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Torsional Stiffness Measuring Machine (TSMM) & Automated Frame Design Tools

William Thomas Steed March. 6, 2010 Bachelor of Science in Mechanical Engineering Masters of Science in Mechanical Engineering College of Engineering Committee Chair: Randall Allemang

Abstract

Designing an automotive chassis is not an intuitive process. It, at times, can be very difficult depending on the geometry of the structure. Research was conducted at the

University of Cincinnati to alleviate the burden of this task. Software tools were developed to help speed the design process. A new technique of measuring the torsional stiffness of a Formula SAE chassis design was created. Finally, a recommended process is presented to perform the design and validation of a Formula SAE chassis.

As engineers we turn to different tools that we have access to in order to understand and iterate a design. In the area of space frames, design tools can be limited.

To get an understanding of a chassis design, engineers turn to Finite Element Analysis

(FEA) to gain a better understanding of these types of structures. Ultimately, manual iterations are not enough to completely optimize a structure to a desired goal. Software tools need to be developed in order to have a deep understanding of how the structure performs at each iteration. Two tools, a sensitivity and optimization tool, were written and the out come of each is discussed.

Until 2007, the UC Formula SAE team has validated only the current year’s frame design and not the entire chassis design. In the world of Formula One racing it is essential to have knowledge not only of frame stiffness but also hub to hub chassis stiffness. Various ways to test chassis stiffness were investigated and designed. A static test was developed and performed. A finite element model and its correlation to this static test is discussed.

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Acknowledgement

This thesis has been the greatest culmination to an engineer-in-training process. I have great admiration for the following people because of their eagerness to help, their ambition to learn and their patience to listen and mature my ideas.

Thank you:

• To the “man upstairs” for giving me all the wonderful blessings of this life and sharing with me in all these years.

• To my family for always believing in me, providing for me and giving me inspiration to be the best engineer I know how to be.

• To the University of Cincinnati for providing a faculty of the best engineering professors and learning facilities to chase a student’s dream.

• To Doctor Randall Allemang, for giving me the freedom to explore my ideas and for being a superb engineering role model.

• To Doctor Allyn Phillips for aiding in the development of my Matlab skills and for your patience while I shared the lab’s equipment.

• To my thesis committee. Thank you for your thoughts and time.

• To Douglas Hurd and David Breheim. Thank you for expert advice and patience.

• To the 2005 - 2007 University of Cincinnati FSAE teams for sharing your ideas, your talents and your passion for building race cars and believing that this research can provide a deeper understanding of each design.

• To my colleague Benjamin Stoney; without your help this would not have been possible. Thanks brother, for working as hard on these cars as you do and for all the great welds.

• To my colleague Fredrick Jabs for conversing with me to mature my ideas and pushing the limits of engineering design.

• To my colleague Ryan Lake for setting great examples for future teams and engineering students. Thanks for your thoughts and time. It has been fun!

• To my colleague David Moster for all the long loud years of learning how to become great engineers. Thanks for keeping us fast!

• To my colleagues Ben Rawe, Abbey Yee, Ravi Mantrala and Bill Wise for the extra thoughts and hands they provided during testing.

• To my colleague Dan Alford for your support and dedication to getting the University of Cincinnati FSAE back to top 5.

• To Carroll Smith for creating a collegiate activity that challenges engineers to be better than ever could have thought they could be. Preparing for and competing in this series has been the one of the greatest accomplishment of my life.

This thesis is dedicated to my family and friends: Margaret and Ray Winialski, William, Brian, Kathleen, Edward & Jean Steed, Robert Boehm, Sara, Grant, & William Leto, Mary Ann & Norman Noe, Josh Kullis, Sindney Tippet & Paul Tinetti.

Table of Contents

Chapter 1: Development of the Race Car Frame ...... 1 The Ladder Frame ...... 2 The Space Frame...... 3 The Composite Monocoque ...... 4 Chapter 2: Background ...... 7 Chapter 3: Frame Model ...... 11 Geometry Construction ...... 12 Element Types ...... 14 Material & Section Properties ...... 16 Meshing...... 18 Frame Model Design Iterations & Constraints ...... 19 Chapter 4: Chassis Model ...... 24 Why Model the Chassis? ...... 25 Revolute Joint ...... 30 Model Constraints ...... 33 Chapter 5: Sensitivity Analysis & Optimization Tools ...... 36 Chapter 6: Torsional Stiffness Measuring Machine (TSMM) ...... 44 Fixture ...... 46 Mechanical Fuse ...... 49 Strain Gauge Setup ...... 52 Strain Gage Installation...... 53 Strain Gage Wiring ...... 53 LVDT Calibration ...... 55 Testing...... 56 Chapter 7: Conclusion / Future Recommendations ...... 61 Conclusion ...... 61 Design Tools ...... 63 Torsional Stiffness Measuring Machine ...... 65 Appendix A FEA Checklist ...... 70 Appendix B Scripts ...... 71 Torsional Stiffness Script ...... 71 Sensitivity/Eigen Value Analysis Script ...... 72 Create Combo Script ...... 74 TSMM Post-Processing Script (ctorsion.m) ...... 77 Appendix C: ITER06 Sensitivity Analysis ...... 78 Appendix D: ITER07 Sensitivity Analysis ...... 85 Appendix E: LVDT Calibration Curves ...... 93 Appendix F: Load Cylinder Calibration Curves ...... 94 Appendix G: Torsional Stiffness Measuring Machine Assembly/Test Procedure……..G.1

List of Figures Figure 1: Ladder Frame Automobile [1] ...... 2 Figure 2: Space Frame Automobile [1] ...... 4 Figure 3: Carbon Composite Tub [1] ...... 5 Figure 4: Frame Design Iteration Spreadsheet...... 9 Figure 5: Design Process Flow Chart ...... 10 Figure 6: ITER05, ITER06, ITER07 [11] ...... 11 Figure 7: ANSYS GUI [11] ...... 11 Figure 8: Formatted Key point ANSYS Input [11] ...... 12 Figure 9: ANSYS Line Creation [11] ...... 13 Figure 10: ANSYS Line Geometry [11] ...... 14 Figure 11: Beam188 & Beam4 Deflection Results [11] ...... 15 Figure 12: Common Beam Tool [11]...... 17 Figure 13: Setting Global Element Size [11] ...... 18 Figure 14: Setting Cross Section [11] ...... 19 Figure 15: ITER05 TSTIFF Setup [11] ...... 20 Figure 16: Load vs. Deflection & Torsional Stiffness ...... 21 Figure 17: Torsional Stiffness vs. 4 th Natural Frequencies ...... 23 Figure 18: Completed Chassis Model [11] ...... 25 Figure 19: A-Arm Key point Creation [11] ...... 26 Figure 20: A-arm Geometry Creation [11] ...... 27 Figure 21: Upright Geometry [11] ...... 28 Figure 22: Bell-crank Modeling Comparison [11] ...... 29 Figure 23 Push Rod Geometry [11] ...... 30 Figure 24 Push Rod Connection [11]...... 30 Figure 25: Revolute Joint Locations [11] ...... 31 Figure 26: Revolute Joint Axis Node Creation [11] ...... 32 Figure 27 Completed Chassis Corner [11]...... 33 Figure 28 Spherical Local Coordinate System Creation [11] ...... 34 Figure 29 Completed Chassis model with Boundary Conditions [11] ...... 35 Figure 30: '06 Comp. 1 Torsional Stiffness vs. Cross Sectional Area ...... 36 Figure 31: '06 Component 1 Resorted TSTIFF vs. Cross Section Number ...... 37 Figure 32: TSTIFF vs. Section # Sorted by T.C...... 38 Figure 33: ITER06 Sensitivity Analysis Component Legend[11] ...... 39 Figure 34: Optimization "COMBO" Matrix from ANSYS' Array Editor [11] ...... 41 Figure 35: Optimization Results ...... 41 Figure 36: Optimization Results Resorted ...... 42 Figure 37: Optimization vs. Optimization by Sensitivities ...... 43 Figure 38: Major Automotive Manufacturer's Torsional Stiffness Rig [3] ...... 44 Figure 39: "Backyard" Variety Torsional Stiffness Rig [10] ...... 45 Figure 40: MTS 4 Post Road Simulator in UC-SDRL ...... 45 Figure 41: First Fixture Design ...... 46 Figure 42: Second Fixture Design ...... 47 Figure 43: TSMM Fixture ...... 48 Figure 44: TSMM Fixture Exploded View ...... 49 Figure 45: Strain Gauge Setup [6] ...... 52

Figure 46: Bending, Tension, & Combined [6] ...... 52 Figure 47: Strain Gage Wiring Schematic ...... 53 Figure 48: Strain Gage Conditioner Pin Out Schematic [8] ...... 54 Figure 49: LVDT Calibration ...... 55 Figure 50: (A) LVDT 1 vs. LVDT 3 (B) LVDT3 & LVDT4 ...... 57 Figure 51: ITER06 Chassis Model Results ...... 58 Figure 52: ITER06 Load vs. Time ...... 59 Figure 53: ITER06 Load Steps ...... 60 Figure 54: Deflection Point Legend ...... 60 Figure 55: Commercial Semi-Dynamic Test Rig [9] ...... 68

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List of Tables Table 1: Hand Calc. Beam Properties ...... 15 Table 2: Beam Element Error ...... 15 Table 3: Real Constant Data Table ...... 17 Table 4: ITER05, 06, 07 Frame Model Results ...... 23 Table 5: Torsional Stiffness Property Dependence ...... 37 Table 6: ITER06 Component Sensitivity Ranking ...... 39 Table 7: TSMM Fixture Parts List ...... 48 Table 8: Fuse Design Study ...... 50 Table 9: ITER06 Torsional Stiffness ...... 60 Table 10: ITER06 Experimental Deflections ...... 60 Table 11: ITER06 Chassis Model Deflections ...... 60

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Chapter 1: Development of the Race Car Frame

Since the development of the wheel, humans have been engineering better ways to create modes of transporting goods and people from one place to another. In order to accomplish this, a structure is designed to connect a wheel or a series of wheels together.

In today’s world this structure is more commonly referred to as a chassis. History does not conclude exactly when the first chassis was developed, but information can be found further back in time than the first horse drawn carriage. As time and technology has progressed, these structures have become more dependable, safe, and rigid.

In the racing arena it was determined that the degree of twist for the amount of torque that you are applying to the frame is very important. This degree of twist measurement is known throughout the racing community as torsional stiffness. The torsional stiffness of a race car frame was important because of the need to tune the car for different weight transfer scenarios. A chassis could be described as three spring in series. The spring in the middle would be the frame. If the spring in the middle had a very low stiffness, changing the stiffness of the springs at each end would have little effect on the overall stiffness of the system.

Intuitively, the stiffest structure in torsion is a solid tube. For every bit of material

that is cut out of the tube the weaker the structure becomes. The challenge in

designing/engineering a frame is to keep as much material in a connected pattern as

possible, while at the same time attaching necessary components and creating an

ergonomic space for a driver.

The Ladder Frame

In the world of racing, the modern chassis has been developed over the last

century and a half. The first frames in the beginning of the twentieth century were

constructed using two parallel beams laterally connected. Figure 1 shows an example of

such a construction.

Figure 1: Ladder Frame Automobile [1]

As Indy car racing began, this type of structure, referred to as a ladder frame was popular due to its ease of manufacture and good stiffness in vertical bending. Although,

Forbes Aird perhaps said it best “The notable feature of the frame was that it generally flexed and twisted so much, handling was limited to trying to keep the car under control, never mind tune it for cornering.” [1] This in itself was a great example of what should not be happening while a chassis is making laps around a race track.

During the early years in the development of the racecar found the design focus to

be on engine development, not on chassis development. At this time, the role that chassis

stiffness played to create a controllable racecar was unclear. In the following years, this

role would be realized, leading to further development of the chassis. The ladder frame

in its infancy was a good start. Designers and engineers had the ability to easily

reconfigure different systems using this design. The simplicity of the design made it

extremely desirable. In fact, today the ladder frame is still implemented in most truck

and sport utility vehicle designs. Remnants can also be seen in the front structure of

modern stock cars.

The Space Frame

As conclusions were drawn about stiffness in torsion, engineers turned to space frame construction in the 1950s and 1960s. Breakthroughs in stiffening the ladder frame design were small and typically undesirable. Designers came to realize that adding a second set of axially mounted beams connected with smaller tubing in a truss like structure greatly increased the magnitude of torsional stiffness. As iterations of space frames progressed, designers were able to orient tubes in the frame in order to better handle and distribute the applied forces from the suspension. Initially there were not huge leaps in frame stiffness; however with some persistence and use of triangulation, designers were able to create a much more rigid frame. Connecting tube to tube in this fashion allowed forces to act only along the axis of the tube, putting the tube only in compression or tension. [1] A member loaded in this orientation only required a small amount of material on its cross section to withstand the load. Figure 2 depicts an example of a space frame that was developed in this era.

Figure 2: Space Frame Automobile [1]

With the advent of the space frame, the racecar finally evolved. Racecars became lighter, faster and more predictable. Nevertheless, the space frame design has drawbacks.

They are complex to build and elaborate fixturing has to be created to hold points relative to each other, prior to welding. Joints in the design(s) can be difficult to weld, which can lead to manufacturing challenges. Despite these issues, the space frame was a major improvement over the ladder frame.

The Composite Monocoque

A new technology was discovered in the aircraft industry that would lead to the next evolution in frame design. The combination of stressed skin structures developed in the depression and fibrous materials in the late 1960s resulted in the birth of the composite monocoque. [1] This technology revolutionized Formula One and Indy car racing. Designers now had the ability to create a structure that was multi-purpose. The monocoque served as the car’s structure and body, as well as provided aerodynamic flow

paths. Composites gave engineers the ability to construct a structure that had no

dislocations in front of the driver. Combinations of carbon fiber and aluminum

honeycomb in a sandwich construction created an extremely light weight, but stiff

structure. The ratio of torsional stiffness to weight increased exponentially. Figure 3 is

an example of an early 1990’s Indy car composite monocoque.

Figure 3: Carbon Composite Tub [1]

There are obvious benefits to having a composite tub, but there were also drawbacks. Composite tubs were hard to design and layers of composites needed to be organized in a fashion to create a desired stiffness. Complex laminate schemes were developed in order to stiffen mounting locations for hardware attachment. Also, at that point in time, there were no software tools developed to help the engineers determine the laminate layout scheme. Engineers had to solely design the schemes from test coupons.

The following Chapters had three major objectives. The first was to develop a procedure for designing and validating a space frame for future teams to follow. To this end, Chapter 2 describes how this process was previously performed and a new recommended process. The second objective was to develop software tools that would help speed the frame design and automate the process. The final objective was to develop an accurate experimental test to obtain chassis stiffness on FSAE vehicles. The text also had two less important objectives. Chapters 3 & 4 describe/document how the frame and chassis Finite Element models are constructed for future teams to follow. The second was to explore optimization methods for future teams to pursue.

Chapter 2: Background

The University of Cincinnati (UC) Formula Society of Automotive Engineers

(SAE) team has built and designed a new open-wheel chassis every year since 1993.

Traditionally, the design stage of each one of these structures was limited to three (3) months. Throughout the infancy of the program, few analysis tools were available, so students relied on their intuition to determine what would and would not create a rigid chassis. Team members only utilized computers to visualize and check the clearances of their design concepts.

Historically, UC Formula SAE vehicles have been constructed utilizing a space frame design. Constructed from 1020 drawn over mandrel (DOM) mild steel, chassis tubes were joined using the gas tungsten arc welding process (GTAW). The team utilized this process because of the availability of steel, the ease of manufacturing, and various aspects of the FSAE rules. Composite tubs would be the first choice if the facility to produce the structure and associated expertise was available.

Frames were designed with a minimum amount of analytical and experimental validation, prior to 2004. Typically, chassis and frame stiffness was greatly overlooked.

The time it took to understand how the frame and chassis performed was outweighed by the time it took to actually build a car that could operate in the annual competition.

Through many of these years the UC FSAE chassis did not progress, but instead was an annual reinvention. These structures were built with one-inch tubing, which in the end were highly under-designed and significantly heavier than necessary.

In 2004, an analytical tool was fully introduced into the design process to help understand how frame designs performed. ANSYS ® Academic Research [11], a computer based finite element analysis program was utilized in very new ways that were not previously undertaken by the Formula SAE team. Several manual iterations with a beam element model were performed to understand how the orientation of frame members affected torsional stiffness as well as providing an estimate of overall weight.

With this tool also came the ability to validate the software model by correlating to experimental modal (vibration) analysis test data. The need for a static torsion test of the actual chassis was thought to be unnecessary at this point since the focus was on improving torsional stiffness and reducing weight. Correlating to modal analysis data was a reasonable and acceptable way to conclude that the FEA model was accurate. This design process was adopted and has been implemented into each frame since 2004.

Beginning in 2005, the design process became more complicated when multiple frame concepts were simultaneously evaluated. These design iterations were conducted manually and an on going spreadsheet was used to document their progression and guide the decision making process. An example of this spreadsheet can be seen in Figure 4. In each case the ultimate goal was to drive the designs’ natural frequencies as high as possible without adding significant amounts of mass, thus increasing the efficiency of the frame. Once manual iterations concluded, a static solution was run to obtain a torsional stiffness value. This process took many hours of tedious work. Attempting to understand a single frame design was difficult enough, thus concurrently handling multiple designs became excessively challenging. In addition, the bookkeeping was not adequately identifying a single solution to pursue. Time eventually expired on the design process, as

a final product had to be built. As might be expected, cars were fabricated without great

confidence that the design chosen was the best it could be.

Figure 4: Frame Design Iteration Spreadsheet

The frame design process at the University of Cincinnati did not advance again until 2007 when the notion of automating the design process through computer simulation was thought to be possible. In addition, the desire existed to create a physical test to measure the torsional stiffness of an assembled chassis. A breakthrough in automation was made in early October 2007 when the results of ANSYS Parametric

Design Language (APDL) scripting proved to be promising. Outlined in Figure 5 was the outcome of the 2007 design process and is the recommended way for future teams to design and validate a Formula SAE chassis. The results of these works are described in detail in the following Chapters.

Create a design Build Finite concept in a 3D Element Model Perform FEA Validate Rules solid Modeling using Beam188 Checklist Program Elements

Finalize the design Perform Run based on sensitivity Experimental Optimization Run Sensitivity and optimization Modal Analysis Analysis Analysis results

Correlate Build Finite Correlate Establish Frame Beam188 Model Element Model Beam4 Model to analytical to Experimental using Beam4 Experimental stiffness with Modal Analysis Elements Modal Analysis Beam4 Model

Correlate Perform Establish Frame Experimental Experimental Build Chassis & Chassis Torsional Stiffness Torsional Stiffness Model stiffness values data to Chassis Test (TSMM) Model

Build Shell Sub-models & Analyze

Figure 5: Design Process Flow Chart

Chapter 3: Frame Model

The “frame model” was, as the name implies, a model of the frame and engine combined. The engine was included due to the fact that it was assumed to be a significantly stressed structural member of the combined frame/engine structure. The model was built with simplicity in mind along with basic required features because of the need for quick computational speed. Figure 6 depicts three different frames that will be referred to throughout this document as ITER05, ITER06, and ITER07 respectively.

Figure 6: ITER05, ITER06, ITER07 [11]

The software used to build these models was called ANSYS, which gives engineers the ability to understand both simple and complex engineering problems. In this case, ANSYS provided a means for the UC FSAE team to understand the amount of stiffness a frame concept possessed. Figure 7 displays the ANSYS graphical user interface (GUI).

Figure 7: ANSYS GUI [11]

Geometry Construction

The UC FSAE team’s model began its creation in another program called Solid

Edge [15], a three dimensional solid modeling program. Before any analysis work

commenced, all tubes were modeled as an assembly to ensure proper orientation and

fitment of a driver and engine. Once a geometry had been defined, a coordinate “x,y,z”

list of nodes was created from the 3-D model. The list was formatted in a word processor

(i.e. Microsoft Notepad) to match the proper syntax for the ANSYS key point command

(k,npt,x,y,z). Figure 8 provides an example of a formatted list ready for input into the

ANSYS preprocessor.

Figure 8: Formatted Key point ANSYS Input [11]

Once organized properly, the list was imported into ANSYS using the

“/input,filename,ext” command. This process created a set of key points in the ANSYS workspace. The next step was to connect these points using lines. Lines could be created in ANSYS in a variety of ways. In a Cartesian coordinate system (csys, 0) straight lines could be made by issuing the “l,p” command. Using the GUI, the path to the line command was: >>preprocessor> modeling> create> lines> lines> straight line .

Figure 9 depicts the process of creating a line between two key points 1 and 2.

Figure 9: ANSYS Line Creation [11] This process was repeated until all key points were connected to create the wireframe model. The engine was represented as a solid volume and was modeled to closely represent the relative geometry of the engine. It was not intended to be a detailed model. To improve this part of the process, it is recommended that a 3D solid modeling program is used to model the engine, followed by importing the model into the analysis software in a proper file format, such as *.prt or a *.iges file. These file types eliminate the need for any scaling of the geometry. Nevertheless, if a parasolid (*.para) is imported, it is important to recognize that scaling is needed to achieve proper dimensional characteristics using a unit conversion factor. At this point in the process the model looked similar to that of Figure 10.

Figure 10: ANSYS Line Geometry [11]

Element Types

In ANSYS, there were multiple options for defining an element type for this purpose. The first was the 3-D finite strain beam element called “Beam188”. This element was particularly useful due to some display options available in ANSYS. The

Beam188 element’s cross-sectional properties could be defined with the Section Tool within ANSYS. Once the line geometry was meshed, the elements could be displayed with their element shapes visible (ANSYS command string: /eshape,1). This displays the beams as they appear in real life. This visual reference gave confirmation that the line was meshed with the correct cross-sectional properties. The second option was a 3D elastic beam element called “Beam4.” However, this element’s cross-sectional properties could not be defined with the Section Tool. Its properties must be defined using a real

constant [13]. Nevertheless, with either option there were distinct advantages, as well as

disadvantages. For example, the Beam4 was found to be a more accurate element to

solve for deflections. Hand calculations were performed using a simple cantilever beam

of 1” diameter with a point load of 100 lbf. Table 1 defined the necessary mechanical

properties.

Hand Calc. Beam Properties Property Value Units P 100 lbf. L 12 in. E 2.97E+06 psi. 4 I 0.048986 in Table 1: Hand Calc. Beam Properties

PL 3 Using the cantilever beam deflection equation δ = produces a deflection of 3EI

0.039591 inches. Table 2 compares ANSYS results from Figure 11.

BEAM188 BEAM4

Figure 11: Beam188 & Beam4 Deflection Results [11]

Beam Element Error Method δδδ % Error Hand Calc. 0.03959 --- Beam188 0.03973 0.36 Beam4 0.03959 0.00 Table 2: Beam Element Error

Table 2 verifies that the overall accuracy of the Beam4 element was quite good.

However, the decision to use the Beam188 element in this research was solely based on 15

the ability to write scripts quickly, with less complexity, utilizing section properties as

opposed to real constants. For the purpose of stiffness calculations, the Beam188

element was sufficient for doing comparison and design studies. For deriving an “actual”

empirical number for frame and/or stiffness the Beam4 element was the correct element

to use.

Material & Section Properties

Material and Section properties were the next items to be defined in the model.

Young’s Modulus (EX), Poisson’s Ratio (PRXY), and density had to be defined at a minimum. Material properties were quite simple to define, yet were the most overlooked item when the model was not responding properly. In particular, it was important to make some assumptions as to how the gravity field was defined. Since this research involved a racecar operating in a 1-G field, it was necessary to define that in the model.

Gravity could be defined in two ways. The first and recommended way was to scale the density down by 1-G. Another way was to define an inertial gravity field using the

“accel” command in ANSYS. If the gravity field is not defined, natural frequencies cannot be accurately measured for a simulation in a 1-G field. Temperature effects were not considered because testing for torsional stiffness was a static measurement done with the engine off in a controlled environment, indoors. Therefore, it was not necessary to define a temperature dependant material property table in ANSYS.

Sections in ANSYS, which are the cross-sections of the tubes in the frame design, were created using the ANSYS common beam section tool for the Beam188 elements.

The path to the tool in ANSYS was >>Preprocessor> Sections> Common Sections .

Figure 12 was a display of this tool. This tool was easily implemented when using

Beam188 elements.

Figure 12: Common Beam Tool [11]

For Beam4 elements, it was useful to create a spreadsheet in Microsoft Excel to aid in the

creation of real constants. Once this spreadsheet was fashioned, it was used recursively

throughout the creation of other models. The necessary inputs to create real constants for

a beam element were the cross sectional area and the area moments Ixx, Iyy, and Izz.

The equations for cross-sectional area and area moment for a square and round tube are

presented below.

Square: Round: 2 2 π Area = OD − ID Area = (OD 2 − ID 2 ) 4 = = I xx 2 I xx I xx 2 I xx 1 π I = I = (OD 4 − ID 4 ) I = I = (OD 4 − ID 4 ) yy zz 12 yy zz 64

Section # OD ID Ro Ri Wall Thickness Area Iyy =I ZZ Ixx 1 1.000 0.902 0.500 0.451 0.049 0.1464 0.016594 0.033188 2 1.000 0.870 0.500 0.435 0.065 0.1909 0.020965 0.041931 3 1.000 0.810 0.500 0.405 0.095 0.2701 0.027957 0.055914

Table 3: Real Constant Data Table

Meshing

A line model was the simplest model to mesh. The mesh density could be defined

all at once since there are no dislocations in the geometry such as holes or fillets. To

assign the element size of the mesh, this path was followed: >>Preprocessor> Meshing>

Mesh Tool to get to the mesh tool menu depicted in Figure 13. To select the appropriate

value or the mesh size, the following path was chosen: Set>Global . The tool and this

process are depicted in Figure 13.

Figure 13: Setting Global Element Size [11]

The next step during the line meshing process was to issue the “latt” command for each line of the model. The “latt” command assigns the line the appropriate cross section number at the seventh entry (latt,,,,,,,#) to all the lines currently selected. This was beneficial because selecting lines by its associated cross section was now possible using the “lsel,s,sec,,#” command. Calculating the weight of the entire model was then easily done with the use of the “lsum” and “vsum” commands. To switch between meshing different cross sections, the “secnum, #” command could issued at the command line or it could be found in the GUI at: >>Preprocessor> Meshing> Mesh Tool> Global Drop

Down “Set” Button. Figure 14 illustrates this process. Once meshing was complete the

model looked very close to Figure 15.

Figure 14: Setting Cross Section [11]

Frame Model Design Iterations & Constraints

Frame design iterations could be conducted in two distinct ways. The first was to perform iterations using torsional stiffness as the measured characteristic. Torsion stiffness could be calculated by constraining all degrees of freedom of the rear most suspension points of the frame and applying a force couple at the front suspension pickup points. This setup is pictured in Figure 15.

Figure 15: ITER05 TSTIFF Setup [11]

This analysis was a very good way to understand how well the geometry was

oriented and if the cross sectional material was associated with the right frame members.

However, it did not mimic a loading condition that was possible on the track. The setup

in Figure 15 establishes infinite stiffness of the points that are fixed, which is not possible

in the real world. Furthermore, the loading of the front pickup points on the track would

only have a slight vertical reaction force while the bell crank mounts would take the

majority of the vertical load. Nevertheless, this was the simplest model to construct and

evaluate the frame design.

The amount of load that was applied to the front pickup points was of no

particular concern. The model is created with linear assumptions; therefore the same

torsional stiffness should result with any load. Figure 16, shows deflection results while varying the load on the ITER06 frame model. Figure 16 proves that the frame model provides linear results between the different load schemes. The ultimate goal with this

model was to evaluate the frame’s stiffness and not its strength, no concern was given to

operating in the material’s plastic region. Therefore, keeping the load (displacement)

small, there was no need to calculate results using the large displacement feature in

ANSYS. Activating the large displacement feature in ANSYS enables it to recalculate

the stiffness matrix while incrementally adding load.

ITER06 - Load vs. Deflection & Torsional Stiffness 0.14 920

919.8 0.12 y = 0.0001x + 919.43 919.6

0.1 919.4

919.2 0.08 919 0.06 Load vs. Deflection 918.8

Deflection (in.) Load vs. Torsional Stiffness

0.04 918.6 Torsional Stiffness lb)/Deg. (Ft. y = 0.0002x - 2E-05 918.4 0.02 918.2

0 918 100 150 200 250 300 350 400 450 500 Force Couple Load (lbs.) Figure 16: Load vs. Deflection & Torsional Stiffness

Conducting iterations using this method allowed for a direct evaluation of frame stiffness. However, changing tube orientations and cross-sections led to constraints and applied loads having to be removed and re-applied. The task was tedious and there was no efficient way to conduct and document all the iterations quickly.

The second way to iterate with the frame model was to perform a free-free modal analysis. This analysis required no constraints, but the correct value for density or the proper gravity field had to be defined correctly in order to obtain the proper values for natural frequencies. An evaluation of the frame stiffness could then be made by looking at the magnitude of the natural frequencies. Simplistically, the natural frequencies of the

K structure are theoretically linked to frame stiffness through the equation, . M

Therefore, organizing the frame tubes and cross-sections to shift natural frequencies into

a higher frequency band, while minimizing the mass, stiffens the frame.

Running a modal analysis in ANSYS was very easy, but at times it could be

difficult to understand how the design was improving. While, conducting iterations with

modal analysis and comparing the natural frequencies from one iteration to the next

evaluating the design’s improvement could get confusing. It was essential to have a deep

understanding as to what was happening from one iteration to the next. When a cross

section of a certain tube was iterated, both mass and stiffness were changing. In some

instances, this produced a result where one natural frequency went up and while another

natural frequency went down. Figure 17 gives a representative possibility of how

torsional stiffness could be increased but a certain natural frequency drop off. In this

case as the cross section of component 26 of the ITER06 frame was increased, the 4th natural frequency dropped off. One possible reason that might have caused this was that the components mass was influencing the frequency of the 4 th mode more than the

additional stiffness. A second reason could have been that the stiffness associated with

this mode is not influenced by component 26.

ITER06 Comp. 26 Torsional Stiff. vs. 4th Natural Freq. 820 75 800 74 780 760 73

740 72 y = 9.0182x + 651.42 720 71 700 70

680 (Hz) Frequency Torsional Stiffness 660 4th Natural Frequencies 69 640 Torsional Stiffness (Ft.*lb)/Deg. TorsionalStiffness 68 620 Linear (Torsional Stiffness) 600 67 1 2 3 4 5 6 7 8 9 10111213141516 Ansys Cross Section Number

Figure 17: Torsional Stiffness vs. 4 th Natural Frequencies

Ultimately, the idea of this type of iterating was to raise all of the structures’

K natural frequencies to increase the efficiency, of the frame. To be more efficient at M

iterating using modal analysis, the first torsion mode needed to be identified and tracked.

Table 4 below presents the Frame Model results for the 05, 06 & 07 iterations.

Table 4: ITER05, 06, 07 Frame Model Results ITER-05 ITER-06 ITER-07 Tstiff (ft*lbs/Deg.) 588 1004 1100 Weight (lbs.) 55.2 57.7 52.2 1 32.5 50.561 71.853 2 72.3 71.665 78.647 3 84.4 74.413 86.826 4 102.2 97.776 108.44 5 114.25 106.45 146.18 With Engine Modes 1-6 (Hz) 1-6 Modes 6 126.44 126.23 148.75

Chapter 4: Chassis Model

Trying to model a fully operational chassis in ANSYS was not a simple task. For this research, a sound knowledge of the ANSYS software program was essential. For the novice ANSYS user, this particular task could be very intimidating until a good knowledge base has been established. The following outlines the modeling techniques to assist in making this easier.

It would be ideal at this point in the analysis effort that the frame model be correlated to experimental modal data. If experimental modal data is not available, the frame model should at least be run through a series of model checks to gain confidence in the results that it will produce. Refer to Appendix A for a representative checklist to aid in this process. This checklist, in most cases, will save time and minimize frustration. It suggests that a modal solution be run on the model to make sure that the first natural frequency (Mode 1 or 7) should be at or above 10 Hz. If this was not the case, more than likely there was an unconnected line at an existing key point. As an extra precaution, it was good habit to plot the first six mode shapes and to ensure everything looks like a system mode and not a local mode due to unconnected nodes. Also, prior to running a modal solution, a 1 G static solution should be run. This check verifies that densities have been correctly assigned and the sum of the reactions at all the constraint points equals the predicted weight of the frame. A reaction printout in ANSYS can be obtained by typing “prrs” at the command line while in the post processor (/post1) with the results file loaded.

Why Model the Chassis?

A model of the chassis was necessary to gain an understanding of how the

complete vehicle system worked together. It gave the opportunity to understand the

contribution that frame stiffness had to chassis stiffness. Modeling the chassis allowed

for a direct correlation to an experimental torsional stiffness test. From it, conclusions

could be drawn about sufficient a-arm and bell-crank stiffness. It also provided data to

understand how track loads were reacted and distributed to the mass of the vehicle under

operating conditions. Most importantly, it provided an accurate measure of chassis

stiffness as opposed to just frame stiffness. If on track data could be obtained, it could

also be applied to the model for a deflection stack-up for evaluating suspension

performance characteristics. Figure 18 provides a representation of a completed chassis

model.

Figure 18: Completed Chassis Model [11]

Model Construction

Construction of the chassis model began by using the frame model as a building block. The steps covered in Chapter 3 were repeated to import upper and lower ball joints and bell crank pivot locations. Because of the need for a revolute joint, creation of 25

a-arm geometry was postponed until an extra set of key points were created on top of

existing suspension pickup points on the frame (coincident nodes). This was an arduous

task. It required the use of the work-plane. Moving the work-plane from one pick up

point to the next allowed for the creation of a key point at the origin of the work-plane.

To move the work-plane to a suspension pickup key point the path was >>Main

Toolbar> Work-plane> Offset WP to> Key point . Once moved, a key point could be created at the work-plane origin using the GUI path: >>Preprocessor> Modeling>

Create> Key point> On Working Plane . Once chosen, a menu with the option to be in

Global Coordinates or Working Plane Coordinates appeared. Working Coordinates

needed to be checked and 0, 0, 0 entered at the menu prompt. Figure 19 graphically

describes the process that was performed.

Figure 19: A-Arm Key point Creation [11]

The end result was a key point on top of the one that was already there. This process was then repeated at each of the fifteen remaining suspension pick up points.

Upon completion, it was necessary to select the key points that were just created. These key points did not have a line “connected” to them. This made selection of the duplicate

key points fairly difficult. This issue was dodged by issuing the “allselect” command,

which selected everything in the database. Next, the “allselect,below,line” was issued,

which selected only the key point that were associated under a line. Finally, the

“ksel,inve” command was issued and the key points were re-plotted. Issuing these three

commands consecutively selected the duplicate key points and any new key points not

associated with geometry. Now only the key points that defined a-arm geometry were

selected and the creation of a-arm geometry could then begin by connected the key points

with lines. Figure 20 depicts the a-arm geometry for the ITER07 chassis model.

Figure 20: A-arm Geometry Creation [11]

Uprights were next to be modeled. A detailed model of the upright was thought to be unnecessary, because the goal of the model was to understand stiffness and not stress. To keep the database size small, the uprights were modeled with beams assigned with stiffness from a detailed shell model.

To model the uprights, the steps described above were repeated to create separate key points at the a-arm rod end locations. The key points to make the lines that will define the uprights were selected again by using the “allsel,below,line” and “ksel,inve” process. At that state, the a-arm and upright geometry “looked” connected as in Figure

21. Figure 21 also depicts that at each upright to a-arm attachment there existed two key

points.

Figure 21: Upright Geometry [11]

The next step in the process was to import the points that defined the bell-crank geometry. The bell-crank, push rod, and shock pivots points were imported. This created the coincident node at the bell-crank pivot necessary to define a revolute joint.

For the chassis model it was not important to represent the bell-crank with a detailed model. A triangle of beam elements was simple and effective. However, defining the correct bell-crank stiffness was very important. The beams representing the bell-crank were iterated, so that the stiffness would match a detailed model of the bell- crank.

Figure 22: Bell-crank Modeling Comparison [11] Figure 22 compares a simple and complex representation of the bell-crank. The detailed bell-crank on the right required a complex series of constraints whereas the bell- crank on the left did not require constraints. In this portion of the analysis effort, keeping the model simple led to less debugging and shorter solution time.

To continue building the chassis model, the push/pull rods were constructed. The push/pull rod outer connection points were imported. With the creation of the bell-crank, the connection point between the bell-crank and push/pull rod had been defined.

However, a coincident node needed to be created to define the revolute element between the two. The process of moving the work-plane that was described previously was repeated to create this key point. A corner of the chassis model now looked like Figure

23.

Figure 23 Push Rod Geometry [11]

To connect the push rod to the a-arm, a simple pyramid of lines was created at the end of the a-arm. As Figure 24 shows, modeling the outer push rod connection joint could be simple or complex. To represent this joint with beams, the stiffness was tuned to match the detailed model.

Figure 24 Push Rod Connection [11] Revolute Joint

To model the connection of either a spherical bearing or a rod end, the revolute joint element in ANSYS was used. The element was found in the element selection menu under “combination”. ANSYS referenced this element as a “Combin7” element. The

process of creating these elements was not trivial. Figure 25 marks the seven locations

where each one of the four corners required a revolute joint.

Figure 25: Revolute Joint Locations [11]

The revolute joint element required three nodes to be present, two to define the joint and a third node to define the axis of rotation. At this stage of the model, all the a- arm, push rod, and bell-crank geometry were meshed and only two of the three necessary nodes for the revolute joints had been defined. To create the third node, one of the work- plane’s axes was oriented to be co-linear with axis of revolution of a particular joint. The work-plane origin was then moved to be coincident with the joint. Finally, a node was created along the work-plane axis but offset 0.25” to the right of its origin. Figure 26 illustrates this process.

Figure 26: Revolute Joint Axis Node Creation [11] After all extra nodes were created and the proper element type number was selected, (type,#) the revolute joint element could be created. The path to the command to create the element was : >>Preprocessor> Modeling> Create> Element> Auto

Numbered> Through Nodes . With the command issued, all three nodes needed to be selected. ANSYS automatically detected that the two nodes that were “coincident” were the nodes required to create the element and the third node off to the side defined the axis of revolution.

The last elements to be defined and created were the elements representing the spring-damper system. Coincident key points for these elements were not required, which made the process very simple. The Combin14 element was created in the database and the line between the bell-crank and frame was drawn. A real constant was used to set a very large (infinite) stiffness for these elements. At this point, all modeling was complete and a completed corner of the model looked like Figure 27.

Figure 27 Completed Chassis Corner [11] Model Constraints

Chassis constraints were very similar to the frame model constraints with a minor addition/modification. The upright connection at the ends of the a-arms needed to be defined. This joint is a spherical joint and was not modeled using the revolute joint element. Instead, the two key points defining the connection were rotated into a local spherical coordinate system. The work-plane was offset to these key points and a coordinate system was created at the origin. The path to creating this coordinate system was >>Work-plane>Local Coordinate Systems>Create Local CS

Figure 28 displays the process of how the coordinate system was created.

Figure 28 Spherical Local Coordinate System Creation [11]

Once the coordinate system was created, ANSYS automatically made it the active coordinated system. The two nodes at the upright connection were then selected using the “nsel,r,p” command. These nodes were rotated into the spherical coordinate system by issuing the “nrot,all” command. This command was available interactively at

>>Preprocessor> Modeling>Move/Modify>Rotate Node CS>To Active CS. Finally, with only the two nodes selected, coupled constraints were applied in all translational degrees of freedom (UX,UY,UZ) using the couple coincident nodes menu at >>

Preprocessor>Coupling / Ceqn>Coincident Nodes . This process was then repeated at the other seven upright connections points.

The model was now ready to be loaded in torsion and displacement constraints applied to allow only movement in the lateral direction (UY). Model checks were performed and Combin14 element stiffness was set low so that any displacement results could be reviewed for any anomalies. Once the model was confirmed to be in working

order, element stiffness was reset and the model was solved. Figure 28 shows the model at the end of construction with all boundary conditions turned on.

Figure 29 Completed Chassis model with Boundary Conditions [11]

Chapter 5: Sensitivity Analysis & Optimization Tools

Sensitivity Analysis

Once geometry had been defined for a frame design, the next task was to determine what size cross section was appropriate for each member in the geometry.

This was not a very intuitive process when manually iterating. It was extremely difficult to get an overall picture as to what tube was more important to stiffness as opposed to another. An automated method was conceived to rank frame members in order of their sensitivity to torsional stiffness, to aid in alleviating this issue.

The sensitivity analysis was developed by conducting some research about how linear the change in torsional stiffness was compared to cross-sectional area. Figure 30 displays some initial results.

'06 Comp. 1 Section # Sorted by Cross Sectional Area 650

648

646

644

642

640 Torsional Stiffness (Ft.*lb)/Deg.

638 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Section # Sorted by Cross Sectional Area Figure 30: '06 Comp. 1 Torsional Stiffness vs. Cross Sectional Area

Figure 30 showed a disconnect in the relationship between cross sectional area

and torsional stiffness. Using some reverse engineering, the next step in the investigation

was to re-sort the torsional stiffness data in ascending order and plot against a “dummy”

array of integers. This allowed for any linear relationship based on physical properties to

reveal itself. Figure 31 depicts the result of this resorting.

'06 Comp. 1 Torsional Stiffness vs. Integer Array 650

648

646

644

642

640 TorsionalStiffness lb)/Deg. (Ft.

638 1 2 3 4 5 6 7 8 9 10111213141516 Integer Array Figure 31: '06 Component 1 Resorted TSTIFF vs. Cross Section Number

Drawing conclusions from Figure 31 it was clear that torsional stiffness had a linear relationship with a particular physical property. Next, Table 5 was organized to compare two physical properties: area moment and torsion constant. This determined which property had a “better” linear relationship with torsional stiffness.

Table 5: Torsional Stiffness Property Dependence Torsional Stiffness Sorted by: TSTIFF Area Moment Torsion Constant 639.467 639.467 639.467 640.054 640.054 640.054 641.282 641.282 641.282 642.112 642.112 642.112 642.430 642.430 642.430 643.077 643.077 643.077 644.036 644.036 644.036 644.697 644.697 644.697 645.401 645.401 645.401 645.711 645.711 645.711 646.115 646.115 646.115 647.151 647.151 647.401 647.401 647.966 647.151 647.966 647.401 647.966 648.381 648.955 648.381 648.955 648.381 648.955

The highlighted cells in Table 5 are the corresponding rows that do not match to

the first column. The first column was torsional stiffness listed in ascending order.

Sorting the data by area moment proved not to be as accurate as sorting the data by

torsional constant. This concluded that, to calculate the sensitivity to torsion stiffness of

each frame member, it was necessary to rank cross section number by torsion constant.

Figure 32 depicts the initial results resorted by torsional constant.

'06 Comp. 1 vs. Section # Sorted by Torsion Constant 650

648

646

644

642

640 Torsional (Ft.*lb)/Deg. Stiffness

638 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Ansys Cross Section Number Figure 32: TSTIFF vs. Section # Sorted by T.C.

After understanding how to best sort the data, linear regression was performed to determine the equation for the best fit line to the data. The sensitivity of the component to torsional stiffness was then established as the slope of the best fit line.

'06 Comp. 1 vs. Section # Sorted by Torsion Constant 650

y = 0.6212x + 639.36 648 R2 = 0.9743

646

644

642

640 Torsional Stiffness (Ft.*lb)/Deg.

638 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Ansys Cross Section Number

To automate the process of obtaining all the information for each component in

the frame, an ANSYS script was written. This script can be found in Appendix B. The

sensitivity analysis took approximately ten hours to complete on a desktop pc. Results of

the ITER06 sensitivity analysis can be seen in Table 6. Figure 33 shows a legend of the

analyzed ITER06 components. Appendix C provides the detailed sensitivity analysis

results for both ITER06 and ITER07.

Figure 33: ITER06 Sensitivity Analysis Component Legend[11]

Table 6: ITER06 Component Sensitivity Ranking Rank 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 Component 26 12 21 6 10 27 2 18 7 25 22 31 17 24 15 19 16 4 3 1 11 8 23 20 9 5 30 14 13 28 29 32 33

In the end, the sensitivity analysis was the ultimate tool for this part of the design stage. The result of the analysis tells the designer/engineer exactly where to place and

take away material. It was a complete answer to the question: How does one determine

what cross-section belongs in the frame?

Optimization

In an effort to take more guess work out of designing a FSAE frame, an automated optimization script underwent experimentation. The idea behind this script was to eliminate all manual iterating when determining the frame design. In theory, the optimization would analyze any ANSYS frame geometry and return the best cross section combination for all frame members to provide the best torsional stiffness. Thus, the ultimate frame design is created.

To begin the optimization process, all the possible combinations of cross-sections needed to be coded. The ITER07 geometry had thirty three components that could have sixteen different possible cross-sections, which computed to 5.4 X 10 39 combinations.

The amount of time to optimize that many combinations was projected to take years. In order to reduce the number of combinations, the top four most sensitive components to torsional stiffness were selected, which reduce the number of combinations to 65,536.

The first challenge faced while writing the optimization script was trying to create a matrix that defined all 65,536 combination automatically. The initial thought was to try and utilize Microsoft Excel’s intelligent fill agent instead of coding it directly in a formatting loop. However, the attempt was unsuccessful when Microsoft Excel failed to recognize the pattern. With ANSYS’ memory swapping issues the code was written in a

Matlab ® routine before it was adapted to ANSYS Parametric Design Language (APDL).

Matlab ® was able to create the matrix in an order of magnitude less time than ANSYS.

However, once the script was run in ANSYS, the matrix could be saved in an empty database so that it did not need to be executed again. Figure 34 represents the first and last

nineteen entries into the completed “COMBO” matrix.

Figure 34: Optimization "COMBO" Matrix from ANSYS' Array Editor [11]

To optimize these components the ratio of torsional stiffness to weight needs to be calculated for each combination. Using the frame model, the task of acquiring the data took ten days to complete on a Pentium IV PC. The optimization script can be found in

Appendix B. Results are displayed in Figure 35. From initial inspection, the data does not have any real definite pattern or have the appearance of a simple mathematical relationship.

Figure 35: Optimization Results

Figure 35 shows 16 distinct patterns for the 16 available cross-sections. It was

fairly easy to see that as cross-sectional area was added, the ratio of torsional stiffness

increased. The first combination produced the lowest ratio of torsional stiffness to

weight, which set all four components to the smallest cross sectional area available. The

last combination created the highest ratio of torsional stiffness to weight, which resulted

from all four components being set to the greatest cross-sectional area. The information

shown in Figure 35 did not show much potential until it was resorted. Figure 36 shows

the optimization results resorted from the smallest ratio of torsional stiffness to the

greatest.

Figure 36: Optimization Results Resorted

It was apparent from Figure 36 that there was a cubic mathematical relationship between the combination and the ratio of torsional stiffness to weight. Further, investigation into how the two were connected was thought to be very difficult with the number of data points to process. Getting the data plotted took several days due to memory issues and software limitations, so further investigation was abandoned. Instead, the realization was made that this data could potentially be produced quicker with the use of the data from the sensitivity analysis.

The thought that optimization data could be produced from the sensitivity analysis came from the insight that the contribution to torsional stiffness of each frame member was independent of other frame members. Investigating further into this, a script was developed to take the sensitivity data along with the matrix of combinations and produce optimization results. As opposed to taking ten days, this script created results for all

65,536 combinations in less than 30 seconds. The results of this new optimization routine were plotted along with the correct optimization results in Figure 37. The data presented in Figure 37 contradicts the assumption that the stiffness of one frame member was not related to the stiffness of other frame members. If the two were truly independent of each other the two curves shown in Figure 37 would overlay exactly.

Next, post processing was conducted to investigate if the combinations appeared in the same order. From a sample of 1000, 60% of the combinations appeared at the same index. With this established, the optimization tool did not produce valuable enough answers to continue the effort. If time permitted, the optimization routine had the potential to evolve into the ultimate design tool.

Figure 37: Optimization vs. Optimization by Sensitivities

Chapter 6: Torsional Stiffness Measuring Machine (TSMM)

The Torsional Stiffness Measuring Machine culminated from a need for the experimental measurement of chassis stiffness. Research showed some very basic ideas of how to go about taking this measurement. Some engineers chose to create their own fixtures to hold the frame and some methods were of the “backyard” variety.

Commercially available systems are referred to as “Kinematic and Compliance Systems.”

Figure 38: Major Automotive Manufacturer's Torsional Stiffness Rig [3]

Figure 38 gives a general idea of how major automotive manufacturers go about testing for torsional stiffness. However, it does not draw any conclusion as to how the force couple was physically applied. Figure 39 shows a very simple, but inaccurate way of measuring torsional stiffness. This approach has been used by many FSAE teams and produces a wide variety of results. A free body diagram would show that by loading the frame as in Figure 39 causes more than just a force couple, but also shear loading.

Another downside for this setup was the post supporting the frame. For better results, the frame should have been placed on a cylinder located at the center line of the car.

However, the intention might have been to correlate this type of loading scheme to a

Finite Element Model instead of acquire torsional stiffness.

Figure 39: "Backyard" Variety Torsional Stiffness Rig [10]

The idea for the TSMM spawned from a four post road simulator that was available at UC-SDRL. This road simulator was designed and built by Mechanical

Testing Systems (MTS). The system was hydraulically driven and controlled with the use of four internal linear variable differential transformers (LVDT). This system was not designed for static testing in its raw form, but instead is used to excite a fully assembled vehicle simulating various road conditions. Figure 40 shows this system with a vehicle installed on the simulator.

Figure 40: MTS 4 Post Road Simulator in UC-SDRL

Initial feasibility runs showed that the system was accurate for controlling in

increments of ten thousandths of an inch of movement. The controller also allowed for

the ability to displace each post independently. With these two capabilities established,

the TSMM concept started to become a reality. The next question that needed to be

answered was how to connect the racecar to the each of the posts.

Fixture

To connect the car to each of the four posts a fixture was needed. Research was conducted to identify the various hole patterns that were available on the “wheel pan” of each post. This set the constraints for the interface at the post. The second interface needed to resemble that of the rim of the FSAE car, so that force could be input at each hub. With these first few constraints set, an initial design was drawn up, which is pictured in Figure 41.

Figure 41: First Fixture Design

As with any fixture, simplicity was highly desired. The intent with the first design was to make the fixture very easy to manufacture and assemble. The base plate allowed the fixture to be attached to the four center bolts but also the “wheel pan” outer bolt pattern. The bolts at the outer locations were later determined to be non-load carrying bolts so the first base plate design was abandoned. Additionally, to be able to take a strain/force measurement a cylinder was required to be incorporated into the fixture design.

Figure 42: Second Fixture Design

The first design being inadequate led to the design shown in Figure 42. This design was improved with the integration of a cylinder and the redesign of the base plate to only capture the four bolts at the center of each post. However, after more discussion and thought, flaws were again revealed. They began with the fact that there was the potential for a lot of bending stress if there were to be any misalignment. The nature of the cars’ suspension systems was to have camber change as the wheel moved vertically. The second fixture design would constrain this motion, leading to some potential load magnification. Lastly, the need for a mechanical fuse was desired to prevent yielding of any suspension components. To remedy these major flaws, a pivot was integrated into the design along with a mechanical fuse.

Figure 43: TSMM Fixture

Figure 43 depicts the assembled final design of the TSMM fixture. The design has a pivot at the top of the load cylinder to keep from constraining rotation and a hole near the base for a mechanical fuse in double shear to be installed. Table 7 and Figure 44 provide a more detailed description of the TSMM fixture.

Table 7: TSMM Fixture Parts List

Item Part Description Material/Grade 1 Hub Adapter Stainless 304 2 Pivot Bolt Nut Steel 3 Load Cylinder w/ strain gages 6061 Aluminum 4 Pivot Bolt (1/2 Shoulder Bolt) 1020 Steel 5 Mechanical Fuse Brass 6 Base Bolts (M12 X 1.75 X 120 MM) Blk. Oxide Grade 8 7 Base Stainless 304 Adjustable Solid Shock Assy. 8 Steel (not pictured )

3 2

5 6

Figure 44: TSMM Fixture Exploded View Mechanical Fuse

The purpose of incorporating a mechanical fuse into the fixture was to protect the hardware during testing. Many of the suspension components are delicate and are not designed to take bending loads. The goal of this type of testing was to gain understanding of how stiff the chassis was without breaking it. Integrating a mechanical fuse between the hardware and the input provided a great deal of safety for the test.

Designing the mechanical fuse proved to be a challenge. Metallic materials were not exactly suitable for this purpose. A brittle or non-yielding material was desirable but

was difficult to locate in a form that could quickly be manufactured. Searching material

supplier databases returned little-to-no results for raw forms of ceramic materials.

Reluctantly, the choice to use brass was made. Brass was chosen because of its low

shear strength and availability. As a backup, nylon was thought to be a second choice if

brass were to become a problem.

To determine the dimensions of the fuse the maximum amount of load while

keeping the hardware safe needed to be established. Stress was extracted from the

chassis model while spring stiffness was set to be infinite (1 X 10 6 lb/in). Results showed positive margin was maintained while loading remained under 150 lbs. With this value established, calculations were carried out to determine the fuse dimensions.

Table 8: Fuse Design Study

2 Trial Do Di Ao Ai Area (in ) Load (lbf) Shear Ult. Stress (psi) Margin 1 0.0625 0.0000 0.00307 0.00000 0.00614 150 31900 12223.100 1.610 2 0.0625 0.0078 0.00307 0.00005 0.00604 150 31900 12417.117 1.569 3 0.0625 0.0156 0.00307 0.00019 0.00575 150 31900 13037.973 1.447 4 0.0625 0.0234 0.00307 0.00043 0.00527 150 31900 14223.243 1.243 5 0.0625 0.0313 0.00307 0.00077 0.00460 150 31900 16297.466 0.957 6 0.0625 0.0391 0.00307 0.00120 0.00374 150 31900 20058.420 0.590 7 0.0625 0.0469 0.00307 0.00173 0.00268 150 31900 27938.513 0.142 8 0.0625 0.0547 0.00307 0.00235 0.00144 150 31900 52151.892 -0.388

Table 8 shows results from the design study for the mechanical fuse. The stress

F documented in Table 8 was calculated using the equation τ = [5]. Margin was ave 2A

then calculated by comparing the calculated stress to the shear allowable of 31,900 psi

Shear [4]. The equation for margin was then M = allow −1. Trial 8 had negative shear F.S *. σ

margin with a factor of safety of 1.0. This fuse would require the inner diameter to be

7 1 in. and the outer diameter to be in. This defined a fuse that was 1.125” long and 128 16

had a wall thickness of 0.003”. Machining a fuse with this small of a wall thickness seemed very unrealistic.

When material for the mechanical fuse arrived, manual machining of an internal diameter proved to be almost impossible. Directing a drill bit through a 1/16” diameter stock of yellow brass, with the help of a center drill, proved to be extremely difficult.

Any wobbling of the drill bit or weakening of the part caused it to shear immediately from the lathe. Eventually, the idea for boring out the 1/16” diameter brass stock was abandoned after a few tries. The backup nylon fuse was then tested as a result of the failure to create the ideal brass fuse. Experimental testing of the nylon fuse showed that it would fail around 100 lbs of load. Testing commenced with the nylon fuse.

Strain Gauge Setup

With the fuse determined, attention was turned to how to setup the strain gauges so that the axial load could be logged during testing. The strain gauges needed to be wired in a manner that would ignore any bending stress that the load cylinder experienced.

Figure 45: Strain Gauge Setup [6]

Using the setup described by Figure 45, bending stresses could be neglected.

Two strain gauges were placed diametrically opposite of each other. [6] The two gages were then wired in series and installed in one leg of a Wheatstone bridge.

Figure 46: Bending, Tension, & Combined [6]

Perry and Lisner describe, “ It is apparent from this illustration (Figure 42) that if the

shank is being bent slightly by non-axial loading, gage A will ‘feel’ a strain somewhat

greater than the uniform strain representative of pure tension. On the other hand, the net

strain felt by gage B will be lower than it should be by exactly the same amount. If these

gages are placed in series electrically, the circuit effectively adds their results and divides

by two, which gives the true tensile strain and eliminates all the strain indication due to

bending.” [6]

Strain Gage Installation

Installing the strain gages on the load cylinders was again no easy task. It required an extreme amount of patience and discipline for following directions. Any step left out led to the strain gage being pulled from the part and discarded. At $7 each, it was very important to complete each step properly. A complete step-by-step installation guide can be found for each individual brand of strain gage. Vishay strain gauges were used for testing and their step by step installation guide can be found in Reference 7.

Strain Gage Wiring

With all the strain gages installed on the load cylinders, attention was focused on how to properly wire both the strain gages and the strain gage conditioner. A quarter bridge was required for this type of setup. To begin the installation of the two strain gages in series, a jumper cable was installed to connect the two. Both the P- and S- wires are soldered together at one of the relief pads and the remaining P+ wire was soldered to the last vacant solder pad on the opposite strain gage. For better clarity, reference the wiring schematic in Figure 47 below.

Figure 47: Strain Gage Wiring Schematic

Wiring the Vishay Strain Gage Conditioner and Amplifier system for the quarter

bridge circuit came next. Previously, the system was configured for a full bridge circuit.

Pinning-out each strain gage amplifier connector took some time. Soldering the

terminals was difficult due to the limited access the connector design provides to the pins.

As with any process, it became easier with practice. The key was to keep the heat on the pin and not the wire. Once the pin was hot enough the old solder would melt and the wire could be inserted. With the addition of each wire, it was important to keep the soldering tip away, so that insulation did not melt. It was also a good practice to keep a set of safety glasses on while soldering. Figure 48 is a modified schematic from the

Vishay Conditioner Instruction Manual, Reference 8.

Figure 48: Strain Gage Conditioner Pin Out Schematic [8]

As the diagram describes, it was necessary to wire an extra resistor in line with

the P- signal. The size of the resistor needed to be equal to the total resistance of the two

strain gages in series. This created the second arm of the bridge circuit that balances the

arm containing the two strain gages. For example, if both strain gage A & B were 350 , the total resistance needed would be 700 . Therefore, the resistance in the second arm

of the bridge needed to balance this resistance, by also having 700 of resistance. This could be achieved through two methods. Method one was to wire a 700 precision resistor at the dummy resistor location, according to Figure 47. The second method was to install a 350 precision resistor at the dummy resistor location and wire this lead to the G pin in Figure 48. Wiring to the G pin uses an internal precision 350 resistor

which creates the 700 resistance needed to balance the bridge. The second method

was chosen because of the availability of 350 resistors.

LVDT Calibration

To record displacement without having any manual interaction, LVDTs were

thought to be the best instrument. Micro Measurement LVDTs were chosen to take the

measurements. These LVDTs need external power in order to operate. To power the

LVDTs a Dymac 24 volt Direct Current (DC) voltage supply was used. The LVDT has

four wires (Ground, Positive, Negative, & Source). Using two conductor shielded wire

the connections between the Dymac power supply and the LVDT were made. A BNC

wire was then terminated to connect the remaining wires of the LVDT.

Calibration curves for each LVDT were acquired by using a dial indicator placed in-line with the axis of the LVDT. The piston was then cycled both up and down while voltage and displacement were recorded. Each instrument proved to be very repeatable.

An example of this calibration method is shown in Figure 49. Calibration curves for these sensors can be found in Appendix E.

Figure 49: LVDT Calibration

Testing

There were many challenges that were overcome during the first session of

testing. The most important challenge was to determine the order in which events should

occur. The ITER06 chassis was installed on the fixture first without installing the solid

shocks beforehand (a rigid shock allowed for a direct calculation of stiffness of the frame

and suspension components alone.) While installing the solid shocks on the fixture, the

ITER06 chassis was overloaded and a lower front a-arm was bent. With the order of

events re-worked, ITER05 chassis was installed next. Solid shocks were installed prior

to installing the chassis on the TSMM. The sequence to installing each post was

documented and can found in the procedure in Appendix G. The order in which these

events needed to occur was critical to the chassis’ safety.

During the first test session using the ITER06 chassis, conclusions about the fuse

and the ability to control the angle of twist were drawn. Initially, the ITER06 chassis was

installed using the plastic mechanical fuses. The load applied to the chassis during

testing was mostly absorbed by the elasticity of the plastic fuse. After a few data points

were collected the fuses were replaced with the solid brass mechanical fuses. The brass

fuses showed no signs of bowing/sinking. However, the brass fuses being solid, the

“fuse” characteristic was lost. Knowing that the controller was accurate in moving in ten

thousandths of an inch and having a dynamic display of the load, this was not a huge

concern. Testing of the ITER05 chassis completed with no harm to the hardware.

For each chassis tested, two approaches were made. The first approach was to

move the front two posts in increments of 0.020”, followed by a second test using 0.050”

increments. The initial theory was that testing with 0.020” increments would allow the

maximum load to be approached carefully. Using 0.020” increments was also initially thought to produce inaccurate data points due to the small offset. Using the 0.020” increments the ITER05 chassis was tested to 0.200” of deflection. The load applied to the chassis at this point was approaching the maximum load capability concluded from the stress analysis. Testing finished when a deflection of 0.200” was reached and the chassis was relaxed back to its zero point in 0.100” increments. The second round of testing was then conducted using the 0.050” increments.

The last concern throughout testing was that as load/deflection was applied to the front of the chassis, would the back remained fixed? Testing showed that while deflection increments were applied to the chassis the hydraulic control system was able to maintain a very small amount of twisting of the rear of the car.

(A) (B)

Figure 50: (A) LVDT 1 vs. LVDT 3 (B) LVDT3 & LVDT4

Figure 50A gives an example from the ITER06 test of how well the control system managed the deflection through the frame (Blue to Black lines). When applying a

0.200” of a couple in the front of the chassis, the rear posts deflected only 0.005”. This small amount of deflection was taken into account during post processing of the data.

The amount of rotation allowed by the two rear post was calculated and subtracted from the amount of rotation that was applied in the front. Chassis stiffness was then calculated using this new rotation. Figure 50B also shows results of the deflection of both rear posts as load was applied.

Post Processing/Results

Once the data was collected on the ITER06 chassis it needed to be post processed in Matlab. A Matlab function called “ctorsion” was written to automate this process.

This script can be found in Appendix B. The script was executed and the torsional stiffness was calculated at every load step. Finally, the average of these torsional stiffness values was calculated and the value was printed to the screen. For the ITER06 chassis stiffness was calculated experimentally to be 965 ft-lb/deg. From analysis results of the ITER06 chassis, Figure 51, torsional stiffness calculated to 925 ft-lb/deg.

Figure 51: ITER06 Chassis Model Results

Loading each chassis was done by moving the two front posts independently.

Since each post could not be commanded to move at the same time there was a short time period when only one post had moved. This caused a period where the chassis was not loaded as desired. A challenge was discovered when trying to post process the data. To account for this, the code was written to identify all the indexes where the load increased.

It then determines the time span in which both posts had been commanded to be at the same deflection. The average of the entire time window was then calculated and sent back to the program to calculate torsional stiffness.

Figure 52: ITER06 Load vs. Time

Figure 52 shows the output from the Load Cylinders from testing the ITER06 chassis. The time spans highlighted in red were the areas of interest. If the areas in between the red areas were averaged into the calculation, the torsional stiffness would be

incorrect. The “ctorsion” script identifies these highlighted red areas and uses them to calculates the torsional stiffness for each load step.

Table 9: ITER06 Torsional Stiffness

Torsional Stiffness Load Step (ft-lb)/deg. 1 946.46 2 968.91 3 981.58 Avg: 965.65

Figure 53: ITER06 Load Steps To further validate how well the ITER06 chassis model corresponds to the experimental data, Tables 9 and 10 were tabulated. Table 9 shows the values that were manually recorded from the dial indicators that were placed at key locations along the frame while the test was being conducted. Table 10 shows the deflection results from the corresponding points as the chassis model was solved while being loaded due to displacement constraints. Comparing Tables 9 and 10, they are remarkably close to being equal.

Table 10: ITER06 Experimental Deflections

ITER06 TSMM Deflection Results Shaker Defl. Point 1 Point 3 Point 4 Point 5 Point 6 Point 7 Point 8 0.05 -0.009 -0.01 0.005 -0.009 0.006 -0.004 0.004 0.1 -0.015 -0.019 0.011 -0.018 0.013 -0.007 0.007 0.15 -0.021 -0.027 0.019 -0.026 0.021 -0.01 0.011

Table 11: ITER06 Chassis Model Deflections

Ansys Results Shaker Defl. Point 1 Point 3 Point 4 Point 5 Point 6 Point 7 Point 8 0.05 -0.007 -0.008 0.008 -0.0109 0.0106 -0.005 0.005 0.1 -0.014 -0.017 0.016 -0.022 0.021 -0.01 0.01 0.15 -0.02 -0.026 0.024 -0.033 0.031 -0.015 0.015 Figure 54: Deflection Point Legend

Chapter 7: Conclusion / Future Recommendations

Conclusion

For Formula SAE teams it is not only a race to the finish line, but also a race to finish the building and validation of a racecar. Having every tool possible to “get there” gives teams the upper advantage. The design and validation of the chassis as a whole will continue to be the focal point at every collegiate racecar competition. Understanding and utilizing the tools presented in the preceding will not only speed the process, but will also provide that extra edge for competition.

The process from frame to chassis model is an engineering process that has been proven to work at the University of Cincinnati. Establishing and documenting this process will allow future teams to achieve the goals they have for their designs.

Following this process also allows for a direct comparison from year-to-year. When rule changes are so widespread that a year-to-year comparison can not be made, engineers can find reassurance that if this process is followed, the result will be a very good working product. This process gives excellent trend (relative) information to evaluate progress as well as accurate absolute (properly scaled) numbers for ultimate design and analysis.

The automation of the sensitivity analysis played a key role in the success of this process for the UC Formula SAE team. Having a global view of how each tube’s stiffness contributed to the overall stiffness of the frame was a huge step forward in the design process. The ability to quickly make changes as manufacturing issues arose was an invaluable asset. The sensitivity analysis tool saved time by pointing the designer in the direction that needed to be taken in order to improve frame stiffness. In the end, this allowed for more time to be dedicated to the building and manufacturing and assembly of

the vehicle. The sensitivity analysis proved not only to be a great tool for this type of design work but it also has the potential to be adapted to aid in the design of any structure.

In the end, the optimization tool presented did not turn out to be the ultimate design tool. The number of combinations needing to be solved in such a short period of time overwhelmed the idea. However, the results of the small subset that was evaluated showed great potential. To have absolutely no human interaction required to complete the design of the frame would be a tremendous feat of ingenuity. It would, without a doubt, give any team the upper hand. With advancements in CPU speed and a more robust code, this tool could quickly become a very valuable engineering tool.

Testing and validation is an important part of any engineering process. Testing allows engineers to prove not only to themselves but to others, that what was designed is that which was built. Having a test rig such as the TSMM allows for a direct comparison from model to hardware. Comparing the data from the rig to analytical data showed that the correct loading scheme was achieved. The results of torsional stiffness showed that it can produce very accurate answers. This gives confirmation that the actual hardware will perform as it was designed to. Results boost team confidence and gives reassurance that the chassis can make it to the finish line. Having this testing process established plays a large role in communicating with design judges in a collegiate competition. The ability to relay that a $500,000 four post dynamic shaker system was modified to statically measure chassis torsional stiffness is an impressing and interesting conversation starter.

Having a test rig like the TSMM, shows design judges that your design innovation does not just stop at the car, but is continued into accurate testing and validation methods.

This also justifies that future designs can proceed analytically with only minimal testing and validation.

Design Tools

Beyond the design tools presented there is much more to consider. A script could

be developed to automatically take a Solid Edge model and turn it into a working

ANSYS frame model. The leap between the frame model to the chassis model would be

much more difficult. With the help of a Matlab GUI, it could be achieved. The notion of

having a set of points loaded into a Matlab GUI and then formatted into an ANSYS

database is very possible. The result would yield an entirely automated process, start to

finish, eliminating the need for the more complicated processes outlined in Chapters 2

and 3.

If the choice to completely automate the analysis process from Solid Edge to

ANSYS is not chosen, the recommended path is to make the solution routines a little

more user friendly. This could be completed with the use of a feature in ANSYS. The

scripts can be added in as a command in the toolbar. The result would be such that each

time the ANSYS GUI is opened, the commands to run the scripts are only one click

away.

The most difficult tool to write would be a geometry optimizer. The scripts

presented in this text do not take into account that, between the defined points, the

arrangement of tubes could be different. A script could be written to identify whether it

is more important for a frame member to be oriented at one angle versus another. A

script of this nature could be derived from the sensitivity routine. Components could be

defined such that at times they are meshed and at others, are not. This would measure the difference in torsional stiffness with and without this component in the frame.

Additionally, the link between modal analysis and experimental modal analysis could be better defined with the help of a cross-orthogonality script. This script would extract the modal vectors (mode shapes) of the analysis and do the same for the experimental data. These two vector pairs can then be compared for each mode and a better understanding of how well the analysis actually compared to experimental data.

Once the set of vectors are defined for each mode they can be compared for how parallel they are. This would be the ultimate modal analysis correlation tool.

The Taguchi Method could also be implemented to help optimize the frame. The

Taguchi Method was developed to optimize manufacturing processes, however it could be adapted to perform case studies on the frame. The Taguchi method utilizes orthogonal arrays. Orthogonal arrays are tables which define a minimum number of experiments to be able to understand the importance of one parameter versus another. When the data has been collected, signal to noise ratios are calculated for each parameter. The parameters with the largest signal to noise ratios are then considered more important [4].

Another optimization process that could considerably improve the frame design would be to implement the use of objective functions. A function could be developed, along with a set of inequalities, that when solved using differential calculus could generate the optimal frame design [15]. An example problem using objective functions has been illustrated in Chapter 2 of Reference 15. This optimization technique was also found to be in current Finite Element (F.E.) Programs and should be investigated to determine its value in improving future frame designs.

Torsional Stiffness Measuring Machine

The TSMM was designed and built because it is extremely versatile and possesses opportunities for improvement. There are some basic upgrades that could be made and some extensive ones. All of these upgrades should be completed to better understand the ability of the chassis to do its job and perform at its peak.

To begin, there are various minor modifications that should be made to the rig.

First, the holes that were created in the base of the each fixture were reamed to the size of the fixture bolts. These bolts when purchased were bowed. This did not allow for a very easy installation. There are two options that could be executed that would easily remedy this situation. Better grade bolts could be purchased or the sixteen holes could be reamed out with an over-sized reamer. Knowing that the bolts of this type, length and grade are expensive, the recommended way is to use the over-sized reamer.

The solid shocks designed for the TSMM were difficult to use because the correct rod ends were not available. Therefore, thin spacers needed to be created to hold the center-line of the solid shock at the correct height. Trying to install two spacers above and below the rod end inside the frame pickup tube presented a frustrating challenge. For the future, it is recommended that, each year, a custom set of solid shocks be made at the correct width of the shock mating interface. The other option would be to make a tapered sliding dovetail joint that could be adjusted for length and locked at the correct height. Depending on the construction of this joint, it may pose problems while testing.

The dovetail could potentially slip if it is not pinned. The recommended way to fix this issue is to make a custom set of solid shocks. Each year, a solid shock assembly should

be an automatic item to be fabricated by the suspension team. This solid shock assembly should be designed to be integrated into the TSMM.

To increase the confidence in the results of the TSMM data, an easy upgrade would be to acquire some steel pins to replace the “fuse” in the fixture. The solid brass fuses performed without any indication of yielding. However, the fuses were under constant load when vehicles were attached to the rig. Replacing these fuses with a material that has a higher shear modulus would be recommended.

For testing, a great addition to the TSMM would be to connect the two forward posts to move in unison with one button press of the controller. This would eliminate the pause from the movement sequence of each front post. Inherently, this would eliminate the need to identify the correct time period in which both post have been moved. In order to accomplish this, internal coding in the hydraulic controller software may be required.

This would probably involve some heavy “C” coding and would take quite a few months to integrate. A better solution would be to go back to the software design group and ask if this option could be added into the next revision of the software.

The TSMM was conceptualized and built to have many more capabilities than just a torsional stiffness measuring rig. The rig is capable of being setup to test suspension parameters. If a table was designed and built to hold the frame fixed, a single post could be translated while suspension parameters are measured. This type of testing eliminates the use of solid shocks and poses less harm to the car. This test would replace the need to travel to Goodyear to utilize their suspension parameter measuring machine and would give the Formula team that much more time to understand the current suspension design.

Having built and designed a suspension parameter measuring machine would also

provide more justification that the Formula Team understands the suspension and how it is suppose to perform, when presenting to the competition judges. The rig would need some modification to accomplish this. A three point sensor system would need to be developed. This could be done with the use of string potentiometers or perhaps a laser tracking system. In addition, a kinematic table would need to be developed to pitch and yaw the frame. The cost of materials and sensors to create this addition would probably overwhelm the budget and consume valuable design time. The system would take many years to develop. The software alone to process and create the curves would require the suspension team leader’s time and some heavy Matlab code training.

The more desirable addition would be to use the TSMM rig as a quick way to simulate on track conditions if weather or track availability presented issues. A Motec data acquisition system was purchased in 2007 for acquiring on track data. Information from the Motec data acquisition system could be used to produce a time history of displacement at each wheel. This data could be formatted as input into the four post simulation software. With the input established the simulation could be run and team members could closely monitor chassis performance. During the simulation, strain gauge information could be logged on any part of the vehicle. This would also provide the chance for team members to check operating clearances, which could warrant design changes and prevent hardware failure.

Figure 55: Commercial Semi-Dynamic Test Rig [9]

Figure 55 shows a commercially available rig to do this type of testing. In this instance a Nextel Cup series chassis has been installed and track conditions are simulated.

The rig is able to translate in all three translational degrees of freedom. This poses a problem for the TSMM, but could be remedied. The four post MTS system of the

TSMM was not designed to allow for in-plane translations. The posts have an air ride system that makes moving them much easier, but it requires a large demand for air. The air supply system could be upgraded to allow for all four posts to be run at the same time.

The other option is to place two steel plates underneath each post with an oil film in between. This is a relatively simple solution if oil is applied manually. A more permanent solution would be to use granite slabs attached to the floor with a steel top plate and an oil pump. This system if built properly would be fairly easy to maintain and would be dependable. In any case, the first two solutions would be more economical.

References

1. Aird, Forbes. Race Car Chassis: Design and Construction . Osceola:MBI, 1997

2. Sakkis, Tony. Anatomy & Development of the Indy Car . Osceola: MBI, 1994

3. Weissler, Paul “Body by the numbers.” Automotive Engineering International Sep. 2007: 26+

4. Roy, Ranjit. A Primer on the Taguchi Method . Dearborn, MI: Society of Manufacturing

Engineers, 1990

5. Beer, Ferdinand, E. Johnson, and John DeWolf. Mechanics of Materials . New York, NY:

McGraw Hill, 2001.

6. Perry, C., and H. R. Lissner. The Strain Gage Primer . New York, NY: McGraw Hill, 1962

7. Student Manual for Strain Gage Technology . Raleigh: North Carolina, 1992

8. Strain Gage Conditioner and Amplifier System Instruction Manual . Raleigh: North Carolina:

TD, 1992.

9. Monaghan, Matt “New Simulation Rig Help ‘Tighten’ Racecar Performance.” Automotive Engineering International Dec. 2007: 62-63

10. Adams, Herb. Chassis Engineering . New York, NY: HP Books, 1993

11. ANSYS Academic Research, v. 8.0

12. ANSYS Academic Research,8.0, Help System, Command Reference, ANSYS Inc.

13. ANSYS Academic Research 8.0, Help System, Element Reference, ANSYS, Inc.

14. Solid Edge Academic ,V17

15. Haftka, Raphael and Zafer G ϋrdal. Elements of Structural Optimization . Dordrecht,

Netherlands: Kluwer, 1992

Appendix A FEA Checklist Project Name: ______Date: ______Engineer: ______Reviewer: ______

Model Data

Jobname: ______Solved Using: (ANSYS Ver. ______Other______) # of Nodes: ______Analysis Type: ( Static Modal Thermal Other______) # of Elements:______Equation Solver: (Frontal PCG Block-Lanczos Other______) # of D.O.F.:______Hardware Used: ( Pentium HP Sun Other______) File size (.db):______Memory Required for Run (Total/Database):______/______File size (.rst):______Disk Space Required for Executing a Run:______Units: (English Metric) Run Time (CPU/Clock): ______/______Source of Geometry (Drawing #, CAD filename): ______Software used for Mesh Generation: (ANSYS PATRAN I-DEAS Other______) Model Description: ______Loading Description: ______Restraint Description: ______

Model Checks Input Check Runs Model Dimensions Apply Unit Displacement Sufficient Mesh Density Apply Uniform Temperature No Cracks/Discontinuity Apply 1G Acceleration No Distorted or Warped Elements Modal Analysis (Modes and Frequencies) Correct and Consistent Units for Properties/Loads Deformation Check Element Type Keyopts Flexibility Check Component Separation with Gap Elements

Temperature (TREF, TUNIF, and applied temps) Heat Transfer Coefficients and Gas Temperatures View and/or Plot Model by Displacements and Restraints Element Types Couples Real Constants Constraint Equations Material Properties Pressures Boundary Conditions Forces and/or Moments Rotational Velocity and/or Accelerations View and/or Print Listing by Rotated Nodes Element Types Large Deflection Real Constants Stress Stiffening Material Properties

Output 70 Check Reaction Forces Check Mass vs. Supplied Data or Hand Calc’s

Appendix B Scripts

Torsional Stiffness Script ! tstiff.txt !******************************************************************** ! W.T. Steed ~ 5/14/07 ! Step 4: Define what node to take displacement from to ! University of Cincinnati ! calculate the angle the frame twisted ! EMAIL: [email protected] !******************************************************************** ! TEL:(513) 260-8955 dnode=fc1 ! !-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- ! PURPOSE: Calculates the torsional stiffness of an SAE !******************************************************************** ! Frame ! Step 5: Apply Boundary Conditions ! OUTP UT: Torsional Stiffness to background screen and to ! !************************************************** ****************** tstiff variable /prep7 !-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- allsel ! d,d1,all !******************************************************************** d,d2,all ! Notes: d,d3,all ! - This script is meant to be used with a Frame Model in ANSYS d,d4,all ! - Meant be run INTERACTIVELY ! - Assumes that CYLINDRICAL coordinate systems ! Force ! 200-205 have been created at the loading and restraint f,fc1,fz,fval ! locations on the frame f,fc2,fz,-fval !********************************************************************

!******************************************************************** !******************************************************************** ! Step 1: Define Track Width ! Step 6: Define Static Solution !******************************************************************** !******************************************************************** couple_length=17/12 ! Input in feet /solu antype,0 !******************************************************************** allsel ! Step 2: Define Restraint Nodes !******************************************************************** !******************************************************************** !d1=7158 ! Step 7: Solve !d2=7190 !******************************************************************** !d3=7202 solve !d4=7236 csys,200 !******************************************************************** nsel,s,loc,x,0,0.1 ! Step 8: Post Process Results *get,d1,node,0,num,min !******************************************************************** csys,201 /post1 nsel,s,loc,x,0,0.1 set,1 *get,d2,node,0,num,min csys,0 csys,202 *afun,deg nsel,s,loc,x,0,0.1 *get,dnode_u,node,dnode,u,z *get,d3,node,0,num,min *get,dnode_y_loc,node,fc2,loc,y csys,203 theta=atan(dnode_u/dnode_y_loc) nsel,s,loc,x,0,0.1 tstiff=((couple_length*fval)/theta) *get,d4,node,0,num,min

!******************************************************************** ! Step 3: Define Force Nodes and Value !******************************************************************** fval=100 !f1=6614 !f2=6643 csys,204 nsel,s,loc,x,0,0.1 *get,fc1,node,0,num,min csys,205 nsel,s,loc,x,0,0.1 *get,fc2,node,0,num,min

Sensitivity/Eigen Value Analysis Script

! tstif_eigen_analysis.ain allsel ! W.T.Steed 11/20/06 allsel,below,volu ! University of Cincinnati lsel,inve ! EMAIL: [email protected] ! Set Section number and material to begin the first ! TEL:(513) 260-8955 mesh with secnum,1 !-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- mat,1 ! PURPOSE: cmsel,all ! - Calculates Torsional Stiffness and Computes first 6 Modes ! Loop through each cross section ! - To track how modes of vibration change with tor. stiffness *DO,jj,1,17,1 ! OUTPUT: EIGEN.TXT cmsel,s,line%ii% !-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- /prep7 lclear,all !******************************************************************** latt,,,,,,,jj ! Notes: secnum,jj ! - This script is meant to be used with a Frame Model in ANSYS lmesh,all ! - It should be run in BATCH Mode ! - It assumes that CYLINDRICAL coordinate systems 200-205 couple_length=17/12 ! have been created at the loading and restraint locations on the ! frame csys,200 !******************************************************************** nsel,s,loc,x,0,0.1 *get,d1,node,0,num,min !******************************************************************** csys,201 ! Instructions: nsel,s,loc,x,0,0.1 ! 1. Create a component for each pair of symmetric members in the *get,d2,node,0,num,min ! FRAME Model csys,202 ! - Name each component "line1, line2, line3, etc." nsel,s,loc,x,0,0.1 ! - Note how many components there are *get,d3,node,0,num,min ! csys,203 ! ******Make sure that there are no lines from the engine in any of nsel,s,loc,x,0,0.1 ! these components***** *get,d4,node,0,num,min ! ! 2. Make sure there are 17 sections defined, ensure that section fval=100 ! 17 is the same as section 1 csys,204 ! nsel,s,loc,x,0,0.1 ! 3. Save a copy of the Database *get,fc1,node,0,num,min ! csys,205 ! 4. Modify the /filn command to be /filn,"database name" nsel,s,loc,x,0,0.1 ! *get,fc2,node,0,num,min ! 5. Modify the number 39 with the number of the "line" ! components in the database dnode=fc1 ! ! 6. Execute in Batch Mode and watch check EIGEN.txt every so /prep7 ! often allsel !******************************************************************** d,d1,all d,d2,all !******************************************************************** d,d3,all ! Step 1: Read in Database d,d4,all !******************************************************************** /batch ! Force /filn,07-tstiff-eigen f,fc1,fz,fval resu f,fc2,fz,-fval

!******************************************************************** /solu ! Step 2: Define initial parameters antype,0 !******************************************************************** allsel /prep7 solve *get,max_secp,secp,num,max *get,count_line,line,0,count /post1 *DIM,eigen_stiff,array,max_secp,7,39 set,1 csys,0 !******************************************************************** *afun,deg ! Step 3: Begin Solution Routine *get,dnode_u,node,dnode,u,z !******************************************************************** *get,dnode_y_loc,node,fc2,loc,y *DO,ii,1,39,1 theta=atan(dnode_u/dnode_y_loc) /prep7 tstiff=((couple_length*fval)/theta) Page 1 Page 2

! Store torsional stiffness in first column of eigen_stiff array

eigen_stiff(jj,1,ii)=tstiff

! Clear Boundary Conditions /prep7 lsclear,all ! Start Modal Analysis /solu antype,modal MSAVE,0 MODOPT,LANB,12 EQSLV,SPAR MXPAND,0, , ,0 LUMPM,0 PSTRES,0 MODOPT,LANB,12,0,10000, ,OFF solve /solu ! Loop through Modes 7 to 12 and store in colums 2 ! through 7 of eigen_stiff *DO,kk,2,7,1 xx=kk+5 *get,freq,mode,xx,freq eigen_stiff(jj,kk,ii)=freq *ENDDO

*ENDDO

/prep7 ! Save all Parameters to eigen.txt PARSAV,ALL,'eigen','txt',' ' allsel

*ENDDO Page 3

Create Combo Script ! create_combo.txt counter3=counter3+1 ! W.T.Steed *IF,counter3,eq,4097,then ! University of Cincinnati counter3=1 ! EMAIL: [email protected] dummy3=dummy3+1 ! TEL:(513) 260-8955 *ENDIF *IF,dummy3,eq,17,then !-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= dummy3=1 ! PURPOSE:- Creates Matrix of all possible combinations for optimization *ENDIF ! OUTPUT: COMBO Matrix in ANSYS Parameters COMBO(i,1)=dummy3 !-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= *ENDDO !******************************************************************** ! Note: ! 1. Takes approximately ten minutes to execute

!********************************************************************

!******************************************************************** ! Instructions: ! 1. Run interactively in any ANSYS database ! 2. Save Database ! 3. Run Optimization Routine !********************************************************************

! Dimension the "COMBO" Matrix *DIM,COMBO,array,65536,4,1

*DO,i,1,4096,1 *DO,j,1,16,1 x=(i-1)*16 COMBO(x+j,4)=j *ENDDO *ENDDO counter1=0 counter2=0 counter3=0 dummy1=1 dummy2=1 dummy3=1

*DO,i,1,65536,1 counter1=counter1+1 *IF,counter1,eq,17,then counter1=1 dummy1=dummy1+1 *ENDIF *IF,dummy1,eq,17,then dummy1=1 *ENDIF COMBO(i,3)=dummy1 counter2=counter2+1 *IF,counter2,eq,257,then counter2=1 dummy2=dummy2+1 *ENDIF *IF,dummy2,eq,17,then dummy2=1 *ENDIF COMBO(i,2)=dummy2

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Optimization Script

! Optimization.txt XAREA(1,1)=x1 ! W.T.Steed XAREA(2,1)=x2 ! University of Cincinnati XAREA(3,1)=x3 ! EMAIL: [email protected] XAREA(4,1)=x4 ! TEL:(513) 260-8955 XAREA(5,1)=x5 !-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- XAREA(6,1)=x6 ! PURPOSE: XAREA(7,1)=x7 ! - Optimize 4 components of the Frame Model XAREA(8,1)=x8 ! OUTPUT: Paramaeters.txt XAREA(9,1)=x9 !-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- XAREA(10,1)=x10 XAREA(11,1)=x11 !******************************************************************** XAREA(12,1)=x12 ! Notes: XAREA(13,1)=x13 ! - This script is meant to be used with a Frame Model in ANSYS XAREA(14,1)=x14 ! - It should be run in BATCH Mode XAREA(15,1)=x15 ! - It assumes that CYLINDRICAL coordinate systems 200-205 XAREA(16,1)=x16 ! have been created at the loading and restraint locations on the ! frame ! - This analysis takes multiple weeks *get,starttime,active,0,time,cpu ! - Analysis blocks may need to be split into smaller block sizes *DO,i,1,65536,1 ! i.e. 1-65536 may need to be 1-20000, the 20001 to 40000, etc. /prep7 ! - Analysis may be done on multiple computers to speed solution cmsel,s,line4 !******************************************************************** lclear,all secnum=COMBO(i,1) !******************************************************************** latt,,,,,,,secnum ! Instructions: lmesh,all ! 1. Run the sensitivity analysis (tstiff_eigen_analysis.ain) cmsel,s,line12 ! 2. Post process the results and determine the 4 most sensitive lclear,all secnum=COMBO(i,2) ! components to torsional stiffness latt,,,,,,,secnum ! 3. Find the four commands "cmsel,s,line#" in this script and change lmesh,all ! "#" to the "line" component numbers to reflect the new results cmsel,s,line24 ! 4. Start/resume the new frame database in ANSYS and run the lclear,all ! create_combo.txt script secnum=COMBO(i,3) ! 5. Save the database, exit, and make a copy of it latt,,,,,,,secnum lmesh,all ! cmsel,s,line7 ! 6. Modify the /filn command to be /filn,"database name" lclear,all ! secnum=COMBO(i,4) ! 7. Execute in Batch Mode and check parameters.txt every so latt,,,,,,,secnum ! often lmesh,all !******************************************************************** /batch, *DO,j,1,16 lsel,s,sec,,j /filn,07_Optimization *get,lselect,line,0,count resu *IF,lselect,eq,0,then lsum%j%=0 *DIM,TSTIF,ARRAY,65536,1,1 *ELSEIF,lselect,ne,0 *DIM,RATIO,ARRAY,65536,1,1 lsum *DIM,ITERWEIGHT,ARRAY,65536,1,1 *get,lsum%j%,line,0,leng *DIM,WEIGHT,ARRAY,16,1,1 *ENDIF WEIGHT(j,1)=lsum%j%*XAREA(j,1)*dens *DIM,XAREA,ARRAY,16,1,1 *ENDDO dens=0.284 *vscfun,sumweight,sum,WEIGHT ITERWEIGHT(i,1)=sumweight *Get,x1,secp,1,prop,area *Get,x2,secp,2,prop,area *Get,x3,secp,3,prop,area *Get,x4,secp,4,prop,area *Get,x5,secp,5,prop,area

*Get,x6,secp,6,prop,area *Get,x7,secp,7,prop,area *Get,x8,secp,8,prop,area *Get,x9,secp,9,prop,area *Get,x10,secp,10,prop,area *Get,x11,secp,11,prop,area *Get,x12,secp,12,prop,area

*Get,x13,secp,13,prop,area *Get,x14,secp,14,prop,area *Get,x15,secp,15,prop,area *Get,x16,secp,16,prop,area Page 1 Page 2

! This is the distance in ft between the two forces

couple_length=17/12

csys,200 nsel,s,loc,x,0,0.1 *get,d1,node,0,num,min csys,201 nsel,s,loc,x,0,0.1 *get,d2,node,0,num,min csys,202 nsel,s,loc,x,0,0.1 *get,d3,node,0,num,min csys,203 nsel,s,loc,x,0,0.1 *get,d4,node,0,num,min

fval=100 csys,204 nsel,s,loc,x,0,0.1 *get,fc1,node,0,num,min csys,205 nsel,s,loc,x,0,0.1 *get,fc2,node,0,num,min

! Enter in the node where vertical displacement should be taken from

dnode=fc1

! Apply Loading condition

! Displacement constraints

/prep7 allsel d,d1,all d,d2,all d,d3,all d,d4,all

! Force f,fc1,fz,-fval f,fc2,fz,fval

/solu antype,0 allsel solve

/post1 set,1 csys,0 *afun,deg *get,dnode_u,node,dnode,u,z *get,dnode_y_loc,node,fc2,loc,y theta=atan(dnode_u/dnode_y_loc) tstiff=((couple_length*fval)/theta)

TSTIF(i,1)=tstiff RATIO(i,1)=tstiff/sumweight /prep7 *get,endtime,active,0,time,cpu PARSAV,ALL,'parameters','txt',' ' *ENDDO fini /exit,nosave

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TSMM Post-Processing Script (ctorsion.m) function[avgtstiff]=ctorsion(data) % Average the two force data streams % ctorsion.m avg(i)=((abs(ch9_avg(i+1)- % Thomas Steed ch9_avg(1))+(abs(ch10_avg(i+1)-ch10_avg(1)))))/2; % University of Cincinnati % Calculate the degree of twist % E-MAIL: [email protected] deg1(i)=atan((abs(ch1_avg(i+1)-ch1_avg(1)))/24)*(180/pi); % TEL: (513) 260-8955 deg2(i)=atan((abs(ch3_avg(i+1)-ch3_avg(1)))/24)*(180/pi); %************************************************************************** deg(i)=deg1(i)-deg2(i); % Description: Calculates the Experimental Torsional Stiffness of a FSAE % Calculate the numerator to the tstiff equation % chassis for data acquired on the Tosional Stiffness Measuring Machine num(i)=avg(i)*twidth; %************************************************************************** % Caluclate the torsional stiffness tstiff(i)=num(i)/deg(i); %~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ end % Instructions: % 1. Rename the time_data_sum variable from the TSMM *.mat to a variable % called data %------% 2. Issue the command "ctorsion(data)" at the Matlab prompts % Step 6: Calculate the average Torsional Stiffness from %~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ all data steps %------%------avgtstiff=sum(tstiff)/length(tstiff); % Step 1: Resample data to smaller working size %------ch1=data(1:500:length(data),1); % Shaker LVDT 1 ch2=data(1:500:length(data),2); % Shaker LVDT 2 ch3=data(1:500:length(data),3); % Shaker LVDT 3 ch4=data(1:500:length(data),4); % Shaker LVDT 4 ch9=data(1:500:length(data),9); % Strain Gage Force ch10=data(1:500:length(data),10); % Strain Gage Force

%------% Step 2: % Calculate the difference between the next point and the point prior to % locate where the next data step is %------for i=1:length(ch1)-1 j=i+1; diff1(i,1)=ch1(i)-ch1(j); diff2(i,1)=ch2(i)-ch2(j); end

%------% Step 3: Find the index where the step occurs and determine wether the % index is a point where the load is being applied or relaxed %------

% Find the index where the shaker movement occurs indx1=find((diff1)>=0.010); indx2=find((diff2)>=0.010); indx3=find((diff1)<=-0.010); indx4=find((diff2)<=-0.010); if length(indx1)

%------% Step 4: Calculate the average for each data step %------ch1_avg(1)=sum(ch1(1:indx1(1))/length(1:indx1(1))); ch2_avg(1)=sum(ch2(1:indx1(1))/length(1:indx1(1))); ch3_avg(1)=sum(ch3(1:indx1(1))/length(1:indx1(1))); ch4_avg(1)=sum(ch4(1:indx1(1))/length(1:indx1(1))); ch9_avg(1)=sum(ch9(1:indx1(1))/length(1:indx1(1))); ch10_avg(1)=sum(ch10(1:indx1(1))/length(1:indx1(1))); for ii=1:length(indx2)-1 ii=ii+1; ch1_avg(ii)=sum(ch1(indx2(ii-1)+1:indx1(ii)))/length(indx2(ii-1)+1:indx1(ii)); ch2_avg(ii)=sum(ch2(indx2(ii-1)+1:indx1(ii)))/length(indx2(ii-1)+1:indx1(ii)); ch3_avg(ii)=sum(ch3(indx2(ii-1)+1:indx1(ii)))/length(indx2(ii-1)+1:indx1(ii)); ch4_avg(ii)=sum(ch4(indx2(ii-1)+1:indx1(ii)))/length(indx2(ii-1)+1:indx1(ii)); ch9_avg(ii)=sum(ch9(indx2(ii-1)+1:indx1(ii)))/length(indx2(ii-1)+1:indx1(ii)); ch10_avg(ii)=sum(ch10(indx2(ii-1)+1:indx1(ii)))/length(indx2(ii-1)+1:indx1(ii)); end ch9_avg(ii)=sum(ch9(indx2(ii-1)+1:indx2(ii)))/length(indx2(ii-1)+1:indx2(ii)); ch10_avg(ii)=sum(ch10(indx2(ii-1)+1:indx2(ii)))/length(indx2(ii-1)+1:indx2(ii));

%------% Step 5: Calculate Torsional Stiffness for each Step %------twidth=4; % ft for i=1:length(indx2)-1 Page 1 Page 2

Appendix C: ITER06 Sensitivity Analysis

'06 Frame Component 1 Sensitivity '06 Frame Component 2 Sensitivity 650 690 y = 0.6212x + 639.36 y = 3.0444x + 635.54 648 R2 = 0.9743 680

646 670

644 660

642 650

640 640 Torsional Stiffness (Ft.*lb)/Deg. Torsional Stiffness (Ft.*lb)/Deg.

638 630 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1 2 3 4 5 6 7 8 9 10 11 12 13 1415 16 Ansys Cross Section Number Ansys Cross Section Number

'06 Frame Component 3 Sensitivity '06 Frame Component 4 Sensitivity 654 658

652 656 y = 0.83x + 642.32 y = 0.7753x + 638.56 654 650 652 648 650

646 648

646 644 644 642 642 Torsional Stiffness (Ft.*lb)/Deg. Torsional (Ft.*lb)/Deg. Stiffness 640 640

638 638 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Ansys Cross Section Number Ansys Cross Section Number

'06 Frame Component 5 Sensitivity '06 Frame Component 6 Sensitivity 643 720

y = 0.1869x + 639.15 710 642 y = 4.0564x + 641.77 700 642 690

641 680

641 670

660 640 650

Torsional Stiffness (Ft.*lb)/Deg. 640 Torsional Stiffness (Ft.*lb)/Deg. 640

639 630 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1 2 3 4 5 6 7 8 9 10 11 12 13 1415 16 Ansys Cross Section Number Ansys Cross Section Number 78

'06 Frame Component 7 Sensitivity '06 Frame Component 8 Sensitivity 680 648

647 675 y = 2.3035x + 638.01 y = 0.5019x + 638.77 670 646 645 665 644 660 643 655 642 650 641 645 640 Torsional Stiffness (Ft.*lb)/Deg. Torsional Stiffness (Ft.*lb)/Deg. 640 639

635 638 1 2 3 4 5 6 7 8 9 10 11 1213 1415 16 1 2 3 4 5 6 7 8 9 10 11 1213 1415 16 Ansys Cross Section Number Ansys Cross Section Number

'06 Frame Component 9 Sensitivity '06 Frame Component 10 Sensitivity 644 644

643 643

643 643 y = 0.2142x + 639.04 y = 0.2142x + 639.04 642 642

642 642

641 641

640 640 Torsional Stiffness (Ft.*lb)/Deg. Torsional Stiffness (Ft.*lb)/Deg. 640 640

639 639 1 2 3 4 5 6 7 8 9 1011 12 13 14 15 16 1 2 3 4 5 6 7 8 9 10 11 12 1314 15 16 Ansys Cross Section Number Ansys Cross Section Number

'06 Frame Component 11 Sensitivity '06 Frame Component 12 Sensitivity 649 644 648 y = 0.5504x + 638.48 644 y = 0.2705x + 639 647 643 646 643 645 642 644 642 643 641 642 641 641 640 640 Torsional (Ft.*lb)/Deg. Stiffness Torsional Stiffness (Ft.*lb)/Deg. 639 640

638 639 1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 1 2 3 4 5 6 7 8 9 10 11 12 1314 15 16 Ansys Cross Section Number Ansys Cross Section Number

'06 Frame Component 13 Sensitivity '06 Frame Component 14 Sensitivity 641 641

641 y = 0.0691x + 639.34 641 y = 0.0835x + 639.35

640 640

639 639 Torsional Stiffness (Ft.*lb)/Deg. Stiffness Torsional Torsional Stiffness (Ft.*lb)/Deg. Stiffness Torsional 639 639 1 2 3 4 5 6 7 8 9 1011 12 13 1415 16 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Ansys Cross Section Number Ansys Cross Section Number

'06 Frame Component 15 Sensitivity '06 Frame Component 16 Sensitivity 660 656.000

y = 1.2156x + 638.25 654.000 655 y = 0.943x + 637.97 652.000

650.000 650 648.000

646.000 645 644.000 ((Ft.*lb)/Deg.))

Torsional Stiffness Stiffness Torsional 642.000 640 640.000 Torsional Stiffness (Ft.*lb)/Deg. Stiffness Torsional 638.000 635 1 2 3 4 5 6 7 8 9 10111213141516 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Ansys Cross Section Number Ansys Cross Section Number

'06 Frame Component 17 Sensitivity '06 Frame Component 18 Sensitivity 665 685 y = 1.441x + 637.62 660 680 y = 2.4959x + 639.86 675

655 670

665 650 660

655 645 650

640 645 Torsional Stiffness (Ft.*lb)/Deg. Stiffness Torsional Torsional Stiffness (Ft.*lb)/Deg. Stiffness Torsional 640 635 635 1 2 3 4 5 6 7 8 9 10111213141516 1 2 3 4 5 6 7 8 9 10 1112 1314 1516 Ansys Cross Section Number Ansys Cross Section Number

'06 Frame Component 19 Sensitivity '06 Frame Component 20 Sensitivity 645 658 644 656 y = 0.9999x + 639.82 y = 0.2811x + 639.51 644 654 643 652 643 650 642 648 642 646 641 644 641 642 640 Torsional Stiffness (Ft.*lb)/Deg. Stiffness Torsional Torsional Stiffness (Ft.*lb)/Deg. Stiffness Torsional 640 640 638 639 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1 2 3 4 5 6 7 8 9 1011 121314 1516 Ansys Cross Section Number Ansys Cross Section Number

'06 Frame Component 21 Sensitivity '06 Frame Component 22 Sensitivity 720 670

710 y = 4.4591x + 638.96 665 y = 1.6508x + 638 700 660 690

680 655

670 650 660 645 650 Torsional Stiffness (Ft.*lb)/Deg. Stiffness Torsional Torsional Stiffness (Ft.*lb)/Deg. Stiffness Torsional 640 640

630 635 1 2 3 4 5 6 7 8 9 101112 13141516 1 2 3 4 5 6 7 8 9 10 11121314 1516 Ansys Cross Section Number Ansys Cross Section Number

'06 Frame Component 23 Sensitivity '06 Frame Component 24 Sensitivity 648 665 647 y = 0.4772x + 639.85 660 y = 1.4349x + 636.83 646

645 655

644 650 643

642 645

641 640 Torsional Stiffness (Ft.*lb)/Deg. Stiffness Torsional Torsional Stiffness (Ft.*lb)/Deg. Stiffness Torsional 640

639 635 1 2 3 4 5 6 7 8 9 101112 13141516 1 2 3 4 5 6 7 8 9 1011 1213 1415 16 Ansys Cross Section Number Ansys Cross Section Number

ITER06 Frame Component 26 Sensitivity '06 Frame Component 25 Sensitivity 820 675 800 y = 9.0182x + 651.42 670 y = 1.8111x + 640.66 780 760 665 740 660 720

655 700 680 650 660

645 640 Torsional Stiffness (Ft.*lb)/Deg. TorsionalStiffness 620

Torsional Stiffness (Ft.*lb)/Deg. Stiffness Torsional 640 600 635 1 2 3 4 5 6 7 8 9 10 11121314 1516 1 2 3 4 5 6 7 8 9 10111213 141516 Ansys Cross Section Number Ansys Cross Section Number

'06 Frame Component 27 Sensitivity '06 Frame Component 28 Sensitivity 720 639 710 y = 3.8566x + 648.45 639 y = -5E-12x + 639.47 700

690 639

680 639 670

660 639

650 639 Torsional Stiffness (Ft.*lb)/Deg. Stiffness Torsional Torsional Stiffness (Ft.*lb)/Deg. Stiffness Torsional 640

630 639 1 2 3 4 5 6 7 8 9 101112 1314 1516 1 2 3 4 5 6 7 8 9 101112 13141516 Ansys Cross Section Number Ansys Cross Section Number

'06 Frame Component 29 Sensitivity '06 Frame Component 30 Sensitivity 639 643

639 642 y = 0.1836x + 639.01 639 642 639

639 641

639 y = -3E-09x + 639.47 640 639

Torsional Stiffness (Ft.*lb)/Deg. Stiffness Torsional 640 Torsional Stiffness (Ft.*lb)/Deg. Stiffness Torsional 639

639 639 1 2 3 4 5 6 7 8 9 10 1112 1314 1516 1 2 3 4 5 6 7 8 9 1011 1213141516 Ansys Cross Section Number Ansys Cross Section Number

'06 Frame Component 31 Sensitivity '06 Frame Component 32 Sensitivity 670 639

639 665 y = 1E-09x + 639.47 y = 1.5052x + 640.32 639

660 639

639 655 639 650 639

645 639

639

Torsional Stiffness (Ft.*lb)/Deg. Stiffness Torsional 640 Torsional Stiffness (Ft.*lb)/Deg. Stiffness Torsional 639

635 639 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1 2 3 4 5 6 7 8 9 101112 13 141516 Ansys Cross Section Number Ansys Cross Section Number

'06 Frame Component 33 Sensitivity 639 639

639 639 639 639 639 y = -1E-09x + 639.47 639 639 639 Torsional Stiffness (Ft.*lb)/Deg. Stiffness Torsional 639 639 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Ansys Cross Section Number

Appendix D: ITER07 Sensitivity Analysis

'07 Frame Component 1 Sensitivity '07 Frame Component 2 Sensitivity 547 575

546 y = 0.5199x + 538.16 570 y = 2.0367x + 539.54 545 565 544 560 543

542 555

541 550 540 545 539 540 Torsional Stiffness (Ft.*lb)/Deg. Torsional Stiffness (Ft.*lb)/Deg. 538

537 535 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Ansys Cross Section Number Ansys Cross Section Number

'07 Frame Component 3 Sensitivity '07 Frame Component 4 Sensitivity 539 630 620 y = 4.8064x + 542.75 539 y = 0.0683x + 537.81 610

600 539 590

538 580 570 538 560 550 538 Torsional Stiffness (Ft.*lb)/Deg.

Torsional Stiffness (Ft.*lb)/Deg. 540

538 530 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1 2 3 4 5 6 7 8 9 10111213141516 Ansys Cross Section Number Ansys Cross Section Number

'07 Frame Component 5 Sensitivity '07 Frame Component 6 Sensitivity 565 900

850 y = 15.943x + 577.15 560 y = 1.1907x + 542.21 800 555 750

550 700

650 545 600 540

Torsional Stiffness (Ft.*lb)/Deg. Torsional Stiffness 550 Torsional Stiffness (Ft.*lb)/Deg.

535 500 1 2 3 4 5 6 7 8 9 10 11 1213 1415 16 1 2 3 4 5 6 7 8 9 10 11121314 1516 Ansys Cross Section Number Ansys Cross Section Number

'07 Frame Component 7 Sensitivity '07 Frame Component 8 Sensitivity 585 552 580 y = 2.7754x + 535.57 550 y = 0.7183x + 538.45 575 548 570

565 546

560 544 555 542 550 540 545

Torsional Stiffness (Ft.*lb)/Deg. Torsional Stiffness 538 540 Torsional(Ft.*lb)/Deg. Stiffness

535 536 1 2 3 4 5 6 7 8 9 1011 1213 1415 16 1 2 3 4 5 6 7 8 9 101112 13 14 15 16 Ansys Cross Section Number Ansys Cross Section Number

'07 Frame Component 9 Sensitivity 565 y = 1.1907x + 542.21 560

555

550

545

540 Torsional Stiffness (Ft.*lb)/Deg. Torsional Stiffness

535 1 2 3 4 5 6 7 8 9 10 111213141516 Ansys Cross Section Number

'07 Frame Component 10 Sensitivity '07 Frame Component 11 Sensitivity 554 545

552 y = 0.8929x + 537.13 544 y = 0.3962x + 536.98 550 543 548 542 546 541 544 540 542

540 539 Torsional Stiffness (Ft.*lb)/Deg.

538 Torsional Stiffness (Ft.*lb)/Deg. 538

536 537 1 2 3 4 5 6 7 8 9 10 1112 13141516 1 2 3 4 5 6 7 8 9 101112 13141516 Ansys Cross Section Number Ansys Cross Section Number

'07 Frame Component 12 Sensitivity '07 Frame Component 13 Sensitivity 610 550

600 y = 4.3827x + 533.68 548 y = 0.7807x + 535.72

590 546

580 544

570 542

560 540

550 538

Torsional Stiffness (Ft.*lb)/Deg. 540 536 Torsional Stiffness (Ft.*lb)/Deg.

530 534 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1 2 3 4 5 6 7 8 9 10111213 141516 Ansys Cross Section Number Ansys Cross Section Number

'07 Frame Component 14 Sensitivity '07 Frame Component 15 Sensitivity 542 541

541 y = 0.2011x + 537.49 540 y = 0.1301x + 537.66 541 540 540

540 539

539 539 539 538

538 Torsional Stiffness (Ft.*lb)/Deg. Torsional Stiffness (Ft.*lb)/Deg.

538 538 1 2 3 4 5 6 7 8 9 10111213 141516 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Ansys Cross Section Number Ansys Cross Section Number '07 Frame Component 16 Sensitivity '07 Frame Component 17 Sensitivity 542 540

540 541 y = 0.108x + 537.83 y = 0.2083x + 537.7 539 541 539

540 539

540 539 539 539 538 539 538 Torsional Stiffness (Ft.*lb)/Deg. Stiffness Torsional Torsional Stiffness (Ft.*lb)/Deg. 538 538

538 538 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1 2 3 4 5 6 7 8 9 10 11121314 1516 Ansys Cross Section Number Ansys Cross Section Number '07 Frame Component 18 Sensitivity '07 Frame Component 19 Sensitivity 547 565 546 y = 0.5635x + 536.64 560 y = 1.4437x + 536.02 545 544 555 543 542 550 541

540 545 539

538 540 Torsional Stiffness (Ft.*lb)/Deg. Torsional Stiffness (Ft.*lb)/Deg. 537 536 535 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Ansys Cross Section Number Ansys Cross Section Number

'07 Frame Component 20 Sensitivity '07 Frame Component 21 Sensitivity 575 550 y = 2.1857x + 536.25 570 548 y = 0.6915x + 537.65

565 546 560 544 555 542 550 540 545

540 538 Torsional Stiffness (Ft.*lb)/Deg. Torsional Stiffness (Ft.*lb)/Deg.

535 536 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Ansys Cross Section Number Ansys Cross Section Number

'07 Frame Component 22 Sensitivity '07 Frame Component 23 Sensitivity 546 547 545 y = 0.4402x + 538.2 546 y = 0.4359x + 539.16 544 545 544 543 543 542 542 541 541 540 540

539 539 538 Torsional Stiffness (Ft.*lb)/Deg.

Torsional Stiffness (Ft.*lb)/Deg. 538

537 537 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Ansys Cross Section Number Ansys Cross Section Number

'07 Frame Component 24 Sensitivity '07 Frame Component 25 Sensitivity 600 543 542 y = 0.2249x + 538.5 590 y = 3.2324x + 540.19 542

580 541 541 570 540

560 540 539 550 539

540 Torsional Stiffness (Ft.*lb)/Deg. 538 Torsional Stiffness (Ft.*lb)/Deg.

530 538 1 2 3 4 5 6 7 8 9 10 111213 141516 1 2 3 4 5 6 7 8 9 1011 121314 15 16 Ansys Cross Section Number Ansys Cross Section Number

'07 Frame Component 26 Sensitivity '07 Frame Component 27 Sensitivity 575 550

570 y = 1.9791x + 536.93 548 y = 0.6604x + 538.7 565 546 560 544 555 542 550 540 545

538 Torsional Stiffness (Ft.*lb)/Deg.

Torsional Stiffness (Ft.*lb)/Deg. 540

535 536 1 2 3 4 5 6 7 8 9 1011 1213 14 1516 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Ansys Cross Section Number Ansys Cross Section Number

'07 Frame Component 28 Sensitivity '07 Frame Component 29 Sensitivity 547 570 546 y = 0.4729x + 538.08 565 y = 1.8494x + 534.66 545

544 560

543 555 542 550 541

540 545 539 540 Torsional Stiffness (Ft.*lb)/Deg.

Torsional Stiffness (Ft.*lb)/Deg. 538

537 535 1 2 3 4 5 6 7 8 9 10 11 1213 14 15 16 1 2 3 4 5 6 7 8 9 10 11 12 1314 1516 Ansys Cross Section Number Ansys Cross Section Number

'07 Frame Component 30 Sensitivity '07 Frame Component 31 Sensitivity 540 541 540 y = 0.0981x + 538.09 y = -0.0547x + 539.53 540 539

539 540 539

539 539

539 539 538

538 538 Torsional Stiffness (Ft.*lb)/Deg. Torsional Stiffness (Ft.*lb)/Deg. 538

538 538 1 2 3 4 5 6 7 8 9 1011 12 1314 1516 1 2 3 4 5 6 7 8 9 10 11121314 1516 Ansys Cross Section Number Ansys Cross Section Number

'07 Frame Component 32 Sensitivity '07 Frame Component 33 Sensitivity 539 539

539 y = 0.0729x + 538.11 539 y = 0.0386x + 538.03

539 539 538 539 538 539 538 538 538 538 538 538 Torsional Stiffness (Ft.*lb)/Deg.

Torsional Stiffness (Ft.*lb)/Deg. 538

538 538 1 2 3 4 5 6 7 8 9 1011 12 13 14 1516 1 2 3 4 5 6 7 8 9 10 1112 1314 1516 Ansys Cross Section Number Ansys Cross Section Number

'07 Frame Component 34 Sensitivity '07 Frame Component 35 Sensitivity 541 600

590 540 y = 0.1417x + 537.63 y = 1E-10x + 537.93 580

540 570 560

539 550

540 539 530

538 520 Torsional Stiffness (Ft.*lb)/Deg. Torsional Stiffness (Ft.*lb)/Deg. 510

538 500 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1 2 3 4 5 6 7 8 9 10 11 1213 1415 16 Ansys Cross Section Number Ansys Cross Section Number

'07 Frame Component 36 Sensitivity '07 Frame Component 37 Sensitivity 544 538 538 543 y = 0.2939x + 538.53 y = 5E-10x + 537.93 538

542 538 538 541 538 538 540 538 539 538 538 538 Torsional Stiffness (Ft.*lb)/Deg. Torsional Stiffness (Ft.*lb)/Deg. 538

537 538 1 2 3 4 5 6 7 8 9 10 11 1213 1415 16 1 2 3 4 5 6 7 8 9 1011 12 1314 1516 Ansys Cross Section Number Ansys Cross Section Number

'07 Frame Component 38 Sensitivity '07 Frame Component 39 Sensitivity 560 543 y = 1.2312x + 536.63 543 y = 0.2854x + 537.78 542 555 542 541 550 541 540 545 540 539

540 (Ft.*lb)/Deg. Stiffness Torsional 539

Torsional Stiffness (Ft.*lb)/Deg. 538

535 538 1 2 3 4 5 6 7 8 9 1011 12 13 1415 16 1 2 3 4 5 6 7 8 9 10 1112 13 1415 16 Ansys Cross Section Number Ansys Cross Section Number

Appendix E: LVDT Calibration Curves LVDT 1 Calibration Curve LVDT 2 Calibration Curve 7.7 11.4

7.6 y = 5.7871x + 6.9107 11.3 R2 = 0.9999 y = -4.8564x + 11.282 7.5 2 11.2 R = 0.9961 7.4 11.1 Voltage 7.3 11 7.2 Voltage 10.9 7.1 10.8 7

6.9 10.7 6.8 10.6 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Displacement (in.) Displacement (in.)

LVDT 4 Calibration Curve LVDT 5 Calibration Curve 10.3 16.3

10.2 y = -5.9068x + 10.259 16.2 y = 5.2587x + 15.575 2 R = 0.9991 R2 = 0.9994 10.1 16.1

10 16

9.9 15.9 Voltage Voltage 9.8 15.8

9.7 15.7

9.6 15.6

9.5 15.5 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Displacement (in.) Displacement (in.)

LVDT 6 Calibration Curve 16.3

y = 5.2587x + 15.575 16.2 R2 = 0.9994

16.1

15.9 Voltage 15.8

15.7

15.6

15.5 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Displacement (in.)

Appendix F: Load Cylinder Calibration Curves

Load Cylinder 1 Calibration Curve 600

500 y = 5.3432x - 4.0147 R2 = 0.9996

400

300 STRAIN

200

100

0 0 20 40 60 80 100 LOAD (in.)

Load Cylinder 2 Calibration Curve 600

y = 5.1684x - 2.039 500 R2 = 0.9996

400

300 STRAIN

200

100

0 0 20 40 60 80 100 LOAD (in.)

Appendix G: Torsional Stiffness Measuring Machine Assembly/Test Procedure

Torsional Stiffness Measuring Machine (TSMM) Assembly/Test Procedure

Author: Thomas Steed

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Table of Contents 1. Test Information...... 3 2. Testing Equipment List ...... 3 3. TSMM Fixture Parts List ...... 4 4. Pre-Test Notes ...... 5 4.1 “BUY OFFS” ...... 5 4.2 Bagging & Labeling ...... 5 4.4 *****************************E-Stop******************************* 5 5. TSMM Assembly/Test Procedure...... 6 6. Appendix A: Sensor Record Sheet ...... 20 7. Appendix B: TSMM Test Data Record Tables...... 21 8. Appendix C: Equipment Record ...... 22 9. Appendix D: Channel Record ...... 22

Table of Figures Figure 1: TSMM Fixture Exploded View ...... 4 Figure 2: 4 Post Shaker Software Startup ...... 6 Figure 3: Vishay Amp. Banana Clip Plug-ins ...... 7 Figure 4: 4 Post Height Software Commands...... 9 Figure 5: Vishay Amp. Banana Clip Plug-ins ...... 13 Figure 6: DYMAC Power Supply Terminals ...... 14 Figure 7: TSMM Sensor Locations...... 20

Table of Tables Table 1: Testing Equipment List...... 3 Table 2: TSMM Fixture Parts List ...... 4 Table 3: Strain Gage Wiring Scheme ...... 7 Table 4: Ride Height Shock Lengths ...... 9 Table 5: Strain Gage Wiring Scheme ...... 13 Table 6: Transducer Log ...... 20 Table 7: TSMM Test 1 0.020" Increment ...... 21 Table 8: TSMM Test 2 0.050" Increment ...... 21 Table 9: Equipment Record ...... 22 Table 10: Channel Record ...... 22

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1. Test Information

Car Name:______

Test Conductor:______

Test Team______

______

2. Testing Equipment List

Table 12: Testing Equipment List Item Description Location Quantity 1 VXI Mainframe Vibes Lab 1 2 Vishay Strain Gage Conditioner and Amp. System Vibes Lab/High Bay 1 3 Dymax 24 Volt Power Supply Vibes Lab Cabinet 1 4 LVDTs Frame Cabinet 3+ 5 Dial Indicators SMLab/SAE Cabinet 5+ 6 MTS 4 Post Simulation System High Bay 1 7 Data Acquisition PC Vibes Lab 1 8 Fire Wire Cable Vibes Lab 1 9 HP ICP Break Out Box Vibe Lab Cabinet 2 10 LVDT Uni-Strut Fixture High Bay 1 FSAE & Vibes Lab 11 C-Clamps 3+ Toolboxes 12 Safety Straps High Bay Cabinet 6 13 Red Cherry Pickers High Bay 2 14 Rolling Cart FSAE Area 1 15 Weight Set [5-20,1-10,1-5,(Qty-lb)] High Bay 7 16 Video Camera Your House? 1 17 Long BNC Cables (Under Lattice) High Bay 4

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3. TSMM Fixture Parts List

Table 13: TSMM Fixture Parts List Quantit Item Part Description Material/Grade Location y 1 Hub Adapter Stainless 304 Frame Cabinet 4 2 Pivot Bolt Nut Steel Frame Cabinet 4 3 Load Cylinder w/ strain gages 6061 Aluminum Frame Cabinet 4 4 Pivot Bolt (1/2 Shoulder Bolt) 1020 Steel Frame Cabinet 4 5 Mechanical Fuse Brass Frame Cabinet 4 6 Base Bolts (M12 X 1.75 X 120 MM) Blk. Oxide Grade 8 Frame Cabinet 16 7 Base Stainless 304 Frame Cabinet 4 8 Adjustable Solid Shock Assy. Steel Frame Cabinet 4

3 2

5 6

Figure 56: TSMM Fixture Exploded View

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4. Pre-Test Notes In preparation for testing, organizing equipment and hardware will save time and frustration. It is recommended that the equipment list and procedure are thoroughly read over. Depending upon the extravagance of the suspension some major modifications to the adjustable solid shocks and alignment spacers may be required. Consulting the current suspension team leader for the length and the proper spacer thickness is strongly suggested when using the solid shocks. Any miscommunication between the test conductor and the suspension and/or frame team leader could potentially be very hazardous to the car. Having this person on hand at the time of the test is suggested. However, with the knowledge in this procedure and use of the step by step instructions will create an environment that is safe for all team members and the car.

4.1 “BUY OFFS”

This procedure has been written in a manner in which each step is intended to be bought off by the test conductor. It is EXTREMELY important that each step is read and executed as written. If at any time a step is read and not understood testing should halt and a group consensus should be met before proceeding. This is not a test that should be conducted at a time where personnel are fatigued. Each step MUST be bought off for completion to protect the hardware, NO MATTER how juvenile or tedious it might be. Buying off shall be completed by any member in the testing team. “Buy offs” shall be completed by initialing and dating the “Buy off” cell in each step of the procedure. The team member who “Buys Off” takes the responsibility that the step has been completed.

4.2 Bagging & Labeling

Throughout the testing process hardware should be bagged and labeled accordingly. Bagging and labeling all the removed parts will prevent any problems remembering the hardware configuration during re-installation. Having extra hardware after re-installing all the parts is not acceptable. Tires should be labeled RF, LF, RR, or LR before they are removed from the car. Each shock should be bagged and labeled with RF, LF, RR, or LR and an orientation arrow to ensure proper re-installation.

4.3 Testing Duration

Following this procedure should limit the test duration to no more than 6 hours. However, assuming that Murphy’s Law is always in effect, expect to dedicate a full day to testing. It is absolutely necessary to remove the car from the TSMM fixture at the end of the day. With that said, do not start testing in the late afternoon.

4.4 *****************************E-Stop*******************************

The MTS 4 Post Simulation System is equipped with two E-Stop buttons. These buttons are an EXTREME Hazard to the car. If at any time the car is connected to the fixture with solid shocks installed these buttons MUST NOT be tripped. The E-Stop buttons when depressed will cause each post to return to a natural zero based on the hydraulic pressure in the system. These positions are reached very quickly and at different rates. If an E-Stop is tripped there will be damage to the chassis. All members of the test team must be made aware of this.

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5. TSMM Assembly/Test Procedure STEP DESCRIPTION BUYOFF 5.1 In the high bay at the 4 post shaker, remove the center cover of each wheel pan by removing the M4 X 0.70MM X 20MM socket head cap screws (Qty 4). Store the center covers and socket head cap screws in a labeled plastic bag and place in the control room.

5.2 Install the base plate of the TSMM fixture on each post using M12 X 1.75 MM X 120 MM (Qty 4) socket head cap screws. Each screw shall be torqued in a star pattern.

**************************NOTE************************ The base plate must be seated against the horizontal surface of each wheel pan to be installed correctly. It may be necessary to lubricate the shoulder of each socket head cap screw to aid in installation. If lubrication is necessary make sure base plate identification labels are not destroyed by the lubricant. ******************************************************* 5.3 Install the corresponding labeled aluminum load cylinder on each base plate. Insert a 1/8” Ø brass fuse to orient and connect the base plate and cylinder together.

5.4 Plug in and turn on the strain gauge amplifier. Allow the amplifiers to warm up for 15-30 minutes so that a stable measurement can be made.

5.5 Using the FlexTest software on the pc in the control room turn on the hydraulic shaker system. Make sure that “External” and “High” are selected and press “Run.” Refer to Figure 57 below.

Figure 57: 4 Post Shaker Software Startup

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5.6 Plug in and secure two HP Patch Boxes to the VXI mainframe making sure to install each bank of channels to the corresponding pin connector. (1-4, 5-8 markings)

5.7 Plug in the fire wire cable into the VXI mainframe and then to the back of the PC. Power up the VXI first followed by the PC.

5.8 Start Matlab. Make a new working directory, locate and copy the following scripts: ttest.m, vxiarnge.m, vxierror.m, vxiacquire.m, vxiacquire2.m, vxiinit.m, vxisetup.m, vxi_sae.m

5.9 Unwind the cables for each Load Cylinder and the banana clip connectors into the Vishay 2100 Strain Gage Amplifier system using Figure 58 and Table 14 as a guide. Match the shaker LVDT order sequentially.

Figure 58: Vishay Amp. Banana Clip Plug-ins

Table 14: Strain Gage Wiring Scheme Wire Color Plug-in Color RED RED BLACK BLACK SILVER (braided) GREEN GRAY WHITE

Using the BNC to banana clip wires connect the RED wire to the OUTPUT RED plug-in and the BLACK wire to the OUTPUT BLACK plug-in. Using Table 10 as a guide plug in the BNC connectors into the HP Break Out Box.

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5.10 Place the stack of weights outlined in Table 1 next to one of the posts.

5.11 Start the torsion test MATLAB script by issuing “ttest” at the MATLAB command line while in the correct working directory.

5.12 Turn the monitor towards you so that you can see the display as weights are stacked onto the Load Cylinder.

5.13 Confirm that the amount of weight that is stacked onto the Load Cylinder is the value that is displayed on the digital readout on the screen.

5.14 If the displayed value matches the amount of weight that is on the Load Cylinder skip this step and step 5.16.

If the displayed value does not correspond with the amount of weight that is stacked on the Load Cylinder, use the values on the Strain Gage Amplifier display to create a new calibration curve. Plot this curve, take its slope and enter in the new calibration value into the top of the “ttest.m” MATLAB script. 5.15 Repeat steps 5.11 to 5.15 for the remaining Load Cylinders.

5.16 Unplug and coil the Load Cylinder cables from the Vishay Strain Gage Amps and place them with each post so that they can move together.

**********************WARNING*********************** Make sure to support each Load Cylinder cables so that their weight is not pulling on the strain gauge. *******************************************************

5.17 Turn on the green air compressor in the high bay.

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5.18 Measure the length of each shock as the car supports it’s own weight and record in Table 15:

Table 15: Ride Height Shock Lengths Location Length Left Front Right Front Left Rear Right Rear

5.19 *******************Multiple Person Operation***************

Lift the car onto a rolling cart. Be sure that the weight of the car rests on the frame and not the suspension components. Lift the car by having a person at each corner bear hug the wheel.

5.20 Remove each wheel, label and set aside. Make sure to place each wheel lug in a safe and easily accessible place for use in the next step.

5.21 Install a TSMM fixture Hub Adapter (Qty 4) on each corner of the car, using the car’s wheel lugs. Hand tighten each nut until it is seated at the outer face of each adapter. Using a 19 MM open ended wrench tighten each wheel lug in a star like pattern. It may be necessary to have another person hold the brakes while the lugs are tightened. 5.22 Return to the control room and iterate on the setpoint of each post until the External Readout reads the same for each post. Type in the setpoint box, hit enter, and watch the external readout value. Repeat until all the Shaker LVDTs read the same.

Figure 59: 4 Post Height Software Commands

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5.23 Consult the current suspension team leader if doubtful of measurement accuracy of Table 15. Adjust the length of the solid shocks to match that of Table 15 and label accordingly.

5.24 *******************Two Person Operation******************

While supporting the suspension at the hub, remove the shock/damper by backing out the ¼” – 28 bolts at the bell-crank and frame mount. Make sure to carefully watch for any loose spacers. Bag, label and store shock and any necessary hardware.

5.25 Install solid shock with alignment spacers using ¼”-28 bolts. Properly torque each bolt.

5.26 Repeat steps 5.25 and 5.26 for each corner of the car.

5.27 Raise the blue lift in the high bay all the way up and rotate the support arms away from the 4 Post Shaker area.

5.28 Roll the cart/car into the middle of the 4 Post Shaker area so that the front point towards SMLAB.

5.29 Place a cherry picker at the front of the car. Install a strap on the cherry picker’s hook/clip and raise it so that the boom will not hit the car. Position the cherry picker so that the strap wraps around the front end and supports the bottom frame rails.

5.30 Roll the second cherry picker to the rear of the car. Install a strap on the clip and raise the boom. Position the cherry picker so that the strap will wrap around the jack bar.

5.31 With another person raise each cherry picker together so that the car will clear each post.

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5.32 Lower the blue lift a small amount and as a safety measure wrap a strap around the bottom side impact tube of the frame and up to each arm. Provide each strap with ample slack so that when the frame is attached to the fixture it will not be supported.

5.33 Return to the control room and check that the external readout of each post’s LVDT still reads as it did before. If it has made any significant change more time is needed for the fluid to reach a constant operating temperature. Wait 10 minutes if LVDTs are still fluctuating. 5.34 Make any adjustments to the height of the rear of the car so that the hub adapter and load cylinder pivot points match.

5.35 **********************WARNING*********************** Steps 5.36 through 5.47 must be completed in the sequence described. If not the potential of pre-loading the suspension/frame is greatly increased. ******************************************************* 5.36 Install the air supply at the right rear post and turn on. Gently float the post into a planar position so that the car can be translated with the cherry picker so that the slot of the Hub Adapter can slide around the Load Cylinder. Turn off the air supply!

5.37 Make any vertical adjustments by raising/lowering the cherry picker so that the pivot holes match in each part. Install the pivot bolt and hand tighten the nut.

*************************NOTE************************* A hammer may be necessary to TAP the pivot bolt in. *******************************************************

5.38 Remove the air supply to the right rear post and install on the left rear post. Turn the air supply on.

5.39 Wrestle the left rear post so that it is floating and can be easily moved with a small amount of force. Make sure that the post is floating and not oscillating because of low air pressure ! Very gently float the post so that the Load Cylinder is in the slot of the Hub Adapter. Turn off the air supply!

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5.40 Make any out of plane adjustments by raising/lowering the cherry picker so that the pivot holes match in each part. Install the pivot bolt and hand tighten the nut.

**************************NOTE************************ The air supply may be turned on to make small adjustments if necessary. ******************************************************* 5.41 Adjust the height of the front of the car by raising/lowering the boom of the cherry picker. Position the height so that the pivot point of the Load cylinder matches with the Hub Adapter.

5.42 Remove the air supply and install on the front left post. If necessary wait for air pressure to return before turning on.

5.43 Wrestle the left front post so that it is floating and can be easily moved with a small amount of force. Make sure that the post is floating and not oscillating because of low air pressure ! Very gently float the post so that the Load Cylinder is in the slot of the Hub Adapter. Turn off the air supply! 5.44 Make any out of plane adjustments by raising/lowering the cherry picker so that the pivot holes match in each part. Install the pivot bolt and hand tighten the nut.

**************************Note************************* The air supply may be turned on to make small adjustments if necessary. ******************************************************* 5.45 Remove the air supply from the left front post and install on the right front post. Wait until air pressure has been completely been restored.

5.46 Wrestle the right front post so that it is floating and can be easily moved with a small amount of force. Make sure that the post is floating and not oscillating because of low air pressure ! Very gently float the post so that the Load Cylinder is in the slot of the Hub Adapter. Turn off the air supply! 5.47 Make any out of plane adjustments by raising/lowering the cherry picker so that the pivot holes match in each part. Install the pivot bolt and hand tighten the nut.

**************************Note************************* The air supply may be turned on to make small adjustments if necessary. *******************************************************

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5.48 Lower and roll cherry pickers away from testing area.

5.49 Roll the cart out from underneath the car.

5.50 Position LVDT Fixture underneath the car and place some weight on the lower rails to hold it in position.

5.51 Plug the Shaker LVDTs into Channels 1-4.

**************************Note************************* These cables can be found lying along the control room wall. ******************************************************* 5.52 Unwind the cables for each Load Cylinder and the banana clip connectors into the Vishay 2100 Strain Gage Amplifier system using Figure 60 and Table 16 & 10 as a guide. Match the shaker LVDT order sequentially.

Figure 60: Vishay Amp. Banana Clip Plug-ins

Table 16: Strain Gage Wiring Scheme Wire Color Plug-in Color RED RED BLACK BLACK SILVER (braided) GREEN GRAY WHITE

5.53 Attach the three Frame LVDTs to the fixture using the C-Clamps and record their location in Table 17.

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5.54 Connect the BNC attached to each Frame LVDTs to the HP Patch Boxes according to Table 21.

5.55 Connect the Frame LVDTs 24 VDC and ground wires to the DYMAC power supply. The black wire is 24 VDC and the silver wire is the ground. Refer to the Figure 61 below.

Figure 61: DYMAC Power Supply Terminals

**************************Note************************* Only one power supply is needed to power all three LVDTs. Install two wires in the first two terminals. ******************************************************* 5.56 Plug in the DYMAC 24 Power Supply.

5.57 Start the torsion test MATLAB script by issuing “ttest” at the command line and manually operate each Frame LVDT to confirm that it is operating within the range of each plot window.

5.58 Attach the dial indicators to the LVDT Fixture using a magnetic post and record their location in Table 17.

**************************Note************************* It is much easier to log displacement data from the dial indicators if two people record what is happening from each side of the car at each displacement point of the 4 post shaker. ******************************************************* 5.59 Print out an extra set of Tables 7 & 8 for recording displacements from the dial indicators.

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5.60 Zero the strain gage amps by turning the “Balance” knob so that the red lights are not on and the display reads very close to zero if not zero.

5.61 Start the video camera recording.

5.62 Start the MATLAB torsion test script by issuing “ttest” at the command line.

5.63 Record the external readout of SHAKER LVDT 25 & 26 below:

SHAKER LVDT 25 External Position:______SHAKER LVDT 26 External Position:______

5.64 With the test conductor in the control room, begin the first test as outlined in Table 18 by moving the setpoint in 0.020” increments. Record the deflection from the dial indicators at every increment position in Table 18.

5.65 Save the MATLAB workspace to a file with the formatted name: “TSMM_CARNAME_DATE_20_MIL.mat.”

5.66 Save the MATLAB display with the formatted name: “TSMM_CARNAME_DATE_20_MIL.fig.”

5.67 Unload the frame in four 0.050” increments until the neutral positions recorded in step 5.61 are achieved.

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5.68 Pause the video recorder.

5.69 Re-zero the dial indicators.

5.70 Re-zero the strain gage amps.

5.71 Start the video camera recording.

5.72 Start the MATLAB torsion test script by issuing “ttest” at the command line.

5.73 Record the external readout of SHAKER LVDT 25 & 26 below:

SHAKER LVDT 25 External Position:______SHAKER LVDT 26 External Position:______

5.74 With the test conductor in the control room, begin the second test as outline in Table 19. Record the deflection from the dial indicators at every increment position in Table 19.

5.75 Save the MATLAB workspace to a file with the formatted name: “TSMM_CARNAME_DATE_50_MIL.mat.”

5.76 Save the MATLAB display with the formatted name: “TSMM_CARNAME_DATE_50_MIL.fig.”

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5.77 Pause the video recorder

5.78 Unload the frame in four 0.050” increments until the neutral positions recorded in step 5.73 are achieved.

5.79 Make a backup copy of the data files and figures onto a removable media storage device.

5.80 Roll the two red cherry pickers back into their previous positions, install the straps and jack the cherry pickers up until the straps are taught.

5.81 Remove the pivot bolt from each Load Cylinder.

5.82 ******************Three Person Operation****************** With a person in between two shaker posts jack up each cherry picker simultaneously until the Hub Adapters are clear of all the Load Cylinders.

**************************Note************************* The person in the middle of the shakers should have a hand on the frame to stabilize it once the Hub Adapters clear the Load Cylinders.

5.83 Turn off the hydraulic pressure to the shakers by using the software in the control room

5.84 Unplug and detach all instrumentation that is attached to the LVDT fixture. Coil and tape all instrumentation wires and store the instrumentation in the frame cabinet.

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5.85 Remove the LVDT fixture from underneath the car and place it along side the railing in the high bay.

5.86 Unplug and coil the Load Cylinder cables from the Vishay Strain Gage Amps and place them with each post so they can move together.

**********************WARNING*********************** Make sure to support each wire so that its weight is not pulling on the strain gage. ******************************************************* 5.87 Attach the air supply to each shaker post and float the post out of the way to make room for the rolling cart.

5.88 Roll the cart underneath the car.

5.89 Remove the security straps from the frame to the lift arms and store the straps in the high bay cabinet.

5.90 Lower the car onto the rolling cart, detach the straps on the cherry picker and store the cherry pickers where they were located previously.

5.91 Roll the car/cart out from the testing area.

5.92 Remove each solid shock assembly from the suspension system and replace with the bagged hardware.

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5.93 Remove and properly store all TSMM fixturing and hardware back in the frame cabinet.

5.94 Return the VXI mainframe, patch boxes, DYMAC power supply, and PC to the vibrations lab.

5.95 Turn off the Vishay 2100 Strain Gage Amplifier System.

5.96 Install the center cover of each wheel pan back onto each post.

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6. Appendix A: Sensor Record Sheet

Table 17: Transducer Log Location Sensor Description Model Number Serial Number Calibration 1 2 3 4 5 6 7 8 9 10

Figure 62: TSMM Sensor Locations

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7. Appendix B: TSMM Test Data Record Tables

Table 18: TSMM Test 1 0.020" Increment Location # (Refer to Figure 62 CAR NAME: Defl. 1 2 3 4 5 6 7 8 9 10 0.020 0.040 0.060 0.080 0.100 0.120 0.140 0.160 0.180 0.200

Table 19: TSMM Test 2 0.050" Increment Location # (Refer to Figure 62 ) CAR NAME: Defl. 1 2 3 4 5 6 7 8 9 10 0.050 0.100 0.150 0.200

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8. Appendix C: Equipment Record

Table 20: Equipment Record Item Description Model Number Serial Number 1 PC Station 2 HP Breakout Box 3 HP Breakout Box 4 Dymax Power Supply 5 VXI Main Frame 6 Strain Gage Amp 7 Strain Gage Amp 8 Strain Gage Amp

9. Appendix D: Channel Record

Table 21: Channel Record Channel # Description Location 1 Shaker LVDT 2 Shaker LVDT 3 Shaker LVDT 4 Shaker LVDT 5 Strain Gauge 6 Strain Gauge 7 Strain Gauge 8 Strain Gauge 9 Frame LVDT 10 Frame LVDT 11 Frame LVDT 12 Frame LVDT

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