Test Stand for Calibrating Strain Gaged Drive Shafts
1. 1
Indiana University Purdue University β 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 β 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
3. 3
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
4. 4
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 unitβs 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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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.
ο· Torque Applied- The variable should be anywhere from 0 ft. lbs. to 3500 ft. lbs. It needs
to be applied, held, and safely released.
ο· Application Display- It needs easy to read calibration values, applied torque, and simple
input interface.
ο· Drive shaft Configuration- One requirement is that it accommodates Dana Spline
Configuration.
ο· Measure of Applied Torque- An accurate measure of applied torque will be displayed on
the readout.
ο· Mechanical safety guards must be included to restrain a drive shaft in the event of failure
ο· 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.
ο· 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.
β Drive shaft Dimensions- The dimensions are approximately 0 to 104 inches in length, and
3 to 6 inches in diameter.
β 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.
8. 8
Design Variables
The below variables allow for flexibility in the design of the project in order to meet the given
requirements.
β Torque Application- Manual or automated (hydraulic, pneumatic, etc.)
β Drive shaft Connector- Accommodates different drive shaft spline configuration, along
with short-tool change/setup (10 to 15 minutes).
β Stand Construction- Different materials are allowed in construction.
β Test Stand Mobility- Portable or fixed unit, either is viable.
β 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.
β Torque measurement method- may be a torque cell or a load arm.
β 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.
β 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.
β Budget- The entire project must fall below the given budget of $7500.
β 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.
β Safety Cage- Safety system (e.g., safety collar or full cage) to account for drive shaft
failure.
β Emergency Fail Safe- Emergency stop that acts as a disconnect.
β Hydraulic System- Must have hydraulic spill containment plan (if said system is used).
β Safety Regulations- Test Stand must comply with all Eaton, OSHA, and other safety
regulations.
β Power Supply- The system should be 120 volts (standard outlet voltage).
11. 11
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 standβone 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 β 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.
ο· Torque multiplier
ο· Chain gear box configuration
ο· Epicyclic gearing
ο· Hydraulic system
ο· Pneumatic system
Electrical Interface β 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
12. 12
ο· National Instruments DAQ
ο· Measurement Computing USB - 3102
User Interface β This is the subsystem that the user will interface with, that accepts and provides
all necessary data to calibrate the strain gages.
ο· LabView
ο· Visogram
ο· MyOpenLab
ο· SENSIT Test and Measurement Software
Safety Guards β This is the safety system that protects the apparatus and end user against drive
shaft failure.
ο· Full box (Plexiglass)
ο· Padded bar (ergonomics/safety)
ο· Safety Loop/Brace
ο· Interlock on guarding to disengage torque applicator if guard is open (mechanical)
ο· Solenoid actuated guard that is locked during operation (electrical)
Strain Gages β These are the different strain gages that could be used to take measurements on
the drive shaft.
ο· Single axis strain gages
ο· 90 biaxial strain gages
Fixture β This sub-system is the main fixture that will house the torque multiplier, and secure the
test stand to the ground.
ο· Slotted rail in the floor to accommodate variable length
ο· Tube steel frame
ο· That can be wheeled around
ο· Bolted to the ground
ο· Bed plate
13. 13
Torque Measurement β 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.
ο· Torque load cell capable of 3500 ft. lbs.
ο· 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
ο· This component will require a costly and complex torque multiplier that could heavily cut
into the test stand budget.
ο· 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:
ο· High cost associated with a hydraulic system.
ο· 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
ο· A pneumatic system contains a lower threshold for maximum applied torque compared to
a hydraulic system.
ο· 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
ο· The NIDAQ can be somewhat costly; and with our budget being at $7,500, it could cost
us 1/7 of our budget.
ο· 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
16. 16
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:
ο· 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 Server 2008 R2 (64-bit)
Windows Server 2003 R2 (32-bit)
Windows 8.1/8/7/Vista (32-bit and 64-bit)
Windows XP SP3 (32-bit)
Windows Server 2012 R2 (64-bit)
Windows Server 2008 R2 (64-bit)
Windows Server 2003 R2 (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
Pentium 4/M 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
18. 18
Disadvantages:
ο· The computer we chose to use for our user interface will need an operating system which
adds to the cost of our system.
ο· 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:
ο· Will be more expensive than a similar safety βcageβ.
ο· 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:
ο· 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
19. 19
operation of the test stand could be implemented to achieve the same results as the
interlock system.
Disadvantages
ο· Not as safe as a Full Plexiglass Box because small parts could get past the
brace in the event of failure.
ο· 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.
90Β° 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:
ο· 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.
ο· Should the movable portion not be correctly braced or fixed down before load
is applied, the safety of the entire system could be compromised.
20. 20
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:
ο· 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.
ο· 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:
ο· 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:
ο· 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.
21. 21
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:
ο· 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.
ο· This application system will be less complex, whereas hydraulic and pneumatic systems
require storage/compression tanks for fluid/air.
Disadvantages:
ο· 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.
22. 22
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 βpawlβ
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:
ο· Chain and Sprocket assembly will allow for cheap and simple torque multiplication
compared to expensive and complex alternatives.
Disadvantages:
ο· 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.
23. 23
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:
ο· Both systems would be easier to use than a manual torque application
ο· Use of a torque multiplier is not required, thus reducing system complexity
ο· Possibly easier to incorporate safety features to the system via the control system
Disadvantages:
ο· Significantly higher cost than a manual torque application system
ο· Use of hydraulic system requires a hydraulic spill containment plan
ο· Possible additional safety threats from having a system capable of such high torque
25. 25
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%
26. 26
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 componentβs ranking within each attribute
between the six memberβs 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 memberβs 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
27. 27
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
90Β° 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. 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. 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 90Β° 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
31. 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 πΉπ =
33 ππ π 16.3 ππ π β 2β . 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 πΉπ = 19.8 ππ π 9.5 ππ πβ β 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. 32
For A36 Steel, the yield strength is 36 ksi. With a maximum stress of 5.9 ksi, the resulting factor
of safety is πΉπ = 36 ππ π 5.9 ππ π β 6β .
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:
β π = 0
3500 β 10 β π β (7.25 12β ) = 0
(Reaction forces equal from symmetry)
β π = 3000 πππ
Figure 10: Sliding Base FEA
Equation 1: Moment Balance
34. 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. 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.
β π = 0
3500 β 10 β πΉ β 3.5 12β = 0
β πΉ = 1200 πππ
Figure 15: Finding Shear Stress on Bolts
Figure 16: Bolt Hole Pattern is for Adapter Piece
36. 36
Once the force on each bolt was found, the area of contact was calculated for each bolt. The βaβ
dimension is the thickness of the adapter plate, 0.5β, and the βdβ dimension is half the
circumference of the bolt (for a 10 mm bolt, it is 0.618β).
With all the information present, the shear stress on the bolts could be calculated.
π = π ππβ
π = 1200 πππ (.5" β .618")β
β π = 3.9 ππ π
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. 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.
π(πππ) =
ππΏ
πΊ π
2
(π·4βπ4)
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. 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 βlocksβ 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. 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. 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.
πΊπππ π ππ‘ππ = 1 +
π
π
= 1 +
48
12
= 5
For a 2-stage epicyclic, the output of the first stage is the input of the second stage
πΊπππ π ππ‘ππ = (
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.
πππ’π‘ = πππ(25) β 3500 = (3 ππ‘)(πΉππ)(25) β πΉππ = 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.
π+π
π
= πΌππ‘ππππ =
18+48
3
= 22 [ππππππ‘π πππ ππ πππ ππ‘πππππ 120 πππππ‘]
(π + 2) < (π + π) β sin (
180
π
) β (18 + 2) < (12 + 18) β sin (
180
3
) β 20 < 25.98
2π + π = π β 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. 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 Shigleyβs
Mechanical Engineering Design Ninth Edition textbook.
ππ = πΆ π [(π π‘
)(πΎπ)(πΎπ£)(πΎπ ) (
πΎ π»
π π€1 π
) (
π π
π πΌ
)]
1
2
πΆ π= [
1
π(
1β π£ π
2
πΈ π
+
1β π£ πΊ
2
πΈ πΊ
)
]
1
2
= [
1
π(
1β 0.3052
28(10)6 +
1β 0.3202
10.6(10)6)
]
1
2
= 1648.92
Where,
πΆ π = ππππ π‘ππ πππππππππππ‘
π£ π = ππππ π ππβ²
π πππ‘ππ ππ π‘βπ π π’π ππππ
π£ πΊ = ππππ π ππβ²
π πππ‘ππ ππ π‘βπ ππππππ‘ ππππ
πΈ π = ππππ’ππ’π ππ ππππ π‘ππππ‘π¦ ππ π π‘ππππππ π π π‘πππ
πΈ πΊ = ππππ’ππ’π ππ ππππ π‘ππππ‘π¦ ππ ππππππ§ππ πππ’ππππ’π
π π‘
= π‘ππππ πππ‘π‘ππ ππππ
πΎπ = ππ£ππππππ ππππ‘ππ
πΎπ£ = ππ¦πππππ ππππ‘ππ
πΎπ = π ππ§π ππππ‘ππ
πΎ π» = πΉπππ ππππ β πππ π‘ππππ’π‘πππ ππππ‘ππ
π π€1
= πππ‘πβ ππππππ‘ππ ππ π π’π
π = π‘πππ‘β π‘βππππππ π
Equation 4: Contact Stress Equation
42. 42
The transmitted load (π π‘
) 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.
π π‘
=
π ππ(π π)
π(
π
2
)
cos(β )
where,
πππ = ππππ’π‘ π‘ππππ’π πππ‘π π‘βπ π π¦π π‘ππ (ππ‘ ππ)
π π = π‘ππππ’π πππ‘ππ ππ ππππ π‘ π π‘πππ
N = number of planetary gears
d = pitch diameter of the sun gear
β = ππππ π π’ππ πππππ
π π‘
=
140(5)
3(
1
2(12)
)
cos(20) = 5262 ππ
The overload factor (πΎπ) was chosen to be unity because the system is assumed have uniform
shock. Also, the dynamic factor (πΎ π) 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 (π π£) of 10. From this
information, the dynamic factor is calculated using the following equation.
πΎ π = [
50+56[1β0.25(12βπ π£)
2
3]+βπ
50+56[1β0.25(12βπ π£)
2
3]
]
0.25(12βπ π£)
2
3
πΎ π = 1.004
The size factor (πΎπ ) is based on the Lewis form factor (Y) found in Table 14-2 in Shigleyβs
book, the face width of the gears, and the diametral pitch (teeth/in).
πΎπ = 1.192 (
πΉβπ
π
)
0.0535
= 1.192 (
1.5β.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 (πΎπ ). This is dependent upon the mesh alignment and pinion proportions.
πΎ π» = 1 + πΆ ππ(πΆ ππ πΆ ππ + πΆ ππ πΆπ)
Equation 5: Transmitted Load Equation
Equation 6: Dynamic Factor Equation
Equation 7: Load Distribution Factor
43. 43
where,
πΆ ππ = ππππ πππππππ‘πππ ππππ‘ππ
πΆ ππ = ππππππ πππππππ‘πππ ππππ‘ππ
πΆ ππ = ππππππ πππππππ‘πππ ππππππππ
πΆ ππ = πππ β πππππππππ‘ ππππ‘ππ
πΆπ = πππ β πππππππππ‘ πππππππ‘πππ ππππ‘ππ
The load correction factor (πΆ ππ) for uncrowned teeth and the mesh alignment factor (πΆπ) 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.
πΆ ππ =
πΉ
10π
β 0.0375 + 0.0125 πΉ = 0.13125
The pinion proportion factor is (πΆ ππ) is also one because
π1
π
< 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 π =
1.5
2
+
1
2
= 1.25. Furthermore, the distance π1can be calculated by subtraction
π1 = 1.25 β (0.625 + 0.5) = .125. Therefore,
π1
π
=
.125
1.25
= 0.1 < 0.175.
Figure 21: Definition of sun gear to planetary gear proportions
44. 44
The mesh alignment factor (πΆ ππ) is calculated with empirical constant A, B, and C from Table
14-9 of Shigleyβs Mechanical Engineering Design. The mesh alignment factor for open gearing
is defined as,
πΆ ππ = π΄ + π΅(πΉ) + πΆ(πΉ)2
= 0.247 + 0.0167(1.5) + (β0.765(10β4))(1.5)2
= 0.2718
Consequently,
πΎ π» = 1 + 1((0.05)(1) + (0.2718)(1)) = 1.3218
Therefore,
πΎ π»
π π€1 π
= 0.8812
π π
π πΌ
=
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:
ππ = 254212.03 ππ π
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:
ππ,πππ = (
π π π π πΆ π»
π π» πΎ π πΎ π
)
where,
ππ,πππ = πππππ€ππππ πππππππ π π‘πππ π
ππ = πππππ€ππππ ππππ‘πππ‘ π π‘πππ π ππ’ππππ
π π» = π ππππ‘π¦ ππππ‘ππ (πππ‘π‘πππ)
π π = π π‘πππ π ππ¦πππ ππππ‘ππ πππ πππ‘π‘πππ πππ ππ π‘ππππ
πΎ π = π‘πππππππ‘π’ππ ππππ‘ππ
πΆ π» = βππππππ π πππ‘ππ ππππ‘ππ
πΎ π = ππππππππππ‘π¦ ππππ‘ππ
45. 45
The calculated factor of safety is determined by solving for the pitting factor of safety (π π») and
computing the ratio of the tooth contact stress previously calculated to the allowable contact
stress.
π π» = (
π π π π πΆ π»
π π πΎ π πΎ π
)
An estimated value of the allowable stress was found in Shigleyβs Mechanical Engineering
Design book to be:
ππ = 180000 psi
The stress cycle factor is determined from Fig. 14-15 of Shigleyβs textbook. The gears are
designed for 104
number of cycles. Therefore, after 10,000 loading cycles, the gears should be
replaced.
π π = 1.55
The hardness ratio factor (πΆ π») is based on the Rockwell hardness of 303 Stainless Steel and
Anodized Aluminum. The hardness ratio is given by:
πΆ π» = 1.0 + (
π» π΅π
π» π΅πΊ
) (ππππ πππ‘ππ β 1.0) = 1.9717
Because the speed at which the input gear rotates is very small (~3 ft/min), the temperature factor
(πΎ π) 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 π π» = 1.13.
AGMA Spur Gear Bending
First, the modified gear tooth bending stress is calculated with the help from Shigleyβs
Mechanical Engineering Design Ninth Edition textbook. Some of the factors are the same as
those used to calculated contact stress (π π‘
,πΎπ, πΎπ£, πΎπ , πΎ π»).
π = (π π‘
)(πΎπ)(πΎπ£)(πΎπ ) (
π π
πΉ
) (
πΎ π» πΎ π΅
π½
)
πΎ π΅ = π ππ π‘βππππππ π ππππ‘ππ
π½ = πΊπππππ‘πππ ππππ‘ππ πππ πππππππ π π‘πππππ‘β
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.
πΎ π΅ = 1.6 ln (
2.242
π π΅
) where,
Equation 8: Hardness Ratio Factor
Equation 9: Rim Thickness Factor
46. 46
π π΅ = πππππ’π πππ‘ππ =
π‘ π
β π‘
=
π ππ πβππππππ π
π‘πππ‘β βπππβπ‘
=
0.25
0.1853
= 1.35 > 1.2
πΎ π΅ = 1.6 ln (
2.242
1.35
) = 0.811
The geometric factor for bending strength (π½) defines the effect of stress concentration due to the
tooth profile. The stress-concentration factor (πΎπ) and the load-sharing ratio (π π) are
components of that contribute to this effect and are defined as follows. For spur gears, π π = 1.
π½ =
π
πΎ π π π
where, Y = tooth form factor
The stress-concentration factor (πΎπ) which are related to the dimensional information of the gear
teeth profile.
πΎπ = π» + (
π‘
π
)
πΏ
(
π‘
π
)
π
where,
π» = 0.34 β 0.4583662β = 0.180
πΏ = 0.316 β 0.4583662β = 0.156
π = 0.290 β 0.4583662β = 0.45
π =
(πβπ π)
2
π
2
+πβπ π
=
(0.102β0.02)2
1
2
+0.102β0.02
= 0.0115
where,
π = πππππππ’π
ππ = π‘πππ‘β ππππππ‘ πππππ’π
πΎπ = 0.018 + (
0.1309
0.01155
)
πΏ
(
0.1309
0.1653
)
π
= 1.495
Consequently,
π½ =
0.245
1.495(1)
= 0.164
Evaluating the bending stress at the second stage of the epicyclic gear train yields:
π = (5262.28)(1)(1.004)(1) (
12
1.5
) (
1.3012(1)
0.164
) = 335349 ππ π
47. 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 πΎ π and πΎ π are
the same as calculated for contact stress. The AGMA bending strength (ππ‘) is estimated to be
55,000 psi (obtained from Table 14-4 in Shigleyβs Mechanical Engineering Design textbook).
The stress cycle factor for bending (ππ) is estimated from for (104
) number of load cycles to be
1.55.
π πΉ = (
ππ‘ π π
π π πΎ π πΎ π
)
where,
ππ‘ = π΄πΊππ΄ πππππππ π π‘πππππ‘β
ππ = ππ‘πππ π ππ¦πππ ππππ‘ππ πππ πππππππ π π‘πππππ‘β
As a result, the bending factor of safety is,
π πΉ = (
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.
ππ,πππ = (
55000(1.55)
(2)(1)(1.00196)
) = 42541.62 ππ π
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 Shigleyβs 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. 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 (π½) by the equation below, and the plot is shown in Figure 23 on the next page.
ππππ‘β = π·πππππ‘πππ πππ‘πβ (πππ‘πβ ππππππ‘ππ)
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 ππ π.
Figure 23: Plot of the bending stress vs pitch diameter
y = 0.114ln(Teeth) - 0.0246
RΒ² = 0.9753
0.2
0.25
0.3
0.35
0.4
0 10 20 30 40
Lewisformfactor(Y)
Number of teeth
Lewis Form Factor vs. Number of Teeth
Series1
Log. (Series1)
y = 529768x-3.742
RΒ² = 0.9954
0
20000
40000
60000
80000
100000
1 1.5 2 2.5 3
BendingStress(psi)
Pitch Diameter (inch)
Bending Stress vs. Pitch Diameter
Series1
Power (Series1)
1.95
49. 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:
ππ =
π
π΄
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
gearβs overall bore hole diameter and length.
π = ππ‘ = 4745.4 π
π΄ = .19ππ β .25ππ = .0475 ππ2
= 0.00003065 π2
ππ =
4745.4 [π]
π΄ [π2]
= 154.851 πππ
50. 50
Factor of safety was calculated using the maximum shear strength for titanium of 550.0 MPa.
πΉπ =
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 60Β° 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. 51
Input Torque (to sun gear): 140 ft.lbs.
Primary Equations:
Equation 11: for allowable torque on the ratchet: π = πΉπ β ππ‘
Equation 12: for allowable transmission force: πΉπ = ππ β
πΉβπ2
6
β
1
β
β
1
πΉπ
Equation 13: for Bending Stress: ππ =
ππ‘βπ π
πΉβπ
Where ππ‘is 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, ππ‘is the tangential load, π πis the diametral pitch, and Y is the
Lewis form factor.
Secondary Equations:
Equation 14: Tooth Radius: ππ‘ =
[ππ£πππππ π·πππππ‘ππβ(2ββ)]
2000
Equation 15: Modulus: π =
ππ£πππππ π·πππππ‘ππ
# ππ π‘πππ‘β
Equation 16: Pitch Diameter: π π =
25.4
ππππ’ππ’π
Equation 17: Root Length: π = β β tan (60 β
360
# π‘πππ‘β
)
Equation 18: Tangential Load: ππ‘ =
350 ππ‘.πππ .
ππ£πππππ πππππ’π
Using these equations, the tangential load was calculated to be 3796.4 N, with a diametral pitch
of 38138.14 πβ1
, a root length of 2.408mm, and tooth radius of .0484m.
Using the primary equations, a bending stress ππof 2.7053 π₯ 1010
[
π
π2
] was calculated, along
with an allowable transmission force πΉπof 98041.15 N. From this, the maximum allowable
torque on the ratchet gear was calculated to be 4745.19 ππ. 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.
ππ‘,πππ₯ =
π π β πΉ β π
π
=
90,000 (
1
3
) (. 472ππ)(. 446)
3.14
= 2011.26πππ = 8946.53π
52. 52
Where π πis 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.
πΉπ =
8946.53
3796.4
= 2.36
53. 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. 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 Β± 0.05% and a linearity of Β± 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.
ππππππ πππ (ππ) =
πππππ (ππ)
2(πππ‘ ππππππ πππ)
=
40
214
= 0.00244 ππ
Equation 19: Precision in mV over the range of -20 to +20 mV using 14 bit precision.
55. 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. 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. 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 βCalculate Cal. Factorβ 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 βTake pointβ 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. 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. 59
Figure 32: Steps are
given for allowing
data from Windaq to
be sent to LabView.
60. 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 βWireβ in the
βToolsβ 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 βToolsβ box there is the βOperate Valueβ 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.
βGetScaledDataβ 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 βShowβ then clicking on βLabelβ.
61. 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.
63. 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. 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 Bergβs
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: $897.54
65. 65
Safety Guard
In summary of the cost analysis of the safety box, there is a need of twelve 4 ft. x 2 ft. cold-rolled
weldable steel sheet metal to make up the front back and top of the safety box. There is a need of
eight 2ft-1ft cold-rolled plate to cover the sides. The two hinges are so that the box can open and
close, while the two latches are used to keep it closed.
Table 10: Safety Guard Cost
Cost/Unit
($)
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. 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-
f039wmRun-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
Pentium 4/M 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. 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 projectβs 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 $6677
68. 68
Conclusions
It is anticipated that the chosen design will meet all of the design criteria better than the other
conceptual design ideas. Where the design rated the worst was in cost, because it was the most
expensive design, but this helped the design rate higher in other areas that were a higher priority.
Even with this design being more expensive the budget for the project was not excessed.
The outcome of the project is to allow for the Auburn Eaton to run their own strain gage tests on
a drive shaft, and not have to use an outside faculty to run these tests. These results from
applying a torque to a drive shaft will be given on a user interface. They will have the ability to
increment the torque applied to the drive shaft to test over a range for more results.
This design has been dimensioned appropriately to the size of the space in the faculty it will be
placed.
It has been designed with durability in mind in order to reach a lifetime of 10,000 cycles before
parts will start needing to be replaced.
The estimated cost of the project is 6677$ 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. 69
References
ο· Wheatstone Bridge β Last used on 9/12/14
http://www.electronics-tutorials.ws/blog/wheatstone-bridge.html
ο· System Requirements for LabView Development Systems and Modules-
Last used on 10/14/14
http://www.ni.com/labview/requirements/
ο· 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
ο· Metals Depot- Last used on 12/1/14
www.metalsdepot.com
ο· Fastener Fundamentals- Last used on 12/1/14
http://www.strengthandstiffness.com/4_basic/images/bearing_stress.gif
ο· McMASTER-CARR- Last used on 12/1/14
http://www.mcmaster.com/
ο· Mechanical Engineering Design, by Shigley, Nineth Editions
ο· AMERICAN GEAR MANUFACTERS ASSOCIATION, Revision of AGMA 226.1
ο· AMERICAN NATIONAL STANDARDβFundamental Rating Factors and
Calculation Methods for Involute Spur and Helical Gear Teeth
ο· KHK Gears β Last used on 12/3
http://www.khkgears.co.jp/world/break/SRT%20SRTB%20SRT-C.pdf
ο· Berg Precision PartsβLast used on 12/3
http://precisionparts.wmberg.com/gears/spurGears/en
ο· QTC Gears (prices)βLast used on 12/3
http://www.qtcgears.com/RFQ/default.asp?Page=../KHK/newgears/KHK316.html
76. 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
