Test Stand for Calibrating Strain Gaged Drive Shafts

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Indiana University Purdue University – Fort Wayne

Department of Engineering

ENGR 410

Capstone Senior Design Project

Report #1

Project Title: Test Stand for Calibrating Strain Gaged Drive Shafts

Team Members: Alex Yarian EE

Joseph Carnes EE

Isaac Larson ME

Curtis Coverstone ME

Darin Taylor ME

Aaquib Asif ME

Sponser: Eaton Corporation – Clutch Division

Faculty Advisors: Dr. C. Chen and Dr. Younis

Date: December 04, 2014

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Table of Contents

Acknowledgements ........................................................................................................................4

Abstract ...........................................................................................................................................5

Section I: Problem Statement .......................................................................................................6

a.) Problem Statement .........................................................................................................7

b.) Requirements and Specifications ...................................................................................7

c.) Given Parameters ...........................................................................................................7

d.) Design Variables ............................................................................................................8

e.) Limitations and Constraints ...........................................................................................8

f.) Safety, Environment, Economic, and Other Considerations .........................................9

Section II: Conceptual Design ....................................................................................................10

a.) Conceptual Designs Generation ...................................................................................11

b.) Subsystem Categories ..................................................................................................11

c.) Subsystem Concepts ....................................................................................................13

1.) Torque Application ..........................................................................................13

2.) Electrical Interface ...........................................................................................14

3.) User Interface ...................................................................................................16

4.) Safety Guards ...................................................................................................18

5.) Strain Gage.......................................................................................................19

6.) Fixture ..............................................................................................................19

7.) Torque Measurement .......................................................................................20

d.) Conceptual Designs .....................................................................................................21

1.) Concept A ........................................................................................................21

2.) Concept B.........................................................................................................22

3.) Concept C.........................................................................................................23

Section III: Evaluation of Conceptual Designs .........................................................................24

a.) Attribute Weighting .....................................................................................................25

b.) Design Decision Matrix ...............................................................................................26

c.) Conceptual Evaluation Summary ................................................................................28

Section IV: Detailed Design.........................................................................................................30

a.) Calibration Test Stand..................................................................................................31

b.) Epicyclic Gear Train Design ........................................................................................39

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1.) Gear Selection ..................................................................................................39

2.) AGMA Stress Analysis ....................................................................................41

3.) AGMA Contact Stress .....................................................................................41

4.) AGMA Spur Gear Bending .............................................................................45

c.) Safety Guard ................................................................................................................53

d.) Data Acquisition System Selection ..............................................................................54

1.) Hardware Setup ................................................................................................56

2.) User Interface ...................................................................................................57

3.) ActiveX Setup for Lab View ...........................................................................58

4.) LabView Software Setup .................................................................................61

Section V: Cost Analysis/Estimation ..........................................................................................62

a.) Strain Gage Test Stand.................................................................................................63

b.) Gears ............................................................................................................................64

c.) Safety Guard ................................................................................................................65

d.) LabView, Computer, and DAQ System ......................................................................66

e.) Overall Project Cost .....................................................................................................67

Conclusion ....................................................................................................................................68

References .....................................................................................................................................69

Appendices ....................................................................................................................................71

a.) Appendix A: Decision Matrix ......................................................................................71

b.) Appendix B: Drive Shaft Dimensions .........................................................................74

c.) Appendix C: Test Stand Drawings ..............................................................................77

d.) Appendix D: Drawings of the Gears ............................................................................85

e.) Appendix E: Safety Components .................................................................................89

f.) Appendix F: Additional Parts ......................................................................................90

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Acknowledgements

The team would like to thank Eaton Clutch Corporation for their support of this project and for

sponsoring our senior design Capstone Project at IPFW.

In particular, the team thanks Andrew Temple and Jim Hurl from Eaton Labs in Auburn for all of

their help, support, and for being the primary contacts for the project at Eaton. They have given

hours of their own time answering questions as well as meeting with the team at Eaton.

Finally, the team would like to express their gratitude to Dr. C. Chen and Dr. Younis who are the

advisers for the project and have spent many hours of their time guiding and helping the team.

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Abstract

Eaton Clutch requested the design of a test stand for calibrating strain gauged drive shafts for its

staff to use in their Auburn Lab to perform in-house calibration tasks. The lab currently uses

drive shafts with strain gages applied to the surface to measure the output torque from the

transmissions of large trucks. A relationship between the output voltage of the strain gages and

the input torque to the drive shaft must be found by applying a known torque value to the drive

shaft. This calibration is currently done outside of the lab at one of two facilities that are several

hours away. By developing a new calibration fixture, the company will save many hours of

technician time by eliminating the transportation time to and from facilities. Additionally, this

stand will be a cost savings for the Auburn Lab, as the other facilities charge for use of their

calibration fixtures.

The calibration will be accomplished by first installing the drive shaft into the test stand with one

end fixed. The opposite end will be attached to a load cell, and the load cell will be attached to a

torque multiplier. The user will apply a torque, through the multiplier, which is measured by the

inline torque cell, and that data will be used to generate a calibration curve to be used for the

strain gage output. The test stand itself will be a self-contained unit; that is, the input torque,

output strain gage voltage, and final calibration curve will all be displayed on the unit’s monitor.

The team chose seven subsystems and brainstormed ideas for each subsystem. After

brainstorming was completed, the ideas were narrowed down to between two and four ideas per

subsystem. The team then used an attribute weighting matrix and a design decision matrix to

quantitatively choose first and second choices for each subsystem.

Once the final conceptual design was chosen, the detailed design was completed. The system

was simplified into four main subsystems, and a full analysis was completed on each subsystem.

After completing the final detailed design, a cost analysis was performed for the entire system.

The estimated cost of the test fixture is about $6700. Eaton has allowed a budget of $7500 for

the project; so, currently the design meets criteria.

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Section 1: Problem Statement

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Eaton Clutch requested the design of a test stand for calibrating strain gaged drive shafts for its

staff to use in the Auburn lab to perform in-house calibration tasks. This stand should be able to

apply a variable torque load to said drive shaft with the capability of handling torque inputs up to

3500 ft. lbs. The stand must be able to accommodate different size drive shafts with variable

length and diameter, and it is preferable to accommodate different spline configurations. A

simple to read/use interface for the test stand is requested. The integrated user interface must be

able to display the applied torque in real time. The interface should also be able to produce

ready-to-use calibration factors that can be inputted directly into the equipment that reads the

strain gage.

Requirements and Specifications

The test stand needs to apply a known torque to obtain strain gage calibration values.

Torque Applied- The variable should be anywhere from 0 ft. lbs. to 3500 ft. lbs. It needs

to be applied, held, and safely released.

Application Display- It needs easy to read calibration values, applied torque, and simple

input interface.

Drive shaft Configuration- One requirement is that it accommodates Dana Spline

Configuration.

Measure of Applied Torque- An accurate measure of applied torque will be displayed on

the readout.

Mechanical safety guards must be included to restrain a drive shaft in the event of failure

If a powered/automated means of torque application be used, then an e-stop (emergency

stop) must be located on the front of the equipment that disables all systems

instantaneously.

Method of measuring torque applied must be able to be calibrated.

Given Parameters

The following fixed-design parameters will strictly govern a portion of the project.

● Drive shaft Dimensions- The dimensions are approximately 0 to 104 inches in length, and

3 to 6 inches in diameter.

● Stand-alone Unit- This must give calibration results without additional calculations,

input, or system related parts. It must also contain control systems and torque application

systems all-in-one.

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Design Variables

The below variables allow for flexibility in the design of the project in order to meet the given

requirements.

● Torque Application- Manual or automated (hydraulic, pneumatic, etc.)

● Drive shaft Connector- Accommodates different drive shaft spline configuration, along

with short-tool change/setup (10 to 15 minutes).

● Stand Construction- Different materials are allowed in construction.

● Test Stand Mobility- Portable or fixed unit, either is viable.

● Device output- range of means for output of test stand.

a.) The bare minimum is to read applied torque and voltage output of the strain gage.

b.) The desired system should be computer integrated with the Test Stand. It is one

that will accept a full range of applied torque vs voltage readout and calculates

usable calibration data. The system should also control the applied load if an

automated loading system is used.

● Torque measurement method- may be a torque cell or a load arm.

● Computer interface system- could use a variety of software and data acquisition devices.

National Instruments data acquisition system (NI-DAQ) is preferred; however, it is not

specified. LabView software is preferred but not specified.

● Multipoint Calibration- Software should accommodate multiple calibration points across

the entire applied load range to allow for accurate characterization of the strain gage(s)

and drive shaft system.

Limitations and Constraints

The test stand must follow given constraints as well as budgetary limitations.

● Budget- The entire project must fall below the given budget of $7500.

● Test Stand Footprint- Space is limited, and stand should be as compact as allowable per

tested drive shaft. It must be able to fit reasonably within an Eaton test cell.

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Safety, Environmental, Economic, & Other Considerations

Safety is of the utmost importance for every part of the project; additionally, ensuring that the

project is environmentally friendly is also a key concern.

● Safety Cage- Safety system (e.g., safety collar or full cage) to account for drive shaft

failure.

● Emergency Fail Safe- Emergency stop that acts as a disconnect.

● Hydraulic System- Must have hydraulic spill containment plan (if said system is used).

● Safety Regulations- Test Stand must comply with all Eaton, OSHA, and other safety

regulations.

● Power Supply- The system should be 120 volts (standard outlet voltage).

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Section 2: Conceptual Design

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Conceptual Designs Generation

Once the Requirements and Specifications for the test stand were established, the next step in the

project was to begin the formulation of conceptual designs. This process began with a

brainstorming session where multiple possibilities for each subsystem were provided. Eaton

requires this test stand to provide 3500 ft. lbs. of torque to drive shafts of variable length,

diameter, and spline configuration. Figure 1 illustrates that two main processes may be used in

this test stand—one being a powered system utilizing some type of motor for automated torque

application, and the other consisting of a manual torque application system utilizing more

operator input.

Manual User Application:

Electric Torque Application:

Figure 1: Two Primary Conceptual Processes

Subsystem Categories

In order to analyze the concepts more efficiently, the design of the test stand was divided into

seven different categories where conceptual designs and their alternatives were generated. These

different subsystems will be put together to create the final concept for the test stand.

Torque Application – This subsystem applies the known torque to the drive shaft through the use

of torque multipliers. Below is a list of several concepts for torque application systems.

Torque multiplier

Chain gear box configuration

Epicyclic gearing

Hydraulic system

Pneumatic system

Electrical Interface – This is the electrical subsystem that will interface between the drive shaft

and the user interface software to gather data and make necessary calculations.

Manual Torque

Applicator

Torque

Multiplier Load Cell Drive Shaft

Electric Motor-

Automated

Gear System/TQ

Multiplier Load Cell Drive Shaft

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National Instruments DAQ

Measurement Computing USB - 3102

User Interface – This is the subsystem that the user will interface with, that accepts and provides

all necessary data to calibrate the strain gages.

LabView

Visogram

MyOpenLab

SENSIT Test and Measurement Software

Safety Guards – This is the safety system that protects the apparatus and end user against drive

shaft failure.

Full box (Plexiglass)

Padded bar (ergonomics/safety)

Safety Loop/Brace

Interlock on guarding to disengage torque applicator if guard is open (mechanical)

Solenoid actuated guard that is locked during operation (electrical)

Strain Gages – These are the different strain gages that could be used to take measurements on

the drive shaft.

Single axis strain gages

90 biaxial strain gages

Fixture – This sub-system is the main fixture that will house the torque multiplier, and secure the

test stand to the ground.

Slotted rail in the floor to accommodate variable length

Tube steel frame

That can be wheeled around

Bolted to the ground

Bed plate

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Torque Measurement – This will be the subsystem that takes the input torque from the operator

after the torque goes through a multiplier, and will then read the applied torque to the drive shaft.

Torque load cell capable of 3500 ft. lbs.

Load arm of specified length with force gage to measure torque.

Subsystem Concepts

1. Torque Application

This subsystem would be a part of a manual torque application process. In this system, the

operator would apply a torque manually, which then passes through a torque multiplier to the

drive shaft.

Torque Multiplier: This will be a required component for torque application for manual user

input, as a user cannot apply a high enough torque load without a multiplier. This multiplier will

be in the form of epicyclic gearing or a chain gear box configuration. These torque multipliers

will allow for the appropriate applied torque of 3500 ft. lbs. to be applied to the drive shaft for

strain gage calibration.

Figure 2: Example of Epicyclic Gearing Setup for Multiplying Applied Torque.

Disadvantages

This component will require a costly and complex torque multiplier that could heavily cut

into the test stand budget.

The operator will still have to exert a significant physical force in operating the system.

This could cause potential issues, such as extreme fatigue should the system must be used

multiple times a day.

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Hydraulic System: This component would be implemented with an automated torque application

system, wherein the torque is supplied by a hydraulic actuator to the drive shaft. This component

would not necessarily require a torque multiplier which reduces costs significantly.

Disadvantages:

High cost associated with a hydraulic system.

Requires a containment system for hydraulic fluids, as well as spill containment plan that

complies with both Eaton and OSHA safety regulations.

Pneumatic System: This component of the subsystem would be implemented with an automated

torque application system. The torque is supplied by a pneumatic actuator to the drive shaft.

Pursuing this option would cut costs significantly because the pneumatic system would not

necessarily require a torque multiplier. This allows for the budget to be utilized elsewhere. It

would also not require a fluid containment system or spill plan like the hydraulic system.

Disadvantages

A pneumatic system contains a lower threshold for maximum applied torque compared to

a hydraulic system.

A pneumatic system would have a slower response time because the air tank(s) would

need to build pressure before torque is applied.

2. Electrical Interface

This subsystem would be a part of the system that reads data from the gages and load cell,

interprets and analyzes it, and then computes necessary output values such as applied torque,

thermal and mechanical strain, and provides these values to the user interface.

National Instruments Data Acquisition unit: This component will allow for the voltage change in

the strain gages to be read and interpreted as a strain value, which will then be output to the user

interface. It will also be able to read the output of the torque load cell and feed this value to the

computer user interface so it can be displayed and used in the calibration calculations. If a

powered system is used for applying torque than the NIDAQ device can be used for controlling

torque application from the user interface.

Disadvantages

The NIDAQ can be somewhat costly; and with our budget being at $7,500, it could cost

us 1/7 of our budget.

Also the NIDAQ could be easily damaged in the lab if consideration is not taken with the

use of heavy duty equipment nearby.

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Figure 3: Electrical System to be implemented if a Manual System for applying Torque is used.

Figure 4: Electrical System to be implemented if a Powered System for applying Torque is used.

LabVIEW

Software

DC Power

supply

NIDAQ

Wheatstone

bridge

Strain gages

Torque Cell

LabVIEW

Software

DC Power

supply

NIDAQ

Wheatstone

bridge

Strain gages

Torque Cell

Torque

application

system

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Wheatstone Bridge in a quarter, half, or full bridge configuration:

Quarter Bridge: This works by having one strain gage for one of the resistors in this circuit, and

when that resistance changes it produces an output voltage.

Half Bridge: Instead of just using one strain gage, it uses two strain gages for two of the resistors

in the bridge. This will allow for minimizing the effect of temperature.

Full Bridge: This circuit uses four strain gages for the four resistors of the circuit.

Figure 5: Shown here is the Wheatstone Bridge configuration.

Disadvantages:

The change in resistances that the Wheatstone Bridge measures are very small; so, the

wire resistance can have a significant effect on the output voltage.

3. User Interface

The user interface of this system will be used to observe the calculated measurements of the

torque from the load cell on the drive shaft. The actual value of torque applied to the drive shaft

as measured by the load cell or load arm will be displayed on the user interface. The raw voltage

value that is outputted by the Wheatstone Bridge will be displayed as well. A computer running a

LabView program will be used as the user interface, and it will need to meet the requirement of

the software chosen for the system.

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Table 1: Computer System Requirements

Computer Requirements:

Windows

Run-Time Engine Development Environment

Processor Pentium III/Celeron 866 MHz or equivalent

Pentium 4/M or equivalent

RAM 256 MB 1 GB

Screen Resolution

1024 x 768 pixels 1024 x 768 pixels

OS Windows 8.1/8/7/Vista (32-bit and 64-bit)

Windows XP SP3 (32-bit)

Windows Server 2012 R2 (64-bit)



Windows 8.1/8/7/Vista (32-bit and 64-bit)

Windows XP SP3 (32-bit)




Disk Space

500 MB 5 GB (includes default drivers from NI Device Drivers DVD)

Linux

Run-Time Engine Development Environment

Processor Pentium III/Celeron 866 MHz or equivalent


RAM 256 MB 1 GB

Screen Resolution

1024 x 768 pixels 1024 x 768 pixels

OS Linux kernel 2.4x, 2.6x, or 3.x and GNU C Library (glibc) Version 2.5.1 for the Intel x86_64 architecture.

The LabVIEW Installation Guide inaccurately omits Linux kernel 3.x from this list.

Red Hat Enterprise Linux Desktop + Workstation 6 or later, open SUSE 12.3 or 13.1, or Scientific Linux 6 or later.

Disk Space

115 MB (32-bit)

131 MB (64-bit)

1.2 GB for the complete installation of each bitness

1.4 GB for the complete installation of both 32- and 64-bit LabVIEW

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Disadvantages:

The computer we chose to use for our user interface will need an operating system which

adds to the cost of our system.

LabView software is also more expensive to use.

4. Safety Guards

This subsystem is a safety requirement where a safety harness, loop, or cage will protect the

operator(s) against unwanted drive shaft failure. This will involve securing either a safety loop or

safety cage of some type around the drive shaft/test stand to act as a barrier.

Full Box (Plexiglass): This component, if implemented, would be a large steel and

plexiglass covering that encompasses the entire testing apparatus. The benefit of this

component would be that it is inherently safe and is structurally rigid, without

compromising the visibility of the drive shaft during testing. Also, the plexiglass cover

would not allow any small pieces of debris to escape the safety barrier.

Disadvantages:

Will be more expensive than a similar safety “cage”.

Cumbersome to open/close, and swap out different sized drive shafts.

Padded Bar (Ergonomics/Safety): This safety bar would be used if the manual torque

application system was interrupted. With a high torque load being applied during testing,

severe whiplash could occur if the operator were to release the application lever. The

padded bar would act as a guard against the lever hitting the operator, or damaging

equipment.

Disadvantages:

Not as safe as a ratchet system (similar to a parking pawl in vehicle

transmissions) where applied torque could be held within the gears without

operator input.

Safety Loop/Brace: This component would act as a safety brace against drive shaft

failure. Should the drive shaft fail during testing, this brace would hold it in place and not

allow the shaft components to shift significantly. This component would be significantly

less cumbersome than a full encasing and restrict less movement of the drive shaft.

Should a safety loop be used, an interlock to disengage the torque applicator may be

implemented to restrict the user from being injured by opening the loop/brace during

operation. Similarly, a solenoid actuated guard that automatically locking during the

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operation of the test stand could be implemented to achieve the same results as the

interlock system.

Disadvantages

Not as safe as a Full Plexiglass Box because small parts could get past the

brace in the event of failure.

Much costlier than alternatives, should the interlock(s) (mechanical/electrical)

be implemented.

5. Strain Gages

This subsystem consists of two or more strain gages connected to the DAQ system and will

collect the necessary strain data from the drive shaft being tested. This will be done by reading a

voltage change logged by the Wheatstone bridges located on the gages, which then can be

interpreted into a strain value. This value will then be separated into mechanical and thermal

strain then applied to calibration data.

Single axis strain gages: This component would read the strain value as a change in

voltage on the Wheatstone bridge.

90° biaxial strain gages: This component would read the strain value as a change in

voltage on the Wheatstone bridge. And it may be needed to measure torque applied more

accurately.

6. Fixture

This is the physical subsystem that will fix the test stand to the ground. It will consist of either a

bed plate or tube steel frame that will be connected directly to the test stand and the floor of the

lab.

Slotted rail in the floor to accommodate variable length: This slotted rain system would

allow for the opposite end of the test stand to move freely in one axis toward or away

from the other end of the test stand (where torque is applied). This would allow the test

stand to accommodate different length drive shafts, as well as allow for easier setup when

attaching the shaft to the test stand.

Disadvantages:

This component could be a potential weak point for the test stand as it must be

easily movable and maintain rigidity during high torque load application.

Should the movable portion not be correctly braced or fixed down before load

is applied, the safety of the entire system could be compromised.

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Tube steel frame: This component would be a simple steel tube frame that is directly

bolted to the ground, which would have no moving parts, and will maintain rigidity. This

tube frame system could either be a wheeled component for easy movement throughout

the test lab or a component bolted directly to the ground.

Disadvantages:

This component would not be able to compensate for different length drive

shafts and would have a fixed length. One possible way to compensate for

this would be to add connectors for smaller shafts. However, doing this would

further complicate the test stand.

Added wheels would completely remove the rigidity aspect of the tube frame

in exchange for marginal mobility. However, without wheels the test stand

would be bolted directly to the ground and have little chance for repositioning

in the future.

7. Torque Measurement

This subsystem reads the input torque from the operator after the torque has passed through a

multiplier and is being applied to the drive shaft.

Torque Load Cell (Capable of 3500 ft. lbs.): This system will measure the applied torque

to the drive shaft and will output this value as an electrical signal which can then be read

by the NIDAQ and displayed on the user interface.

Disadvantages:

This component is a very costly device for the torque range that it is needed.

Load arm of a precise length with a calibrated force gage: This system will measure

force, which can be converted into torque since the arm length is a known value. This

calculation can be done by the LabVIEW user interface.

Disadvantages:

This system will add some complexity to the mechanical design as a load arm

will need to be added as well as an anchor for the force gage.

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Conceptual Designs

Concept A

Figure 6: Conceptual Design A (w/ epicyclic gearing)

This conceptual design incorporates manual torque application, along with epicyclic gearing, as a

torque multiplier to achieve high torque input values. As is shown in Figure 6, the torque

application will be manually done by the operator, pass through the multiplier, then to the load

cell, and finally to the drive shaft.

Advantages:

A primary advantage of this system is the low cost to incorporate a manual torque

application system as opposed to a hydraulic or pneumatic system.

This application system will be less complex, whereas hydraulic and pneumatic systems

require storage/compression tanks for fluid/air.

Disadvantages:

This system may require more than a single torque multiplier, depending on the

performance of the gearing system chosen. This could significantly increase the cost

associated with the design.

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Concept B

Figure 7: Conceptual Design B (w/ Chain and Sprocket Assembly)

This conceptual design, shown in Figure 7 above, incorporates manual torque application along

with a ratchet assembly for torque delivery to the drive shaft. This design incorporates a “pawl”

or ratchet assembly feature in the gearing to allow the operator to hold the torque being applied

at a set point, illustrated in DETAIL A, without the load being removed once the operator

releases the crank bar. This is beneficial from a safety standpoint, as well as an ergonomic one.

Advantages:

Chain and Sprocket assembly will allow for cheap and simple torque multiplication

compared to expensive and complex alternatives.

Disadvantages:

Chain and Sprocket assembly as well as the ratchet system are potential high wear items

with a limited lifespan. These components must be replaced for the test stand to continue

functioning indefinitely. For this reason, common size, tooth, and chain lengths must be

chosen to easily source replacements for these components.

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Concept C

Figure 8: Conceptual Design C (Hydraulic or Pneumatic torque application)

This conceptual design depicts a system in which either a hydraulic or pneumatic cylinder is

used to apply a torque to an arm, which then applies the torque to the drive shaft through the test

stand. This design most likely would need to incorporate the pawl mentioned in Concept B

above in the event of rapid loss of power to the hydraulic or pneumatic system.

Advantages:

Both systems would be easier to use than a manual torque application

Use of a torque multiplier is not required, thus reducing system complexity

Possibly easier to incorporate safety features to the system via the control system

Disadvantages:

Significantly higher cost than a manual torque application system

Use of hydraulic system requires a hydraulic spill containment plan

Possible additional safety threats from having a system capable of such high torque

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Section 3: Evaluation of Conceptual Designs

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Once brainstorming and concept generation processes were completed, the next step involved

analyzing and evaluation of each concept, and finally, a decision on which concepts would be

used as the primary and alternative design.

Attribute Weighting

The design of the test stand was initially divided into 7 different subsystems, each with several

different components that could accomplish the requirements for that subsystem. Each of these

components was evaluated under different attribute criteria. Safety, cost, ease of use, reliability,

reparability, environmental impact, design simplicity, and company acceptance were the

attributes chosen, and from the matrix shown in Table 2, each attribute was compared

individually against one another for their individual attribute weight towards the final score of

each component. This was done by taking the attributes in each column and comparing them to

each attribute in the rows of Table 2. If the attribute in the column was deemed more important

than the attribute in the corresponding row, it was given a 9. If the attribute was deemed less

important it was given a 1, and if they were of equal importance, it was given a 4. These values

were then totaled for each column and converted to a fraction of the whole. These fractions are

the weighting factors or attribute weights that were then used in the decision matrices shown in

Appendix A. The percent value of their weight versus the total was also provided.

Table 2: Attribute Weighting Matrix showing total score and rank of each Design Attribute

Safety Cost Ease

of Use

Reliability Reparability Environmental

Impact Design

Simplicity Company

Preference

Safety - 1 1 1 1 1 1 1

Cost 9 - 1 9 4 4 4 9

Ease of Use 9 9 - 4 9 4 4 9

Reliability 9 1 4 - 1 1 1 1

Reparability 9 4 1 9 - 4 4 1

Environmental Impact

9 4 4 9 4 - 1 9

Design Simplicity

9 4 4 9 4 9 - 9

Company Preference

9 1 1 9 9 1 1 -

Totals 63 24 16 50 32 24 16 39

Weight 0.239 0.091 0.061 0.189 0.121 0.091 0.061 0.148

Percent 23.9% 9.1% 6.1% 18.9% 12.1% 9.1% 6.1% 14.8%

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Design Decision Matrix

The individual weights of each attribute in the weighting matrix (Table 2) were used in the

design decision matrix (Appendix A). All 7 subsystems were placed within the decision matrix,

along with each component that was being considered to accomplish the task of the subsystem.

These components were then rated with respect to each attribute in the form of a ranking from

first to last. For example, the torque application subsystem had four component choices; each of

these choices was ranked from first to last against one another in terms of its safety attribute, cost

attribute, etc. by each group member. Next, each component’s ranking within each attribute

between the six member’s submitted decision matrices was averaged, and then multiplied by the

attribute weight calculated from Table 2. This was done for each component, under each

attribute, and then the values were added together for a total score for each component. The

component with the highest score was determined to be the most favorable, as this system

factored in each attribute as well as each team member’s choice in the matter.

For example, assume the chain gear box received an average ranking of 1.50 for safety between

all group members. This value would then be multiplied by the attribute weight for safety

(0.239). This process is then repeated for each attribute, and then the values are added together

for a total score. This entire process is then repeated again for each component, until a score is

generated for each component of each subsystem, the final scores can be seen in Table 3 below.

Table 3: Scoring Matrices Subsystem Component Score

Torque Application Score

Chain gear box 2.66

Epicyclic Gearing 2.97

Hydraulic 1.96

Pneumatic 2.48

Electrical Interface Score

National Instruments

1.69

Measurement Computing USB -

3102 1.31

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User Interface Score

LabView 3.60

Visogram 2.41

MyOpenLab 2.16

SENSIT 1.79

Safety Guards Score

Full box 3.38

Padded bar 2.30

Loop w/interlock 2.39

Loop w/solenoid 1.93

Strain Gages Score

Single axis 1.46

90° biaxial 1.54

Fixture Score

Slotted rail in floor 2.43

Tube steel w/wheels

1.88

Tube steel w/bolts 2.98

Bed plate 2.71

Torque Measurement

Score

Load Cell 1.63

Load Arm 1.37

28

Concept Evaluation Summary

Several different components were generated for each subsystem; each concept fulfilled the

attributes that were chosen as well as the role of the subsystem within the conceptual design.

However, using the design decision matrix the top choices for each subsystem were chosen by

highest overall score and second highest overall score.

For the subsystem of torque application, the component that was chosen was epicyclic gearing.

This gearing would allow for acceptable torque multiplication, as well as smooth delivery to the

load cell/arm and subsequently the drive shaft. The nature of this component is non-automated,

and will require operator input. The secondary component that was chosen was the chain gear-

box component.

For the electrical interface subsystem, the chosen component was the National Instruments data

acquisition unit. This component will allow for the voltage change in the strain gages to be read

and interpreted as a strain value, which will then be output to the user interface. This component

will also be able to read the output of torque to the load cell/arm and feed this value to the

computer user interface for display/calibration calculations. The secondary component chosen

was Measurement Computing USB - 3102.

For the user interface subsystem, the chosen component was the LabView program. This

interface will be used to observe the calculated measurements of the torque from the load

cell/arm on the drive shaft. An executable in the LabView software for installation and running

on a PC (that meets the hardware requirements of the software), along with running a full version

of MS Windows for basic analysis capability (Excel) will be required for this subsystem. The

secondary component chosen was Visogram.

For the safety guard subsystem, the chosen component was the full box. This component

includes a large steel and plexiglass covering that encompasses the entire testing apparatus. The

secondary component chosen was the safety loop with interlock.

For the strain gage subsystem, the chosen component was multi-dimensional strain gage. This

component will read the strain values as a change in voltage on the Wheatstone bridge, the multi-

dimensional gage allows for a much more accurate measure of the applied torque. The secondary

component chosen was the single-dimensional strain gage.

For the fixture subsystem, the chosen component was tube steel with bolts. This component

would be a simple tube frame that is directly bolted to the ground; this component will have no

moving parts, and will maintain rigidity. This component will not be able to compensate for

different length drive shaft, therefore this subsystem will need revision to accommodate different

length drive shafts. The primary workaround for this would be to incorporate the slotted rail

system into it, allowing for variable drive shaft length, along with the structural rigidity of a tube

steel frame. The secondary component chosen was bed plate.

For the torque measurement subsystem, the chosen component was the load cell. This system

will measure the applied torque to the drive shaft and will output this value as an electrical signal

29

which can then be read by the NIDAQ and displayed on the user interface. The secondary

component chosen was the load arm, requiring an anchor for the calibrated force gage.

Shown below in Table 4 are the primary and secondary components chosen for their respective

subsystems.

Table 4: Conceptual Designs by Subsystem and Component

Conceptual Design 1

Subsystem Component

Torque Application Epicyclic Gearing

Electrical Interface National Instruments

User Interface LabView

Safety Guards Full Box

Strain Gages 90° biaxial strain gages

Fixture Tube Steel w/Bolts

Torque Measurement

Load Cell

Conceptual Design 2

Subsystem Component

Torque Application Chain gear box

Electrical Interface Measurement Computing USB -

3102

User Interface Visogram

Safety Guards Loop w/Interlock

Strain Gages Single axis strain gages

Fixture Bed Plate

Torque Measurement

Load Arm

30

Section 4: Detailed Design

31

Detailed Design Analysis

Calibration Test Stand

Frame:

The frame was modeled as one entire piece in SolidWorks due to the difficultly and inaccuracy

involving welds within SolidWorks Simulation. Using the assembly model of the frame with the

sliding base, the base was placed halfway between the end and the middle of the frame, where

the deflection from a torque would be the highest. The feet of the frame were fixed, and a torque

of 3500 ft-lbs was applied to the bolt holes in the sliding base. The resultant finite element

analysis (FEA) shows that the maximum stress in the frame is equal to 16.3 ksi. The minimum

yield strength of A500 steel is 33 ksi; so, the minimum factor of safety of the frame is 𝐹𝑆 =33 𝑘𝑠𝑖 16.3 𝑘𝑠𝑖 ≈ 2⁄ . A diagram of the stresses found from the simulation is shown in Figure 9.

Figure 9: FEA simulation of torque on the Frame

Additionally, the highest stress at a weld joint is 9.5 ksi. For weld in tension or compression, the

yield strength is multiplied by 0.6, so the minimum yield strength is 19.8 ksi for A500 steel.

Therefore, the factor of safety at the weld joints is 𝐹𝑆 = 19.8 𝑘𝑠𝑖 9.5 𝑘𝑠𝑖⁄ ≈ 2.

Sliding Base:

The base was also modeled and simulated in SolidWorks using FEA. The bottom was fixed, and

the bolt holes were subjected to the drive shaft torque. The bolt holes had the highest resultant

stress, about 5.9 ksi. The highest stress in the rest of the base was about 3.5 ksi. This is shown

in Figure 10.

32

For A36 Steel, the yield strength is 36 ksi. With a maximum stress of 5.9 ksi, the resulting factor

of safety is 𝐹𝑆 = 36 𝑘𝑠𝑖 5.9 𝑘𝑠𝑖 ≈ 6⁄ .

Clamp: The clamps were also simulated with SolidWorks FEA. To determine the load to apply

to the clamps, a moment balance was performed on the sliding base, shown in Figure 10. From

the diagram, the resulting force was shown to be about 3000 lbf. This force was applied to both

surfaces of the clamp bearing load in the structure, as shown in Figures 12 and 13. The resulting

maximum stress is 18.9 ksi. With a yield strength of 36 ksi, the resulting factor of safety is about

1.9.

From the moment diagram:

∑𝑀 = 0

3500 − 10 ∙ 𝑅 ∙ (7.25 12⁄ ) = 0 (Reaction forces equal from symmetry)

→ 𝑅 = 3000 𝑙𝑏𝑓

Figure 10: Sliding Base FEA

Equation 1: Moment Balance

33

Figure 11: Moment Diagram on Sliding Base

Figure 12: FEA of Clamp

34

Figure 13: Back Side FEA of Clamp

Adapter: The adapter piece is required to make the connection between the load cell and the

companion yoke of the drive shaft. This analysis of this piece included FEA as well as bolt shear

analysis. From the FEA analysis, for A36 Steel (tensile strength of 58 ksi, and shear strength of

29 ksi), the shaft diameter necessary was found to be 3.10 inches, which resulted in a maximum

stress of 16.3 ksi, and a resulting factor of safety of 1.8 (shown in Figure 14).

Figure 14: FEA Simulation of Adapter

35

Additionally a bolt analysis was performed to ensure that the bolts between the adapter and the

companion yoke would not shear. Using Figure 15 below as a guide, the shear stress on the bolts

was calculated. The force, P, was found by taking a moment balance with the bolts and the

applied torque. The bolt hole arrangement for the adapter can be seen below in Figure 15.

∑𝑀 = 0

3500 − 10 ∙ 𝐹 ∙ 3.5 12⁄ = 0

→ 𝐹 = 1200 𝑙𝑏𝑓

Figure 15: Finding Shear Stress on Bolts

Figure 16: Bolt Hole Pattern is for Adapter Piece

36

Once the force on each bolt was found, the area of contact was calculated for each bolt. The “a”

dimension is the thickness of the adapter plate, 0.5”, and the “d” dimension is half the

circumference of the bolt (for a 10 mm bolt, it is 0.618”).

With all the information present, the shear stress on the bolts could be calculated.

𝜎 = 𝑃 𝑎𝑑⁄

𝜎 = 1200 𝑙𝑏𝑓 (.5" ∙ .618")⁄

→ 𝜎 = 3.9 𝑘𝑠𝑖

The resulting shear stress of 3.9 ksi is much less than the shear strength of a Class 10.9 fastener,

which is 37.8 ksi.

Equation 2: Bolt

Shear Stress

37

Torsional displacement of the drive shaft

The overall range of torsional displacement was found by entering all of the Dana drive shaft

information into an Excel spreadsheet and by using Equation 3, shown below. From Figure 17

below, L is the drive shaft length, D is the outside diameter of the drive shaft, d is the inside

diameter of the drive shaft, T is the applied torque to the drive shaft, and G is the shear modulus

of the drive shaft. The modulus was estimated using the value for low carbon steel, as the drive

shaft material is not published.

𝜃(𝑟𝑎𝑑) =𝑇𝐿

𝐺𝜋2(𝐷4−𝑑4)

Figure 17: A diagram showing a Hollow Shaft with a Torque Applied

Using these calculations, the maximum and minimum displacements were found, and those

values were converted to degrees, as shown below in Table 5. The maximum drive shaft

displacement found was about 1 degree. Multiplying that back through the gear ratio of 25:1, the

displacement to the load arm is about 25 degrees.

Table 5: Summarized range of Drive Shaft Displacement

Range of Rotational Displacement for all

Spicer Drive Shafts (@ 3000 ft lb of torque)

Radians Degrees

Minimum 0.002 0.111

Maximum 0.017 0.999

Equation 3: Torsional displacement Calculation for a Hollow Shaft

38

Selection of the Ratchet

As shown in Figure 18 below, the proper ratchet size was determined from the calculated 25

degree angular displacement of the sun gear. This was calculated from the torsional displacement

of the driveshaft at the maximum loading condition. Since the sun gear only allows for an

angular displacement of 25 degrees, this severely limits the choices of available ratchets. The

ratchet sizes with the largest diametral pitch allows for the largest amount of teeth to be triggered

by the pawl within the 25 degree rotational displacement limit. The chosen ratchet and pawl

would allow for up to eight “locks” from the ratchet and pawl system, while other ratchets with

smaller diametral pitches would allow for much fewer.

Figure 18: Ratchet Gear with Angular Displacement of Sun Gear shown

39

Epicyclic Gear Train Design

Figure 19: Epicyclic Gear Train Design

Gear Selection

Figure 20: Gear Setup for 1st stage of the multiplier

Planetary

Ring

Planetary

Sun

40

The gears chosen to comprise the epicyclic gear train(s) are listed below in Table 6. The pinion

(sun gear) is chosen to be stainless steel because the input gear will experience the most

revolutions; and therefore, it will experience the most wear. Anodized aluminum is used for the

planetary gears. Meshing stainless steel with aluminum minimizes wear.

Table 6: Dimensions and material specification for gear train design

Epicyclic Gear Specifications

Gear Teeth Diametral Pitch

Pressure Angle Build Material

Sun 12 12 20 Stainless Steel 303

Planetary 18 12 20 Aluminum 2024T4

Ring 48 12 20 Stainless Steel 303

A total gearbox ratio of 25:1 is used to limit the amount of applied force that the operator has to

input into the system. A two-stage epicyclic gear train is used to conserve space.

𝐺𝑒𝑎𝑟 𝑅𝑎𝑡𝑖𝑜 = 1 +𝑅

𝑆= 1 +

48

12= 5

For a 2-stage epicyclic, the output of the first stage is the input of the second stage

𝐺𝑒𝑎𝑟 𝑅𝑎𝑡𝑖𝑜 = (5

1) (

5

1) = (

25

1)

From this, a calculation of the required maximum amount of operator input is computed for a 3

ft. long lever crank.

𝑇𝑜𝑢𝑡 = 𝑇𝑖𝑛(25) ⇒ 3500 = (3 𝑓𝑡)(𝐹𝑖𝑛)(25)

⇒ 𝐹𝑖𝑛 = 46.66 lb

Gear Train Assembly Validation:

The validation process for the gear train assembly was done with three primary equations that

must be satisfied for an epicyclic gear train, these equations are listed below.

𝑃+𝑅

𝑁= 𝐼𝑛𝑡𝑒𝑔𝑒𝑟 =

18+48

3= 22 [𝑝𝑙𝑎𝑛𝑒𝑡𝑠 𝑐𝑎𝑛 𝑏𝑒 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛𝑒𝑑 120 𝑎𝑝𝑎𝑟𝑡]

(𝑃 + 2) < (𝑆 + 𝑃) ∗ sin (180

𝑁)

⇒ (18 + 2) < (12 + 18) ∗ sin (

180

3)

⇒ 20 < 25.98

2𝑃 + 𝑆 = 𝑅 ⇒ 2(18) + 12 = 48

Where P is the number of teeth of the planetary gear, R is the number of teeth of the ring, S is the

number of teeth of the sun gear, and N is the number of planetary gears used in the assembly.

These equations were satisfied using the gears listed in Table 6 above.

41

AMGA Stress Analysis

In order to ensure the safety and reliability of the chosen gears, the AGMA (American Gear

Manufacturers Association) approach is used. The following procedures are performed on the

second stage of the epicyclic gear train because the largest stresses occur after the first torque

multiplication.

AGMA Contact Stress

First, the modified gear tooth contact stress is calculated with the help from Shigley’s

Mechanical Engineering Design Ninth Edition textbook.

𝜎𝑐 = 𝐶𝑝 [(𝑊𝑡)(𝐾𝑜)(𝐾𝑣)(𝐾𝑠) (

𝐾𝐻

𝑑𝑤1𝑏) (𝑍𝑅

𝑍𝐼)]

1

2

𝐶𝑝= [1

𝜋(1− 𝑣𝑝

2

𝐸𝑝+1− 𝑣𝐺

2

𝐸𝐺)

]

1

2

= [1

𝜋(1− 0.3052

28(10)6+1− 0.3202

10.6(10)6)]

1

2

= 1648.92

Where,

𝐶𝑝 = 𝑒𝑙𝑎𝑠𝑡𝑖𝑐 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡

𝑣𝑝 = 𝑝𝑜𝑖𝑠𝑠𝑜𝑛′𝑠 𝑟𝑎𝑡𝑖𝑜 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑢𝑛 𝑔𝑒𝑎𝑟

𝑣𝐺 = 𝑝𝑜𝑖𝑠𝑠𝑜𝑛′𝑠 𝑟𝑎𝑡𝑖𝑜 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑙𝑎𝑛𝑒𝑡 𝑔𝑒𝑎𝑟

𝐸𝑝 = 𝑚𝑜𝑑𝑢𝑙𝑢𝑠 𝑜𝑓 𝑒𝑙𝑎𝑠𝑡𝑖𝑐𝑖𝑡𝑦 𝑜𝑓 𝑠𝑡𝑎𝑖𝑛𝑙𝑒𝑠𝑠 𝑠𝑡𝑒𝑒𝑙

𝐸𝐺 = 𝑚𝑜𝑑𝑢𝑙𝑢𝑠 𝑜𝑓 𝑒𝑙𝑎𝑠𝑡𝑖𝑐𝑖𝑡𝑦 𝑜𝑓 𝑎𝑛𝑜𝑑𝑖𝑧𝑒𝑑 𝑎𝑙𝑢𝑚𝑖𝑛𝑢𝑚

𝑊𝑡 = 𝑡𝑟𝑎𝑛𝑠𝑚𝑖𝑡𝑡𝑒𝑑 𝑙𝑜𝑎𝑑

𝐾𝑜 = 𝑜𝑣𝑒𝑟𝑙𝑜𝑎𝑑 𝑓𝑎𝑐𝑡𝑜𝑟

𝐾𝑣 = 𝑑𝑦𝑛𝑎𝑚𝑖𝑐 𝑓𝑎𝑐𝑡𝑜𝑟

𝐾𝑠 = 𝑠𝑖𝑧𝑒 𝑓𝑎𝑐𝑡𝑜𝑟

𝐾𝐻 = 𝐹𝑎𝑐𝑒 𝑙𝑜𝑎𝑑 − 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑓𝑎𝑐𝑡𝑜𝑟

𝑑𝑤1 = 𝑝𝑖𝑡𝑐ℎ 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 𝑠𝑢𝑛

𝑏 = 𝑡𝑜𝑜𝑡ℎ 𝑡ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠

Equation 4: Contact Stress Equation

42

The transmitted load (𝑊𝑡) to the input gear of the second stage is calculated by using the

pressure angle of 20 degrees and the pitch radius. The transmitted load will be the component of

the load from sun gear onto the planetary gears. Because 3 planet gears are chosen, the load is

distributed evenly across the 3 planet gears.

𝑊𝑡 =𝑇𝑖𝑛(𝑚𝑔)

𝑁(𝑑

2)cos (∅)

where,

𝑇𝑖𝑛 = 𝑖𝑛𝑝𝑢𝑡 𝑡𝑜𝑟𝑞𝑢𝑒 𝑖𝑛𝑡𝑜 𝑡ℎ𝑒 𝑠𝑦𝑠𝑡𝑒𝑚 (𝑓𝑡 𝑙𝑏)

𝑚𝑔 = 𝑡𝑜𝑟𝑞𝑢𝑒 𝑟𝑎𝑡𝑖𝑜 𝑜𝑓 𝑓𝑖𝑟𝑠𝑡 𝑠𝑡𝑎𝑔𝑒

N = number of planetary gears

d = pitch diameter of the sun gear

∅ = 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑎𝑛𝑔𝑙𝑒

𝑊𝑡 =140(5)

3(1

2(12))cos(20) = 5262 𝑙𝑏

The overload factor (𝐾𝑜) was chosen to be unity because the system is assumed have uniform

shock. Also, the dynamic factor (𝐾𝑉) is calculated using an estimated pitch line velocity (V) of 3

(ft/min) of the first stage. During the second stage, the pitch line velocity is estimated to be 0.6

(ft/min). The gears are chosen to obtain a transmission quality factor (𝑄𝑣) of 10. From this

information, the dynamic factor is calculated using the following equation.

𝐾𝑉 = [50+56[1−0.25(12−𝑄𝑣)

23]+√𝑉

50+56[1−0.25(12−𝑄𝑣)23]

]

0.25(12−𝑄𝑣)23

𝐾𝑉 = 1.004

The size factor (𝐾𝑠) is based on the Lewis form factor (Y) found in Table 14-2 in Shigley’s

book, the face width of the gears, and the diametral pitch (teeth/in).

𝐾𝑠 = 1.192 (𝐹√𝑉

𝑃)0.0535

= 1.192 (1.5√.245

12)0.0535

= 1.02711

The distribution of the force on the gear teeth also is considered when calculating the face load

distribution factor (𝐾𝑠). This is dependent upon the mesh alignment and pinion proportions.

𝐾𝐻 = 1 + 𝐶𝑚𝑐(𝐶𝑝𝑓𝐶𝑝𝑚 + 𝐶𝑚𝑎𝐶𝑒)

Equation 5: Transmitted Load Equation

Equation 6: Dynamic Factor Equation

Equation 7: Load Distribution Factor

43

where,

𝐶𝑚𝑐 = 𝑙𝑜𝑎𝑑 𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝑓𝑎𝑐𝑡𝑜𝑟

𝐶𝑝𝑓 = 𝑝𝑖𝑛𝑖𝑜𝑛 𝑝𝑟𝑜𝑝𝑜𝑟𝑡𝑖𝑜𝑛 𝑓𝑎𝑐𝑡𝑜𝑟

𝐶𝑝𝑚 = 𝑝𝑖𝑛𝑖𝑜𝑛 𝑝𝑟𝑜𝑝𝑜𝑟𝑡𝑖𝑜𝑛 𝑚𝑜𝑑𝑖𝑓𝑖𝑒𝑟

𝐶𝑚𝑎 = 𝑚𝑒𝑠ℎ 𝑎𝑙𝑖𝑔𝑛𝑚𝑒𝑛𝑡 𝑓𝑎𝑐𝑡𝑜𝑟

𝐶𝑒 = 𝑚𝑒𝑠ℎ 𝑎𝑙𝑖𝑔𝑛𝑚𝑒𝑛𝑡 𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝑓𝑎𝑐𝑡𝑜𝑟

The load correction factor (𝐶𝑚𝑐) for uncrowned teeth and the mesh alignment factor (𝐶𝑒) for

non-adjustable gear assemblies are unity. The pinion proportion factor is calculated from the

following definition for face widths between 1 and 17 inches.

𝐶𝑝𝑓 =𝐹

10𝑑− 0.0375 + 0.0125 𝐹 = 0.13125

The pinion proportion factor is (𝐶𝑝𝑚) is also one because 𝑆1

𝑆< 0.175, as shown in Figure 1

below. The S dimension is simply the sum of the pitch radii for the sun gear and the planetary

gear 𝑆 =1.5

2+1

2= 1.25. Furthermore, the distance 𝑆1can be calculated by subtraction

𝑆1 = 1.25 − (0.625 + 0.5) = .125. Therefore, 𝑆1

𝑆=.125

1.25= 0.1 < 0.175.

Figure 21: Definition of sun gear to planetary gear proportions

44

The mesh alignment factor (𝐶𝑚𝑎) is calculated with empirical constant A, B, and C from Table

14-9 of Shigley’s Mechanical Engineering Design. The mesh alignment factor for open gearing

is defined as,

𝐶𝑚𝑎 = 𝐴 + 𝐵(𝐹) + 𝐶(𝐹)2 = 0.247 + 0.0167(1.5) + (−0.765(10−4))(1.5)2= 0.2718

Consequently,

𝐾𝐻 = 1 + 1((0.05)(1) + (0.2718)(1)) = 1.3218

Therefore,

𝐾𝐻

𝑑𝑤1𝑏= 0.8812

𝑍𝑅

𝑍𝐼=

1

(1

2) cos(20) sin(20)

(5

5+1) = 5.186

Evaluating the contact stress at the second stage of the epicyclic gear train yields:

𝜎𝑐 = 254212.03 𝑝𝑠𝑖

The analysis is performed on the second stage because the torque has been multiplied by 5 at this

stage; and thus, the stresses are the highest in this region of the gear train.

Calculation of gear wear factor of safety:

The gear wear factor of safety is calculated by utilizing AGMA contact endurance strength

equations and modification factors, as shown in the following equation:

𝜎𝑐,𝑎𝑙𝑙 = (𝑆𝑐𝑍𝑁𝐶𝐻

𝑆𝐻𝐾𝑇𝐾𝑅)

where,

𝜎𝑐,𝑎𝑙𝑙 = 𝑎𝑙𝑙𝑜𝑤𝑎𝑏𝑙𝑒 𝑏𝑒𝑛𝑑𝑖𝑛𝑔 𝑠𝑡𝑟𝑒𝑠𝑠

𝑆𝑐 = 𝑎𝑙𝑙𝑜𝑤𝑎𝑏𝑙𝑒 𝑐𝑜𝑛𝑡𝑎𝑐𝑡 𝑠𝑡𝑟𝑒𝑠𝑠 𝑛𝑢𝑚𝑏𝑒𝑟

𝑆𝐻 = 𝑠𝑎𝑓𝑒𝑡𝑦 𝑓𝑎𝑐𝑡𝑜𝑟 (𝑝𝑖𝑡𝑡𝑖𝑛𝑔)

𝑍𝑁 = 𝑠𝑡𝑟𝑒𝑠𝑠 𝑐𝑦𝑐𝑙𝑒 𝑓𝑎𝑐𝑡𝑜𝑟 𝑓𝑜𝑟 𝑝𝑖𝑡𝑡𝑖𝑛𝑔 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒

𝐾𝑇 = 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑓𝑎𝑐𝑡𝑜𝑟

𝐶𝐻 = ℎ𝑎𝑟𝑑𝑛𝑒𝑠𝑠 𝑟𝑎𝑡𝑖𝑜 𝑓𝑎𝑐𝑡𝑜𝑟

𝐾𝑅 = 𝑟𝑒𝑙𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑓𝑎𝑐𝑡𝑜𝑟

45

The calculated factor of safety is determined by solving for the pitting factor of safety (𝑆𝐻) and

computing the ratio of the tooth contact stress previously calculated to the allowable contact

stress.

𝑆𝐻 = (𝑆𝑐𝑍𝑁𝐶𝐻

𝜎𝑐𝐾𝑇𝐾𝑅)

An estimated value of the allowable stress was found in Shigley’s Mechanical Engineering

Design book to be:

𝑆𝑐 = 180000 psi

The stress cycle factor is determined from Fig. 14-15 of Shigley’s textbook. The gears are

designed for 104 number of cycles. Therefore, after 10,000 loading cycles, the gears should be

replaced.

𝑍𝑁 = 1.55

The hardness ratio factor (𝐶𝐻) is based on the Rockwell hardness of 303 Stainless Steel and

Anodized Aluminum. The hardness ratio is given by:

𝐶𝐻 = 1.0 + (𝐻𝐵𝑃

𝐻𝐵𝐺) (𝑔𝑒𝑎𝑟 𝑟𝑎𝑡𝑖𝑜 − 1.0) = 1.9717

Because the speed at which the input gear rotates is very small (~3 ft/min), the temperature factor

(𝐾𝑇) is chosen to be 1. Also, the reliability factor is calculated based on a 99 % reliability and

yields a factor of close to 1.

As a result the factor of contact stress factor of safety is calculated to be 𝑆𝐻 = 1.13.

AGMA Spur Gear Bending

First, the modified gear tooth bending stress is calculated with the help from Shigley’s

Mechanical Engineering Design Ninth Edition textbook. Some of the factors are the same as

those used to calculated contact stress (𝑊𝑡,𝐾𝑜 , 𝐾𝑣, 𝐾𝑠, 𝐾𝐻).

𝜎 = (𝑊𝑡)(𝐾𝑜)(𝐾𝑣)(𝐾𝑠) (𝑃𝑑

𝐹) (𝐾𝐻𝐾𝐵

𝐽)

𝐾𝐵 = 𝑅𝑖𝑚 𝑡ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 𝑓𝑎𝑐𝑡𝑜𝑟

𝐽 = 𝐺𝑒𝑜𝑚𝑒𝑡𝑟𝑖𝑐 𝑓𝑎𝑐𝑡𝑜𝑟 𝑓𝑜𝑟 𝑏𝑒𝑛𝑑𝑖𝑛𝑔 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ

The rim thickness of the gear has to be sufficiently strong to support the loading on the teeth.

The rim thickness factor accounts for this and is given by the following.

𝐾𝐵 = 1.6 ln (2.242

𝑚𝐵) where,

Equation 8: Hardness Ratio Factor

Equation 9: Rim Thickness Factor

46

𝑚𝐵 = 𝑏𝑎𝑐𝑘𝑢𝑝 𝑟𝑎𝑡𝑖𝑜 = 𝑡𝑅

ℎ𝑡=

𝑅𝑖𝑚 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠

𝑡𝑜𝑜𝑡ℎ ℎ𝑒𝑖𝑔ℎ𝑡=

0.25

0.1853= 1.35 > 1.2

𝐾𝐵 = 1.6 ln (2.242

1.35) = 0.811

The geometric factor for bending strength (𝐽) defines the effect of stress concentration due to the

tooth profile. The stress-concentration factor (𝐾𝑓) and the load-sharing ratio (𝑚𝑁) are

components of that contribute to this effect and are defined as follows. For spur gears, 𝑚𝑁 = 1.

𝐽 =𝑌

𝐾𝑓𝑀𝑁 where, Y = tooth form factor

The stress-concentration factor (𝐾𝑓) which are related to the dimensional information of the gear

teeth profile.

𝐾𝑓 = 𝐻 + (𝑡

𝑟)𝐿

(𝑡

𝑙)𝑚

where,

𝐻 = 0.34 − 0.4583662∅ = 0.180

𝐿 = 0.316 − 0.4583662∅ = 0.156

𝑚 = 0.290 − 0.4583662∅ = 0.45

𝑟 =(𝑏−𝑟𝑓)

2

𝑑

2+𝑏−𝑟𝑓

=(0.102−0.02)2

1

2+0.102−0.02

= 0.0115

where,

𝑏 = 𝑑𝑒𝑑𝑒𝑛𝑑𝑢𝑚

𝑟𝑓 = 𝑡𝑜𝑜𝑡ℎ 𝑓𝑖𝑙𝑙𝑒𝑡 𝑟𝑎𝑑𝑖𝑢𝑠

𝐾𝑓 = 0.018 + (0.1309

0.01155)𝐿

(0.1309

0.1653)𝑚

= 1.495

Consequently,

𝐽 =0.245

1.495(1)= 0.164

Evaluating the bending stress at the second stage of the epicyclic gear train yields:

𝜎 = (5262.28)(1)(1.004)(1) (12

1.5) (

1.3012(1)

0.164) = 335349 𝑝𝑠𝑖

47

Calculation of bending factor of safety:

The bending factor of safety is calculated by utilizing AGMA contact endurance strength

equations and modification factors, as shown in the equation below. The factors 𝐾𝑇 and 𝐾𝑅 are

the same as calculated for contact stress. The AGMA bending strength (𝑆𝑡) is estimated to be

55,000 psi (obtained from Table 14-4 in Shigley’s Mechanical Engineering Design textbook).

The stress cycle factor for bending (𝑌𝑁) is estimated from for (104) number of load cycles to be

1.55.

𝑆𝐹 = (𝑆𝑡𝑌𝑁

𝜎𝑐𝐾𝑇𝐾𝑅)

where,

𝑆𝑡 = 𝐴𝐺𝑀𝐴 𝑏𝑒𝑛𝑑𝑖𝑛𝑔 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ

𝑌𝑁 = 𝑆𝑡𝑟𝑒𝑠𝑠 𝑐𝑦𝑐𝑙𝑒 𝑓𝑎𝑐𝑡𝑜𝑟 𝑓𝑜𝑟 𝑏𝑒𝑛𝑑𝑖𝑛𝑔 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ

As a result, the bending factor of safety is,

𝑆𝐹 = (55000(1.55)

(335349)(1)(1.00196)) = 0.25

Note, this factor of safety suggests that the design needs be re-evaluated.

Re-evaluation of initial design

An estimate of the allowable bending stress can be calculated for a factor of safety of 2. This can

be done by solving the following equation.

𝜎𝑐,𝑎𝑙𝑙 = (55000(1.55)

(2)(1)(1.00196)) = 42541.62 𝑝𝑠𝑖

The allowable bending stress can be used to estimate the necessary pitch diameter of the gears to

yield a reasonable factor of safety. Figure 22 shows a logarithmic regression analysis of

experimental data retrieved from Shigley’s Mechanical engineering design textbook. This data

can be used to back substitute into the AGMA modified gear bending strength equations

previously used. A plot of the bending stress versus the pitch diameter can then be obtained, as

shown in Figure 23 on the next page.

Equation 10: Bending Factor of Safety

48

Figure 22: Plot of Lewis Form Factor vs the Number of Teeth.

The Lewis form factor can be computed for varying pitch diameters by holding the diametral

pitch constant (tooth density). The varying Lewis form factors are used to compute the geometric

factor for bending (𝐽) by the equation below, and the plot is shown in Figure 23 on the next page.

𝑇𝑒𝑒𝑡ℎ = 𝐷𝑖𝑎𝑚𝑒𝑡𝑟𝑖𝑐 𝑃𝑖𝑡𝑐ℎ (𝑝𝑖𝑡𝑐ℎ 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟)

Figure 23 below shows the power relationship between bending stress and pitch diameter. This

was computed by keeping the pitch diameter as a variable in the AGMA modified bending stress

equations. A power equation fits the data with a coefficient of determination of 0.99. As shown,

the necessary pitch diameter is around 1.95 inches for the estimated allowable bending stress of

42541.62 𝑝𝑠𝑖.

Figure 23: Plot of the bending stress vs pitch diameter

y = 0.114ln(Teeth) - 0.0246 R² = 0.9753

0.2

0.25

0.3

0.35

0.4

0 10 20 30 40

Lew

is f

orm

fac

tor

(Y)

Number of teeth

Lewis Form Factor vs. Number of Teeth

Series1

Log. (Series1)

y = 529768x-3.742 R² = 0.9954

0

20000

40000

60000

80000

100000

1 1.5 2 2.5 3

Be

nd

ing

Stre

ss (

psi

)

Pitch Diameter (inch)

Bending Stress vs. Pitch Diameter

Series1

Power (Series1)

1.95

49

Figure 24: Shear Stress on Output Shaft from Planetary Gears

Each planetary gear will have a clevis pin that will take the output torque from each epicyclic

gear train and transfer it to the gear bearing, and subsequently to the drive shaft. This pin is made

from grade 5 titanium Ti-A1-4V, with shear strength of 550.0 MPa. Using the equations below,

calculations were made for the maximum shear stress that will be exerted on these pins.

Shear Stress on Clevis Pins:

Equations:

𝜎𝑏 =𝑃

𝐴

Where P is the maximum amount of shear load, and A is the area of the surface in contact with

the pin.

P was assumed to be the maximum tangential load applied between gears, which will also be

applied on the pins during load application, and the area was calculated using the planetary

gear’s overall bore hole diameter and length.

𝑃 = 𝑊𝑡 = 4745.4 𝑁

𝐴 = .19𝑖𝑛 ∗ .25𝑖𝑛 = .0475 𝑖𝑛2 = 0.00003065 𝑚2

𝜎𝑏 =4745.4 [𝑁]

𝐴 [𝑚2]= 154.851 𝑀𝑃𝑎

50

Factor of safety was calculated using the maximum shear strength for titanium of 550.0 MPa.

𝐹𝑆 =550.0

154.851= 3.6

Ratchet/Pawl System:

Figure 25: This gear is used to hold the torque being applied on the drive shaft.

The chosen ratchet and pawl were chosen from catalogues provided by KHK Gears. The ratchet

gear chosen for the application was designation SRTB1-100 where it was a 100 tooth ratchet

gear with a 60° tooth angle, using S45C Mild Steel. The properties of this ratchet gear are shown

in the table below next to its designation of SRTB1-100.

Table 7: Ratchet Gear Dimensions

This gear was chosen due to its high allowable input torque value, which would benefit our

application greatly and allow for a high number of load cycles before significant wear occurs on

the ratchet. This is evidenced in the equations below where allowable torque on the ratchet is

calculated.

51

Input Torque (to sun gear): 140 ft.lbs.

Primary Equations:

Equation 11: for allowable torque on the ratchet: 𝑇 = 𝐹𝑏 ∗ 𝑟𝑡

Equation 12: for allowable transmission force: 𝐹𝑏 = 𝜎𝑏 ∗𝐹∗𝑒2

6∗1

ℎ∗1

𝐹𝑆

Equation 13: for Bending Stress: 𝜎𝑏 =𝑊𝑡∗𝑝𝑑

𝐹∗𝑌

Where 𝑟𝑡is the tooth radius, F is the face width of the gear, e is the root length, h is the tooth

depth, FS is the factor of safety, 𝑊𝑡is the tangential load, 𝑝𝑑is the diametral pitch, and Y is the

Lewis form factor.

Secondary Equations:

Equation 14: Tooth Radius: 𝑟𝑡 =[𝑂𝑣𝑒𝑟𝑎𝑙𝑙 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟−(2∗ℎ)]

2000

Equation 15: Modulus: 𝑚 =𝑂𝑣𝑒𝑟𝑎𝑙𝑙 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟

# 𝑜𝑓 𝑡𝑒𝑒𝑡ℎ

Equation 16: Pitch Diameter: 𝑝𝑑 =25.4

𝑚𝑜𝑑𝑢𝑙𝑢𝑠

Equation 17: Root Length: 𝑒 = ℎ ∗ tan (60 −360

# 𝑡𝑒𝑒𝑡ℎ)

Equation 18: Tangential Load: 𝑊𝑡 =350 𝑓𝑡.𝑙𝑏𝑠.

𝑜𝑣𝑒𝑟𝑎𝑙𝑙 𝑟𝑎𝑑𝑖𝑢𝑠

Using these equations, the tangential load was calculated to be 3796.4 N, with a diametral pitch

of 38138.14 𝑚−1, a root length of 2.408mm, and tooth radius of .0484m.

Using the primary equations, a bending stress 𝜎𝑏of 2.7053 𝑥 1010 [𝑁

𝑚2] was calculated, along

with an allowable transmission force 𝐹𝑏of 98041.15 N. From this, the maximum allowable

torque on the ratchet gear was calculated to be 4745.19 𝑁𝑚. or ~3500 ft.lbs. which allows for a

factor of safety of 25 when the ratchet/pawl assembly is attached to the sun gear, or a FS = 1.35

should the assembly be attached to the output shaft leading to the load cell. The chosen pawl was

a SRT1-C model.

However, using the Lewis Gear Strength Calculation method yielded a FS of 2.36. This

calculation is shown below.

𝑊𝑡,𝑚𝑎𝑥 =𝑆𝑀 ∗ 𝐹 ∗ 𝑌

𝑃=90,000 (

13)(. 472𝑖𝑛)(. 446)

3.14= 2011.26𝑙𝑏𝑠 = 8946.53𝑁

52

Where 𝑆𝑀is the safe material strength (1/3 of the tensile strength of 303 stainless steel), F is the

face width of the ratchet gear, Y is the Lewis factor of the 100 tooth 20 degree involute gear, and

P is the pitch of the gear.

Factor of safety was calculated using the tangential load that will be applied, and the maximum

allowable tangential load from the equation above.

𝐹𝑆 =8946.53

3796.4= 2.36

53

Safety Guard

Part of designing the Drive Shaft Calibration Test Stand requires developing safety guarding. It

will protect the user in the event of a drive shaft failure. The way this safety guarding was tested

was by doing a drop test to simulate an impact.

To simulate what will happen more accurately, an arbitrary plane inside the box was created and

was used as the reference when the drop test was done. For this test, the safety box was dropped

from 1.5 meters. The results of the test are shown in Figure 26.

Max stress on the body = 200 mpa

Yield Strength of AISI 1020 410mpa

Factor of safety = 2.05

Max stress on the foot 350 mpa

Factor of safety = 1.17

Figure 26: Stress Concentration on the Foot and Stress Distribution along the Body

54

Data Acquisition System Selection

The chosen DAQ model is the DATAQ Instruments Model DI-718B 8-channel USB Data

Acquisition System (see Figure 24) we will be using two of the eight channels for strain gage

measurements so 2 strain gage measurement modules must be purchased for it as well. The two

modules that need to be included for the strain gage measurements are DI-8B38-05 Strain Gage-

based Sensor (see Figure 25).

We selected this device combination for several reasons. It has the correct bridge resistance

range of 300 ohm to 2000 Ohm bridge resistance and the bridge that will be used in the design

has a bridge resistance of 350 Ohm. This module has a 10.0 V excitation voltage for the bridge

as well which is the level that was originally requested by Eaton so no additional voltage source

will need to be added to the setup. It has an input range of +- 20 mV, which according to the

example data provided, will be more than enough to accommodate the anticipated readout range

of +- 1 mV. This device also provides 100 dB reduction to common mode noise which is

essential to reading these very small voltage levels that are involved here. The device has 14 bit

precision which when coupled with the given mV and torque range gives a precision of 0.00244

mV (see equation 19).

This device, although not produced by National Instruments, is still completely LabView

compatible. When both a LabView Plugin (ActiveX) and the driver program for the device

(Windaq) are installed and running then all of the data that is being streamed in by the DAQ can

be read and manipulated by LabView.

The DAQ also has a very high accuracy of ± 0.05% and a linearity of ± 0.02%. The device is a

calibrated instrument; so, it can very accurately measure the torque being applied and the mV

output from the bridge.

This data acquisition unit was chosen because it has sufficient capabilities for the required tasks

while coming in at a much lower price point of ~800 dollars as opposed to the national

instruments version that is in the ~1350 dollar range.

𝑃𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛 (𝑚𝑉) = 𝑟𝑎𝑛𝑔𝑒 (𝑚𝑉)

2(𝑏𝑖𝑡 𝑝𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛)=40

214= 0.00244 𝑚𝑉

Equation 19: Precision in mV over the range of -20 to +20 mV using 14 bit precision.

55

Figure 27: DI-718B Data Acquisition Unit for strain gage based measurements.

Figure 28: DI-8B38-05 amplification module that provides 10V excitation voltage as well as a

very precise measurement range of +-20mV. This module also provides 100 dB reduction in

common mode noise.

56

Hardware Setup

Below in Figure 29 is a diagram of how all the components in the electrical system will be laid

out. The strain gages on the drive shaft are connected in a full Wheatstone Bridge configuration.

There are two 4-wire busses connecting the strain gages to the DAQ and the Torque Cell to the

DAQ. A USB cable then connects the DAQ to the computer. Each of the buses has four wires in

it. Two of them are to apply a 10 V excitation voltage to provide power to the bridge. The other

two wires are to sense the output voltage of the bridge.

Figure 29: Hardware setup of the electrical system showing the wiring of the strain gages and

the Torque cell to the DAQ and the DAQ being connected up to the computer.

57

User Interface

Below in Figure 30, there is a concept for what the user interface will include and how it will be

arranged. On the left side of the screen are meters that will display the applied load and the

output voltage across the bridge in real time. Also, a display is included that will display the

calibration factor for the drive shaft once the ‘Calculate Cal. Factor’ button is pressed (which is

located in the upper right hand corner). Another button is located in the upper right hand corner

which is labeled as ‘Take point’ which will record a data point and plot it on the graph when it is

pressed. This user interface will be developed using LabView.

Figure 30: Screen Layout for the test stand user interface showing meters on the left that will

display real time readouts, buttons that record a test point and calculate the calibration factor, and

a graph that plots each point as it is taken.

58

ActiveX Setup for using LabView

Figure 31: These are the

steps for linking

Windaq, main program

of the DAQ we chose,

and LabView.

59

Figure 32: Steps are

given for allowing

data from Windaq to

be sent to LabView.

60

ActiveX is used for allowing the DAQ software, WinDaq, to be compatible with LabView

(Shown in Figure 31). What ActiveX does, is it links Windaq code to another program. The user

starts by creating a new project in LabView (new projects are created by just opening LabView).

In the functions box of LabView there is the sequence structure, which allows for Windaq

control to start up in the program, place sequence on the Diagram Window. The Diagram

Window plays a main part in deciding what gets executed and the order of it. This window is

where the components also get placed. These components will be connected using “Wire” in the

“Tools” box, which creates a path for the program (LabView) to follow.

The Windaq control located outside of the sequence needs to be connected to the sequence to

allow for the Windaq to have access to all of the frames inside. Frames are used to pass data

around the program. A slider bar needs to be placed in the sequence; this is used to select the

channel that the data is displayed from. In the “Tools” box there is the “Operate Value” tool

which gives the user the option of changing properties of the objects, use it to change the number

values of the channels. The indicators are used to display the data to the user such as the number

of channels or real time data coming from the Windaq can also be displayed. To pass this data,

an Invoke Node is used which allows it to pass data back and forth in the method as needed. The

channel count property is used to tell the number of channels that data can be given on. Setting

limits for the channels will make sure data that is outside the range is not read. This can be done

by using an Attribute Node and setting it to maximum.

“GetScaledData” is used to retrieve data from Windaq (block diagram is Figure 32), which will

be in calibrated engineering units, this will be considered a start loop. A way to continuously get

this data is by using an event structure; but if it is an older version of LabView, use a while loop.

These same steps should be taken again but this time for a stop loop.

To help with the designing of the program, turn on the labels of the components that way you

have a better idea of what is there. A way of doing this can be done by right-clicking the object

or control in the diagram window and going to “Show” then clicking on “Label”.

61

LabView Software Setup

The change in resistance can be calculated by comparing the output voltage to excitation voltage.

So this will be the voltage drop across the terminals as well as the excitation voltage used on the

bridge for the ratio. The program (Figure 33) will need a while loop and a DAQ in it. Wires are

connected from the DAQ to outputs for the voltage drop across the terminals and then other

excitation voltage. There is also an output for the ratio of the two voltages (output/excitation).

In the while loop there is a stop button so the program does not run forever. Even though the

ratio is the only output that is being looked for. The excitation and output voltages are output so

the user can see them to make sure they are close to what is expected in the case of a problem.

Figure 33: This is the

LabView setup for the

program of the DAQ.

62

Section 5: Cost Analysis/Estimation

63

Strain Gage Test Stand

The cost analysis of the frame and related components was completed by finding material cost of

the steel online and estimating the shop labor required to fabricate the components. Eaton may

have some of these items available, which will reduce the overall cost of the

project. Additionally, Eaton may have a preferred supplier which would be able to supply some

items at a discount due to the large volume of material that Eaton purchases. These are options

that can be explored during the next portion of the project.

While the material price was very straightforward, the labor associated with fabrication is just an

estimate of the time that will be required to machine and weld the various components. Some of

the fabrication may be able to be done by the students or in house at Eaton, which will reduce

this cost. However, the rest will need to be sent out to a shop, and will require an estimated 30

hours at $75 an hour. The overall cost of the labor and materials together comes to just under

$3740.

Quantity Description Price ($) Extended ($)

1 1018 HR Steel Round 8" x 1' 469.97 469.97

1 3" x 4" x 1' A36 Steel Bar 104.04 104.04

1 1' x 2' x 1/4" Thick A36 Steel Plate 31.02 31.02

3 2 x 2 x 1/4" Thick Square A500 Tube

Steel 139.68 419.04

1 1' x 2' x 3/4" Thick A36 Steel Plate 101.06 101.06

1 1' x 1' x 3" Thick A36 Steel Plate 219.09 219.09

1 1' x 1' x 2" Thick A36 Steel Plate 134.77 134.77

1 2 x 1-1/2 x 1/8" Thick 2' Angle Steel

A36 6.48 6.48

30 Hours Shop Labor 75.00 2,250.00

Total 3,735.47

Table 8: These are the

costs of the components for

the strain gage stand.

64

Gears

Table 9 below shows an estimated cost of the gears used in the two-stage epicyclic gear train.

These gears are being purchased by either WM Berg or KHK gears. By designing the torque

multiplier from individual off the shelf gears, cost is decreased significantly. For example,

Granger offers a torque multiplier that is capable of meeting our torque output requirements.

However, the unit price is $3,640 dollars, which is 48.5 % of our budget. Purchasing WM Berg’s

stock sized gears would only account for 11.9 % of our budget. As a result, designing the

components of the gear assembly individually instead of purchasing the entire unit from a

supplier decreases cost by 36.53 %.

Table 9: Cost of Planetary Gears

Quantity Description Price

2 Sun Gear $34.81

2 Ring Gear $60.22

6 Planetary

Gears $233.30

Total: $897.54

65

Safety Guard

In summary of the cost analysis of the safety box, there is a need of twelve 4 ft. x 2 ft. cold-rolled

weldable steel sheet metal to make up the front back and top of the safety box. There is a need of

eight 2ft-1ft cold-rolled plate to cover the sides. The two hinges are so that the box can open and

close, while the two latches are used to keep it closed.

Table 10: Safety Guard Cost

Cost/Unit

($) Units Needed

Total

Cost ($)

The hillman Group 4-ft x 2-ft Cold-Rolled Weld

able steel sheet metal 33.21 12 398.52

The hillman Group 2-ft x 1-ft Cold-Rolled Weld

able steel sheet metal 6.27 8 50.16

unfinished type 304 stainless steel surface-mount

hinge 12.47 2 24.94

Black Steel Work-load Rated Draw Latches 7.37 2 14.74

Total Cost

488.36

66

Labview, Computer, and DAQ system

Table 11 shows the requirements of LabView in two of the columns, and the last column shows

the specifications of the computer selected. The laptop chosen meets all of the requirements of

LabView and is a reasonable price.

Table 12 shows the prices of the software needed for use of the DAQ. The student version of

LabView is a reasonable price ($19.99), and the other needed software is free.

Table 13 gives the prices of the DAQ and module needed for the strain gages and Wheatstone

bridge.

Overall, the cost of the electrical part of the project, not including wire needed or other minor

components, costs around 1,000 dollars.

LabView Software Computer Requirements

HP Black 15-

f039wm

Run-Time Engines

Development

Environment

System OS Windows 8.1/ 8/ 7 Windows 8.1/ 8/ 7 Windows 8

Processor Pentium III/Celeron 866

MHz or equivalent


Intel Celeron

N2830 (2.16

GHz)

Screen

Resolution 1024 x 768 pixels 1025 x 768 pixels

1366 x 768

pixels

Disk Space 500 MB 5 GB 500 GB

RAM 256 MB 1 GB 4 GB

Cost $ 278.75

Software Cost ($)

LabView Student

Edition 19.99

ActiveX Free

WinDaq Free

Price ($)

Model DI-718B 595.00

DI-8B38-05 127.00

DI-8B38-05 127.00

Table 11: Cost amount

and requirements of the

computer

Table 12: Here are the costs

of the Software needed.

Table 13: These are the

costs of the DAQ and

module needed.

67

Overall Cost of Project

The overall cost estimate for the project is shown below in Table 14. A cost for a torque cell is

not included because Eaton already has a torque cell that can be used for the project.

Additionally, some of these costs may be reduced as Eaton likely has preferred suppliers that can

source the items at a discounted rate, or if some of the items are found in the Eaton lab and

reassigned for use with this project. Lastly, the cost for one set of companion yokes is shown

(the yokes allow for an interface between the fixture and the drive shaft). Dependent on final

system cost, additional sets may be purchased as part of this project’s budget.

Table 14: Total Project Cost Analysis

Sub-System Cost

Fixture $3740

Torque Applicator (Gear Train) $900

Safety Guarding $490

Companion Yokes (one set) $400

Electrical/User Interface $1147

Total $6677

68

Conclusions

It is anticipated that the chosen design will meet all of the design criteria better than the other

conceptual design ideas. Where the design rated the worst was in cost, because it was the most

expensive design, but this helped the design rate higher in other areas that were a higher priority.

Even with this design being more expensive the budget for the project was not excessed.

The outcome of the project is to allow for the Auburn Eaton to run their own strain gage tests on

a drive shaft, and not have to use an outside faculty to run these tests. These results from

applying a torque to a drive shaft will be given on a user interface. They will have the ability to

increment the torque applied to the drive shaft to test over a range for more results.

This design has been dimensioned appropriately to the size of the space in the faculty it will be

placed.

It has been designed with durability in mind in order to reach a lifetime of 10,000 cycles before

parts will start needing to be replaced.

The estimated cost of the project is 6677$ which is below the budgeted amount of 7500$.

The epicyclic gearing system uses a ratio of 25:1 thus giving the capability of reaching a total

torque load of 3500 ft. lbs. The incorporated ratchet and pawl system allows for the applied load

to be held while a measurement is taken.

69

References

Wheatstone Bridge – Last used on 9/12/14

http://www.electronics-tutorials.ws/blog/wheatstone-bridge.html

System Requirements for LabView Development Systems and Modules-

Last used on 10/14/14

http://www.ni.com/labview/requirements/

Data Acquisition Using LabView- Last used on 11/1/14

http://www.dataq.com/blog/data-acquisition/programming/data-acquisition-using-

labview-dataq-instruments-activex-controls/?print=pdf

Metals Depot- Last used on 12/1/14

www.metalsdepot.com

Fastener Fundamentals- Last used on 12/1/14

http://www.strengthandstiffness.com/4_basic/images/bearing_stress.gif

McMASTER-CARR- Last used on 12/1/14

http://www.mcmaster.com/

Mechanical Engineering Design, by Shigley, Nineth Editions

AMERICAN GEAR MANUFACTERS ASSOCIATION, Revision of AGMA 226.1

AMERICAN NATIONAL STANDARD—Fundamental Rating Factors and

Calculation Methods for Involute Spur and Helical Gear Teeth

KHK Gears – Last used on 12/3

http://www.khkgears.co.jp/world/break/SRT%20SRTB%20SRT-C.pdf

Berg Precision Parts—Last used on 12/3

http://precisionparts.wmberg.com/gears/spurGears/en

QTC Gears (prices)—Last used on 12/3

http://www.qtcgears.com/RFQ/default.asp?Page=../KHK/newgears/KHK316.html

http://www.electronics-tutorials.ws/blog/wheatstone-bridge.html

http://www.ni.com/labview/requirements/

http://www.metalsdepot.com/

http://www.strengthandstiffness.com/4_basic/images/bearing_stress.gif

http://www.mcmaster.com/

http://www.khkgears.co.jp/world/break/SRT%20SRTB%20SRT-C.pdf

http://precisionparts.wmberg.com/gears/spurGears/en

http://www.qtcgears.com/RFQ/default.asp?Page=../KHK/newgears/KHK316.html

70

Measurement Computing – Last used on 11/3/14

http://www.mccdaq.com/usb-data-acquisition/USB-3102.aspx

71

Appendices

Attribute Weights 0.239 0.091 0.061 0.189 0.121 0.091 0.061 0.148

Torque Application Safety Cost

Ease of Use


Impact Design

Simplicity Company

Preference Score

Best = 4 Best = 4 Best = 4 Best = 4 Best = 4 Best = 4 Best = 4 Best = 4

Chain gear box 1.50 3.67 2.33 3.00 3.50 2.50 3.50 2.67 2.66

Epicyclic Gearing 3.50 3.00 2.33 2.50 2.50 3.00 2.50 3.50 2.97

Hydraulic 2.17 1.00 3.00 2.67 1.83 1.00 1.67 1.67 1.96

Pneumatic 2.83 2.33 2.33 2.17 2.17 3.50 2.33 2.17 2.48


Electrical Interface Safety Cost

Ease of Use


Impact Design

Simplicity Company

Preference Score


National Instruments

1.83 1.17 1.83 1.83 1.50 1.67 1.83 1.67 1.69

Measurement Computing USB -

3102 1.17 1.83 1.17 1.17 1.50 1.33 1.17 1.33 1.31

Appendix A

Decision Matrix

72


User Interface Safety Cost

Ease of Use


Impact Design

Simplicity Company

Preference Score


LabVIEW 4.00 2.17 4.00 3.50 4.00 2.83 3.50 4.00 3.60

Visogram 2.50 2.50 2.50 2.33 2.17 2.50 2.67 2.33 2.41

MyOpenLab 2.00 2.67 2.17 2.50 2.00 2.00 2.33 1.83 2.16

SENSIT 1.50 2.67 1.33 1.50 1.83 2.67 1.50 1.83 1.79


Safety Guards Safety Cost

Ease of Use


Impact Design

Simplicity Company

Preference Score


Full box 4.00 1.67 3.00 4.00 2.67 3.00 2.83 3.83 3.38

Padded bar 1.33 3.67 2.83 2.33 2.67 3.33 3.50 1.33 2.30

Loop w/interlock 2.33 2.67 2.00 2.00 2.83 2.33 2.33 2.67 2.39

Loop w/solenoid 2.33 2.00 2.17 1.67 1.83 1.33 1.33 2.17 1.93


Strain Gages Safety Cost

Ease of Use


Impact Design

Simplicity Company

Preference Score


Single axis strain gages

1.33 1.83 1.17 1.40 1.60 1.40 1.80 1.40 1.46

90° biaxial strain gages

1.67 1.17 1.83 1.60 1.40 1.60 1.20 1.60 1.54

73


Fixture Safety Cost

Ease of Use


Impact Design

Simplicity Company

Preference Score


Slotted rail in floor 3.00 2.00 3.17 2.33 1.50 2.17 1.67 2.83 2.43

Tube steel w/wheels

1.17 3.17 2.17 1.17 2.50 2.67 2.00 2.00 1.88

Tube steel w/bolts 2.83 3.17 2.67 3.17 3.17 3.00 3.33 2.67 2.98

Bed plate 3.00 1.67 2.00 3.33 2.83 2.17 3.00 2.50 2.71


Torque Measurement

Safety Cost Ease of

Use Reliability Reparability

Environmental Impact

Design Simplicity

Company Preference Score


Load Cell 1.83 1.00 1.83 1.83 1.17 1.67 1.33 1.83 1.63

Load Arm 1.17 2.00 1.17 1.17 1.83 1.33 1.67 1.17 1.37

74

Heavy Duty

Lengths

(inches)

Inner Diameter

(inches)

Wall Thickness

(inches)

Outer Diameter

(inches)

Displacement

(Radians)

Displacement

(Degrees)

Dia

mon

d

Ser

ies 104 7.97 0.265 8.5 0.002745791 0.157322209

78 6.47 0.265 7 0.003762568 0.215579254

Sli

p B

etw

een

Cen

ter

Driv

e S

haft

16.93 3.934 0.138 4.21 0.007098659 0.406723179

19.01 5.116 0.197 5.51 0.002513159 0.143993418

16.93 3.936 0.197 4.33 0.004750389 0.272177241

17.34 4.726 0.167 5.06 0.003462754 0.198401175

20.81 4.23 0.18 4.59 0.005263579 0.30158085

17.73 4.726 0.167 5.06 0.003540636 0.202863486

17.73 4.726 0.197 5.12 0.002945631 0.168772233

19.99 4.726 0.167 5.06 0.003991952 0.228722001

19.01 5.116 0.167 5.45 0.003016548 0.172835495

19.01 5.116 0.197 5.51 0.002513159 0.143993418

Fix

ed Y

ok

e C

ou

pli

ng S

haft

Ass

emb

ly w

ith

Cen

ter

Bea

rin

g D

rive

Sh

aft

13.79 4.054 0.138 4.33 0.005299943 0.303664368

13.79 3.936 0.197 4.33 0.003869336 0.221696642

14.47 4.724 0.118 4.96 0.004222548 0.241934159

14.45 4.726 0.167 5.06 0.002885628 0.165334313

15.05 4.726 0.167 5.06 0.003005447 0.172199405

15.05 4.726 0.197 5.12 0.002500381 0.143261258

14.61 5.116 0.197 5.51 0.001931471 0.110665115

14.61 5.116 0.167 5.45 0.002318347 0.132831488

Appendix B

Drive Shaft Dimensions

75

Medium

Duty

Lengths

(inches)

Inner Diameter

(inches)

Wall Thickness

(inches)

Outer Diameter

(inches)

Displacement

(Radians)

Displacement

(Degrees)

Fix

ed Y

ok

e

Cou

pli

ng

Dri

ve

Sh

aft

9.17 3.334 0.083 3.5 0.010824812 0.62021607

9.8 3.31 0.095 3.5 0.010212532 0.585134984

11.39 3.81 0.095 4 0.007870463 0.45094432

Dri

ve

Sh

aft

6.28 3.334 0.083 3.5 0.007413285 0.424749937

6.62 3.31 0.095 3.5 0.00689867 0.395264653

8 3.81 0.095 4 0.005527981 0.316729988

Sli

p B

etw

een

Cen

ter

Dri

ve

Sh

aft

14 3.334 0.083 3.5 0.016526431 0.946894763

14.41 3.31 0.095 3.5 0.01501659 0.860387258

16.58 3.81 0.095 4 0.011456741 0.6564229

Ou

tboard

Sli

p

Cou

pli

ng S

haft

14.77 3.334 0.083 3.5 0.017435385 0.998973975

15.34 3.31 0.095 3.5 0.015985739 0.915915373

17.66 3.81 0.095 4 0.012203018 0.699181448

76

Range of Rotational Displacement for all

Spicer Drive Shafts (@ 3000 ft. lb. of torque)

Radians Degrees

Minimum 0.001931471 0.110665115

Maximum 0.017435385 0.998973975

77

Appendix C

Drawings of strain gage test stand components with dimensions

85

Ring Gear

Appendix D

Gear Drawings with Dimensions

86

Planetary Gear

87

Sun Gear

88

Ratchet Gear

89

Safety Box

Appendix E

Safety Components

90

Pawl

Appendix F

Additional Parts

91

Planetary Gear Carrier

92

Epicyclic Assembly

Test Stand for Calibrating Strain Gaged Drive Shafts

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Transcript of Test Stand for Calibrating Strain Gaged Drive Shafts