54
P15453 RIT MSD I Detailed Design Review 1 ROCHESTER INSTITUTE OF TECHNOLOGY & DRESSER- RAND Dynamic Loading Simulation, By EMA, On Journal Bearing Test Rig Detailed Design Review 12/09/14

Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

  • Upload
    others

  • View
    4

  • Download
    0

Embed Size (px)

Citation preview

Page 1: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

1

ROCHESTER INSTITUTE OF TECHNOLOGY & DRESSER- RAND

Dynamic Loading Simulation, By EMA, On Journal Bearing Test Rig

Detailed Design Review

12/09/14

Page 2: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

2

Table of Contents Team Members: ................................................................................................................................................. 3 Meeting Purpose: ............................................................................................................................................... 3 Attendees: .......................................................................................................................................................... 3 Meeting Time & Location: ................................................................................................................................ 3 Problem Definition Review: .............................................................................................................................. 4

Customer Requirements: ............................................................................................................................... 4 Engineering Requirements: ........................................................................................................................... 4 Pareto Analysis: ............................................................................................................................................. 5 Functional Decomposition: ............................................................................................................................ 6 Functional Decomposition - Project Specific: ............................................................................................... 7

Detailed Design .................................................................................................................................................. 8 Bearing Housing Movement Analysis ........................................................................................................... 9 Simulink Model ............................................................................................................................................ 11 Gap and Film Thickness Analysis: .............................................................................................................. 13

Fluid and Bearing Temperature Sensor Analysis ........................................................................................... 14 Actuator Feasibility: ........................................................................................................................................ 16

Required Motor Torque: ............................................................................................................................. 16 Reflected Inertia (backlash): ....................................................................................................................... 17 Motor Acceleration ...................................................................................................................................... 17

Longevity Analysis: ......................................................................................................................................... 21 False Brinnelling .......................................................................................................................................... 21 Heat Produced by Actuator ......................................................................................................................... 21

Controller / Power supply: .............................................................................................................................. 22 System Block Diagram................................................................................................................................. 22 Voltage Requirement Analysis .................................................................................................................... 23 Simulink Model ............................................................................................................................................ 24

First Order Mounting Analysis: ...................................................................................................................... 27 Beam Deflection ............................................................................................................................................... 30 First Order Load Cell Connection: ................................................................................................................. 31

Equations used ......................................................................................................................................... 31 Analysis .................................................................................................................................................... 32

ANSYS Mounting Analysis ............................................................................................................................. 34 Y Direction Mounting Analysis ................................................................................................................... 36 X direction Mounting Analysis - Bottom .................................................................................................... 37

Machine Elements............................................................................................................................................. 38 Bill of Materials ............................................................................................................................................... 40 Risk Assessment ............................................................................................................................................... 41 Deflection Analysis of Shaft ............................................................................................................................ 41 Audible Noise Reduction ................................................................................................................................. 43 Alpha Prototype Bearing Housing Movement Testing ................................................................................. 44 Preliminary Test Transducer Experiment ...................................................................................................... 46 Preliminary Project Plan for MSD II – Test Plans ......................................................................................... 47 Appendix ........................................................................................................................................................... 53

Page 3: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

3

Detailed Design Review Agenda Team Members:

Michael Bush – Project Manager – ME Kevin Burnett – Sensor Engineering Lead – ME Molly Mariea – EMA Engineering Lead – ME Christina Amendola – CAD Engineering Lead– ME Anthony Depina – Simulation Engineering Lead – ME

Meeting Purpose:

The purpose of this meeting is to present a detailed design and final bill of materials for the P15453

Dynamic Loading System for the Journal Bearing Test Rig and receive feedback moving forward into

the build phase. Attendees:

William Nowak – Team Guide Dr. Jason Kolodziej – Primary Customer – RIT Mechanical Engineering Department

Meeting Time & Location: Date: December 9th, 2014 Time: Location: KGCOE - Building 9 – Room 2250

Page 4: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

4

Problem Definition Review: Customer Requirements:

Engineering Requirements:

Page 5: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

5

Pareto Analysis:

Page 6: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

6

Functional Decomposition:

Page 7: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

7

Functional Decomposition - Project Specific:

Page 8: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

8

Detailed Design

Note: for all Drawings and Schematics refer to separate document ‘Drawing Package’

Page 9: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

9

Bearing Housing Movement Analysis To analyze the bearing housing movement we first had to construct a force body diagram that takes into

account all the forces that would be acting on the bearing housing itself. In the positive x direction the

only force that we will have acting on the housing is the force we will be supplying, 𝐹𝐹. Counteracting

that in the negative x direction we have the inertial force of the block, ma or . Also we have the force

of the preloaded spring in the x direction that is equal to kx, k being the spring constant of our selected

spring for the preload which is 3120 lb/in [546.4 N/mm], and x being the displacement of the housing.

Lastly, the final force counteracting our supplied force is the force of the oil inside the bearing housing.

Essentially we are assuming this force can be modeled as a spring because as the area between the

bearing and shaft is compressed the oil pressure rises and exerts a force that counteracts the supplied

force. This force is represented as 𝐹𝐹𝐹, with 𝐹𝐹being our “spring constant” for the oil and x the

displacement of the housing. The oil spring constant was found by pulling data from Markus’s thesis

that correlated the max force of 970.0 lb [4,315 N] on the bearing with a displacement of 0.0006 in

[.00152 mm]. With that being known we can now use the equation 𝐹 = 𝐹𝐹𝐹to solve for 𝐹𝐹and get

1,620,953.33 lb/in [283872.42 N/mm] as the spring constant of the oil. Free Body Diagram

Page 10: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

10

Governing Equations Using our equations of motion, as seen below, we then took the Laplace transform of them and was able

to output a transfer function that with the input of our supply force we would get the displacement of our

bearing housing.

Input Variables

Page 11: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

11

Simulink Model

From the simulink model the graph above shows three outputs. The first output is the direct output from

the transfer function and as you can see there is fluctuation in the output and not a smooth sine wave as

we desired. The second output is a smooth sine wave and represents the curve we wanted to see and was

obtained by not taking the mass into account. When we take the difference of the two outputs we are

able to see the “noise” that is causing the difference in our outputs and can assume that the natura l

frequency of the system which is, √𝑘

𝑚, is what is causing this noise.

Page 12: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

12

From the above graph we took our transfer function and subtracted the noise to get our input and

confirm that if we subtract the noise we would get our desired output for displacement. From this

analysis we can take away that the bearing housing will not displace how we want it to because of the

natural frequency of the system, but an important point in this analysis is that it does not take into

account that the force we will be supplying will have a direct rigid connection to the bearing housing. So

inherently whatever amount we are displacing with our connection, as long as it is rigid, as we supply

our force the displacement that the bearing housing should see is the displacement that the connection

sees.

Page 13: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

13

Gap and Film Thickness Analysis:

To meet customer requirement 1.8 (Measure gap between journal and sleeve) linear variable differential

transformers (LVDT) will be used. The gap is on the order of tens to hundreds of microns therefore

LVDTs are a good fit. LVDTs are commonly used for micro measurements because of their high

accuracy and great repeatability. Signal conditioners are required for the LVDTs which greatly increases

the cost. In our case we won’t have to purchase these items because we have access to two Macro

Sensors’ BBPM-315-020 LVDTs and LVC-2500 signal conditioners. Under the assumption that the

actuators are directly centered on the bearing housing, the resulting forces wouldn’t create any torques

on the bearing housing. This assumption will be validated as a part of our test plans. This means that the

bearing housing will not rotate and that anyplace on the face of the bearing housing will be the same.

This allows us to put the LVDTs in locations that won’t interfere with other components. The mount

will be secured to the table utilizing preexisting hardware and holes. The LVDTs will be held in place

with set screws so that disassembly can be easy. Knowing the position of the bearing housing, provided

by the LVDTs, allows the gap and film thickness to be calculated. Mat lab script has been previously

created by Marcus Holzenkamp for these measurements. However they are specific to the compressor.

This will provide a jumping off point for our analysis.

Assembled model - proposed design

Page 14: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

14

Fluid and Bearing Temperature Sensor Analysis

For the purpose of measuring temperature, in every case, we have found that the best means will be

Thermocouples, as they are affordable (available) and effective. A thermocouple is a thermoelectric

device for measuring temperature, consisting of two wires of different metals connected at two points, a

voltage being developed between the two junctions in proportion to the temperature difference.

Three K-type thermocouples will be used for measuring temperatures. Type K thermocouples are the

most common general purpose thermocouple with a sensitivity of approximately 41 µV/°C (chromel

positive relative to alumel when the junction temperature is higher than the reference temperature).It is

inexpensive, and a wide variety of probes are available in its −200 °C to +1350 °C / -330 °F to +2460 °F

range.

The three K-type thermocouples will be used as follows: 1 for the oil reservoir, 1 for the oil outlet, 1 for

the bearing temperature

Oil Reservoir: Use a rod type to lower into the reservoir from the top. The reservoir’s oil level is

~4.5” high, while the entire height is 8”. Assuming that the thermocouples we buy are similar to

the one we have in the lab, the rod itself will be ~7.6” long. While the temperature difference

throughout the oil should be relatively the same, the tip of the rod should be placed close to the

middle of the pool of oil for the best accuracy. This means the tip should be 2.25” below the

pool’s surface, 5.75” from the ceiling of the oil reservoir (2.25” + the air gap, 3.5”). For the

thermocouple to be resting on a surface with the rod inserted this much into the oil, we would

need a 1.15” base to place it on. The thermocouple being used will be the FieldPiece ATF1 Type

K Rod Thermocouple.

Page 15: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

15

Oil Outlet: The current fitting will be removed and replaced with a T-type Female-Female-Male

fitting. The horizontal female side will be installed onto the bearing housing and the hose fitting

onto the male side. The vertical female would either have an adapter threaded in, which will

allow the rod type to be used, or a reducer can be used to allow the use of a ¼” omega

thermocouple probe which installs directly into the tee fitting.

The thermocouple being used will be the FieldPiece ATF1 Type K Rod Thermocouple.

Bearing: From McMaster Carr, the surface-contact thermocouple probes would be ideal for

reading the temperature of our bearing. By drilling a hole into the housing, we can insert this

probe and allow it to rest at the base of our cavity. We need to find out how far we should

drill/How close we should drill to the bearing to get accurate readings.

The thermocouple being used will be the McMaster Carr Surface-Contact Probe Thermocouple

with flat-pin connector.

Page 16: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

16

Actuator Feasibility: Required Motor Torque: The motor torque required depends on the force required from the load profile. The motor torque

required to replicate the Dresser Rand Reciprocating compressor with the Moog electromechanical

actuator is modeled below:

Force = 1000 lbs (from compressor load profile)

Screwlead = 0.197 in (provided by Moog)

Gear ratio = 1 (provided by Moog)

Efficiency = 85% (including factor of safety)

[Required torque = 4.2 N*m]

Figure EMA 1

EMA 1 shows the required torque (grey line) at a multitude of speeds; the blue line is the maximum

continuous torque and the red line is the peak torque force available. This actuator is capable of meeting

the required torque (36.86 lbf*in / 4.2 N*m) to speeds up to 500 rpm [Set up in a spreadsheet to

calculate the acceleration torque at many points over the complete cycle].

Page 17: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

17

Reflected Inertia (backlash):

The reflected inertia is the inertial load that the motor sees through the system’s drive train. Reflected

inertia is especially important when dealing with servo motors in order to manage the control system’s

stability.

Load weight = 40 lbs

ScrewLead = 0.197 in

GearRatio = 1

g = 32.174 ft/s2 = 386.088 in/ s2

Reflected Inertia = [ .01 N*mm*s^2]

For example, 40 lbs of connecting equipment and/or load cell, this load mass would reflect back to the

motor as .0001 lbf*in*sec^2. This would be added to the actuator/motor inertia for calculating

acceleration torque.

Motor Acceleration

The change in the motor’s velocity over time is the ‘Motor Acceleration’. The motor acceleration takes

into consideration the inertia of the motor/actuator as well as the reflected inertia of the bearing housing.

The required actuator position is shown in EMA 2. 90 µm (±0.0035 inch) @ 12 Hz

Figure EMA 2

Page 18: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

18

Figure EMA 3

Figure EMA 4

In order to achieve the position shown in EMA 2, the actuator would follow the velocity profile shown

in EMA 3 [Equation V= Pi*F*D, along with inputs from loading profile]. The 90 µm (0.0035 inch)

displacement at 12 Hz would result in an acceleration sine wave with peak of 20 in/sec^2 [shown in

EMA 4] .

Page 19: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

19

With a 5 mm lead ball screw, this linear acceleration results in a motor acceleration of 635 rad/sec^2. The resulting motor torque for acceleration then would be:

In sinusoidal motion such as this, the acceleration and force are both sinusoidal but in opposite phase

(the acceleration torque is opposite direction from the load torque) so the torque values subtract to arrive

at the total motor torque required. EMA 5 shows the phase relationship between the load torque and the

acceleration torque. The resulting motor torque required is the difference between the acceleration

torque and the load torque. [For illustration purposes the acceleration torque was increased on the graph

below]

Figure EMA 5

Page 20: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

20

The speed torque requirements for the motor and the RMS values are plotted on the motor curve to

ensure that the peak requirements are met and that the RMS point lies below the motor continuous

curve. These values were obtained by setting up a spreadsheet to calculate the sine waves [using 100

points in a period of 0.083 seconds for 12 Hz] and taking the sum of the square of the motor torque at

each point * time interval (0.0083s) and divide it by the total time (0.083s) and take the square root to

arrive at the RMS value.

Page 21: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

21

Longevity Analysis: False Brinnelling

False Brinnelling is a common failure mode of EM systems in micro motion. The bearing and ball

screw mechanisms will have all the lubrication displaced from between the contacting elements in such

short motion and will run dry resulting in rapid degradation. False Brinnelling starts to occur after

20,000 micro cycles.

One way to mitigate this is to do periodic displacements greater than the micro motion (one or more full

revolutions of the screw) to re-distribute lubrication within the rolling elements (Periodic means once

every 20,000 or so cycles).

Heat Produced by Actuator

As the actuator runs it will produce heat due to inefficiencies. The maximum temperature allowed is 100

degrees celsius (as suggested by Moog, including factor of safety). If the motor was to have to push

2000 lb at 12 hz (worst case scenario, if preload was required).

Conclusion The EMA would be capable of actuating for more than 3 times our planned test time with the worst

possible conditions assumed.

Page 22: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

22

Controller / Power supply: System Block Diagram

High Level System Overview

Servo Drive to Actuator breakdown

PID Controller Breakdown

Page 23: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

23

Voltage Requirement Analysis To ensure that with EMA’s we do not overcome our max force or displacements allowed we ran

simulation a DC servo motor model. Since our bearing housing is directly and rigidly connected to our

actuation we can assume that the displacement of the lead screw is directly related and equal to the

displacement of the bearing housing. We know that we will be inputting about 10 volts to our motor,

according to our moog point of contact, but we also know that we cannot simply supply a 10 volt

sinusoidal input because the motor is a 3 phase servo motor and requires additional analysis, but this

preliminary analysis ensures that we will have results that show our system is responding favorably and

not exceeding our max force or displacement. From our system model below we were able to place the

equations in state space and input it into simulink to get our desired outputs of force, displacement, and

velocity.

System Model

Page 24: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

24

Simulink Model

Force

Page 25: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

25

From our input voltage we can see above that we do not exceed a force of 1500 newtons. Although this

graph is lower than our required force we know by adjusting the voltage slightly we would be able to get

an accurate force output from our model.

Displacement

From the graph above we can see that we are nowhere close to our maximum displacement of 45

micrometers with our input voltage. And have about 40 micrometers free as we adjust the voltage to get

our desired force.

Angular and Linear Velocity

Page 26: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

26

From our calculations done for the EMA’s we can see that from this simulation the velocities never

exceed the capabilities at our required force of the EMA. The max velocity is .25 in/s which equates to

.00635 m/s. From our graph we have a max of .0002095 m/s so we are not in danger of exceeding our

velocity limits.

Page 27: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

27

First Order Mounting Analysis: To mount our EMA’s to our fixture we had to come up with a mounting design that required

some first order analysis on whether the supports would be sufficient in handling the loads under worst

case scenarios and the deflection that the beam would see. A simple diagram of the sketch is shown

below and is what was used for analysis. Point loads were assumed for worst case scenario for the

reaction forces and a load of 500 was used as the applied load to show that the design is capable of

handling this even though the forces should never reach this much during application..

Schematic

Page 28: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

28

Equations Used

For buckling of the mounts the following equations were used:

Euler’s Equation

To ensure our piece can be treated as a long column and euler’s equation can be used we had to ensure

that the slenderness ratio of our beam is greater than the critical slenderness ratio. If it is we would be

able to treat the beam as a “long” beam. If it is less we would have to treat it as a short beam and must

use a different buckling equation to find the critical buckling force.

Page 29: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

29

Before checking the slenderness ratio a calculation was done with euler’s equation and the factor of

safety came out to be 32048, which ensures our support will be acceptable.

Next we checked the slenderness ratio and found that the slenderness ratio is less than the critical which

means we in fact do have to treat it as a short beam and have to use Johnson’s equation for buckling

which is:

After using this equation with the critical stress we found that our factor of safety is virtually the same

and that we can confidently say that our supports will not be subjected to any buckling.

Page 30: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

30

Beam Deflection Schematic

This is the expected loading of our beam.

Equations

For our application the correct max deflection equation to be used is

where

Same elastic modulus and inertia is used from the buckling analysis because they are the same material.

a1 and a2 represent a and b in the above diagram.

From this calculation we found that the max deflection on the beam is going to be 20.620 micrometers.

This is a large number for our application so we can deduce from this number that we might have to add

additional support to our mounting and further analysis is required on the mounting for deflection.

Page 31: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

31

First Order Load Cell Connection:

For our load cell connector from the bearing housing to our actuator rod analysis was conducted

to ensure the pin size that we select is feasible and has a high factor of safety for our application. Point

loads were assumed for the reaction forces to do calculations under worst case scenarios. Also, for the

applied load to the pin we used the max force that it would see in the x direction, 1000 lbs, and said this

was a distributed load across the diameter of the actuator rod.

From the analysis if we pick a pin with a diameter of .75 in we will have a factor of safety of

about 19 which is more than acceptable and ensures our pin will not shear.

We will use this analysis in confidently sizing our pin for our load cell connector.

Equations used

Page 32: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

32

Analysis

Page 33: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

33

Max shear and moment on pin will be 612.5 lb and 243.75 respectively.

From choosing a diameter of .75 in for our pin we can calculate the max shearing and bending stresses

that the pin will see if the material was a2 tool steel. The max shear stress is 1386.416psi and the max

bending moment is 551.737psi. Since an a2 tool steel shear strength was not found we found it

acceptable to compare this data to that of stainless steel. Stainless steel has a shear strength of

26977.012psi which means our pin for our application will have a factor of safety of 19.458, thus

deeming this pin acceptable.

Page 34: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

34

ANSYS Mounting Analysis

An ANSYS analysis was conducted on each load bearing component of the EMA mounts.

Looking first at the deformation of each component, allowed us to identify if each component would

hold its structural integrity as the x and y loads were applied. All components were able to withstand the

applied forces with minimal deformation. Next, both maximum stress and strain were analyzed. Even

though there was deformation indicated there were no structural issues, the stress and strain were

computed to identify weak location. Once again, there were no areas of high enough stress or strain to

affect the structural integrity of the components. Lastly the locations of high shear stress were identified;

the areas of concern had low stress and thus did not affect the structural integrity. For component

information, refer to the summaries below the specific ANSYS analysis. The report only shows the

deformation and maximum stress but additional analysis is available on EDGE.

While the deformation provides enough information of structural integrity, it is still important to

look at the effects of stress. The yield stress of tooling steel is 2.5X108 while the ultimate stress of

tooling steel is 4.6x108. If the stress is below the yield stress the material is elastically deforming and

will return to its original shape and integrity. If the stress exceeds the yield stress the material will

plastically deform, this will change the component permanently. Plastic deformation affects both shape

and structural integrity. If the stress exceeds the ultimate stress of the tooling steel the component will

break. Deformation is occurring at the micron level; because movement is also at the micron level the

EMA controllers will have to be tuned to accommodate expected deformation. Changing geometric

features could reduce the deformation; however some deformation will always occur. Thus, changing

geometries does not circumvent the necessity to tune the controller. As a result, the geometries will be

kept as modeled and the actuation will be adjusted accordingly. Edge conditions where high stresses are

seen can be reduced with a radius or radial weld. All weld joints have been noted in drawing package in

the appendix.

Looking at the master fatigue diagram of AISI 4340 steel (see below) allowed us to determine

the alternating and amplitude stress of the steel components. These stresses, the fatigue and ultimate

strength, and the mod- Goodman equation allowed us to determine the number of stress cycles of our

components. 𝑆𝑎

𝑆𝑒+

𝑆𝑚

𝑆𝑢𝑡=

1

𝑛, where ‘n’ is the fatigue factor of safety.

Page 35: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

35

Fatigue Diagram

Fatigue Life Cycle

If the fatigue life cycle is less than 106 the elements have a finite life cycle. The life cycle computed

above for the x-components are in the finite range, however they are very close to the infinite range. The

y-components however are in the life cycle range. If this is decidedly too low, geometric changes can

occur to move all of the components into an infinite life cycle.

Page 36: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

36

Y Direction Mounting Analysis

Deformation

Max Stress

The bolt connections are not accurately loaded in this model. To correctly apply the load to the bearing

hole above the bottom bolt connections are under “zero loading” when in reality they will experience a

loading force. They are correctly analyzed in the machine elements section in the screw and bolt table.

Page 37: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

37

X direction Mounting Analysis - Bottom Deflection

Max Stress

Page 38: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

38

Machine Elements

The basic depth thread was found for each possible screw from 32(Pitch)

The major diameter, threads per inch and the tensile stress area is given by Table 8-2 in

Mechanical Engineering Design, that s Diameters and Areas of Unified Screw Threads UNC and

UNF

Mean diameter is given by the major diameter subtracted from half the pitch

The torque required to move a load up the thread would be the case of load application it was

determined by where the lead was determined to be one and

Conservatively friction was determined to be 0.15, standard can be as low as 0.5 and as high as

.30 depending on the material and the cleanliness of the screw. Therefore a conservative estimate

of 0.15 was used.

Likewise, the torque required to move the load down the thread was determined by a similar

equation- it was expected to be very low because the screw would no longer be pushing a force

Normal and shear stress of the cross section were determined to provide a reference for the

nominal stress, because a screw does not have an evenly distributed load on each thread this is

just an estimation where T= Torque F= Force to be moved

Failure due to yield was obtained with

Page 39: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

39

The nominal bearing stress was calculated to determine stressed on engaged threads, I am unsure

what to compare this information to and will be looking into it further. It was determined

using

Additionally because shearing the screw is a very likely risk, the maximum shear stress was

calculated using

Page 40: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

40

Bill of Materials

Page 41: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

41

Risk Assessment

Deflection Analysis of Shaft The first order analysis revealed that the possible deflection of the shaft is 10.6 μm. This is a large amount in proportion to our max expected bearing housing displacement of 45 microns. This value is also our max radial clearance. Due to this ratio additional analysis should be done.

P14453 did the analysis previously using A2 tool steel as their material. They found that the minimum factor of safety to be 5.37 and the max deflection would be 5.06μm using a spreadsheet calculator and Ansys respectively. This deflection is 11% of the radial clearance.

The actual shaft is made of high grade AISI 4140 alloy steel. This material has a much higher tensile strength. Running these new properties through the excel calculator produces a minimum factor of safety of 7.7. The max deflection would be a little less than 5.06μm because deflection is inversely related to the modulus of elasticity. A2 tool steel has a E of 29,400 ksi and AISI 4140 has a E of 29,700 ksi, a variation of about 1%.

It is important to note that the secondary analysis was done using a max force of 2000 lbf. Our current setup would only require a max force of 1000 lbf. This would further reduce the deflection of the shaft and increase the factor of safety.

Page 42: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

42

Page 43: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

43

Audible Noise Reduction

To reduce the audible noise of the lubrication system we propose to switch the current chain link drive

to a v belt drive system. This analysis serves as a first order justification of the solution.

We know the chain derived used has sprockets of 1.84” and 6 ⅜” diameters, therefore the speed ratio is

about 3.465. To keep this the same we chose v belt pulleys with a similar speed ratio.

Calculations

Motor torque is greater than required pump torque even without mechanical advantage

Large torque advantage reduces risk of slip. To implement this solution the following items would

needed.

Page 44: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

44

Alpha Prototype Bearing Housing Movement Testing

To understand the movement of the bearing housing block of the alpha prototype an experiment was

conducted using a LVDT and signal conditioner. This test provided other insights to understanding the

system such as time dependencies calibration procedures. Calibration Setup

A dial caliper was clamped to a piece of aluminum. The LVDT was then

clamped in such a manner that it was parallel to length of the dial caliper.

The dial caliper was then positioned so that the free end could displace

the LVDT. The LVDT was displaced to a similar outputted voltage as

tested. Dial caliper was adjusted by 0.001" and voltages were recorded.

The setup is shown on the right. :

A correlation function was created that converts voltages to displacements.

Page 45: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

45

Experiment Setup

An aluminum block bored with a 0.300” hole and perpendicular 4-40 thread set screw was created to

hold the LVDT to the bottom surface of the bearing housing.

Test Results

The first test consisted of starting the alpha prototype and bringing it to 360rpms. The system ran for 10

minutes before testing. Weight was added incrementally to a maximum of 150lbs, 1500lbf applied to the

block, then removed incrementally. System was allowed to run after weight change for 2 minutes before

data was recorded. The data shows a linear relationship between force and displacement up to about

1000lbs. From a thousand pounds of force to the max the displacement is less. We also see that there is a

poor hysteresis. This could be because because the LVDT somehow got moved during the test or that

the system was not at steady state when the test was started.

Page 46: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

46

Preliminary Test Transducer Experiment

The purpose of this design is to provide a fundamental understanding of the construction process

required for a piezo transducer. The piezo stacks can be purchased from the supplier, American Piezo,

with lead or without leads. If they are to be purchased without leads the team will be soldering on our

own. The supplier offers a soldering kit with practice stacks as well. Once the piezo stack is assembled it

will be installed into the fixture assembly. The half inch diameter bolt will allow for an adjusted preload

while the hex nut will serve as a locking mechanism. Voltages will be applied to the stack and force

measurement data will be record as a function of voltage. This experiment will provide an understanding

of how the pzt stack will react to voltages and the correlation will be compared to analytical data.

Additional instruments can be added to this set up such as LVDTs so that the actual displacement can be

observed. If these preliminary tests are successful, further experimentation can take place. An example

would include dynamic loading where a function of voltage would be supplied to the pzt stack. Since

this is low budget project hardware and materials are subject to change depending on what is available

to the team.

Page 47: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

47

Preliminary Project Plan for MSD II – Test Plans System Test Plan:

Page 48: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

48

Page 49: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

49

Page 50: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

50

Page 51: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

51

Preliminary Project Plan for MSD II

Sub System Level Prep/Build (1/26/15 - 2/20/15)

Page 52: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

52

Build and Test Sub System (2/23/15 - 3/27/15)

Page 53: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

53

Appendix

Film Thickness

Email with Steve Lucchesi

Price Quote from Macro Sensors

Page 54: Dynamic Loading Simulation, By EMA, On Journal Bearing ...edge.rit.edu/content/P15453/public/Detailed Design... · Force = 1000 lbs (from compressor load profile) Screwlead = 0.197

P15453 RIT MSD I Detailed Design Review

54

Fluid and Bearing Temperature Analysis http://en.wikipedia.org/wiki/Thermocouple#Type_K http://www.thermometricscorp.com/thertypk.html http://www.mcmaster.com/#thermocouples/=uwrck1 http://www.omega.com/pptst/UTC-USB.html