1 A Complete Multi-Body Model for an FSAE Space Frame Car
A thesis submitted to the
graduate school
of the University of Cincinnati
in partial fulfillment of the
requirements for the degree of
Master of Science
in the Department of Mechanical and Materials Engineering
of the College of Engineering and Applied Sciences
By
Tejas Chothani
Bachelor of Engineering from University of Mumbai
June 2011
Committee Chair: Dr. Randall Allemang
Committee Members: Dr. David Thompson
Dr. Aimee Frame
2 Abstract:
Vehicle dynamics has evolved into an increasingly indispensible discipline to supplement the
design of automobiles, especially racecars. Every single component of the car and the
environment with which it interacts contributes to the overall dynamic behavior of the vehicle.
For Formula Society of Automotive Engineers (FSAE) cars in particular, these parameters
become extremely critical and hence require robust and accurate physical testing methods, which
are expensive and time consuming, warranting the need for virtual testing methods. The Bearcat
Motorsports team (BCMS) lacked this capability of predicting vehicle dynamic behavior, relying
on previously available test data and the performance of the car after fabrication. Hence, a
thorough multi-body dynamics model has been developed to overcome this inadequacy. The
2013 race car is used for this study and ADAMS/Car is used as a multi-body development
platform. ADAMS/Car multi-body model consists of different automotive subassemblies
modeled as independent subsystems, which can interact amongst themselves to mimic the overall
dynamics of a physical car model. Each subsystem requires data pertaining to its characteristics
such as mass, inertia, center of gravity, which can be tuned to calibrate and eventually validate
the model against data obtained from physical testing. This makes it imperative to bring together
the work done by all sub-system teams over the course of the year. For simulation of road-tire
interface, the PAC2002 tire model [2] is used, which is the latest Pacejka Tire Model. A new
ADAMS template is made for the anti-roll bars and the strut structure. The model can predict full
vehicle dynamic behavior apart from generating sub-system specific vehicle dynamic
parameters. The validation of a full vehicle model is a multi-year project and is not within the
scope of this thesis. However, the initial dynamic model is now able to help the team predict
vehicle dynamic trends and evolve their designs based on previous design ideologies. The future
3 work for this project will include further calibration and validation of the model and then running
the simulation model on a complete virtual endurance track.
4 5 Acknowledgements
I take this opportunity to thank my parents for making my dream come true and for their
continued support throughout my Graduate school.
Thank you to all the members of the Faculty and team members at Orion Racing India,
KA-Raceing and Bearcat Motorsports for making my time in FSAE the best experience till date.
A special thanks to Dr. Randall Allemang for his guidance and expertise without whom my
graduate work and thesis wouldn’t have been possible.
To all my friends, in India and Cincinnati for giving me support and pushing me to achieve what
I always wanted to.
The Bearcat motorsports Lab, UC- Machine shop and UC-SDRL lab facilities have also
contributed in every way possible.
I would take the opportunity to thank Dr. Aimee Frame and Dr. David Thompson for all the help
and guidance.
A special thanks to Nishant, Suresh, Madhura, Devanshi and Murli for making me believe in my
work and helping me in any and every way possible.
6 Table of Contents
Abstract............................................................................................................................................2
Acknowledgement............................................................................................................................5
Table of Contents.............................................................................................................................6
List of Figures...................................................................................................................................8
List of Tables..................................................................................................................................11
Acronyms........................................................................................................................................13
1. Introduction.........................................................................................................................................................14
1.1 Formula SAE background................................................................................................................................16
1.2 Bearcat motorsports..........................................................................................................................................16
1.3 Project methodology.........................................................................................................................................18
2. Multi body simulation.......................................................................................................................................19
2.1 Multi body modeling.......................................................................................................................................19
2.2 Sub system modeling.......................................................................................................................................21
2.3 Kinematic joints...............................................................................................................................................22
2.4 Coordinate system........................ ...................................................................................................................23
2.5 Sub-Systems in ADAMS modeling.............. ..................................................................................................24
2.5.1 Front Suspension sub-system...................................................................................................................24
2.5.2 Rear Suspension sub-system....................................................................................................................26
2.5.3 Steering system.............................................. .........................................................................................26
2.5.4 Powertrain, Drivetrain and Brakes sub-systems......................................................................................27
2.5.5 Modeling of flex bodies...........................................................................................................................28
2.6 Part modeling of sub-systems…………………………………………………………………………………30
2.6.1 Tire development......................................................................................................................................30
2.6.2 Shock absorbers........................................................................................................................................34
2.6.3 Springs......................................................................................................................................................37
7 3. Calibration...........................................................................................................................................................38
3.1 Vehicle mass moment of inertias.........................................................................................................................38
3.1.1 Test procedure – Vehicle inertia measurement........................................................................................39
3.2 Weight audit for Bearcat 2013............................................................................................................................43
3.3 Coordinate measurement for the hardpoints.............................. ........................................................................44
3.4 Pseudo static calibration ......................................................................................................................................45
3.4.1Spring file calibration...............................................................................................................................45
3.4.2 Adams motion ratio plot............................... ...........................................................................................47
3.4.2.1 Experimental calibration of the front and rear suspension subsystems.................................................47
3.4.2.2 Test Procedure.………………………………………………………...................................................48
3.5 Calibration examples....................................................................................................................................49
4. Conclusions and Recommendations for Future work..............................................................................................51
4.1 Future Scope......................................................................................................................................................51
4.2 References..........................................................................................................................................................53
Appendix A...............................................................................................................................................................55
Appendix B...............................................................................................................................................................79
8 List of Figures:
Figure 1: Time-line based analysis .............................................................................................................................14
Figure 2: Static and dynamic points distribution..........................................................................................................16
Figure 3: Suspension_2012…………...................................................................…...................................................17
Figure 4: Suspension_2013…....................................…....................................…......................................................17
Figure 5: ADAMS/car front suspension template........................................................................................................19
Figure 6: FSAE template_1..........................................................................................................................................20
Figure 7: FSAE template_2..........................................................................................................................................20
Figure 8: Hierarchical template model..........................................................................................................................21
Figure 9: Quarter car model..........................................................................................................................................21
Figure 10: Damper cap setup........................................................................................................................................24
Figure 11: ISO view- steering sub-system…................................................................................................................27
Figure 12: Three-part ARB CAD model.......................................................................................................................28
Figure 13: ADAMS flex body template........................................................................................................................29
Figure 14: Coefficients- tire development....................................................................................................................33
Figure 15: Damper test facility.....................................................................................................................................34
Figure 16: Internal Schematics-_TTX-25.....................................................................................................................35
Figure 17: Spring design_ADAMS ..............................................................................................................................37
Figure 18: Vehicle inertia measurement method..........................................................................................................39
Figure 19: Vehicle inertia measurement facility...........................................................................................................41
Figure 20: Vehicle inertia measurement results_1........................................................................................................42
Figure 21: Vehicle inertia measurement results_2........................................................................................................42
Figure 22: Experimental weight measurement.............................................................................................................43
Figure 23: Spring stiffness experimental setup.............................................................................................................45
Figure 24: Test procedure_motion ratio........................................................................................................................48
Figure 25: % error- FVSA vs. camber change..............................................................................................................49
Figure 26: SAE tire axis system....................................................................................................................................55
Figure 27: TYDEX W-axis system ………………………………………………......................................................55
9 Figure 28: Front view- front suspension…………………………………………………...........................................56
Figure 29: Plan view - front suspension.......................................................................................................................56
Figure 30: ISO view- front suspension.........................................................................................................................56
Figure 31: Front view- rear suspension.........................................................................................................................57
Figure 32: Plan view - rear suspension.........................................................................................................................57
Figure 33: ISO view- rear suspension...........................................................................................................................57
Figure 34: BCMS coordinates_1...................................................................................................................................58
Figure 35: BCMS coordinates_2...................................................................................................................................58
Figure 36: Damper testing- Penske...............................................................................................................................59
Figure 37: Damper testing- Ohlins................................................................................................................................59
Figure 38: Internal schematics-high speed rebound_TTX-25......................................................................................60
Figure 39: Internal schematics-high speed compression_TTX-25...............................................................................60
Figure 40: Joints- names and types- front suspension..................................................................................................61
Figure 41: Joints- names and types- rear suspension....................................................................................................62
Figure 42: Brake system sample requirements.............................................................................................................63
Figure 43: Engine system sample requirements...........................................................................................................63
Figure 44: Linkage diagram- front suspension.............................................................................................................64
Figure 45: Linkage diagram- rear suspension...............................................................................................................64
Figure 46: Front suspension kinematics.......................................................................................................................65
Figure 47: Rear suspension kinematics........................................................................................................................65
Figure 48: Force vs. Velocity curves - Ohlins..............................................................................................................66
Figure 49: Force vs. Displacement curves – Ohlins.....................................................................................................66
Figure 50: Spring Stiffness test apparatus.....................................................................................................................67
Figure 51: Strain gauge based load cell........................................................................................................................67
Figure 52: Spring stiffness testing model.....................................................................................................................68
Figure 53: Spring stiffness testing_1............................................................................................................................68
Figure 54: Spring stiffness testing_2............................................................................................................................69
10 Figure 55: Spring stiffness testing_3............................................................................................................................69
Figure 56: Spring stiffness testing_4............................................................................................................................70
Figure 57: Damper input file........................................................................................................................................70
Figure 58: Force- Velocity curves Penske....................................................................................................................71
Figure 59: Force- Velocity curves Ohlins.....................................................................................................................71
Figure 60: ADAMS motion ratio test results................................................................................................................72
Figure 61: Experimental motion ratio test results .......................................................................................................72
Figure 62: Front static kingpin inclination....................................................................................................................73
Figure 63: Front suspension roll rate............................................................................................................................73
Figure 64: Rear suspension FVSA................................................................................................................................74
Figure 65: Sub-system test bench.................................................................................................................................74
Figure 66: Gantt chart representation of BCMS_2013 ................................................................................................75
Figure 67: Gantt chart representation-- thesis timeline.................................................................................................76
Figure 68: MR calibration_1.........................................................................................................................................77
Figure 69: MR calibration_2.........................................................................................................................................77
Figure 70: MRcalibration_3..........................................................................................................................................77
Figure 71: Engine curves_1..........................................................................................................................................78
Figure 72: Engine curves_2..........................................................................................................................................78
11 List of Tables:
Table 1:BCMS_2013....................................................................................................................................................17
Table 2: Subsystem Weight audit ……………………………………………………………………………………44
Table 3: Calspan tire data channels…………………………………………………………………………………..79
Table 4: PAC2002 tire modeling coefficients 1-..........................................................................................................80
Table 5: PAC2002 tire modeling coefficients 2............................................................................................................80
Table 6: PAC2002 tire modeling coefficients 3............................................................................................................80
Table 7: PAC2002 tire modeling coefficients 4............................................................................................................80
Table 8: PAC2002 tire modeling coefficients 5............................................................................................................80
Table 9: PAC2002 tire modeling coefficients 6............................................................................................................81
Table 10: PAC2002 tire modeling coefficients 7..........................................................................................................81
Table 11: PAC2002 tire modeling coefficients 8..........................................................................................................81
Table 12: PAC2002 tire modeling coefficients 9..........................................................................................................82
Table 13: PAC2002 tire modeling coefficients 10........................................................................................................83
Table 14: PAC2002 tire modeling coefficients 11........................................................................................................83
Table 15: PAC2002 tire modeling coefficients 12.......................................................................................................84
Table 16: Weight and inertia properties -1..................................................................................................................85
Table 17: Weight and inertia properties -2...................................................................................................................86
Table 18: Hardpoint location coordinates (Front)........................................................................................................87
Table 19: Hardpoint location coordinates (Rear).........................................................................................................88
Table 20: Weight audit - drivetrain..............................................................................................................................89
Table 21: Weight audit - powertrain.............................................................................................................................89
Table 22: Weight audit – miscellaneous parts..............................................................................................................90
Table 23: Spring stiffness test results - 1......................................................................................................................91
Table 24: Spring stiffness test results - 2......................................................................................................................91
Table 25: Spring Stiffness test results - 3.....................................................................................................................92
Table 26: Spring Stiffness test results - 4.....................................................................................................................92
Table 27: Damper file (front) ......................................................................................................................................93
12 Table 28: Joints characterization..................................................................................................................................94
Table 29: Constraints characterization.........................................................................................................................95
Table 30: Joints description – front suspension ..........................................................................................................96
Table 31: Joints description –rear suspension..............................................................................................................97
Table 32: Joints description – steering system.............................................................................................................97
Acronyms:
A/car- ADAMS/Car software/ Default template database.
SAE- Society of Automotive Engineers
ECU – Engine control unit
CAD – Computer aided designing
CG – Center of gravity
DOF - Degrees of freedom
UC – University of Cincinnati
BCMS: Bearcat Motorsports
ARB- Anti-roll bar
HPL - hard point left
HPR - hard point right
HOK- Hooke joint
REV- Revolute joint
UBJ – Upper ball joint
LBJ – Lower ball joint
CMM- Coordinate measuring machine
PE- Performance Electronics
TTC- Tire test consortium
FVSA- Front view swing arm
13 14 1. Introduction:
The scope of this thesis is to develop an initial, working version of a complete multi-body model
of an open wheeled space frame racecar. An operational ADAMS model is a first step in
developing the dynamic simulation capabilities of the team. This model will be available to
simulate suspension, steering, tire and other vehicle sub-systems contributing to the development
of the Bearcat Motorsports 2013 race vehicle that would enhance the performance of the team at
the Formula SAE competitions. This model was developed as a consequence of identifying the
reasons for increase and decrease in the points earned at the event over the years. Figure 1 shows
a time-line based analysis, showing the need for a simulation model. The increase and decrease
Figure 1: Timeline Based Analysis
in design event points is indicated by the yellow boxes and blue arrows The first row of red
boxes indicate the method that were used to develop a sub-system model and it also indicates the
reasons for the team scoring less points at the design event. The third row boxes show the
capability of the simulation model to enhance point-scoring ability in the engineering design
15 event. The black boxes indicate the years in which the team has used the tire data accurately for
suspension design development. In order to develop this model, previously available work done
for the BCMS Team was coalesced in to useable mathematical models. The multi-body platform
chosen for simulation was ADAMS (Automated Dynamic Analysis of Mechanical Systems). It is
force-joint based software capable of performing full vehicle dynamic analysis. These references
include theses on frame stiffness by Thomas Stead [16], vehicle dynamics by Fred Jabs [11] and
engine development by David Moster [17] respectively. The prime focus of this thesis was to
ensure that the ADAMS model is furnished with correct input parameters to facilitate good
results for static and dynamic calibration tests. The input parameters include tire property files,
damper and spring curves, hardpoint geometry, engine and brake data. All the links and bodies
are assumed to be rigid, but a procedure is laid out to accurately model flexible bodies along with
their bushings and mounts in ADAMS. Knowledge of solid modeling and finite element
development software is, therefore, a pre-requisite for this project. The errors generated in the
calibration process are partly human and partly due to resolution problems in the sensors used.
Effort was taken to keep these errors minimal. A lot of ideas and work has been done while
keeping in mind that the race car is constructed by a team of engineers in training trying to
improve upon their design year round.
16 1.1 Formula SAE Background:
Formula SAE is an international engineering design event in which students have to design,
fabricate, test and compete with their formula-styled racecars. The target marketing group for the
team would be a non-professional weekend autocross racer. Formula SAE vehicles are an
equivalent system to that of any complex road car with enhanced performance benchmarks. The
dynamic events (4-7) comprise of 65 % of the total points in the competition. The static events
include engineering design, cost analysis and business plan presentation and the dynamic events
include acceleration, skid pad, autocross and endurance.
Figure 2: Static and Dynamic points distribution
1.2 Bearcat Motorsports:
Bearcat Motorsports started taking part in Formula SAE events in 1994, and since then has
competed in various locations including the Silverstone Formula 1 track at Silverstone (UK). The
team has had a successful history with many top 10 finishes in FSAE Michigan and the events in
Virginia and Lincoln (Nebraska). Every year, a majority of the team is comprised of senior level
students who are using this activity as part of their Senior design requirements. These team
members have little or no experience working on the Formula SAE project hence, carrying
17 forward the designs and evolving them becomes a difficult task. Since the team had changed the
front and rear suspension type in 2013 from a double wishbone push-rod actuated spring-damper
setup to a double wishbone direct acting damper setup, kinematic trend patterns had to be
developed for this suspension type. The project was initiated keeping these factors in mind.
Figure 3-4 depicts the change in suspension type.
Figure 3: Suspension 2012 Figure 4: Suspension 2013 The team needed a platform to analyze previous year designs and come up with their own set of
ideas using these previous designs as a reference. This gives the team a head start into their
design period and providing the team with trends, which can be used to compare designs from
the previous years.
An overview of BCMS 13 is as follows:
Model Type
Frame type
Engine type
Suspension type (Front, rear)
Transmission
Track (m) (Front, rear)
Tires (Front, rear)
Electronics
Steering
Brakes (Front, rear)
Formula SAE Race car
Open wheeled space frame
Single cylinder Yamaha 450 Rear wheel
driven
Double Wishbone, direct acting dampers
5 speed Manual
(1.118,1.08)
Hoosier 18/6-10 Front (R-25B), WET
PE DAQ, Motec data logger
Rack and Pinion
Disc (Brembo, AP-racing)
Table1: Overview BCMS 2013 18 1.3 Project Methodology
The ADAMS model has three levels of hierarchy: the full-vehicle, system (for example, front
suspension) and the sub-system (for example, dampers) levels. In order to develop the model, the
software makes use of templates. The project made use of the appropriate (ADAMS/Car)
templates and not the standard FSAE template, since there are no FSAE templates for a directacting setup which the current team was going to use. Modifying the standard FSAE template is
not an option due to difficulties that arise in ADAMS template modification. In order to input
data for the templates and sub-system, data files in the form of mass properties of each
component, rotational inertia values of all the components in roll, pitch and yaw, suspension
hardpoint coordinates, damper curves, spring stiffness graphs, steering ratio, tire property files,
engine power and torque curves have been measured. Verification is done at each step to check
the adherence of the ADAMS model with the theoretical model developed using Solidworks and
the actual car. For part of the calibration of the model, an experiment to check the motion ratio of
the front and the rear suspension is done. Along similar lines, graphs are generated to check for
correct trends. Mounts were made for using appropriate sensors to extract real time data using
the (Performance Electronics Version 3) data acquisition system with the electronics sub-team.
The data will be used for future model calibration and validation exercises. The major steps of this thesis can be outlined as follows:
Multi-body model building (Chapter 2)
Verification (Chapter 3)
Calibration (Chapter 3)
Validation (Chapter 4
The subsequent chapters handle the above in detail
19 2. Multi-Body Simulation:
2.1 Multi-Body Model Building:
As mentioned earlier, an ADAMS model consists of several independent automotive subsystems. The ADAMS/car template is used to modify these sub-systems as per team
requirement. Figure 5 depicts a front suspension sub-system ADAMS/car template. These
templates are used as a start point for sub-system development. An ADAMS/car template
essentially, is an assembly of rigid bodies connected to each other via simple mechanical joints
and kinematic constraints.
Figure 5: Template-­‐ Front Suspension
These templates are used for sub-system modeling in place of the FSAE templates. An FSAE
template defines automotive sub-systems traditionally developed for FSAE events and used by a
majority of student teams. Figure 6 and Figure 7 show sample FSAE templates.
20 Figure 6: FSAE_template_1
Figure 7: FSAE_template_2
The BCMS 13 uses a non-traditional suspension setup. Therefore a more generic approach is
essential. The actual BCMS 13 suspension setup will be explained in Section 2.5.1. The type of
template used establishes the complexity of the effort required. Modifying standard templates to
a great extent poses significant increase in sub-system modeling time and effort. The scope of
this thesis does not warrant making these templates from scratch.
The ADAMS/car template gives the user enough opportunities to achieve acceptable simulation
results and the availability of these templates at no cost is a major contributing factor for their
use. For the development of the entire model, all the sub-system templates have to be defined,
calibrated and validated. A custom ADAMS/car template has also been made for the anti-roll bar
(ARB) of the car since the ARB made by the team is a non-traditional approach for countering
the roll of the vehicle. The template for this is explained in Section 2.5.5.
Figure 8 shows a hierarchical template model, depicting bottom to top construction in ADAMS
for full vehicle analysis.
21 Figure 8: Hierarchy template model
2.2 Sub- System Modeling:
A quarter car representation is shown in Figure 9. This figure shows a sample of how subsystems are connected via joints in order to explain sub-system modeling using ADAMS/car
template.
Figure 9: Quarter-­‐ car model
22 In the ADAMS virtual environment, the geometric positions of these sub-system templates are
fully defined by points having ‘x’ y’ and ‘z’ coordinates in space. In ADAMS terminology, these
are called as ‘hardpoints’. Since a coordinate measuring machine (CMM) is not available, two
methods have been used to arrive at the coordinates of the hardpoints. The value of the
coordinate is the average of the two methods. The methods are explained in detail in Chapter 3.
2.3 Kinematic Joints:
A multi-body system is a collection of multiple bodies connected via different types of joints. A
list of joints along with their properties is shown in Table 28, Appendix B. A sample list of joints
is given below:
•
Fixed
•
Translational
•
Revolute
•
Universal
•
Spherical
•
Inplane
•
Motion
Kinematic joints impose constraints on the relative movement of two rigidly connected bodies.
For instance, a spherical (SPR) joint defines the connection between the upright and the
wishbone, which are a part of the front suspension (double-wishbone) ADAMS/car template,
shown in Figure 5. It allows rotational motion in three directions and attaches constraints on the
translational motion, which is a characteristic of the double wishbone suspension. A second
instance would be the revolute (REV) joint, defined at the hub of the suspension system. It
23 constrains the relative motion between the hub, upright and the wheel in two ways, translation
and rotation. It allows motion of the two components along a common axis. The joints within the
ADAMS/car template have been changed to match the BCMS 2013. While changing the
template for joints, it is not advisable to over-constrain the template. The Gruebler count of a
system is a quantity to explain the under-constrained and over-constrained multi-body
systems.
The Gruebler-Kutzbach criterion determines the degrees of freedom of a kinematic linkage [4].
Table 28 presents the degrees of freedom at associated with each joint. The sub-systems can be
modeled using bushings in place of joints, which introduces non-linearity in behavior of the
connection. Since racecars are relatively rigid automobiles, there is an attempt to reduce this nonlinearity in connections. Due to resource constraint, the BCMS 2013 has not been able to make
use of a kinematics and compliance (K&C) rig to determine the real extent of modeling the
quarter car with bushings or joints to check for hardpoint compliances.
2.4 Coordinate System:
The coordinate system used for the development is a fixed Cartesian coordinate system. This
system is defined using unit vectors X, Y and Z shown in the Fig 33-34. In this system, the ‘X’
coordinate is aligned with the longitudinal axis of the vehicle, the ‘Y’ coordinate is aligned with
the lateral axis of the vehicle and the positive ‘Z’ coordinate aligned vertically pointing towards
the top of the vehicle. The x-y plane defines the ground and is placed at the tire contact patch of
the vehicle with the ground. The measurements for the hardpoints are taken from the origin of
the vehicle coordinate system; in this case, it is the vehicle back-axle centerline. The
measurement methods have been explained in Section 3.3.
24 The sub-systems are explained in further detail in the following subsections.
2.5 Sub-Systems in ADAMS modeling:
This section discusses all the sub-system templates, defining the purpose of each in the full
vehicle model, and the way in which these sub-systems have been modeled in the ADAMS
environment.
2.5.1 Front Suspension system:
A suspension system is used to isolate wheel movement relative to the frame, which determines
how a vehicle moves and turns. This is accomplished with a kinematic arrangement of linkages,
dampers and springs. The wheels and tires are attached to the system using a revolute joint,
which allows translational movement in the y-z plane and rotational movement on the z-axis.
The front suspension for the BCMS 2013 is a double wishbone suspension system, with a unique
spring-damper arrangement. The damper is connected to the wishbone via a ‘Damper Cap’. A
picture of the damper cap is shown in Figure 10.
Figure 10: Damper cap setup
25 This setup is termed as a ‘Direct-Acting’ suspension setup. This setup manages each wheel
independently, hence providing control over modifying wheel and tire parameters. The motion
ratio describes the amount of damper travel for a certain change in wheel travel. In this system,
the vertical wheel movement directly actuates the shock absorbers, eliminating the need for a
‘bell-crank’. This design also eliminated other components associated with the bell crank,
namely, the ‘push-rod to bell crank’ and the ‘bell-crank to shock absorber’ that are used to
adjust the motion ratio. This eliminates the need to describe the bell-crank mechanism in the
model but has a possible negative characteristic of more limited motion ratios. Fig 44 shows the
arrangement of the front suspension, mounted onto the frame rigidly via mounts. The damper for
BCMS 2013 is modeled as a separate part, as explained in Section 2.6.2.
A steering system is attached to the front suspension system using a link called the tie rod via
spherical joints. The attachments for one of the ends are on the rack, which is a part of the
steering sub-system, and for the other end on the upright. The steering controls the wheels via its
attachment at the upright. The kingpin and the castor axis allow the tire to rotate about itself and
are defined by the positions of the upper and the lower ball joint. (UBJ and LBJ). These are
spherical joints.
An anti-roll bar was originally included in the design, but later replaced by spring snubbers
(rubber coil to coil inserts) to supplement roll stiffness. The use of spring snubbers results in a
quicker tuning approach that changes the balance of the car without affecting the tire spring rate.
Along with the above advantage, they are inexpensive, easily replaceable and save money and
time in machining as compared to an ARB.
26 2.5.2 Rear Suspension System:
The rear suspension system supports the weight of the engine, drivetrain system, sprung and
unsprung rear suspension mass, which constitutes for approximately 55% of the total car weight.
The rear suspension sub-system has attachment points on the frame. It is an independent wheel,
double wishbone system with a direct acting setup, similar to the front suspension. The geometry
differs from the front, in terms of constraints attached to the wheel movement. The wheel cannot
have angular motion along the z-axis of the vehicle, due to the constraints associated with the
drivetrain system. The axle attaches to the upright and prevents the movement of the wheel in the
x-axis direction, but the axle has a linear movement in the lateral direction inside the hubs. The
toe-rod is mounted on the upright via support brackets on one end and is either bolted/ welded to
the lower wishbone on the other end. The toe-rod controls the rear steer of the vehicle.
2.5.3 Steering System:
The steering system of BCMS 2013 is a traditional ‘rack and pinion’ arrangement, which
allows the driver to control the wheels of the car via a set of linkages and a gear reduction
system. The tie-rod is attached to the rack at one end using rod-end bearings and the other end is
attached to the upright in the front suspension system via a spherical (SPR) joint. The lateral
translation of the tie-rod facilitates the angular movement of the wheels, which are attached to
the front suspension via a revolute joint. In order to fully define the ADAMS/car steering
template, the gear reduction ratio for the rack and pinion along with the steering ratio was
defined. The ADAMS/car steering template is shown in Figure 11.
27 Figure 11: ISO-­‐ Steering System
By entering values for coordinates of the hardpoints, the percentage Ackerman steering can be
defined. Percentage Ackerman is a quantity that indicates the movement of the inner wheels of a
car relative to its outer wheels during vehicle cornering. The rotary motion of the steering wheel
is converted into the linear motion by the rack and pinion arrangement via a steering column and
this linear motion is translated to the wheels by the tie rod.
2.5.4 Powertrain and Drivetrain and Brakes:
The Powertrain and Drivetrain sub-systems define the amount of power and torque output of the
engine and how effectively it is transferred to the wheels. Curves generated from the engine
dynamometer testing are entered into ADAMS as input files [17]. The BCMS team currently
uses both eddy-current and water brake dynamometer, to generate these curves. Figure 71 and
72, in Appendix A, shows the final power and torque curves for the BCMS 2013. ADAMS does
not include the internal components of the engine in the template, since it increases the difficulty
of the work, and inertia values for rotary components are difficult to find. The non-availability of
28 inertia values for internal components of the engine pose a major challenge in developing the
ADAMS/car engine template and this has not been attempted at this point.
The drivetrain system comprises of the axles, tripod, tripod housing (constant velocity joints) and
differential. It deals with the amount of torque transferred to the wheels. It is connected to the
rear suspension sub-system using revolute joints at the hubs. The engine system is connected to
the frame using bushings with finite value of stiffness, which is an equivalent of soft mounts
used in the car to accommodate engine vibration. Attached also are the parametric values that are
associated with the engine and the drivetrain sub-systems.
The brake system is comprised of the brake rotors, brake pads and the brake calipers. This
system is represented graphically in ADAMS with no associated mass and inertia properties
associated with it. Based upon the location of these components (at the four wheels of the car)
this means that the overall vehicle inertia in yaw (rotation around the z axis) will not be
completely defined. This will need to be corrected in future revisions of the model. The
parameters required to fully define the engine and brake sub-system are listed in Figure 42 and
Figure 43 in the Appendix A.
2.5.5 Modeling of Flex Bodies:
The anti- roll bar (ARB) for BCMS 2013 is a Z-bar in the x-y plane working in bending instead
of torsion. Introduction of flexible bodies in a future revision of the model is essential to predict
accurate behavior of this body and the final handling and tuning characteristics of the
suspension. A CAD model of a three-part ARB working in bending is shown in Figure 12.
Figure 12: Three-­‐part ARB
29 As shown in Figure 13, a new template that has been made in ADAMS since this is a nontraditional way of using an ARB in the modeling of an FSAE vehicle in ADAMS.
Figure 13: ADAMS ARB template
The solid body model is imported into ANSYS as a parasolid (.x_t*) file. The flex body is
modeled as a MASS21 element since there is mass and inertia associated with the anti-roll bar.
Kinematic constraints define how the structural system (rigid and flexible body) is held together,
since rigid and flexible bodies are going to be connected in the ADAMS environment.[6]
Material property and element type is defined in ANSYS for the flexible body for meshing
purposes. A triangular mesh is generated of fine grade. The ANSYS-ADAMS interface is used to
save this meshed component as a modal neutral file keeping scaling factors in mind, since
flexible bodies change dimensions when imported from different software packages
30 2.6 Part Modeling of Sub-systems:
2.6.1 Tire Development:
There are parts within the ADAMS/car templates, which are modeled independently and then
included in the sub-systems. The first part chosen was ‘Tires’, since the team has experimental
data with regards to the accurate numerical model of the tires. The tires in the multi-body system
are modeled as rigid bodies attached to the hub at the front and the rear suspension sub-system.
The tire model in consideration is a “Magic Formula” based model developed by Hans Pacejka.
[2]. It is not a predictive tire model but a means to represent the force and moment curves and is
still in continual development. ADAMS 2011 allows the usage of this model since it has a lot of
inherent advantages over the previously used Pacejka94 tire model.
Pacejka 2002 Tire handling model for BCMS 2013:
Fred Jabs [1] had extracted fitted models from the raw data given to the team by the Tire Testing
Consortium (TTC). The tire testing facility runs data analysis tests on different tires every two
years. The data used to develop the current tire model is from Round 5. Stackpole Engineering
also provides numerical tire models for ADAMS use, based on PAC2002 model. The agency
uses the same tire data, which is generated by the TTC. But these models had inherent
disadvantages over the one developed for the BCMS by Fred [10]. The Magic Formula on which
the model is based is as follows:
Equation: General form of the “Magic Formula”
y = D sin[C tan-1 {Bx-E (Bx-tan-1 Bx)}] +Sv
(1)
x=X+ Sh
(2)
Sh= Horizontal Shift; X = Slip angle or Longitudinal slip
SV = Vertical Shift; C= Shape factor; D= Peak factor
31 The handling performance and directional response of a vehicle are greatly influenced by the
mechanical force and moment generating characteristics of the tire. In vehicle dynamics all the
interaction that can happen with the car, happens only at the four small tire contact patches.
Hence an accurate tire model is critical in aiding the virtual model to become more real. In order
to carry forward and use the work done in accurately quantifying the tire forces for the team, the
PAC2002 model was incorporated in the best possible way and fitted according to the multibody software tire test rig requirement.
Since the team is part of the TTC (Tire Testing Consortium) the Team had raw data from the
TTC machines (Round 4 and 5), for which scripts were developed to extract, analyze and
implement the tire data for the selection of the best possible tire[14][15]. The TTC is a research
group, which analyses tires for a variety of parameters at the ‘Calspan Tire Research Facility’,
based in Buffalo, NY. Stackpole Engineering utilizes the same data to create tire models for
ADAMS. The Hoosier R25B tires used by the Bearcat Motorsports were part of the Round 5
testing. These tires were tested on 2 sets of rim widths. The wheels were Keizer aluminum
wheels. The wheel stiffness is assumed to remain constant for the wheels used on the car.
Regardless of the rim width or diameter, all wheels have appropriate backspacing to align the
wheel center with the center of the tire tread. To achieve more accuracy over the previous rounds
of tire testing, attempts were made to enhance data extraction from the model [12] [14] [15]. The
highlights for Round 5 over the previous rounds are as follows:
1) Full drive/brake/combined testing was done for the 10inch tires
2) Each tire/rim combination was put through a full matrix of load, inclination angle and
pressure combinations.
32 3) A “cold to hot” series of sweeps was added to each test to track the break-in of a new
tire and watch performance change as tread temperature increased. The number of these
sweeps has been increased from Round 4.
4) Certain operating conditions are repeated throughout the test for comparison. This
includes a full repeat of the first pressure (12 psi) after the other test pressures were
recorded. The tire data collected is structured in the SAE tire coordinate system. In this
system the X-axis is the intersection of the wheel plane and the road plane with the
positive direction taken for the wheel moving forward. The Z-axis is perpendicular to the
road plane with a positive direction assumed to be acting downward. The Y-axis is in the
road plane, its direction dictated by the use of a right-handed orthogonal axis system. The
angles ‘
’ represent the slip angle and the camber angle respectively.
For fitting the data, the TYDEX (tire data exchange wheel axis system) is used. Figure 22,
Appendix A, shows this wheel axis system. It is also the tire system used by ADAMS/Tire for
the implementation of the magic formula. A tire PAC2002 file was made for the Hoosier R25B
tire model. The units are in the metric system since the raw tire data was in metric. The file type
is ‘. tir’ and the tire version is PAC2002. The tire details are as follows:
1) Tire dimensions: 18*6 6 inch rim (0.457 m * 0.1524 m, 0.1524 m rim)
2) Manufacturer: Hoosier
3) Nominal Section Width (m): 0.205 m
4) Nominal Aspect Ratio: (- 35)
5) Inflation pressure considered: 68947.57 Pascal
6) File Format: ASCII
33 This file is used for the PAC2002 Tire data and Fitting tool in ADAMS. This file includes the
tire model parameters to model the influence of the inflation pressure (Ip) on the steady-state tire
behavior. The units are as follows:
1) Length: meter
2) Force: newton
3) Angle: radians
4) Mass: Kg
5) Time: second
6) Pressure: Pascal
Table 2, Appendix B, lists the data channels used for tire data acquisition at the Tire Test
Consortium, Calspan Facility. The PAC2002 tire model is constructed using the coefficients
shown in Figure 14.
Figure 14: Coefficients-­‐ tire development
34 2.6.2 Shock absorbers
A shock absorber consists of a spring and damper assembly. In BCMS 2013, a coil spring is used
with the damper in a concentric manner. The dampers (OHLINS –TTX25 FSAE special) were
tested on a hydraulic damper dynamometer setup test facility at ThyssenKrupp Bilstein INC of
North America, shown below.
Figure 15: Damper test facility, ThyssenKrupp Bilstein of North America
The dampers, manufactured by Penske, were also tested for the same setup in bump and droop at
similar gas pressures. Using the results of the ‘Force-Velocity’ and ‘Force-Displacement’ graphs
and a comparison made by the Team, a decision was taken to use the TTX-25 shocks. A lot of
testing has been done to compare the two shocks, but the simulation model acts as a tool to select
the best spring-damper setup by providing the ability to input spring and damper files to check
for the ride characteristics of the car. It simultaneously shows the effect of these files on other
suspension sub-system parameters. The current shocks have an overall weight of ~ 480gms,
overall length of 200mm. (center to center of spherical bearings) and a stroke of 57mm. It is a
four way adjustable shock with high and low rebound and compression damping.
35 A figure of the internal schematics of the damper is given in Figure 16. The internal schematics
of the damper in high-speed rebound, and high-speed compression are shown in Figures 38 and
39 in Appendix A respectively.
Cane Creek DB-1
Check valve
Check valve
Piston
Solid Stroke
Compression
(low speed)
Twin Tube
Solid Stroke
Rebound
(low speed)
High Speed
Compression
Reservoir
High Speed
Rebound
Dividing Piston
Nitrogen
gas
Figure 16: Internal Schematics_ TTX-­‐25
This damper uses a piston-cylinder arrangement. It has two work cycles: compression and
extension. The upper part is attached to the frame (i.e. sprung weight) and the lower mount is
attached to the lower wishbone of the front and rear suspensions (unsprung weight) of the BCMS
2013. The piston sits in a hydraulic fluid; the fluid properties and the way it travels through the
orifices of the piston determine the damping. An additional chamber, comprising of pressurized
nitrogen is attached to the main body. It allows for the accommodation of the volume of
hydraulic fluid displaced under compression or extension strokes, providing additional stiffness
36 from the damper. The input for the ADAMS environment is a force-velocity file and the two
figures have been attached which show the damper testing results.
The full force-velocity curve is used to show the hysteresis in the damper. The curves at different
gas pressures are shown in Figure 45, Appendix A. With this damper, the extension and
compression curves (each way) are almost directly on top of each other. This shows very little
hysteresis. With the Kaz Technologies dampers (used in the past), in the rebound direction the
two corresponding curves are very far apart, showing a large amount of hysteresis, which will
show up as inconsistent damping, and slow reactions.
The force-displacement curve (also called a ‘football’ curve) shows damping force along the Yaxis and piston rod displacement along the X-axis. This curve is shown in Figure 46, Appendix
A. For the dampers used by BCMS 2013, the curves are smooth as seen in Figure 46. The Kaz
Technologies dampers have a “flutter” to the force-displacement curve lines, created by their
base valves. This also happens in everyday twin tube dampers in an auto or truck implementation
with their base valves. Something else to look for on these plots is lag/cavitation. If, at any point,
the force becomes extremely linear rather than the football shape shown in Figure 46, Appendix
A, the gas pressure is too low, and the fluid is cavitating. The lag will show up on the direction
change (near zero force), when the damper will not have the parabolic-like curve. Instead, the
curve will face the other way (parabolic in the opposite direction), until pressure builds in the
damper, which causes the oil to become liquid again, and the damper will generate more normal
damping force.
37 2.6.3 Springs:
The spring template in ADAMS requires a force-displacement curve or it calculates the
installed length required based on the force input and the number of coils of the spring. The
spring used has a linear relationship until reaching a non-linearity as it approaches maximum
compression or rebound. Springs with linear characteristics are chosen, since spring behavior
becomes predictable. The ADAMS/car template provides bumpstops to limit spring travel, that
bumpstops have a very high stiffness value. The spring template in ADAMS/car uses
interpolation techniques to estimate stiffness values. Spring definition in ADAMS/car is shown
below in Figure 17.
Figure 17: Spring Design_ ADAMS
The direct acting damper setup is essentially a spring-damper setup attached to a damper cap. It
facilitates in easy adjustment for ride height of the car by adding thin aluminum plates called
shims. Fewer number of parts leads to a reduced unsprung mass and elimination of a motion
ratio results in increased linearity in load-transfer pattern from wheel to shock. The load directly
gets transferred to the frame via bolted joints. The setup is relatively rigid as compared to a
push-rod/pull-rod setup. The effects of changes in spring and damper setup are hence more
predictable.
38 3. Calibration
3.1 Vehicle Mass Moment of Inertia:
This section describes the static calibration procedures adopted for the multi-body model.
Dynamic calibration methods are described in a later section, Section 3.4.
As explained earlier, calibration of sub-systems is an important step in the development of the
multi-body model. The calibration procedures have been divided into static and dynamic parts.
The static parts include furnishing the sub-systems with mass, rotary inertia and geometry data.
Likewise, the dynamic calibration techniques are used to improve the quality of results expected
from the full vehicle and sub-system simulations. Dynamic calibration techniques involve
accelerating or braking of vehicle parts or sub-systems while performing experiments for
collecting numerical data models.
The mass moment of inertia of the rigid body is a fundamental requirement for the virtual
environment to achieve mass balance in the rigid body system. The CAD model developed in
Solidworks calculates the mass moment inertia of the rigid bodies based on simple geometry of
the rigid bodies and the density of the material associated to the part modeled. This mass
moment of inertia is calculated with respect to the back axle centerline of the car. Unfortunately,
the ADAMS model does this with respect to the front axle centerline. To calibrate the simulation
model for the correct inertia values of the entire car in terms of roll, pitch and yaw, experimental
validation of the inertia values was done on a test rig at the Vehicle Inertia Measurement Facility
(VIMF) at the SEA Inc. facility in Columbus, OH.
The test values serve as a starting point for calibration of the inertia model of the rigid body and
also provide an accurate value of the vehicle center of gravity with and without the driver. This
serves as a point for comparison between the design and actual CG of the car. The comparison of
39 the measured and calculated test is associated with measurement of the inertias, the errors
associated with the derived CG height of the car and ways to account for it. The measured inertia
values allow a more realistic simulation and thus better estimate the vehicle response
characteristics.
3.1.1 Test procedure – Vehicle Inertia Measurement
For the vehicle inertias to be accurate, the total car mass was measured. The total car mass was a
summation of four corner masses. This was done to compare the experimental and designed curb
weight of the car with and without the driver. Apart from the vehicle inertia, the center of gravity
of the vehicle is an important vehicle dynamic parameter. The location of the vehicle CG is
important since ADAMS/Car does not have mass associated with all the rigid bodies in the
BCMS 2013 assembly. The total theoretical inertia value is adjusted to match the experimental
value. This is achieved by adjusting the mass and inertia properties of major, rigid bodies, which
contribute most to the total mass of the full vehicle assembly. This exercise is performed to
correlate the CG values. The test rig has been designed by SEA Inc. and consists of a huge
aluminum platform used as ground for the subject car in concern as seen in Figure 18.
Figure 18: Vehicle inertia measurement method
40 After getting the car weights from the corner weight load cells, the track width and wheelbase of
the car were accurately measured. The equations used to measure the vehicle mass moment of
inertia are dependent on several variables. They are as follows:
• CG= Center of gravity height (m)
• K= Approximation constant (dependent on inertia property and vehicle class)
• L= Overall length of the car (m)
• m= Vehicle mass
• TW= Track width
To get the inertia values, the CG value must first be known. The procedure is outlined below:
The VIMF test calculates the CG height by averaging four individual CG heights (two tilting the
vehicle forward and two backwards) by attaching weights to the aluminum platform. A thorough
effort has been made to enlist important rigid bodies whose inertia values would be required in
ADAMS. The variables used for CG calculations at the test rig are as follows. [5]
•
Hv= Vehicle center of gravity distance below pivot axis
•
Hp= Platform’s center of gravity distance below the pivot axis
•
Wv= Weight of the vehicle
•
Wp= Weight of the platform
•
p
= Tilt angle of the platform
•
Xv = Movement if the vehicle relative to the platform in the platform’s X- axis
•
HA= Position relative to the pivot axis of the applied weight in the platform’s Z-axis.
•
LA= Position relative to the pivot axis of the applied weight in the platform’s X-axis
•
WA= Applied weight.
41 Figures 19 through 21 show the vehicle inertia test setup and the results of the vehicle inertia
measurement test.
Figure 19: Vehicle Inertia test facility
42 Figure 20: Vehicle Inertia Test Results_1
Figure 19: Vehicle inertia measurement facility
Figure 21: Vehicle Inertia Test Results_2
43 3.2 Weight Audit of Bearcat Motorsports 2013:
Achieving mass equivalency is the initial key to calibration of the simulation model. The
theoretical and the experimental weight audit acts as a metric for mass calibration of the full
vehicle ADAMS model. The measurement of the theoretical mass of the car was done by
carefully entering material details for sub-system components in the Solidworks model,
assuming the volume of the CAD model is as close to the real part as possible. The CAD model
calculates the mass based on simple volume and density values.
Experimental weight audit was achieved by measuring the mass of every single component of all
sub-systems using a calibrated scale, which had a resolution up to two decimal places. Figure 22
shows car on calibrated scales at the SEA VIMF facility to confirm the accurate weight
measurements.
Figure 22: Experimental weight measurement
Tables, in Appendix B, show the values generated after the theoretical and the experimental
weight audit. The material densities were closely monitored and the CAD model materials were
re-entered to match the experimental masses of the component. The percentage error in weight
44 values comparing the theoretical weight measured from Solidworks and experimental values
from a weigh scale in the table below:
Sub-system
Table 2-Subsystem weight audit
Theoretical Weight
Experimental Weight
Percentage Error
Front suspension
10.64
11.22
5.16
Rear suspension
9.54
10.77
11.4
Engine
58.63
47.60
23.17
Frame
29.96
35.92
16.59
Miscellaneous
19.498
21.683
10.07
The percentage error in the frame and Engine systems is high due to the lack of modeling
expertise of components associated with this system in Solidworks since the number of
components associated with these systems is very high.
3.3 Coordinate measurement for the hardpoints:
The simulation model has to accurately match in shape its digital twin in space; hence, it is
imperative to accurately define the geometry of the hardpoints as mentioned in the previous
chapter. In order to arrive at the best approximation for these values, both modeling and
experimental methods were adopted. In the modeling approach, the measurements for the X, Y
and Z locations of the hardpoints were taken from CAD model of the BCMS 2013. Readings
were taken by measuring the values of all three coordinates from the origin of the Cartesian
coordinate system for the vehicle. This method was followed by an experimental approach. It is
necessary to supplement the CAD data with the physical test data, to account for the inaccuracies
and compliances that are generated in the hardpoint coordinate values during the fabrication
process.
45 In order to perform this test, two steel plates, which acted as reference planes, were used.
Measurements of the hardpoint coordinates were taken using a tape from the origin of the
Cartesian coordinate system. The coordinates of all the hardpoints in both the methods were
measured from the back- axle centerline of the car. Table 18-19 shows the values associated
with these hardpoints. These include suspension connection points on the frame, the drivetrain
and engine connection points on the frame and also the steering connections for the rack and the
pinion steering system adopted by the team. ADAMS virtual environment measures the same set
of hardpoints from the front-axle of the vehicle; hence a lot of care was taken to translate the
coordinates of the hardpoints from the back-axle to the front-axle
3.4 Pseudo static Calibration
3.4.1 Spring File Calibration
In order to supplement the static calibration procedures, some pseudo static calibrations were
performed. In order to achieve results with minimal errors, multiple numbers of tests can be
performed. Due to time and resource constraints, only few tests have been performed and are
described below. The following procedure describes the tests performed to generate accurate
spring stiffness data, which will be used as an input for the spring model, part of the front and the
rear suspension sub-systems. A hydraulic ram was used to compress springs by applying load at
one end of the spring. A hydraulic test bench was used in a closed loop circuit to measure the
Force versus displacement curve for the springs. Figure 23 shows the spring stiffness setup.
Figure 23: Spring stiffness experiment setup
46 The spring input files for the Adams files are as follows:
Four sets of springs were tested using the procedure, with the following results.
The default position of the hydraulic piston is 38.1mm on the left of its complete travel.
1) The details of the load cell used are as follows:
The force/ load applied on the spring was measured by a rod-style load cell, with a
capacity of 8.89kN, with sensitivity number of 2mV/V, having a 6-pin connector, with an
overload limit (side force) of 13.34kN and a side force load limit of 0.2224kN.
2) A medium duty hydraulic cylinder has been used as part of the rig with a nominal
pressure rating of 6894744.82 N/m^2(1000psi), depending on bore size. The cylinder has
been connected to a closed loop hydraulic rig whose oil pressure and piston position is
controlled by knobs attached on the electrical panel, which is a part of the rig
construction.
3) A National Instrument data acquisition system was used with Matlab based Mini-X
software (UC developed) to read the data.
Due to the mounting conditions of the plate and the spring, a static load exists on the load cell.
The table for the Force vs. Displacement characteristics of the spring was made using a
resolution of 0.1 inches. Four sets of springs were tested to validate the test setup and minimize
the random and the bias errors. Two sets of readings were taken for each spring to minimize
human errors.
47 Test Case 1: The spring in concern here is 13134.51 N/m (75 pounds / inch) and the free length
of the spring is 0.12 m (4.8 inches). The static load for this setup is 17.79 N (4 pounds.)
Test case 2: The spring in concern here is 14885.78 N/m (85 pounds/ inch) and the free length of
the spring is 0.126 m (4.97 inches). The static load for this setup is 17.79 N (4 pounds.)
Test case 3: The spring in concern here is 95-pounds/ inch and the free length of the spring is
4.80 inches. The static load for this setup is 20.5 pounds.
Test case 4: The spring in concern here is 170 pounds / inch and the free length of the spring is
4.85 inches. The static load for this setup is 14.6 pounds. The results for the above test cases are
shown in Appendix A.
3.4.2 Adams motion ratio plot:
A second type of dynamic calibration determines the motion ratio calibration of the vehicle. This
calibration test was divided in to two parts. The theoretical motion ratio test, which was
performed in the ADAMS environment, is part of the conclusions chapter and will be explained
in Section 4.1. The experimental approach is as follows:
3.4.2.1 Experimental Calibration of the front and rear suspension subsystems:
The front suspension subsystem is experimentally tested for its motion ratio, values for which
will be used as a reference for the theoretical motion ratio test performed in ADAMS simulation
environment. The motion ratio tested in this procedure is the (wheel travel/damper travel.) The
additional motion ratio of (bell-crank travel)/ (damper travel) are non-existent due to the absence
of bell-crank in the system which is replaced by direct acting dampers.
The test apparatus uses the MINI-X data acquisition software system to which a ‘National
Instruments’ DATA ACQ is connected, which is the hardware used for gathering data from the
48 two sensors used. The first sensor is a string potentiometer and the second, is a ‘Linear Variable
Differential Transformer’ commonly known as an ‘LVDT’
3.4.2.2 Test Procedure:
The string pot was attached to the lower wishbone mount and the LVDT was connected to the
damper (Ohlins TTX-25) in parallel. A figure to depict the experiment is attached below.
Figure 24: Test procedure-­‐ Motion ratio
A wooden spacer was made for the shaft of the sensor to activate the nut on the damper cap. The
string pot was rigidly placed/ mounted on the ground, and the string was kept as parallel to the
lower wishbone mount as possible to measure the exact pull of the string. The exact experimental
setup is shown in the Appendix A, Fig 68, Fig 69 and Fig 70.
Sections 3.4.1 and 3.4.2 were two sample cases of making the simulation environment more real.
Multiple calibration tests, experimental and otherwise could be performed on all the sub-systems
to achieve a good ADAMS model.
49 3.5 Calibration examples:
An example would be Figure 25 which shows a percentage error of 4.6511 for FVSA at a static
camber angle of(-1 degree).
Figure 25: FVSA vs. camber change-­‐ % error
Similarly, Figure 62 and Figure 63 in Appendix A, shows the value of static kingpin inclination
and front suspension roll rate in ADAMS to be 6.3 degrees and 185 N-mm/ deg, the theoretical
values being 5.8 degrees and 201N-mm/ deg respectively.
A Front suspension motion ratio test was also conducted in the Adams simulation environment.
The results were used as a reference for the same test performed experimentally.
A front suspension file, comprising of a direct acting setup was used with the parameters that
made the system are as follows: On the abscissa is the damper travel, and on the ordinate is the
wheel travel. Motion ratio for the front suspension is defined as a ratio to measure the wheel
travel to the shock travel. In the test case performed in Adams, the value comes out to be 0.76,
vis-à-vis the value for the front motion ratio, which was experimentally obtained, is 0.88. The
graph associated with the test in the simulation environment is shown on Figure 60. The graph
associated with the experimental test is shown in the Figure 61.
50 The discrepencies in theoretical weight and experimental weight introduces error in experimental
tests which involve measuring the modal parameters of the car (refer to table 2).There is
approximately 12 % error in weight measurements for the front and the rear suspension subsystems. An example in that direction would be the modal testing of the frame for torsional
stiffness[16] .The error in resonance frequencies as measured in FEA software and experimental
work, may be as a result of weight error.This helps to optimize designs in CAD softwares
keeping in mind the material proeprties offered in the software and the properties of materials
used in the car are different.
51 4.0 Conclusions and Recommendations for Future work
The thesis work has established an initial working multi-body model that has the capability to
predict vehicle behavior. More calibration tests have to be performed for the different subsystems to improve the accuracy of the parameter files used for making the model. The objective
was to correlate the vehicle static and dynamic parameters extracted from the model after
calibration. The static portion of this goal has been minimally achieved but it is clear that getting
even a completely calibrated model with respect to statics has been an enormous undertaking.
The further development of the static calibrations and dynamic calibrations will need to be left
for others, achieving sufficient levels of accuracy between the theoretical model of BCMS 2013
and the simulated model of BCMS 2013. At this point, the model is working and is primarily
useful for trending of suspension kinematics, since the BCMS 2013 has been mainly calibrated
for the front and rear suspension sub-system.Visualizing those trends aids in understanding
abstract suspension development parameters. After running sub-system simulations in ADAMS,
graphs were generated to determine the values of a selective set of parameters used for vehicle
dynamic calculations, comparing it with the theoretical model generated from empirical
calculations. Error in the values generated was used as a benchmark for the ‘correctness’ of the
model. Error between verified and calibrated files range from approximately 5-15% .Full car
analysis requires extensive calibration and verification which is a part of the future scope of the
project. The bigbest unforeseen
challenge was to match similar sub-systems models from
different software platforms.
4.1 Future Scope:
In order to achieve better simulation results, more correlation techiniques have to be used.
Dynamic full-car simulations have been performed in ADAMS, but lacks accurate calibrated
52 input data, an example of which is, the inertia of the rotary components of the engine, hence
future work would include measuring accurate engine inertias. The accuracy of the power and
torque curves is a function of the dynamometer used, hence there is a need for better engine test
setup. The use of a CMM for hardpoint location measurement would go a long way in making
the location of suspension hardpoints in space more accurate. A lot of work has been completed
by electronics team for data acquisition using the Performance Electronics data acquisition
system and the Motec data logger. Validation of longitudinal and lateral tire slip using wheel
speed sensors and damper travel using shock travel sensor etc using the above DAQ system,
would aid in correlating the calibrated with the actual test data. ADAMS platform allows the
user to generate custom driver profiles to mimic real driver ( .dcf ) files. It is imperative to use
this functionality since it allows the team to understand the race lines a driver would take on a
defined path.
53 4.2 References
[1] Milliken, William F., and Douglas L. Milliken. Race car vehicle dynamics. Ed. L. Daniel
Metz. Warrendale, PA: Sae International, 1995.
[2] Pacejka, Hans. Tyre and vehicle dynamics. Elsevier, 2005.
[3] Gillespie, Thomas D. "Fundamentals of vehicle dynamics (R-114)." SAE International,
March (1992).
[4] Blundell, Michael, and Damian Harty. The multibody systems approach to vehicle dynamics.
Access Online via Elsevier, 2004.
[5] Ronald, A. "Bixel et al: Development in Vehicle Center of Gravity and Inertial Parameter
Estimation and Measurement.”
[6] Chunhuaa, Z. H. A. O., et al. "Study on modeling methods of flexible body in ADAMS."
(2011).
[7] http://www.ohlinsusa.com/files/files/Schematic.pdf
[8] Smith, Carroll. Tune to win. Fallbrook: Aero Publishers, 1978.
[9] C. Rouelle, Vehicle Dynamics & Race Car Engineering Seminar, Denver, CO: Optimum G
LLC, 2008
[10] M. J. Stackpole, A. Stackpole and T. Stackpole, "PAC2002 Fitting Results - FSAE Tire
Testing Program - ADAMS/2005r2 Support," Stackpole Engineering Services, Inc., North
Canton, OH, 2008.
[11] Simplified Tools and Methods for Chassis and Vehicle Dynamics Development for FSAE
Vehicles – Fred Jabs
[12] Kasprzak, E., and David Gentz. "The formula SAE tire test consortium—tire testing and
data handling." SAE Paper (2006): 01-3606.
[13] "TTX25 MkII." Öhlins Performance Suspension, Shocks, Struts, and Dampers Home.
Ohlins, n.d. Web. 17 Oct. 2013.
[14] "Milliken Research Associates, Inc. -- FSAE Tire Test Consortium." Milliken Research
Associates, Inc. -- FSAE Tire Test Consortium. Milliken Research Associates, n.d. Web. 17 Oct.
2013.
[15] Calspan TIRF; FSAE TTC; "Round 5 Data," 3 April 2012. [Online]. Available:
54 http://sae.wsu.edu/ttc/viewtopic.php?f=22&t=78. [Accessed 3 April 2012].
[16] Torsional Stiffness Measuring Machine and Automated Frame Design tools- Thomas Steed
[17] Intake manifold design for an air restricted design- David Moster
55 Appendix A: Figures
Figure 26: SAE Tire Axis System
Figure 27: TYDEX W-­‐ axis System
56 Figure 28 Front view-­‐ Front suspension
Y Z X Figure 29: Plan-­‐ Front Suspension
Figure 30: ISO-­‐ Front Suspension
57 Figure 31: Front View-­‐ Rear suspension
Z
Y
Figure 32: Plan: Rear Suspension
X
Figure 33: ISO-­‐ Rear Suspension
58 Figure 34: BCMS_coordinates_1
Figure 35: BCMS_Coordinates_2 59 Figure 36: Damper Testing-­‐ Penske
Figure 37: Damper Testing-­‐ Ohlins
60 High Speed Rebound Stroke
High Speed Compression Stroke
Piston
rebound
shim stack
opens
Rebound
poppet opens
(high speed)
Compression
poppet opens
(high speed)
Piston
compression
shim stack
opens
Displaced oil
Figure 38: Internal schematics-­‐ High speed rebound
Displaced oil
Figure 39: Internal schematics-­‐ High speed compression ion 61 Figure 40 Joints-­‐names and Types -­‐Front Suspension
62 Figure 41: Joints-­‐Names and Types-­‐ Rear Suspension
63 Figure 42: Brake System Sample Requirements
Figure 43: Engine System Sample Requirements
64 Figure 44: Linkage Diagram-­‐ Front Suspension
Figure 45: Linkage Diagram-­‐ Rear Suspension
65 Figure 46: Kinematics-­‐ Front Suspension
Figure 47: Kinematics-­‐ Rear Suspension
66 Figure 48: Force vs. Velocity-­‐ Ohlins
Figure 49: Force vs. Displacement-­‐ Ohlins
67 Figure 50: Spring Stiffness Testing-­‐ Apparatus
Figure 51: Strain Gauge based load cell
68 Figure 52: Spring stiffness test apparatus
Figure 53: Spring stiffness Test_1 69 Figure 54: Spring Stiffness Test_2
Figure 55: Spring Stiffness test_3 70 Figure 56: Spring Stiffness test_4
Figure 57: Damper input file
71 Figure 58: Force-­‐ Velocity-­‐ Penske Figure 59: Force-­‐ Velocity Ohlins
72 Figure 60 ADAMS motion ratio test results
Figure 61: Experimental Motion ratio test-­‐results
73 Figure 62: Front static kingpin inclination
Figure 63: Front suspension roll rate
74 Figure 64: Rear suspension-­‐FVSA
Figure 65: ADAMS sub-­‐system test bench
75 Figure 66: Gantt chart Representation -­‐ 2013
76 Figure 67: Thesis timeline
77 Figure 68: Experimental setup-­‐ motion ratio test
Figure 69: Experimental setup-­‐ motion ratio test
Figure 70: Experimental setup-­‐ motion ratio test
78 Figure 71: Engine_input_1
Figure 72: Engine_input_2
79 Appendix B Table 3: Calspan Tire Data Channels Channel
Description
TIRF USCS
TIRF SI
‘ET’
Elapsed time
seconds
seconds
TYDEX
units
seconds
‘testid’
Calspan TIRF ID number
-
-
-
‘tireid’
Tire Description
-
-
-
‘P’
Inflation Pressure
Psi
KPa
Pascal
‘N’
Tire RPM
Rpm
Rpm
Radian/sec
‘V’
Roadway Velocity
Mph
Kmph
Meter/sec
‘SA’
Slip Angle- SAE J2047
Degrees
Degrees
Rad
‘SL’
Slip Longitudinal- SAE J2047
-
-
-
‘SR’
Slip Ratio – Calspan TIRF
-
-
-
‘FZ’
Normal Force SAE J2047
Lbf
Newtons
Newtons
‘IA’
Inclination Angle SAE J2047
Degrees
Degrees
Rad
‘FX’
Longitudinal Force SAE J2047
Lbf
Newtons
Newtons
‘FY’
Lateral Force SAE J2047
Lbf
Newtons
Newtons
‘NFX’
FX/FZ- Longitudinal Coefficient
-
-
-
‘NFY’
FY/FZ- Lateral Coefficient
-
-
-
‘MX’
Overturning Moment SAE J2047
Lbf*ft.
N*meter
N*meter
‘MZ’
Aligning Moment SAE J2047
Lbf*ft.
N*meter
N*meter
‘AMBTMP’
Ambient Temperature
Degree F
Degree C
Degree K
‘RST’
Roadway Surface Temperature
Degree F
Degree C
Degree K
‘TSTC’
Center Tire Tread Surface Temperature
Degree F
Degree C
Degree K
‘TSTI’
Inner Tire Tread Surface Temperature
Degree F
Degree C
Degree K
‘TSTO’
Outer Tire Tread Surface Temperature
Degree F
Degree C
Degree K
‘RE’
Effective Rolling Radius
Inch
Cm
Meter
‘RL’
Loaded Radius
Inch
cm
Meter
80 Table 4: PAC2002 Tire Model Coefficients_1 Sr. No
1
2
3
4
Property
Property File Format
USE_MODE
VXLOW
LONGVL
Value
PAC2002
14
1
16.6
Comment
Tire use switch
Measurement speed
Table 5: PAC2002 Tire Model Coefficients_2 Sr.no
Property
Value
Comment
1
Unloaded radius
0.2236
Free tire radius
2
Width
0.205
Nominal section tire width
3
Aspect ratio
0.35
Nominal aspect ratio
4
Rim radius
0.127
Nominal rim radius
5
Rim width
0.1524
Rim width
Table 6: PAC2002 Tire model Coefficients_3 Sr.no
Property
Value
Comment
1
KPUMIN
-1.5
Minimum valid wheel slip
2
KPUMAX
1.5
Maximum valid wheel slip
Table 7: PAC2002 Tire Model Coefficients_4 Sr.no
1
2
Property
ALPMIN
ALPMIN
Value
-1.5708
1.5708
Comment
Minimum valid slip angle
Maximum valid slip angle
Table 8: PAC2002 Tire Model Coefficients_5 Sr.no
1
2
Property
CAMMIN
CAMMAX
Value
-0.26181
0.26181
Comment
Minimum valid camber angle
Maximum valid camber angle
81 Table 9: PAC2002 Tire Model Coefficients_6 Sr.no
1
2
Property
FZMIN
FZMAX
Value
225
10125.0
Comment
Minimum valid wheel load
Maximum valid wheel load
Table10: PAC2002 Tire Model Coefficients_7 Sr.no
1
Property
QSX1
Value
0.0086
2
3
QSX2
QSX3
0.8313
0.0594
Comment
Lateral force induced overturning
moment
Camber induced overturning couple
Fy induced overturning couple
Table11: PAC2002 Tire Model Coefficients_8 Sr.no
1
2
3
4
5
6
Property
Vertical Stiffness
Vertical damping
BREFF
DREFF
FREFF
FNOMIN
Value
107000.0
3100.0
-2.1464
15.655
2.8975
852.93
Comment
Tire vertical stiffness
Tire vertical damping
Low load stiffness e.r.r.
Peak value of e.r.r.
High load stiffness e.r.r.
Nominal wheel load
82 Table 12: PAC2002 Tire Model Coefficients_9 Sr.no
Property
Value
Comment
1
LFZO
1.0
Scale factor of nominal (rated) load
2
LCX
1.0
Scale factor of Fx shape factor
3
LMUX
1.0
Scale factor of Fx peak friction coefficient
4
LEX
1.0
Scale factor of Fx curvature factor
5
LKX
1.0
Scale factor of slip stiffness
6
LHX
1.0
Scale factor of horizontal shift
7
LVX
1.0
Scale factor of vertical shift
8
LGAX
1.0
Scale factor of camber for Fx
9
LCY
1.0
Scale factor of Fy shape factor
10
LMUY
1.0
Scale factor of Fy peak friction coefficient
11
LEY
1.0
Scale factor of Fy curvature factor
12
LKY
1.0
Scale factor of Fy cornering stiffness
13
LHY
1.0
Scale factor of Fy horizontal shift
14
LVY
1.0
Scale factor of Fy vertical shift
15
LGAY
1.0
Scale factor of camber for Fy
16
LTR
1.0
Scale factor of peak of pneumatic trail
17
LRES
1.0
Scale factor of offset of residual torque
18
LGAZ
1.0
Scale factor of camber for Mz
19
LXAL
1.0
Scale factor of alpha influence on Fx
20
LYKA
1.0
Scale factor of alpha influence on Fx
21
LVYKA
1.0
Scale factor of kappa induced Fy
22
LS
1.0
Scale factor of Moment arm of Fx
23
LSGKP
1.0
Scale factor of Relaxation length of Fx
24
LSGAL
1.0
Scale factor of Relaxation length of Fy
25
LGYR
1.0
Scale factor of gyroscopic torque
26
LMX
1.0
Scale factor of overturning couple
27
LVMX
1.0
Scale factor of Mx vertical shift
28
LMY
1.0
Scale factor of rolling resistance torque
83 Table 13: PAC2002 Tire Model Coefficients_10 Sr.no
1
2
Property
PCX1
PDX1
Value
1.7917
2.5626
Comment
Shape factor Cfx for longitudinal force
Longitudinal friction Mux at Fznom
3
4
PDX2
PDX3
-0.8766
10.9922
Variation of friction Mux with load
Variation of friction Mux with camber
5
6
7
PEX1
PEX2
PEX3
0.5970
0.6872
0.9788
Longitudinal curvature Efx at Fznom
Variation of curvature Efx with load
Variation of curvature Efx with load squared
8
9
10
11
12
PEX4
PKX1
PKX2
PKX3
PHX1
-0.1083
70.7751
-15.6214
0.0130
0.0020
Factor in curvature Efx while driving
Longitudinal slip stiffness Kfx/Fz at Fznom
Variation of slip stiffness Kfx/Fz with load
Exponent in slip stiffness Kfx/Fz with load
Horizontal shift Shx at Fznom
13
14
15
PHX2
PVX1
PVX2
0.0015
-0.0798
-0.0969
Variation of shift Shx with load
Vertical shift Svx/Fz at Fznom
Variation of shift Svx/Fz with load
16
17
18
19
20
RBX1
RBX2
RCX1
REX1
REX2
-21.2425
-29.7784
0.8081
-2.3930
9.3902
Slope factor for combined slip Fx reduction
Variation of slope Fx reduction with kappa
Shape factor for combined slip Fx reduction
Curvature factor of combined Fx
Curvature factor of combined Fx with load
21
22
23
RHX1
PTX1
PTX2
-0.0153
0.85683
0.00011
Shift factor for combined slip Fx reduction
Relaxation length SigKap0/Fz at Fznom
Variation of SigKap0/Fz with load
24
PTX3
-1.3131
Variation of SigKap0/Fz with exponent of load
Table 14: PAC2002 Tire Model Coefficients_11 Sr.no
1
Property
QSY1
Value
0.01
2
3
4
QSY2
QSY3
QSY4
0
0
0
Comment
Rolling resistance torque coefficient
Rolling resistance torque depending on Fx
$Rolling resistance torque depending on speed
Rolling resistance torque depending on speed ^4
84 Table 15: PAC2002 Tire Model Coefficients_12 Sr.no
Property
Value
Comment
1
QBZ1
10.0298
Trail slope factor for trail Bpt at Fznom
2
QBZ2
-21.7061
Variation of slope Bpt with load
3
QBZ3
57.4837
Variation of slope Bpt with load squared
4
QBZ4
-3.2488
Variation of slope Bpt with camber
5
QBZ5
0
6
QBZ9
-14.9000
Slope factor Br of residual torque Mzr
7
QBZ10
-0.1552
Slope factor Br of residual torque Mzr
8
QCZ1
1.8690
Shape factor Cpt for pneumatic trail
9
QDZ1
1.0368
Peak trail Dpt" = Dpt*(Fz/Fznom*R0)
10
QDZ2
-2.6120
Variation of peak Dpt" with load
11
QDZ3
-3.1727
Variation of peak Dpt" with camber
12
QDZ4
43.8455
Variation of peak Dpt" with camber squared
14
QDZ6
-0.0254
Peak residual torque Dmr" = Dmr/(Fz*R0)
15
QDZ7
0.0019
Variation of peak factor Dmr" with load
16
QDZ8
-2.1903
Variation of peak factor Dmr" with camber
17
QDZ9
0.2102
Variation of peak factor Dmr" with camber and load
18
QEZ1
1.0365
Trail curvature Ept at Fznom
19
QEZ2
-0.0242
Variation of curvature Ept with load
20
QEZ3
0.0072
Variation of curvature Ept with load squared
21
QEZ4
0.0029
Variation of curvature Ept with sign of Alpha-t
22
QEZ5
-0.0716
Variation of Ept with camber and sign Alpha-t
23
QHZ1
0.0071
Trail horizontal shift Sht at Fznom
24
QHZ2
0.00098
Variation of shift Sht with load
25
QHZ3
-0.2925
Variation of shift Sht with camber
26
QHZ4
0.1884
Variation of shift Sht with camber and load
27
SSZ1
-0.0370
Nominal value of s/R0: effect of Fx on Mz
28
SSZ2
-0.0469
Variation of distance s/R0 with Fy/Fznom
29
SSZ3
0.9717
Variation of distance s/R0 with camber
30
SSZ4
-1.3253
Variation of distance s/R0 with load and camber
31
QTZ1
0
32
MBELT
0
Variation of slope Bpt with absolute camber
Gyration torque constant
85 Table 16: Weight and Inertia Properties_1 Sr.
no
Sub-system-Suspension
Part Name
Theoretical
Mass (Kg)
Experiment
al Mass
(Kg)
2.9
3.5
Center of Mass Location
X
Y
Z
(m)
(m)
(m)
0
0.0013
0
Mass Moment of Inertia
Ixx
Iyy
Izz
Kg-m^2
Kg-m^2
Kg-m^2
0.10642
0.171
0.10642
1
Hoosier R25B
2
Wheels
2.5537
2.2
0
-0.033
0
0.025699
0.0357
0.025699
3
Calipers P34G
0.6985
0.0675
0.0246
0.03302
0.00161
0.004541
0.004175
4
Damper-TTX 25
0.448
With
upright
0.93
0.0202
-0.021
0.02288
3.048
0.56305
0.80584
5
Hub
0.6304
With
upright
0
0
-0.0297
0.001428
0.001428
0.000834
6
Upright
0.7393
3.1
0.0050
0.0071
0.00457
0.000921
0.001498
0.002
7
Steering Mount (Upright)
8
Damper strut
0.06123
With
damper
9
Ride height Adjusters
0.03628
N/A
10
ARB Mounting plate
0.04895
11
Shock mounting plate
0.04895
With
Chassis
12
Front rotor
0.6803
With
upright
0
0.0025
0
13
Upper Wishbone
0.2086
0.25
-0.033
0
-0.0005
14
Lower Wishbone
0.3129
0.300
-0.036
-0.172
0
0.01206
0.00163
0.01368
15
Tie-rod
0.1288
0.11
0
0
-0.0005
0.003825
0.003825
7.023E-6
16
GE-8C bearing
0.01
0.01
17
Chassis Mounts (upper F)
0.14968
0.15
18
Chassis Mounts (upper R)
0.14968
0.15
19
Chassis Mounts (lower F)
0.210
0.235
20
Chassis Mounts (lower R)
0.210
0.235
21
Upper Damper Mounts
0.13
With
Chassis
22
Springs
0.188
0.220
10.64332
11.12
Total
0.12
With upright
With Upright
0.000287
0.00029
0.000032
0.001656
0.0033
0.00166
0.00382
0.00436
0.000550
Inconsequential
N/A
With Chassis
With Dampers
86 Table 17: Weight and Inertia Properties_2 Sr.
no
Sub-system-Suspension
Part Name
(Rear-Left)
Theoretical
Mass(Kg)
Experimental
Mass(Kg)
Center of Mass Location
X
Y
(m)
Mass Moment of Inertia
Z
(m)
Ixx
(m)
Kg-m^2
Iyy
Kg-m^2
Izz
Kg-m^2
1
Hoosier R25B
2.9
3.5
0
0.0013
0
0.10642
0.171
0.10642
2
Wheels
2.5537
2.2
0
-0.033
0
0.025699
0.0357
0.025699
3
Caliper- AP Racing 4226
0.24
0.24
0.0675
0.0246
0.03302
0.00161
0.004541
0.004175
4
Damper-TTX 25
0.448
0.895
0.0202
-0.021
0.02288
3.048
0.56305
0.80584
5
Hub
0.5125
With upright
0
0
-0.0297
0.001428
0.001428
0.000834
6
Upright
0.893577
2.77
0.0050
0.0071
0.00457
0.000921
0.001498
0.002
7
Steering Mount(Upright)
8
Damper strut
0.05805
0.0579
0.000287
0.00029
0.000032
9
Ride height Adjusters
0.03628
10
ARB Mounting plate
11
Shock mounting plate
0.02585
With Chassis
12
Rear rotor
0.3084
With upright
0
0.0025
0
0.001656
0.0033
0.00166
13
Upper Wishbone
0.15875
0.29
-0.033
0
-0.0005
0.00382
0.00436
0.000550
14
Lower Wishbone
0.2222
0.33
-0.036
-0.172
0
0.01206
0.00163
0.01368
15
Tie-rod
0.0821
0.15
0
0
-0.0005
0.003825
0.003825
7.023E-6
16
GE-8C bearing
0.01
0.01
17
Chassis Mounts(upper F)
0.160571
0.12
18
Chassis Mounts(upper R)
0.1179
0.06
19
Chassis Mounts(lower F)
0.2
0.2
20
Chassis Mounts(lower R)
0.2
0.2
21
Upper Damper Mounts
0.13
With Chassis
22
Springs
0.188
0.220
Total
N/A
With damper
0
0
N/A
Inconsequential
N/A
9.5439
10.775
N/A
With Chassis
With Dampers
87 Table 18: Hardpoint Location Coordinates (Front) Sr.no
Point Name
X-location
(mm)
Y-location
(mm)
Z-location
(mm)
1
Driveshaft inner
267.0
-200.0
255.0
2
Lower control arm front
-98.59
-280.075
116.052
3
Lower control arm outer
-3.722
-525.91
130.35
4
Lower control arm rear
69.282
-280.075
116.052
5
Lower strut mount
-5.689
-470.12
180.0
6
(S) Rack house mount
40.74
-280.075
144.625
7
Sub frame front
-133.0
-450.0
180.0
8
Sub frame rear
667.0
-450.0
180.0
9
Tierod inner
40.794
-274.07
144.625
10
Tierod outer
30.515
-587.026
175.97
11
Top damper mount
30.0
-202.61
548.245
12
Upper control arm front
98.592
-280.5115
272.989
13
Upper control arm outer
11.415
-517.75
306.275
14
Upper control arm rear
-53.573
-280.07
272.754
15
Wheel center
57.029
-605.15
259.697
16
Global part reference
0.0
0.0
0.0
17
(S) Intermediate shaft forward
116.994
-5.145
271.628
18
(S) Intermediate shaft rear
279.4
-5.145
436.728
19
(S) Pinion pivot
40.794
-5.145
144.628
20
(S) Input rotation
200.0
200.0
0.0
21
(S) Input slider
200.0
0.0
0.0
22
(S) Input translation
200.0
-200.0
0.0
23
(S) Steering wheel center
469.9
-5.145
512.928
88 Table 19: Hardpoint Location Coordinates (Rear) Sr.no
Point Name
X-location
(mm)
Y-location
(mm)
Z-location
(mm)
1
Drive shaft inner
1550.51
-157.13
213.15
2
Lca front
1225.50
-212.38
129.04
3
Lca outer
1542.48
-502.75
145.60
4
Lca rear
1631.57
-211.94
127.08
5
Lower strut mount
1540.65
-452.39
162.80
6
Subframe front
1250.0
-220.0
180.0
7
Subframe rear
1600.0
-220.0
180.0
8
Tierod inner
1631.57
-211.34
147.97
9
Tierod outer
1648.07
-499.33
164.6
10
Strut top mount
1401.32
-192.10
455.60
11
Uca front
1397.24
-275.1305
263.34
12
Uca outer
1574.72
-471.80
325.39
13
Uca rear
1619.72
-274.95
268.54
14
Wheel center
1606.42
-605.15
223.61
15
global part reference
0.0
0.0
0.0
16
Steering input rotation
200.0
200.0
0.0
17
Steering input slider
200.0
0.0
0.0
18
Steering input translation
200.0
-200.0
0.0
89 Table 20: Weight Audit -­‐ Drivetrain Sr. No
Sub-system - Part Name
Theoretical Mass (Kg)
Experimental Mass
(Kg)
1
Frame
29.9688
35.92
2
Axle (Left)
0.8618
0.66
3
Axle (Right)
1.108
0.85
4
Tripod
0
0
5
Tripod Housing
0.7
0.72
6
Differential
2.8803
3.15
7
Differential (1,2,3)
0.7244
1.15
8
Chain
0.74
0.74
9
Sprocket and Chain Guard
1.02
1.05
Table 21: Weight Audit -­‐ Powertrain Sr.
No
Sub-system-Suspension
Part Name
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
(Engine)
Engine (WET)
Twinkie (Restrictor side)
Airbox (Middle part)
Airbox (Twinkie side)
Restrictor – ABS plastic
Throttle body
Bell mouth
Air filter
Exhaust pipe
Muffler + cover
Fuel Tank
Radiator core fins
Radiator upper Tank
Radiator lower Tank
Fuel Tank Bracket *4
Swirl Pot
Fuel Lines + Pressure Regulator
Fuel Pump
19
Catch Cans
Total
Theoretical Mass (Kg)
Experimental Mass
(Kg)
34.0194
0.76203
0.4173
0.8255
0.1769
0.0816
0.0952
0.6803
1.0750
7.983
8.178
1.9323
0.0997
0.1088
0.097
36.5
2.6
0.1
0.1133
1.1
2.8947
0.097
0.3
0.9
0.8
0.11
58.635
47.6078
90 Table 22: Weight audit -­‐ Miscellaneous Parts Sr. No
Sub-system - Part Name
Theoretical Mass (Kg)
1
Impact Attenuator
0.75
Experimental Mass
(Kg)
0.8
2
Pedal Cluster
2.455
2.5
3
Shifter
0.25
0.3
4
Electronics
5
Battery
0.8
6
Driver
~65
7
Body
2.3
8
Seat
1.45
9
Head Rest
10
Nuts, Bolts and Circlips
11
Router
0.3
12
Firewall
0.58
0.6
13
Sidewall
0.35
0.4
14
Undertrays
2.013
2.7
15
Brake Light
0.25
5
4.533
1.1
1.7
0.25
Total
3
15.848
20.435
91 Table 23: Spring Stiffness Test Results_1 Sr.no
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Displacement
(Inches)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
Displacement
(mm)
2.54
5.08
7.62
10.16
12.7
15.24
17.78
20.32
22.86
25.4
27.94
30.48
33.02
35.56
38.1
Force Required
(Pounds)
14
21.6
31
40
48.7
59.1
66.6
75.5
83.9
91.1
96.8
101.7
107.8
113.6
118.2
Force Required
(Newton)
62.275
96.081
137.894
170.928
216.628
262.889
296.251
335.840
373.205
405.232
430.587
452.384
479.518
505.317
525.779
Table 24: Spring Stiffness Test Results_2 Sr.no
1
2
Displacement
(inches)
0.1
0.2
Displacement
(mm)
2.54
5.08
Force Required
(pounds)
30
38.7
Force Required
(Newton)
133.446
172.146
3
0.3
7.62
49.6
220.631
4
5
0.4
0.5
10.16
12.7
62.8
76.6
279.348
340.733
6
7
0.6
0.7
15.24
17.78
90.3
101.5
401.674
451.494
8
0.8
20.32
114.0
507.097
9
10
0.9
1.0
22.86
25.4
127.3
140.9
566.258
626.754
11
1.1
27.94
154.0
685.026
12
13
1.2
1.3
30.48
33.02
166.8
182.3
741.963
810.910
14
1.4
35.56
197.8
879.858
15
1.5
38.1
210.3
935.461
92 Table 25: Spring Stiffness Test Reults_3 Sr.no
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Displacement
(Inches)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
Displacement
(mm)
2.54
5.08
7.62
10.16
12.7
15.24
17.78
20.32
22.86
25.4
27.94
30.48
33.02
35.56
38.1
Force Required
(Pounds)
30
38.7
49.6
62.8
76.6
90.3
101.5
114.0
127.3
140.9
154.0
166.8
182.3
197.8
210.3
Force Required
(Newton)
133.446
172.146
220.631
279.348
340.733
401.674
451.494
507.097
566.258
626.754
685.026
741.963
810.910
879.858
935.461
Table 26: Spring Stiffness Test Results_4 Sr.no
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Displacement
(Inches)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
Displacement
(mm)
2.54
5.08
7.62
10.16
12.7
15.24
17.78
20.32
22.86
25.4
27.94
30.48
33.02
35.56
38.1
Force Required
(Pounds)
31.1
43.7
57.7
71.1
86.8
100.1
112.5
128.6
142.5
159.0
175.3
189.4
216.3
231.6
257.8
Force Required
(Newton)
138.339
194.387
256.662
318.937
386.105
445.266
500.424
572.041
633.871
707.267
779.773
842.493
962.150
1030.156
1146.24
93 Table 27: Front Damper File Sr.No
Velocity
Damping Force
(mm/sec)
(Newton)
1
-1270
-747.75
2
-254.0
-404.75
3
-152.4
-327.40
4
-127.0
-293.55
5
-101.6
-266.90
6
-76.2
-227.75
7
-50.8
-185.05
8
-25.4
-103.20
9
0.0
0.0
10
25.4
231.30
11
50.8
347.70
12
76.2
427.0
13
101.6
483.2
14
127.0
542.55
15
152.4
585.7
16
254.0
711.7
17
1270
1609.05
94 Table 28: Joints Characterization Sr.no
Name
Abbreviation
Dof
Type of motion
1
Translational
TRA
1
Translation of one part with respect to another while all
axes are co-directed
2
Revolute
REV
1
Rotation of one part with respect to another along a
common axis
3
Cylindrical
CYL
2
Translation and Rotation of one part with respect to
another
4
Spherical
SPH
3
Three rotations of one part with respect to the other
while keeping two points, one on each part, coincident
5
Planar
PLA
3
The x-y plane of one part slides with respec to another
6
Fixed
FIX
0
No motion of any part with respect to another
7
Inline
INL
4
One translational and three rotational motions of one
part with respect to another
8
Inplane
INP
5
Two translational and three rotational motions of one
part with respect to another
9
Orientation
ORI
3
Constraints the orientation of one part with respect to
the orientation of another one, leaving the translational
degree of freedom free.
10
Parallel axes
PAX
4
Three translational and one rotational motions of one
part with respect to another
11
Perpendicular
PER
5
12
Convel
CNV
2
Three translational and two rotational motions of one
part with respect to another
Two rotations of one part with respect to the other
while remaining coincident and maintaining a constant
velocity through the spin axis
13
Hooke
HX
2
Two rotations of one part with respect to the other
while remaining coincident.
95 Table 29: Constraints Characterization Constraint Element
Translational
Constraints
Rotational
Constraints
Coupled Constraints
Total Constraints
Cylindrical joint
2
2
0
4
Fixed Joint
3
3
0
6
Planar Joint
1
2
0
3
Rack and Pinion Joint
0
0
1
1
Revolute Joint
2
2
1
5
Spherical Joint
3
0
0
3
Translational Joint
3
3
0
5
Universal joint
2
1
0
3
Atpoint joint primitive
3
0
0
3
Inline joint primitive
2
0
0
2
Inplane joint primitive
1
0
0
1
Orientation joint
primitive
Parallel joint primitive
0
3
0
3
0
2
0
2
Perpendicular joint
primitive
0
1
0
1
Motion (translational)
1
0
0
1
Motion (rotational)
0
1
0
1
Coupler
0
0
1
1
96 Table 30: Joints Description -­‐ Front Suspension Sr.No
Part (A)
Part (B)
Joint Name
Joint Type
1
Joint
No
1
uca
Upright
Uca_outer
SPR
2
2
Uca
Frame
Uca_front
FIX
3
3
uca
Frame
Uca_rear
SPR
4
4
Damper
Frame
Shock_frame
HOK
5
5
Damper
Frame
Shock_frame
HOK
6
6
uca
Frame
Uca_front
SPR
7
7
uca
Frame
Uca_rear
SPR
8
8
uca
Upright
Uca_outer
SPR
9
9
Lca
Upright
Lca_outer
SPR
10
10
Front Suspension
Damper
Shock_lca
FIX
11
11
Lca
Frame
Lca_rear
SPR
12
12
Lca
Frame
Lca_front
SPR
13
13
Front Suspension
Steering
Tie_rod_inner
SPR
14
14
Front Suspension
Steering
Tie_rod_inner
SPR
15
15
Lca
Frame
Lca_rear
SPR
16
16
Lca
Frame
Lca_front
SPR
17
17
Front Suspension
Damper
Shock_lca
FIX
18
18
Front Suspension
Upright
Lca_outer
SPR
19
19
Upright
Hub
Wheel _center
REV
97 Table 31: Joints Description -­‐ Rear Suspension Sr.No
Joint No
Part (A)
Part (B)
Joint Name
Joint Type
1
1
uca
Upright
Uca_outer
SPR
2
2
Uca
Frame
Uca_front
SPR
3
3
Uca
Frame
Uca_rear
SPR
4
4
Damper
Frame
Shock_frame
HOK
5
5
Damper
Frame
Shock_frame
HOK
6
6
Uca
Frame
Uca_front
SPR
Uca
Frame
Uca_Rear
SPR
Uca
Upright
Uca_Outer
SPR
axle
Upright
Drive_shaft_outer
CNV/ TRA
lca
Upright
Lca_outer
SPR
Toe-Rod
Upright
Toe_rod_inner
SPR
Damper
lca
Damper_lca
FIX
lca
Frame
Lca_front
SPR
lca
Frame
Lca_rear
SPR
7
8
9
7
8
9
10
10
11
11
12
12
13
13
14
14
15
15
lca
FRame
Lca_front
SPR
16
16
Lca
Frame
Lca_rear
SPR
17
17
Toe-rod
Upright
Toe_rod_inner
SPR
18
18
Toe-rod
Upright
Toe_rodouter
SPR
19
19
lca
Upright
Lca_outer
SPR
20
20
axle
Upright
Drive_shaft_outer
CNV/ TRA
Table 32: Joints Description Steering System Sr.No
1
Part A
Steering wheel
Part B
Steering column (1)
Joint Type
Fixed
2
Steering Column (1)
Steering Column (2)
Revolute
3
Rack
Tie Rod
Spherical