in table 5-l of

    AGMA go&B89 for load sharing and is therefore

    considered to be loaded at the tip of the teeth.

    4

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    AGMA 91 A93

    3.1.3 Conventional helical gears

    This example demonstrates a conventional helical

    gearset wher e the mesh face width is greater than

    the axial pitch.

    It also includes an addendum

    modification coefficient in the pinion and protuber-

    ance in the rack cutter used to generate both

    components.

    3.1.4 Low axial contact ratio (LAM) helical

    gears

    This example, which uses the same basic geometry

    as 3.1.3, demonstrates an LACR helical gearset

    where the face width has been reduced to less than

    the axial pitch. The effect on both geometry factors

    under these conditions can readily be seen.

    3.1.5 Conventional helical gears, different tools

    This example demonstrates a conventional helical

    gearset with addendum modification. The pinion is

    generated by a hob and the gear by a pinion type

    shaper cutter. Both cutters have protuberance.

    3.1.6 Spur sun and planet gear

    This example combines with 3.1.7 to demonstrate

    the geometry factor calculation for a spur sun/planet

    gear combination. Here, the I factor for the

    sun/planet mesh and the J factor for each compo-

    nent are calculated.

    3.1.7 Spur planet and ring gear

    This example combines with 3.1.6 and demon-

    strates the effect on the I factor when the same

    planet meshes with the internal ring gear of the

    same set. The calculated J factor for the planet in

    the planet/ring mesh is diierent from that in the

    sun/planet mesh (3.1.6). TheJfactorcalculationfor

    the ring gear is beyond the scope of this information

    sheet (see 1.3).

    3.1.8 Helical sun and planet gear

    This example combines with 3.1.9 to demonstrate

    the geometry factor calculation for a helical sun/

    planet gear combination. The Z factor for the

    sun/planet mesh along with the J factor for each

    component is calculated.

    3.1.9 Helical planet and ring gear

    This example combines with 3.1.8 and demon-

    strates the effect on the Z factor when the same

    planet meshes with the internal ring gear of the

    same set. The calculated J factor for the planet in

    the planet/ring mesh is different from that in the

    sun/planet mesh (3.1.8). TheJfactorcalcula tion for

    the ring gear is beyond the scope of this information

    sheet (see 1.3).

    3.1 I0 Conventional double helical gears

    This example demonstrates the method for consid-

    ering the double face width encountered in this type

    of gearing.

    3.1 I1 Herringbone gears

    This exampledemonstrateshow transverse diametral

    pitch, usually associated with this type of gearing, is

    accommodated.

    3.2 Tabulation of examples

    Tables 2B through 12B tabulate all the information

    relating to each example as described in 3.1. The

    format is based on the flow chart as presented in

    clause 4 and includes all basic geometry (input

    data) and results of the calculations for every

    variable applicable to that gearset. These example

    were calculated to 14 significant digits and the

    results rounded as shown. For those variables

    found by iteration, the final iterative value is listed.

    See tables 2A through WA for the specific value of

    each variable at each iteration loop. Figures 2

    through 12 illustrate the various cutting tool profiles.

    Specificdata relating o each gearset or component

    is listed in the individual example tables.

    5

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    AGMA 91&A93

    Table 2A - Accurate spur gears , example 3.1.1

    Pinion: iteration for generating pressure angle

    Variable 1 2 3 4 5 6

    inv $; 0.014910 0.014910 0.014910 -

    cp - 0.349386 -

    nz

    0.358675 0.349112

    fb

    n(i +l)

    0.349386 0.349112 0.349111 -

    Variable 1

    a

    Pn

    no

    K

    S

    P

    If

    c.F

    P

    UT

    Y

    IYl

    ant

    0.785398

    0.000187

    -1.325365

    -1.761865

    0.099917

    0.685481

    1.179814

    24.257896

    1.142721

    4.452621

    0.689143

    0.689143

    0.630626

    Pinion: iteration for critical point

    2 3

    4

    0.630626 0.605889

    0.605442

    0.000257 0.000270

    0.000271

    -1.589244 -1.645464

    -1.646525

    -2.025744 -2.081964

    -2.083025

    0.113499

    0.116204

    0.116255

    0.517127 0.489685 0.489187

    1.127191

    1.119292

    1.119150

    24.334854 24.349198 24.349464

    1.065763 1.051418 1.051153

    3.441053 3.322607

    3.320554

    0.085121 0.001485

    0.000000

    0.085121 0.001485

    0.000000

    0.605889 0.605442

    0.605442

    Gear: iteration for generating pressure angle

    6

    Variable 1 2 3 4 5 6

    inv $; 0.014894 0.014894 0.014894

    v- 0.358546 0.349263 0.348989

    nl

    v -

    n(i +l)

    0.349263 0.348989 0.348988

    Gear : iteration for critical point

    Variable

    1 2 3 4 5 6

    an

    ho

    ‘CS

    9

    (32

    Bn

    GlF

    %F

    k

    Y’

    Y

    IYl

    %i

    0.785398

    0.586171

    0.541381 0.539939 0.539938

    0.000232 0.000349

    0.000386

    0.000387

    0.000387

    -1.641409 -2.097854

    -2.251830

    -2.257242

    -2.257248

    -2.077909 -2.534354

    -2.688330 -2.693742 -2.693748

    0.053295 0.064581 0.068083 0.068205

    0.068205

    0.732103 0.521590 0.473298 0.471734

    0.471733

    1.224450 1.158420

    1.144696

    1.144259

    1.144259

    50.535758 50.627373

    50.652661

    50.653515

    50.653516

    1.239255

    1.147640

    1.122352 1.121498

    1.121497

    5.034538 3.586125

    3.374076 3.367760

    3.367754

    1.003017 0.160620

    0.004867 0.000005 0.000000

    1.003017 0.160620 0.004667 0.000005 0.000000

    0.586171 0.541381 0.539939

    0.539938

    0.539938

  • 8/15/2019 AGMA 918-A93

    13/49

    AGMA 916-A93

    Table 2B - Accurate spur gears , example 3.1.1

    Gearset

    Pinion

    mn =

    0.2WOW q = 51

    on = 20.0000 n,1

    = lWO0

    Input data

    g&g

    kzol =

    1.4565

    n2 = 104

    Pa01 =

    0.4365

    nc2

    = low0

    ha02 =

    1.4

    w = o.owo

    , =

    15.5000

    F 2.5000

    FI = I

    53 = I

    Rol

    =

    5.3225

    %zol

    =

    0.0099

    Ro2

    = 10.5774

    Pa02

    =

    0.4

    Xl

    =

    0.1127

    Asnl =

    0.0215

    x2

    =

    -0.1127

    6

    a02 =

    0.0

    x01 =

    O.WW

    x02 = o.owo

    As,.,2 =

    0.0

    Cutter

    figure

    2

    Cutter figure 2

    62

    %

    w

    cr

    F

    Rol

    Ro2

    “G

    Rl

    R2

    9

    Rbl

    Rb2

    %

    ‘b

    pN

    vb

    ‘6

    Cl

    %

    c4

    %

    c,

    z

    “P

    G3.64. G5

    nr =

    Px =

    mF =

    na =

    L,h =

    “zN =

    Yr =

    9

    nr =

    0.349066

    o.owow

    77.5WOW

    12.500000

    26.612500

    52.887000

    2.039216

    25.5WOW

    52.OWOW

    0.349066

    23.962162

    48.664016

    0.349066

    2.952131

    2.952131

    o.owow

    26.506561

    6.274342

    8.721514

    9.226474

    11.577563

    8.625431

    5.303220

    1.796404

    Z subroutine

    d =

    51 .WWW

    Rml =

    25.612750

    Pl = 8.625431

    P2 =

    17.881130

    P

    ml =

    9.045870

    P

    m2 =

    17.460691

    cy = 1 OOOOW

    I = 0.107

    G6 pinion

    n1 = 51 .OOWW

    Rol =

    26.612500

    RI =

    25.5OWOO

    Rbl =

    23.962162

    c4 =

    9.226474

    x =

    0.112700

    Asn =

    O.o215W

    nC = 10000.000000

    h, =

    1 A56500

    x0 =

    o.wwoo

    Pa0 =

    0.436500

    sm =

    O.W99W

    J factor Pinion

    n

    =

    51 .WWW

    rn =

    25.5OWW

    0.796404 ‘& =

    23.962162

    cn4 = -

    rd = -

    r&2 = -

    12.5WOW ‘~2 = -

    l.OOOOW cn6 = -

    O.OWOW Cnl = -

    0.349066 ‘m = -

    m@nW=

    0.385043

    5 =

    0.083165

    sn

    $d

    rnL

    nO

    =

    1.631335

    Y

    = 0.904103

    = 0.338152

    J =

    0.46

    =

    25.400616

    = 10000.000000

    gear6

    ‘no

    ‘nbo

    $0

    +ns

    inv%zs

    Sno

    inv%zpo

    hnsf2

    ilV@;

    +“ni

    m”

    r,“0

    = 5Wo.W0000 ni

    = 4698.463104 mG

    = 5W1.02OWO To1

    = 0.349626 R,l

    = o.ol4wg

    R,:

    = 1.570796 T1

    =

    0.015061 R1

    an

    kzo

    KS

    KF

    ;:

    h?.F

    %F

    hF

    Y’

    Y

    “nl

    pF

    co

    ch

    SF

    H

    L

    M

    9

    3f

    =

    -0.WOW8

    = 0.014910

    = 0.349111

    = 25.500422

    = 5000.082737

    = 0.605442

    = 0.00027 1

    = -1.646525

    = -2.083025

    = 0.116255

    = 0.489187

    R2

    Rbl

    cfl

    x

    Asn

    nC

    h

    a0

    X0

    Pa0

    6

    a0

    =

    104.000000

    = 0.490385

    = 26.612500

    = 52.887000

    = 26.612500

    =

    25.5WWO

    =

    52.OWWO

    =

    25.5WWO

    = 48.864016

    = 17.881130

    = -0.112700

    =

    0.0215oo

    = 10000.000000

    = 1.456500

    =

    o.owwo

    = 0.436500

    = 0.009900

    1.119150

    24.349464

    1.051153

    3.320554

    o.wowo

    0.605442

    0.469891

    0.000000

    1 ooowo

    2.238300

    0.18OWO

    0.150ooo

    0.45owo

    1.955632

    1 wowo

    J factor aear

    n

    = 104.000000

    rn

    =

    52.OWWO

    ‘nb =

    48.864016

    cn4 = -

    ‘n2 =

    ‘nb2 = -

    ‘na2 =

    c,6

    = -

    C

    nl = -

    ‘na =

    fN)nW=

    0.365937

    5 = -0.142235

    sn =

    1.467257

    +& =

    0.336924

    rnL =

    51.7

    nO

    = 1 oooo.00

    ‘no = 5000.

    ‘nbo = 4698.4

    GO

    = 5001.0

    qns =

    0.3

    invqns = 0.0

    sno =

    1.5

    in3 npo = 0.0

    hnsi

    inv+n

    vii

    5i

    GO

    an

    ho

    KS

    KF

    ;:

    LF

    qnF

    hF

    Y’

    Y

    anl

    pF

    0

    ch

    SF

    H

    L

    M

    9

    KY

    Y

    J

    =

    -Q.O

    = 0.0

    = 0.3

    = 51.9

    = 4999.8

    = 0.5

    = 0.0

    = -2.25

    = -2.69

    = 0.0

    = 0.4

    = 1.1

    = 50.6

    = 1.1

    = 3.3

    = 0.0

    = 0.5

    = 0.4

    =

    o.o

    = 1 o

    = 2.2

    =

    0.1

    =

    0.1

    =

    0.4

    = 1.9

    = 1 o

    = 0.8

    = 0.4

    7

  • 8/15/2019 AGMA 918-A93

    14/49

  • 8/15/2019 AGMA 918-A93

    15/49

    AGMA 916-A93

    Table 3B - Inaccurate spur gears , example 3.1.2

    Input data

    Gearset

    Pinion

    m

    m, =

    0.200000

    n1 = 51

    ha01 = 1.4565

    n2

    = 104

    hLlo2 =

    1.456

    0, = 20.0000

    n,l = 10000

    P

    a01

    =

    0.4365

    nc2

    =lOooO

    Pa02 =

    0.436

    w = 0.0000

    Rol

    =

    5.3225

    6

    a01 = (

    .0099

    RA =

    “A

    10.5774

    6 nn3 = 0.009

    c, =

    15.5000

    LIv.2

    0.1127

    O.Ml5

    =

    F =

    2.5000

    Xl =

    Asnl =

    7

    =

    -0.1127

    AS,2

    0.021

    Fl

    1

    x01 =

    0.0000

    x02 = 0.0000

    F2

    Cutter

    figure

    2

    = 2

    Cutter figure 2

    62

    %l

    w

    cr

    F

    Rol

    %2

    mG

    Rl

    R2

    +

    Rbl

    Rb2

    6

    ‘6

    pN

    vb

    C6

    Cl

    c3

    c,

    C5

    c2

    2

    “P

    63.64. G5

    nr =

    Px =

    mF =

    na =

    L,h =

    mN =

    Yr =

    nr =

    0.349066

    0.000000

    77.5ooooo

    12.500000

    26.612500

    52.887000

    2.039216

    25.500000

    52.OOOOOO

    0.349066

    23.962162

    48.864016

    0.349066

    2952131

    2.952131

    0.000000

    26.506561

    6.274342

    8.721514

    9.226474

    11.577563

    8.625431

    5.303220

    1.796404

    Z subroutine

    d =

    51.oooooo

    Rml =

    25.612750

    Pl =

    8.625431

    P2 = 17.881130

    P

    ml =

    9.045870

    P&l =

    17.460691

    cy = 1.000000

    I = 0.107

    G6 pinion

    nl = 51.000000

    ROI = 26.612500

    Rl =

    25.5OOOOO

    Rbl =

    23.962162

    c4 =

    9.226474

    x =

    0.112700

    Asn =

    o.o215oo

    nC = 10000.000000

    h, =

    1.456500

    x0 = 0.000000

    Pm =

    0.436500

    aa0 = 0.009900

    J factor Pinion

    n

    =

    51.000000

    rn =

    25.5OOOOO

    0.796404 '& =

    23.962162

    C

    n4 = -

    rn2 = -

    t-h2 = -

    12.5OOOOO '~2 = -

    l.OOOOOO cnfj = -

    0.000000

    C,l = -

    0.349066 rm =

    26.612500

    @4)nW=

    0.483160

    xg =

    osI83165

    sn =

    1.631335

    Y

    = 0.438626

    qjjL = 0.436269

    J = 0.30

    rnL =

    26.438538

    no =

    10000.000000 G6

    ‘no

    ‘nbo

    rs

    no

    ns

    inv4 zs

    sno

    ‘“vOnpo

    hnsli

    iI-@;

    Vni

    4

    Go

    = 5000.000000

    n1

    = 4698.463104

    mG

    = 5001.020000

    T,l

    = 0.349626

    Rol

    = 0.01 979

    4,~

    = 1.570796

    T1

    ,= o.015061 R1

    an

    ko

    KS

    KF

    en

    pn

    %lF

    %.F

    hF

    Y’

    Y

    anl

    pF

    w

    ch

    SF

    H

    L

    M

    Kf

    KY

    =

    -o.oooou8

    =

    0.014910

    = 0.349111

    = 25.500422

    = 5000.082737

    = 0.413704

    = 0.000427

    = -2.330347

    = -2.766847

    = 0.146833

    = 0.266871

    R2

    Rbl

    c4

    n

    Asn

    nC

    h

    a0

    X0

    Pa0

    6

    a0

    =

    104.000000

    = 0.490385

    = 26.612500

    = 52.887000

    = 26.612500

    =

    255OOOOO

    =

    52.OOOOOO

    = 25.500000

    = 48.864016

    = 17.881130

    = -0.112700

    =

    0.0215oo

    =1oooo.oooooo

    = 1.456500

    = 0.000000

    = 0.436500

    = 0.009900

    1.061951

    24.496365

    1.942172

    5.404074

    0.000000

    0.413704

    0.469891

    0.000000

    1.000000

    2.123901

    0.180000

    0.150000

    0.450000

    1.485424

    1.000000

    J factor aear

    n

    = 104.000000

    rn =

    52.OOOOOO

    ‘nb =

    48.864016

    C

    n4 = -

    rn2 = -

    ‘nb2 = -

    ‘na2 =

    c,fj = -

    C,l = -

    ma =

    52.887000

    mn4nW=

    0.414051

    xg = y-:5;

    sn = .

    d =

    0.385039

    rnL

    nO

    ‘no

    ‘nbo

    rs

    no

    +

    ns

    hv+ns

    sno

    inV npo

    hns I2

    in@‘;,

    +Li

    ri

    Go

    an

    f-G20

    KS

    KF

    en

    Pn

    LZF

    ^‘ln.F

    hF

    Y’

    Y

    “nl

    PF

    w

    ch

    SF

    H

    L

    M

    Kf

    KY

    Y

    J

    =

    52.7242

    =1oooo.ooooo

    = 5ooo.ooam

    = 4698.4631

    = 5001.0200

    = 0.349

    = 0.014

    = 1.570

    = 0.015

    = -0.0000

    = 0.014

    = 0.348

    = 51.998

    = 4999.8592

    = 0.364

    = 0.000

    = -3.2540

    = -3.6905

    = 0.089

    = 0.275

    = 1.092

    = 50.788

    = 1.935

    = 5.208

    =

    o.ooo

    = 0.364

    = 0.462

    = 0.000

    = 1.000

    = 2.184

    =

    0.18O

    = 0.150

    =

    0.45o

    = 1.513

    =

    1.ooo

    = 0.451

    = 0.30

    9

  • 8/15/2019 AGMA 918-A93

    16/49

    Table 4A - Conventional helical gears, example 3.1.3

    Pinion: iteration for generating pressure angle

    Variable

    1

    2

    3

    4

    5 6

    inv @;

    0.014937

    0.014937

    0.014937

    $"-

    0.358888

    0.349589

    0.349314

    -

    Ill

    $”

    n(i +l)

    0.349589

    0.349314

    0.349313

    Pinion: iteration for critical point

    Variable

    1

    2

    3

    4

    5 6

    a

    0.785398

    0.530778

    0.484332

    0.483773

    co

    0.000102

    0.000174

    0.000194

    0.000194

    K

    -0.801380

    -1.119323

    -1.216848 -1.218144

    s

    P

    -1.210580.186208

    -1.528523.220419

    -1.626048.229993 -1.627344.230119

    <

    s"

    0.599190

    0.310360

    0.254339

    0.253654

    c.F

    1.157476

    1.092056

    1.082560

    1.082451

    IIs

    F

    10.767751.256396

    10.903191.120957

    10.935968.088180 10.936387.087760

    Y'

    7.558439

    5.779360

    5.652986

    5.651830

    Y

    1.924528

    0.268428

    0.003165

    0.000000

    IYl

    1.924528

    0.268428

    0.003165

    0.000000

    an1

    0.530778

    0.484332

    0.483773

    0.483773

    Gear: iteration for generating pressure angle

    Variable

    1

    2

    3

    4

    5 6

    inv i$;

    0.014902

    0.014902

    0.014902

    -

    $2

    0.358611 0.349324 0.349050 -

    %(i + 1)

    0.349324

    0.349050

    0.349050

    -

    Gear: iteration for critical point

    Variable

    1

    2

    3

    4

    5 6

    an

    0.785398

    0.470846

    0.370221

    0.366647 0.366645

    -

    bl0

    0.000198

    0.000389

    0.000510

    0.000516 0.000516

    -

    %

    -1.554759

    -2.422778

    -3.036768 -3.064963

    -3.064981

    -

    KF

    -1.963959

    -2.831978

    -3.445968 -3.474163

    -3.474181

    -

    &

    0.056632

    0.078839

    0.092918

    0.093552 0.093552

    -

    fin

    0.728766 0.392006 0.277303 0.273096 0.273093 -

    &IF

    1.235535

    1.140587

    1.112683

    1.111685 1.111685

    -

    %lF

    46.328373

    46.482618

    46.563564 46.567096

    46.567098

    -

    F

    2.223231

    2.068985

    1.988040

    1.984507 1.984505

    -

    Y'

    8.691103

    5.665191

    5.332131

    5.325511 5.325507

    -

    Y

    2.733809

    0.570059

    0.019054

    0.000012 0.000000

    -

    IYl

    2.733809

    0.570059

    0.019054

    0.000012 0.000000

    -

    ani

    0.470846

    0.370221

    0.366647

    0.366645 0.366845

    -

  • 8/15/2019 AGMA 918-A93

    17/49

    AGMA 919-A93

    Table 4B - Conventional helical gears, example 3.1.3

    input data

    Gearset

    Pinion

    @g

    ln =

    0.166667 q = 21

    kzol =

    1.4760 n2 = 86

    ha02 =

    1.4760

    0, = 20.0000 n,1 =lOOOO P

    a01 =

    0.4092

    nc2

    =lOOOO

    Pa02 =

    0.4092

    w =

    15.0000

    Rol

    =

    2.0667

    ~~~

    6 ,A =

    U”I

    0.0061

    Ro2

    =

    7.5865

    =

    0.0061

    c, =

    9.3175

    6

    a02

    Xl = 0.5343

    -

    F =

    3.7500

    *w -

    n n34n

    “.“,s-T”

    x2

    =

    - ----

    o.uuuo

    *

    “Sn2

    =

    - _^~^

    0.024u

    Fl = I

    F2

    =Notrequireci

    x01 =

    0.0000

    Cutter figure 3

    x02 = 0.0000

    Cutler figure 3

    G2

    %2

    Y

    cr

    F

    Rol

    Ro2

    “G

    4

    R2

    4,

    Rbl

    Rb2

    @r

    i

    )N

    vb

    c6

    Cl

    %

    c4

    C5

    c,

    Z

    “P

    63.64.65

    nr =

    Px =

    “F =

    na =

    L,h =

    mN =

    Yj- =

    0

    nr =

    0.349066

    0.261799

    55.904888

    22.499955

    12.400175

    45.518909

    4.095238

    10.870400

    44.516876

    0.360356

    10.172208

    41.657612

    0.384177

    3.043517

    2.952131

    0.245674

    20.952955

    2.605900

    4.112262

    5.649417

    7.091582

    4.048065

    4.485682

    1.473848

    0.473848

    12.138182

    1.853651

    0.853651

    33.224468

    0.677210

    0.264134

    0.372068

    I subroutine

    d =

    21.943975

    Rml =

    11.393077

    Pl =

    5.131121

    P2 =

    15.821834

    P

    ml = -

    Pn.Q= -

    cy = 1.000000

    I = 0.242

    G6 oinion

    nl =

    21.000000

    ROI = 12.400175

    Rl =

    10.870400

    Rbl =

    10.172208

    c4 = 5.649417

    x = 0.534300

    AS,, = 0.024000

    nC

    =10000.000000

    h, =

    1.476000

    x0 = 0.000000

    pa0 =

    0.4092W

    6

    a0

    =

    0.006100

    J factor Dinion

    n =

    23.301719

    rn =

    11.650859

    rnb =

    10.948227

    C

    n4 = -

    rn2 = -

    rnb2 = -

    rna2 = -

    c,,fj = -

    C,l = -

    ma =

    13.180635

    tantp,W =

    0.670365

    X8 =

    0.501330

    sn = 1.935735 Y = 0.580609

    9d = 0.572388 .f = 0.58

    rnL =

    13.024147

    no =

    11096.056659 G6

    ‘no

    ‘nbo

    GO

    qns

    inv4ns

    Sn0

    i”v%zPo

    hnsi2

    illV@;l

    Vni

    mt-i

    GO

    = 5548.028330

    nl

    = 5213.441281 mG

    = 5549.095130

    T,l

    =

    o.swi94 R,l

    = o.ol4974

    R,2

    =

    1.570796

    T1

    =

    0.015046 R1

    an

    ko

    KS

    KF

    %z

    pn

    %F

    9n.F

    hF

    Y’

    Y

    anl

    PF

    w

    ch

    SF

    H

    L

    M

    Kf

    KY

    =

    -0.000006 R2

    =

    0.014937

    Rbl

    =

    0.349313

    c4

    =

    11.651910 X

    = 5548.528439 ASn

    0.483773 nc

    o.ooom ha0

    -1.218144 X0

    -1.827344

    Pa0

    0.230119 6ao

    0.253654

    =

    86.000000

    = 0.244186

    = 12.400175

    = 45.518909

    = 12.400175

    = 10.870400

    = 44.516876

    = 10.870400

    = 41.657612

    = 16.904890

    = 0.000000

    = 0.024000

    =10000.000000

    = 1.476000

    = 0.000000

    = 0.409200

    = 0.006100

    1.082451

    10.936387

    2.087760

    5.651830

    0.000000

    0.483773

    0.435535

    5.236189

    1.286597

    2.164902

    0.180000

    0.150000

    0.450000

    1.472865

    0.932426

    J factor aear

    n

    =

    95.426087

    rn =

    47.713044

    ‘nb =

    44.835595

    cn4 = -

    rn2 = -

    ‘nb2 = -

    ‘na2 =

    c,(j

    = -

    C,l = -

    ‘na =

    48.715077

    mOnW=

    0.424901

    xg = -y.ozo;;

    s, = .

    @A =

    0.393787

    rnL = 48.551604

    nO = 11096.056659

    'no = 5548.028330

    ‘nbo

    = 5213.441281

    GO = 5549.095130

    9 ns = 0.34959

    inv~,, =

    0.014974

    sno =

    1.570796

    inv+npo = 0.015046

    hns6

    in@ >

    I;zi

    r;

    GO

    an

    kzo

    KS

    KF

    ;I

    LF

    qn.F

    hF

    Y’

    Y

    “nl

    pF

    0

    ch

    sF

    H

    L

    M

    9

    KY

    Y

    J

    = -0.000006

    = 0.014902

    = 0.349050

    = 47.712763

    = 5547.995640

    = 0.366645

    = 0.000516

    = -3.064981

    = -3.474181

    = 0.093552

    = 0.273093

    = 1.111685

    = 46.567098

    = 1.984505

    = 5.325507

    = 0.000000

    = 0.366645

    = 0.434174

    = 5.236189

    = 1.286597

    = 2.223369

    = 0.180000

    =

    0.15OoO

    = 0.450000

    = 1.524664

    = 0.932426

    = 0.558144

    = 0.54

    11

  • 8/15/2019 AGMA 918-A93

    18/49

    Table 5A - Low axial contact ratio (LACR) helical gears, example 3.1.4

    Pinion: iteration for generating pressure angle

    Variable 1 2 3 4 5 6

    inv @; 0.014937 0.014937 0.014937 -

    $ * 0.358888 0.349589 0.349314 -

    nl

    9” - -

    n(i +l)

    0.349589 0.349314 0.349313

    Pinion: iteration for critical point

    Variable 1

    2 3 4 5 6

    a 0.785398 0.664320 0.651858 0.651758

    Pn 0.000102 0.000130 0.000134 0.000134

    no

    K -0.801380 -0.919094 -0.934027 -0.934149

    s

    3 -1.210580.186208 -1.328294.199679 -1.343227.201299 -1.343349.201312

    P 0.599190 0.464641 0.460559 0.450446

    CF 1.157476 1.123738 1.120528 1.120502

    TlF 10.767751 10.825179 10.831698 10.831751 -

    hF 1.222488 1.165060 1.158541 1.158488

    Y' 4.231279 3.548075 3.492580 3.492145

    Y 0.512316 0.044217 0.000348 0.000000 -

    IYl 0.512316 0.044217 0.000348 0.000000

    an1 0.664320 0.651858 0.651758 0.651758

    Gear: iteration for generating pressure angle

    Variable 1 2 3 4 5 6

    inv Q; 0.014902 0.014902 0.014902

    t$ - 0.358611 0.349324 0.349050 -

    m

    0”

    n(i +l)

    0.349324 0.349050 0.349050

    Gear : iteration for critical point

    Variable 1 2 3 4 5 6

    an 0.785398 0.541421 0.476957 0.474521 0.474518 -

    lllzo 0.000198 0.000329 0.000383 0.000386 0.000386 -

    Ks -1.554759 -2.132880 -2.394107 -2.405443 -2.405456 -

    KF

    -1.963959 -2.542080 -2.803307 -2.814643 -2.814656 -

    en 0.056632 0.071897 0.078164 0.078431 0.078432 -

    Pn 0.728766 0.469524 0.398793 0.396090 0.396087 -

    LF 1.235535 1.160451 1.142289 1.141610 1.141609 -

    %.F 46.328373 46.439304 46.478542 46.480158 46.480160 -

    hF 1.516735 1.405803 1.366566 1.364950 1.364948 -

    Y' 6.035126 4.127370 3.848488 3.839332 3.839321 -

    Y 1.472435 0.266065 0.009375 0.000011 0.000000 -

    IYl 1.472435 0.266065 0.009375 0.000011 0.000000 -

    ani 0.541421 0.476957 0.474521 0.474518 0.474518 -

    12

  • 8/15/2019 AGMA 918-A93

    19/49

    AGMA 916-A93

    Table 5B - Low axial contact ratio (LACR) helical gears, example 3.1.4

    Input data

    Gearset

    Pinion m

    mn =

    0.166667

    q = 21

    &Kd =

    1.4760

    n2 = 86

    kw2 =

    1.476

    9, = 20.0000

    n,l = 10000

    pa01 =

    0.4092

    nc2 = 10000

    Pa02 =

    0.409

    w =

    15.oooo

    Rol =

    2.0667

    6

    a01

    =

    0.0061

    ROIL

    =

    7.5865

    FL-0 =

    0 nm

    .---,

    c, = 9.3175

    -uu.L

    0.5343

    O.o240

    =

    =

    1.8750

    Xl =

    Asnl =

    x2

    0.0000

    As,,2

    0.024

    1

    = Nnt rpntk-od

    x01

    = 0.0000

    Cutter figure 3

    x02 = 0.0000

    Cutter figure 3

    L - ..-.,- l .

    62

    @n

    w

    cr

    F

    Rol

    Ro2

    mG

    Rl

    R2

    cp

    Rbl

    Rb2

    %

    ‘b

    pN

    vb

    c6

    Cl

    %

    G

    C5

    %

    z

    “P

    0.349066

    0.261799

    55.904888

    11.249978

    12.400175

    45.518909

    4.095238

    10.8704oo

    44.516876

    0.360356

    10.172208

    41.657612

    0.384177

    3.043517

    2.952131

    0.245674

    20.952955

    2.605900

    4.112262

    5.649417

    7.091582

    4.048065

    4.485682

    1.473848

    63. G4. G5

    nr =

    0.473848

    Px = 12.138182

    mF

    =

    0.926826

    na =

    L,h =

    mN =

    : .oooooo

    Yr =

    0.264134

    (4

    nr =

    0.372068

    Z subroutine

    d = 21.943975

    Rml = 11.393077

    Pl =

    4.048065

    P2 =

    16.904690

    P

    ml =

    5.131121

    Pm2 =

    15.821834

    cy = 1.320561

    I = 0.241

    G6 pinion

    nl =

    21.oooooo

    ROI =

    12.400175

    R1 =

    10.870400

    Rbl =

    10.1722o6

    c4 =

    5.649417

    x = 0.534300

    Asn =

    0.024000

    nc

    =1oooo.oooooo

    h, =

    1.476000

    x0 =

    0.000000

    Pa0 =

    0.409200

    aa0 =

    O.OO61OO

    J factor pinion

    n

    =

    23.301719

    rn =

    rnb =

    cn4 =

    i-d =

    ‘jIb2 =

    rna2 =

    cn6 =

    cnl =

    rm =

    @@nW=

    X8 =

    11.650859

    10.948227

    5.670768

    47.713044

    44.835595

    48.715077

    21.769309

    2.716636

    0.517962

    0.501330

    sn = 1.935735

    Y =

    0.861107

    4 & = 0.419985

    J =

    0.60

    r-d = 11.990239

    no

    =11096.056659 G6

    ‘no

    = 5548.028330

    ‘nbo

    = 5213.441281

    GO

    = 5549.095130

    0 ns = 0.349594

    iin+,, = 0.014974

    sno =

    1.570796

    hv+npo = 0.015046

    hnsf2 = -O.OOOOO6

    n1

    mG

    To1

    Rol

    Ro2

    T1

    Rl

    R2

    illV l;;

    Vni

    ri

    60

    =

    0.014937

    Rbl

    =

    0.349313

    C4

    =

    11.651910 X

    = 5S8.528439 A Sn

    O1n

    Clno

    KS

    KF

    en

    bz

    LF

    %F

    hF

    Y’

    Y

    “nl

    pF

    Co

    ch

    SF

    H

    L

    M

    Kf

    %

    0.651758 nc

    0.000134

    ha0

    -0.934149 x0

    -1.343349

    Pa0

    0.201312 ijao

    0.450446

    =

    86.OOOOOO

    = 0.244186

    = 12.400175

    = 45.518909

    = 12.400175

    = 10.870400

    = 44.516876

    =

    10.8704oO

    = 41.657612

    = 16.904890

    = 0.000000

    = 0.024000

    =1oooo.oooooo

    = 1.476000

    = 0.000000

    = 0.409200

    = 0.006100

    1.120502

    10.831751

    1.158463

    3.492145

    0.000000

    0.651758

    0.435535

    5.236189

    1.000000

    2.241005

    0.180000

    0.15oooo

    0.45oooo

    1.900525

    1.000000

    J factor aear

    n

    =

    95.426087

    rn =

    47.713044

    ‘nb =

    44.835595

    Cn4 =

    17.382131

    ‘n2

    ‘nb2

    ‘na2

    cn6

    cnl

    =

    11.650859

    =

    10.948227

    =

    13.180635

    =

    21.769309

    =

    14.430000

    ‘na =

    QNnW=

    0.387686

    4 & =

    0.356572

    ‘n.L

    no

    ‘no

    ‘nbo

    rs

    4CS

    inv@ns

    sno

    hv@npo

    hns /2

    invJ h

    +‘;li

    ri

    GO

    an

    hlo

    KS

    KF

    ;:

    hlF

    q?lF

    hF

    Y’

    Y

    anl

    pF

    co

    ch

    sF

    H

    L

    M

    Kf

    KY

    Y

    J

    = 47.845

    = 11096.056

    = 5548.028

    = 5213.441

    = 5549.095

    = 0.349

    = 0.014

    = 1.570

    = 0.015

    = -0.0000

    = 0.014

    = 0.349

    = 47.712

    = 5547.995

    = 0.474

    =

    omo3

    = -2.4054

    = -2.8146

    = 0.078

    = 0.396

    = 1.141

    = 46.480

    = 1.364

    = 3.839

    = 0.000

    = 0.474

    = 0.434

    = 5.236

    = 1.000

    = 2.283

    =

    0.18O

    =

    0.15o

    =

    0.45o

    = 1.796

    = 1.000

    = 0.706

    = 0.52

    13

  • 8/15/2019 AGMA 918-A93

    20/49

    Table 6A - Conventional helical gears, different tools, example 3.1.5

    Pinion: iteration for generating pressure angle

    Variable

    1

    2

    3

    4

    5

    6

    inv I$;

    0.014923

    0.014923

    0.014923

    cp -

    0.358773

    0.349479

    0.349204

    nz

    v

    n(i +l)

    0.349479

    0.349204

    0.349204

    Pinion: iteration for critical point

    Variable

    1

    2

    3

    4

    5

    6

    a

    0.785398

    0.489843

    0.423246

    0.422544

    c

    0.000161

    0.000301

    0.000356

    0.000357

    K

    -1.428714

    -2.146816

    -2 A58926

    -2.462757

    S

    3

    -1.548714.108435

    -2.266816.148603

    -20.16439478926

    -2.582757.164585

    k

    0.676963

    0.341240

    0.258852

    0.257959

    CF

    1.174504

    1.122203

    1.108587

    1.108439

    IIg

    Y<

    20.907868.243744

    21.006137.145476

    21.050445.101167

    21.051005.100608

    8.228124

    6.031137

    5.929895

    5.929600

    Y

    2.431867

    0.401655

    0.004159

    0.000000

    IYl

    2.431867

    0.401655

    0.004159

    0.000000

    ani

    0.489843

    0.423246

    0.422544

    0.422544

    Gear: iteration for generating pressure angle

    Variable

    1

    2

    3

    4

    5

    6

    inv $;

    0.016894

    0.016894

    0.016894

    -

    V-

    0.373767

    0.363741

    0.363431

    nr

    Q

    n(i +l)

    0.363741

    0.363431

    0.363430

    Gear: iteration for critical point

    Variable

    1

    2

    3

    4

    5

    6

    an

    0.785398

    0.478334

    0.388037

    0.384560

    0.384576

    -

    bw

    0.039613

    0.072843

    0.089196

    0.089925

    0.089926

    -

    5

    -1.549491

    -2.268065

    -2.662398

    -2.680317

    -2.680339

    -

    KF

    -1.729491

    -2.448065

    -2.842398

    -2.860317

    -2.860339

    -

    en

    0.068177

    0.091832

    0.103473

    0.103992

    0.103992

    -

    fin

    0.717222

    0.386503

    0.284564

    0280588

    0.280583

    -

    ifl

    1.237266

    1.152564

    1.124054

    1.122925

    1.122924

    -

    %.F

    36.071536

    36.215014

    36.297514

    36.301402r

    36.301406

    -

    F

    2.178133

    2.034656

    1.952155

    1.948268

    1.946263

    -

    V'

    8.343913

    5.576394

    5.196610

    5.183951

    5.183935

    -

    ;I

    2.562113.562113

    0.503535.503535

    0.017965.017965

    0.000022.000022

    o.oooooo.000000

    -

    41

    0.478334

    0.388037

    0.384580

    0.384576

    0.384576

    -

  • 8/15/2019 AGMA 918-A93

    21/49

    AGMA 919-A93

    Table 6B - Conventional helical gears, different tools, example 3.1.5

    Input data

    Gearset

    Pinion

    j&&r

    mn =

    0.083333 nl = 35

    hzol = 1.4460

    n2

    = 59

    ha*: =

    1.41

    on = 20.0000

    n,l =lOOOO

    pa01 =

    0.1200

    nc2 = 42

    Pa02 =

    0.18

    y = 22.1090

    R,l = 1.6843

    6

    a01

    =

    0.0187

    Ro2

    =

    3 7i?aFI

    b.‘ .a..”

    a%-A z

    c,

    4.2837

    --UUL

    -

    n f-l1

    -.-

    0.3498

    0.0240

    =

    F =

    Xl =

    Asnl =

    x2 = 0.3523 Asn2 0.02

    .8750

    Fl = I

    x01 =

    0.0000

    no2 =

    0.0278

    F2

    =Notrequired

    Cutter figure 4

    Cutter figure 5

    G2

    +n

    Y

    cr

    F

    Rol

    Ro2

    “G

    Rl

    R2

    +

    Rbl

    Rb2

    %-

    ‘b

    pN

    wb

    ‘6

    Cl

    C3

    c4

    9

    c2

    z

    “P

    G3. G4.65

    nr =

    0.437722

    Px =

    8.347090

    mF =

    1.257928

    na =

    0.257928

    L,h =

    15.131716

    mN =

    0.693910

    Yr =

    0.390502

    +

    nr =

    0.378768

    0.349066

    0.385875

    51.404606

    10.500042

    20.211681

    33.165733

    1.685714

    18.888911

    31.841306

    0.374334

    17.580881

    29.636343

    0.406423

    3.156112

    2.952131

    0.361494

    20.321595

    5.433579

    7.566551

    8.589692

    9.971191

    6.815079

    4.537612

    1.437722

    I subroutine

    d =

    38.280025

    Rml =

    19.225277

    Pl =

    7.779710

    f32 =

    12.541885

    P

    ml = -

    Pm2 = -

    cy =

    1.000000

    I

    =

    0.166

    G6 oinion

    nl = 35.000000

    ROI = 20.211681

    Rl = 18.888911

    Rbl = 17.560861

    c4 = 8.589692

    x = 0.349800

    As, = 0.024000

    *C

    =10000.000000

    ha0 =

    1.446000

    x0 = 0.000000

    Pa0 =

    0.120000

    s

    a0 =

    0.018700

    J factor oinion

    n =

    44.012358

    rn =

    22.006179

    rnb =

    20.679044

    C

    n4 = -

    rn2 = -

    rnb2 = -

    rna2 = -

    cn6 = -

    C,l = -

    rw =

    23.328949

    mOnW=

    0.522216

    xg =

    0.316830

    ‘n

    %?L

    ‘nL

    nO

    =

    1.801430

    Y

    = 0.541648

    'a = 38.24

    = 0.466382

    J =

    0.46

    no =

    52.81

    = 23.151612

    ‘no =

    26.40

    =12574.959321

    G6 gear

    ‘nbo =

    24.81

    ‘no

    =

    6287.479660

    nl

    ‘nbo

    = 5908.298240 mG

    rs

    no

    = 6288.805660 To1

    6

    ns =

    o.s.ms5 R,l

    invqbns =

    0.014981 R,2

    sno =

    1.570796

    T1

    hv4npo =

    0.015029 R1

    = 59.000000

    rio =

    27.66

    = 0.593220

    (Pns = 0.45

    = 20.211681

    inv~ns = 0.03

    = 33.165733

    sno =

    1.59

    = 20.211681

    hv+

    no0

    = 0.04

    =

    18.888911

    = 31.841306

    = 18.888911

    = 29.636343

    = 13.506516

    = 0.352300

    = 0.024000

    =

    42.OCiWOO

    = 1.411100

    = 0.027800

    = 0.180000

    = 0.012700

    hns 12

    inVqJ’~

    $‘;zi

    r;

    ri0

    an

    CLno

    KS

    KF

    en

    &2

    blF

    = 0.00

    = 0.01

    = 0.36

    = 37.29

    = 26.54

    = 0.38

    = 0.08

    = -2.680

    = -2.860

    = 0.10

    = 0.28

    = 1.12

    = 36.30

    = 1.94

    = 5.18

    = 0.00

    = 0.38

    = 0.25

    = 7.91

    = 1.36

    = 2.24

    = 0.18

    = 0.15

    =

    0.45

    = 1.65

    = 0.85

    = 0.58

    = 0.51

    Ins I2

    inV($

    cP”ni

    r;

    GO

    = 0.000031

    = 0.014923

    = 0.349204

    = 22.007284

    = 6287.795326

    = 0.422544

    = 0.000357

    = -2.462757

    = -2.582757

    = 0.164565

    = 0.257959

    R2

    Rbl

    G

    x

    an

    kzo

    KS

    KF

    en

    Bn

    %lF

    %F

    hF

    Y’

    Y

    “nl

    PF

    0

    ch

    SF

    H

    L

    M

    Kf

    %f

    Asn

    nC

    h

    a0

    x0

    Pa0

    6

    a0

    =

    1.108439

    = 21.051005

    = 2.100608

    = 5.929600

    = 0.000000

    = 0.422544

    = 0.164496

    = 7.910180

    = 1.369671

    = 2.216878

    = 0.180000

    = 0.150000

    = 0.450000

    = 1.693445

    = 0.656723

    J factor Qear

    n

    =

    74.192260

    rn =

    37.096130

    ‘nb =

    34.858960

    Cn4

    = -

    rn2 = -

    ‘nb2 = -

    rna2 = -

    Cn6 = -

    Cnl = -

    ‘na =

    38.420556

    m+nW=

    0.463446

    xg =

    0.319330

    sn =

    1.803250

    $& =

    0.424237

    “nl

    PF

    0

    ch

    SF

    H

    L

    M

    9

    KY

    Y

    J

    15

  • 8/15/2019 AGMA 918-A93

    22/49

    Table 7A - Spur sun and planet gear, example 3.1.6

    Pinion: iteration for generating pressure angle

    Variable 1 2

    3 4 5

    6

    inv $; 0.014928 0.014928

    0.014928 -

    0 . 0.358812 0.349517

    0.349242 -

    rzz

    Q

    n(i +l)

    0.349517 0.349242

    0.349241

    Pinion: iteration for critical point

    Variable 1 2

    3 4 5

    6

    a 0.785398 0.602014

    0.573238 0.572797

    c 0.000151 0.000219

    0.000233 0.000233

    K -1.064773 -1.329401

    -1.388073 -1.389022

    S

    3 -1.489773.168216 -1.754401.192695

    -1.813073.197730 -1.814022.197810

    ff 0.617182 0.409320

    0.375509 0.374987

    CF 1.129153 1.071762

    1.063646 1.063524 -

    P -

    YC

    12.941082.473364 13.043537.370909 13.063152.351294 13.063463.350983

    5.246010 4.090220

    3.970709 3.968983 -

    Y 0.962033 0.117700

    0.001753 0.000000 -

    IYl 0.962033 0.117700

    0.001753 0.000000

    Qhl 0.602014 0.573238

    0.572797 0.572797

    Gear: iteration for generating pressure angle

    Variable 1 2

    3 4 5

    6

    inv $; 0.014928 0.014928

    0.014928 -

    4 . 0.358812 0.349517 0.349242

    ?ZZ

    4

    n(i +l)

    0.349517 0.349242

    0.349241

    Gear : iteration for critical point

    Variable 1 2

    3 4 5

    6

    an 0.785398 0.602014

    0.573238 0.572797

    bzo 0.000151 0.000219

    0.000233 0.000233

    %

    -1.064773 -1.329401

    -1.388073 -1.389022 -

    KF -1.489773 -1.754401

    -1.813073 -1.814022 -

    en

    0.168216 0.192695

    0.197730 0.197810

    Bn 0.617182 0.409320

    0.375509 0.374987

    GZF 1.129153 1.071762

    1.063646 1.063524

    %F 12.941082 13.043537

    13.063152 13.063463

    4F 1.473364 1.370909

    1.351294 1.350983

    Y' 5.246010 4.090220

    3.970709 3.968983

    Y 0.962033 0.117700

    0.001753 0.000000

    IYl 0.962033 0.117700

    0.001753 0.000000 -

    ani 0.602014 0.573238

    0.572797 0.572797

  • 8/15/2019 AGMA 918-A93

    23/49

    AGMA 916-A93

    Table 7B - Spur sun and planet gear, example 3.1.6

    Input data

    Gearset

    Pinion Gear

    m,

    =

    0.200000

    q = 26

    hzol =

    1.4975 722

    = 26

    hao2 = 1.49

    0,

    = 20.0000

    n,l =iwoo

    Pml =

    0.4250 nc2

    =lOooO

    Pa02 = 0.42

    v

    = o.owo

    Rol

    = 3.0750

    6

    a01

    =

    0.0245

    Ro2

    = 3.0750

    8

    a02 =

    0.02

    c, =

    5.7500

    = 0.4096

    =

    0.0650

    0.06

    F =

    Xl

    Asnl

    x2 = 0.4098

    2.5000

    As,; =

    Fl = I

    J-01 =

    O.WW

    x02 =

    o.owo

    F2 = I

    Cutter figure 6

    Cutter figure 6

    G.2

    +n

    v

    cr

    F

    Rol

    Ro2

    mG

    Rl

    R2

    $

    Rbl

    Rb2

    b

    ‘b

    pN

    vb

    c6

    Cl

    c,

    c4

    C5

    ci

    z

    “P

    63.64. G5

    n, =

    Px =

    “F =

    =

    zti =

    mN =

    y- =

    0

    nr =

    0.349066

    o.owow

    26.750000

    12.500000

    15.375000

    15.375000

    1.000000

    14.000000

    14.000000

    0.349066

    13.155697

    13.155697

    0.414645

    2.952131

    2.952131

    0.000000

    11.587626

    3.630348

    5.793613

    6.562460

    7.957276

    5.005146

    4.326929

    1.465697

    I subroutine

    d = 26.750000

    Rlnl = 14.375000

    Pl = 5.005146

    P2 = 6.582480

    P

    ml =

    5.793613

    Pm2 = 5.793813

    cly = 1.000000

    I = 0.091

    G6 Dinion

    nl =

    26.000000

    Rol =

    15.375000

    R1 =

    14.000000

    Rbl =

    13.155697

    c4 =

    6.582480

    x =

    0.409600

    Ass, =

    0.065OW

    %Z

    =1oooo.oooooo

    h, =

    1.497500

    x0 =

    O.WWW

    Pm =

    0.425000

    sao =

    0.024500

    J factor pinion

    n

    =

    26.000000

    rn = 14.000000

    0.465697 '& =

    13.155697

    c,4 = -

    rn2 = -

    rnb2= -

    12.500000 '& = -

    1.000000 c&i = -

    o.owow

    C,l = -

    0.414645 ma = -

    mOnW=

    0.500352

    xg =

    0.320507

    sn =

    1.804106 Y

    = 0.634206

    9d =

    0.421015 J

    = 0.37

    rnL =

    14.414446

    nO

    = 10000.000000 G6

    rno

    = 5000.000000 ni

    ‘nbo

    = 4696.463104 'y%

    GO

    = 5001.072500

    To1

    @

    s =

    0.349655

    ROl

    irwjns = o.olaa3 R,2

    sno =

    1.570796

    T1

    invOnpo =

    O.OISWI R1

    Arts12

    iIN+;

    Vni

    m”

    m"0

    =

    -O.OOOOO6 R2

    =

    0.014926

    Rbl

    =

    0.349241

    C4

    =

    14.oooa95 x

    = 5ooO.319SS A Sn

    an

    Vno

    KS

    KF

    072

    Pn

    ClF

    9n.F

    hF

    Y’

    Y

    anl

    pF

    co

    ch

    SF

    H

    L

    M

    Kf

    Q

    0.572797 n,

    0.000233 ha0

    -1.389022 x0

    -1.614022

    Pa0

    0.197610 tjao

    0.374967

    =

    26.000000

    = 1.000000

    = 15.375000

    = 15.375000

    = 15.375000

    = 14.000000

    = 14.000000

    = 14.000000

    = 13.155697

    = 6.562480

    = 0.409600

    = 0.065000

    = 10000.000000

    = 1.497500

    =

    o.owwo

    = 0.425000

    = 0.024500

    1.063524

    13.063463

    1.350963

    3.966963

    o.wowo

    0.572797

    0.463530

    o.wowo

    1.000000

    2.127047

    0.160000

    0.15ooo0

    0.450000

    1.721566

    1.000000

    J factor ciear

    n = 26.OOOOOO

    rn =

    14.000000

    ‘nb =

    13.155697

    C

    n4 = -

    rn2 = -

    ‘nb2 = -

    ‘na2 =

    c,fj = -

    C,l = -

    ma =

    m+nW =

    osoo352

    xg =

    0.320507

    sn = 1.604106

    Q& =

    0.421015

    rnL = 14.41

    nO = 10000.00

    ‘no = 5000.00

    ‘nbo = 4698.46

    rs

    o = 5001.07

    $

    ns =

    0.34

    inv(bns =

    0.01

    sno =

    1.57

    '"v&p, =

    0.01

    =

    -0.00

    =

    0.01

    =

    0.34

    =

    14.00

    = 5000.31

    hns i

    inv+ n

    Tzi

    r,”

    GO

    an

    klo

    KS

    KF

    %z

    &z

    LF

    qnF

    hF

    Y’

    Y

    “nl

    PF

    co

    ch

    SF

    H

    L

    M

    Kf

    %

    Y

    J

    0.57

    0.00

    -1.38

    -1.61

    0.19

    0.37

    1.0

    13.06

    1.3

    3.96

    0.00

    0.57

    0.46

    o.oo

    1 o

    2.12

    0.1

    0.15

    0.4

    1.7

    l.W

    0.6

    0.3

    17

  • 8/15/2019 AGMA 918-A93

    24/49

    Table 8A - Spur planet and ring gear, example 3.1.7

    Pinion: iteration for generating pmure angle

    Variable

    1 2

    3 4

    5

    6

    inv $;

    0.014928 0.014928

    0.014928

    v-

    0.358812 0.349517

    0.349242

    nr

    v

    n(i +l)

    0.349517 0.349242

    0.349241

    Pinion: iteration for critical point

    Variable

    1 2

    3 4

    5

    6

    an

    0.785398 0.661551

    0.647725 0.647595

    %o

    0.000151 0.000193

    0.000199 0.000199

    K -1.064773

    -1.225493

    -1.247761 -1.247975

    S

    3 -10.168216.89773

    -1.650493.183502

    -1.672761.185507 -1.672975.185526

    s

    0.617182 0.478049

    0.462218 0.462068

    CF

    1.129153 1.089338

    1.085164 1.085125

    TlF 12.941082 13.006523 13.014738 13.014816

    hF

    1.163157 1.097715

    1.089501 1.089422

    Y'

    4.212840 3.485322

    3.421318 3.420729

    Y

    0.521748 0.048189

    0.000446 0.000000

    lYl

    0.521748 0.048189

    0.000446 0.000000

    ani

    0.661551 0.647725

    0.647595 0.647595

    Gear: iteration for generating pressure angle

    Variable

    inv $;

    9”.111

    9”

    n(i +l)

    1

    -

    2

    3 4

    Gear : iteration for critical point

    5

    6

    Variable

    an

    ho

    5

    KF

    &

    Bn

    LF

    %F

    b

    Y’

    Y

    IYl

    clnl

    1 2

    3 4

    5

    6

  • 8/15/2019 AGMA 918-A93

    25/49

    AG MA 91&A93

    Table 8B - Spur planet and ring gear, example 3.1.7

    Gearset

    Pinioq

    Pn =

    0.2WOW q = 28

    t bn = 20.0000 n,l

    =lOOW

    Input data

    Gear

    huol =

    1.4975

    n2 = 85

    &lo2 =

    1.2629

    ezol =

    0.4250

    4.2 = 30

    Pa02 =

    0.1500

    w = o.oooo

    c, =

    5.7500

    F =

    2.5000

    Fl = 2

    F2

    = I

    Rol = 3.0750

    Xl

    = 0.4096

    X01 =

    O.WW

    Cutter figure 6

    %fol = 0.0245

    Ro2

    =

    8.4250

    6

    o.oo

    a02 =

    Asnl

    =

    0.0650

    x2

    =

    0.6678

    Asn2 =

    0.0650

    x02 =

    -0.2229

    Cutter figure 7

    Gz

    +n

    w

    cr

    F

    Rol

    Ro2

    “G

    Rl

    R2

    cp

    Rbl

    Rb2

    4%

    ‘b

    pN

    vb

    c6

    Cl

    c3

    c4

    C5

    F.2

    z

    mP

    63. G4.65

    nr =

    Px =

    mF =

    na =

    L,b =

    mN =

    vr =

    9

    nr =

    0.349066

    o.owow

    28.750000

    12.5WOW

    15.375000

    42.125000

    3.035714

    14.000000

    42.5WOW

    0.349066

    13.155697

    39.936936

    0.372222

    2.952131

    2.952131

    o.owow

    10.455989

    2.943890

    5.136275

    5.896021

    7.957278

    5.005146

    5.013388

    1.698227

    Z subroutine

    d =

    28.245614

    Rml = 14.375000

    PI = 5.005146

    P2 =

    15.461135

    pml =

    5.793613

    P& = 16.249802

    CyJ =

    l.WWW

    I = 0.244

    G6 Dinion

    nl =

    28.WWW

    Rol =

    15.375000

    Rl =

    14.WWW

    Rbl =

    13.155697

    c4 =

    5.896021

    X

    =

    0.409800

    Asn =

    0.065OW

    nC

    =10000.000000

    h, =

    1.497500

    x0 =

    O.WWW

    P&,2 =

    0.425000

    aa0 =

    0.024500

    J factor pinion

    n = 28.WWW

    rn =

    0.698227

    ‘& =

    C

    n4 =

    ‘n2 =

    ‘;Ib2 =

    12.5WOW 'm2 =

    : .owow

    cn6 =

    0.000000

    Cnl =

    0.372222 'na =

    @e,w=

    xg =

    14.OOWW

    13.155697

    0.448172

    0.320507

    sn =

    1.804106 Y =

    0.825562

    qnL =

    0.368836

    J =

    0.43

    rnL =

    14.104239

    no

    =10000.000000

    gear6

    ‘no

    ‘nbo

    60

    @

    s

    hv+ns

    sno

    im’%po

    kI2

    iIW$;f

    cP”ni

    r-i

    GO

    an

    Cl?lO

    KS

    KF

    en

    bl

    LF

    %F

    hF

    Y’

    Y

    anl

    pF

    co

    ch

    SF

    H

    L

    M

    Kf

    Kw

    = 5WO.WOWO

    n1

    = 4698.463104 mG

    = 5W1.072500

    %l

    =

    0.349655

    R,l

    =

    o.o14ga3 R,2

    =

    1.570796

    *1

    =

    0.015061 R1

    =

    -0.WOOO6

    = 0.014928

    = 0.349241

    =

    14.WO895

    = 5000.319535

    = 0.647595

    =

    o.wo199

    = -1.247975

    = -1.672975

    = 0.185526

    = 0.462068

    R2

    Rbl

    c4

    X

    Asn

    nC

    h

    a0

    X0

    pa0

    6

    a0

    1.085125

    13.014816

    1.089422

    3.420729

    o.wowo

    0.647595

    0.463530

    o.wowo

    l.WOWO

    2.170249

    0.18OWO

    0.15owo

    0.45owo

    1.898920

    l.WOOOO

    J factor aear

    n

    =

    rn =

    ‘nb =

    cn4 =

    ‘n2 =

    ‘nb2 =

    ‘na2 =

    cn6 =

    C

    nl =

    ‘na =

    m+nW=

    xi? =

    sn =

    $d =

    rti =

    no =

    ‘no =

    rnbo =

    r-i0 =

    (4

    s =

    invQns =

    sno =

    hvOnoo =

    hnsf2

    in@ >

    %i

    G

    GO

    an

    %zo

    KS

    KF

    en

    fin

    %lF

    qnF

    hF

    Y’

    Y

    anl

    pF

    w

    ch

    SF

    H

    L

    M

    Kf

    %

    Y

    J

    19

  • 8/15/2019 AGMA 918-A93

    26/49

    Table 9A - Helical sun and planet gear, example 3.1.8

    Pinion: iteration for generating pressure angle

    Variable 1 2

    3 4 5

    6

    inv $; 0.030017 0.030017

    0.030017

    $". 0.451838 0.437112

    0.436527

    tll

    v

    n(i +l)

    0.437112 0.436527

    0.436526

    Pinion: iteration for critical point

    Variable 1 2

    3 4 5

    6

    a 0.785398 0.550858

    0.516528 0.516292

    Pn 0.000092 0.000150

    0.000163 0.000163

    n0

    K -0.755647 -1.020756

    -1.081818 -1.082267

    S

    P -0.845647.183552 -1.110756.215756

    -1.171818.222565 -1.172267.222614 -

    s" 0.601846 0.335102

    0.293964 0.293678 -

    CF 1.203951 1.180769

    1.177409 1.177386

    P

    YT

    2.003974.761434 9.808402.957006

    9.818742.946666 9.818818.946590

    6.604027 5.308212

    5.241281 5.240928

    Y 1.548908 0.182230

    0.001237 0.000000

    IYl 1.548908 0.182230

    0.001237 0.000000

    ani 0.550858 0.516528

    0.516292 0.516292 -

    Gear: iteration for generating pressure angle

    Variable 1 2

    3 4 5

    6

    inv $; 0.026131 0.026131

    0.026131 -

    $"* 0.431629 0.418269

    0.417773 -

    Cli +I) 0.418269 0.417773

    0.417772

    Gear: iteration for critical point

    Variable 1 2

    3 4 5

    6

    Cr, 0.785398 0.532078

    0.480780 0.479829 0.479829

    -

    blo 0.019982 0.033342

    0.037361 0.037442 0.037442

    -

    KS -0.595631 -0.815390

    -0.887999 -0.889483 -0.889484

    -

    9 -0.775631 -0.995390

    -1.067999 -1.069483 -1.069484

    -

    &

    0.132923 0.152962

    0.158991 0.159112 0.159112

    -

    fb

    0.652475 0.379116

    0.321789 0.320717 0.320716

    -

    GlF 1.208512 1.173198

    1.166728 1.166610 1.166610

    -

    SF 13.176464 13.239694

    13.257422 13.257776 13.257776

    -

    F 1.837279 1.774049

    1.756320 1.755966 1.755966

    -

    Y' 6.313286 4.684785

    4.524943 4.522425 4.522424

    -

    Y 1.599280 0.240323

    0.004303 0.000001 0.000000

    -

    IYl 1.599280 0.240323

    0.004303 0.000001 0.000000

    -

    %i 0.532078 0.480780

    0.479829 0.479829 0.479829

    -

    L

  • 8/15/2019 AGMA 918-A93

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    AGMA 918-A93

    Table 9B - Helical sun and planet gear, example 3.1.8

    Input data

    Gearset Pinion

    @aJ

    mn

    =

    0.111111

    nl = 18

    hzol =

    1.1460 n2

    = 24

    ha02 = 1.128

    on

    = 25.0000

    n,l =lOOOO

    pa01 =

    0.0900

    nc2

    = 36

    Pa02 = 0.1800

    w

    = 17.7276

    Rol

    = 1.2154

    6

    a01

    =

    0.0000

    c,

    2.5500

    Ro2

    =

    , F.4.c7

    . “-.”

    K.-n -

    WaoL -

    n nnnn

    “.“““I

    Xl

    =

    0.5420

    Asnl =

    0.0180

    F =

    x2

    =

    0.4316

    .5000

    Asn2 =

    0.0180

    =

    Fl

    .x01

    0.0000

    1

    x02

    = 4.6985

    F2

    = Not required

    Cutter figure 8

    Cutter figure 9

    G2

    %l

    w

    Cr

    F

    Rol

    Ro2

    “G

    Rl

    R2

    0

    Rbl

    Rb2

    Qr

    ‘b

    pN

    vb

    c6

    Cl

    c3

    c4

    9

    c,

    z

    “P

    63.64. G5

    n, =

    0.145262

    Px =

    10.317491

    ??aF =

    1.308459

    na =

    0.308459

    L,h =

    15.604712

    mN =

    0.865124

    Yj- =

    0.321240

    0

    nr =

    0.507400

    0.436332

    0.309405

    22.950023

    13.500014

    10.938611

    13.911314

    1.333333

    9.448671

    12.598228

    0.455256

    8.486309

    11.315079

    0.530005

    2.962281

    2.847250

    0.279592

    11.602094

    3.509279

    4.972326

    6.471560

    6.901867

    3.939586

    3.392587

    1.145262

    I subroutine

    d

    =

    19.671448

    Rml =

    9.988660

    Pl =

    5.268385

    l-3

    =

    6.333708

    P

    ml = -

    Pnz; = -

    cy =

    1.000000

    I

    =

    0.146

    G6 pinion

    nl =

    18.000000

    ROI = 10.938611

    RI =

    9.448671

    Rbl = 8.486309

    Cd = 6.471560

    x = 0.542000

    Asn = 0.018000

    nC

    =10000.000000

    h, =

    1.146000

    x0 = 0.000000

    Pm =

    0.090000

    sao =

    0.000000

    J

    factor pinion

    n = 20.828460

    rn = 10.414230

    rnb = 9.488498

    C

    n4 = -

    rn2 =

    ‘nb2 =

    ‘na2 =

    +j

    = -

    C

    nl = -

    ma =

    11.904170

    mOnW=

    0.768580

    xg =

    0.522699

    ‘n

    %.L

    ‘r2.L

    nO

    ‘no

    ‘nbo

    GO

    @ns

    inV4%s

    sno

    inv%zpo

    hns I2

    iIN@;;

    @“ni

    r?i

    riY0

    Orn

    ho

    KS

    KF

    en

    pn

    Gl.F

    Q2.F

    hF

    Y’

    Y

    anl

    pF

    0

    ch

    SF

    H

    L

    M

    Kf

    KY

    =

    2.058274

    =

    0.639785

    =

    11.765408

    =11571X6413

    =

    5785.683206

    =

    5243.609743

    =

    5786.739206

    =

    0.436723

    = 0.030060

    =

    1.570796

    ,=

    0.030111

    =

    0.000033

    =

    0.030017

    =

    0.436526

    =

    10.415169

    =

    5786.204859

    0.516292

    0.000163

    -1.082267

    -1.172267

    0.222614

    0.293678

    1.177386

    9.818818

    1.946590

    5.240928

    0.000000

    0.516292

    0.116121

    7.694021

    1.363320

    2.354772

    0.14oOOo

    0.110000

    0.500000

    1.671480

    0.903789

    Y =

    0.801215

    J =

    0.55

    aear6

    n1

    mG

    %l

    Rol

    Ro2

    T1

    Rl

    R2

    Rbl

    c,

    x

    Asn

    nc

    ha0

    X0

    Pa0

    6

    a0

    =

    24.000000

    = 0.750000

    = 10.938611

    = 13.911314

    = 10.938611

    = 9.448671

    = 12.598228

    = 9.448671

    = 11.315079

    = 7.662508

    = 0.431600

    = 0.018000

    = 36.000000

    = 1.128700

    = -0.698500

    = 0.180000

    = 0.000000

    J factor aear

    n

    =

    27.771279

    rn =

    13.885640

    ‘nb =

    12.584663

    C

    n4 = -

    rn2 = -

    ‘nb2 = -

    rna2 = -

    c,fj = -

    C,l = -

    ‘na =

    15.198726

    @NnW=

    0.677188

    xg =

    0.412299

    sn = 1.955313

    (PnL =

    0.576804

    rnL =

    no =

    ‘no =

    ‘nbo =

    rs

    no =

    $

    ns =

    inv~,, =

    sno =

    inv@npo =

    hns 12

    iIn+ ;z

    %i

    ri

    m”0

    O1n

    bzo

    KS

    KF

    ;:

    &IF

    ‘lnF

    hF

    Y’

    Y

    anl

    PF

    0

    ch

    SF

    H

    L

    M

    9

    Ku’

    Y

    J

    15.0137

    41.6569

    20.8284

    18.8769

    21.0786

    0.4611

    0.0357

    0.9193

    0.0520

    0.0067

    0.0261

    0.4177

    13.7688

    20.6532

    0.4798

    0.037

    -0.8894

    -1.0694

    0.159

    0.320

    1.166

    13.257

    1.755

    4.522

    0.000

    0.479

    0.200

    7.694

    1.363

    2.333

    0.140

    0.110

    0.500

    1.649

    0.903

    0.826

    0.58

    21

  • 8/15/2019 AGMA 918-A93

    28/49

    Table 1OA - Helical planet and ring gear, example 3.1.9

    Pinion: iteration for generating pressure angle

    Variable 1 2 3 4 5 6

    inv 4; 0.026131 0.026131 0.026131 -

    4) . 0.431629 0.418269 0.417773 7

    nr

    4”

    n(i +l)

    0.418269 0.417773 0.417772

    Pinion: iteration for critical point

    Variable 1 2 3 4 5 6

    an 0.785398 0.532078 0.480780 0.479829 0.479829 -

    P 0.019982 0.033342 0.037361 0.037442 0.037442 -

    no

    K -0.595631 -0.815390 -0.887999 -0.889483 -0.889484 -

    S

    2 -0.775631.132923 -0.995390.152962 -1.067999.158991 -1.069483.159112 -1.069484.159112 -

    s 0.652475 0.379116 0.321789 0.320717 0.320716 -

    CF 1.208512 1.173198 1.166726 1.166610 1.166610 -

    F 13.176464.837279 13.239694.774049 13.257422.756320 13.257776.755966 13.257776.755966 -

    Y ; 6.313286 4.684785 4.524943 4.522425 4.522424 -

    Y 1.599280 0.240323 0.004303 0.000001 0.000000 -

    IYl 1.599280 0.240323 0.004303 0.000001 0.000000 -

    ani 0.532078 0.480780 0.479829 0.479829 0.479829 -

    Gear: iteration for generating pressure angle

    Variable 1 2 3 4 5 6

    inv $;

    v- -

    nr

    C(i +l)

    Gear: iteration for critical point

    Variable 1 2 3 4 5 6

    an

    ha0

    5

    KF

    %l

    fin

    &lF

    %F

    4F

    Y’

    Y

    IYl

    ani

  • 8/15/2019 AGMA 918-A93

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    AGMA 916-A93

    Table IOB - Helical planet and ring gear, example 3.1.9

    mn

    +n

    Pinion

    Input data

    g@J

    = 0.111111 nl = 24

    haol =

    1.1287 n2 = 69

    hao2 =

    1.1362

    = 25.0000 n,l

    =

    36 P

    a01 =

    0.1800 nc2

    =

    36 Pa02

    =

    0.1080

    w = 17.7276

    ROI

    = 1.5457 6

    a01

    = 0.0000

    Ro2

    = 3.8846 6

    c, =

    2.5500

    a02 =

    0.0000

    = 0.4316

    =

    0.0180

    =Xl

    Asnl

    -0.1972

    Asn2 =

    0.0180

    1.5000

    x2

    Fl 2

    x01

    =

    -0.6985

    x02 =

    0.1111

    = Notrequired

    Cutter figure 9

    Cutter figure 10

    62

    +n

    w

    cr

    F

    Rol

    Ro2

    mG

    Rl

    R2

    cp

    Rbl

    Rb2

    b

    ‘b

    pN

    vb

    c6

    Cl

    53

    c,

    %

    c;

    z

    “P

    G3. G4.65

    n, =

    0.362671

    Px = 10.317491

    mF =

    1.308459

    n, =

    0.308459

    L,h =

    17.938456

    mN =

    0.752574

    Y, =

    0.301137

    9

    nr =

    0.375282

    0.436332

    0.309405

    22.950023

    13.500014

    13.911314

    34.961435

    2.875000

    12.598228

    36.219905

    0.455256

    11.315079

    32.530852

    0.391249

    2.962281

    2.847250

    0.279592

    8.751830

    4.056199

    4.667643

    7.018480

    8.092814

    5.130533

    4.036615

    1.362671

    I subroutine

    d =

    24.480024

    Rml =

    12.961363

    Pl =

    6.321860

    P2 =

    15.073690

    Pm1 = -

    l-J&= -

    cy =

    1.000000

    I = 0.546

    G6 oinion

    n1 =

    24.000000

    ROI =

    13.911314

    Rl =

    12.598228

    Rbl =

    11.315079

    c4 =

    7.018480

    x =

    0.431600

    Asn =

    0.018000

    nc =

    36.000000

    h, =

    1.128700

    x0 =

    4.698500

    Pa0 =

    0.180000

    6

    a0 =

    0.000000

    J factor Dinion

    n =

    27.771279

    rn =

    13.885640

    rd = 12.584663

    c,4 = -

    rn2 = -

    rnb2 = -

    rna2 = -

    cn6

    = -

    C,l = -

    ma =

    15.198726

    tan(pnW=

    0.677188

    xg =

    0.412299

    ‘n

    %L

    ‘nL

    nO

    ‘no

    ‘nbo

    GO

    @iZS

    ~VQ,,

    Sno

    i”%Zp0

    Ins12

    ilW&

    Q”ni

    ri

    r"0

    an

    &ZO

    KS

    KF

    072

    pn

    h.F

    %F

    hF

    Y’

    Y

    “Rl

    P

    0

    ch

    SF

    H

    L

    M

    Kf

    KY

    1.955313 Y =

    0.885141

    0.576804

    J =

    0.71

    15.013743

    41.656919 G6

    20.828460 ni

    18.876995 mG

    21.078660

    To1

    0.461130

    Rol

    0.035727

    Ro2