1. 1
SAE Commercial Vehicle Conference
October 27, 2004
A Target Setting Procedure for the DesignA Target Setting Procedure for the Design
of the Suspension System of a Tractor andof the Suspension System of a Tractor and
Semi-Trailer CombinationSemi-Trailer Combination
Ragnar LedesmaRagnar Ledesma
Corporate Engineering
ArvinMeritor, Inc.

2. 2
SAE Commercial Vehicle Conference
October 27, 2004
Background: Suspension Design
Procedure (Target Cascading Process)
Vehicle-Level
Targets
Subsystem-Level
Targets

3. 3
SAE Commercial Vehicle Conference
October 27, 2004
Background: Vehicle-Level Targets
• Commercial Vehicle Customer Inputs
• Overall dimensions (wheel base, track width, etc.)
• Axle load ratings
• Desired vehicle handling attributes
• Desired vehicle ride and NVH attributes
• Desired safety attributes
• Durability and warranty goals

4. 4
SAE Commercial Vehicle Conference
October 27, 2004
Background: Current Target Setting
Procedure
• Benchmarking
• Identify market segment leaders (manufacturers and models)
• Procure vehicles (lease or purchase)
• Road tests to measure vehicle ride and handling characteristics
• Rank according to selected set of objective ride and handling
metrics
• Identify target or reference vehicle for each performance metric
• Perform laboratory K&C (kinematics & compliance) tests to
identify the suspension characteristics of reference vehicles
• Define targets for suspension subsystems

5. 5
SAE Commercial Vehicle Conference
October 27, 2004
Project Overview
• Objective:
• To complement the current benchmarking process used in
defining the suspension system targets in the target-cascading
design process with an up-front analytical procedure
• Strategy:
• Use computer modeling and simulation, in conjunction with
designed experiments and optimization, to define the required
suspension system attributes that will produce the vehicle-level
performance characteristics desired by the customer.

6. 6
SAE Commercial Vehicle Conference
October 27, 2004
Analytical Target Setting Procedure
• Key requirement: an appropriate simulation and analysis
model wherein the outputs of the model are the vehicle-
level performance metrics and the inputs to the model
are the suspension subsystem attributes
• The model inputs (suspension subsystem attributes
such as roll center height, wheel rate, etc.) need to be
independent design variables
• The optimization process will determine the required
suspension subsystem attributes, which in turn, become
the targets during the design of the suspension
subsystems

7. 7
SAE Commercial Vehicle Conference
October 27, 2004
Outline of the Target Setting Procedure
• Define the design variables
• Design of experiments (screening DOE)
• Response surface modeling (generate surrogate model)
• Deterministic multi-objective optimization
• Stochastic optimization and robust design
• Source model verification of candidate optimum design
• Target cascading (top-down) and design validation
(bottom-up)

8. 8
SAE Commercial Vehicle Conference
October 27, 2004
Vehicle Dynamics Simulation Model
• TruckSim model of class-8 tractor-semi-trailer combination
• Tractor dimensions and sprung mass properties
Property Value Comments
Tractor:
Wheelbase 5854 mm From front axle to rear tandem center
Sprung mass c.g. x-coordinate 2126 mm From front axle to sprung mass c.g.
Sprung mass c.g. z-location 1118 mm From ground to sprung mass c.g.
Tandem rear axle spacing 1321 mm
5th
wheel hitch x-coordinate 5598 mm From front axle to 5th
wheel hitch
5th
wheel hitch z-coordinate 1212 mm From ground to 5th
wheel hitch
Tractor sprung mass 6,896 kg
Sprung mass roll inertia 5,735 kg-m^2
Sprung mass pitch inertia 30,825 kg-m^2
Sprung mass yaw inertia 30,690 kg-m^2

9. 9
SAE Commercial Vehicle Conference
October 27, 2004
TruckSim Model Inputs
• Tractor front axle and suspension
Front Axle:
Roll center height 488 mm Height from ground (22 mm below wheel center)
Spring spacing 889 mm
Shock spacing 1000 mm
Track width 2070 mm
Unsprung mass 483 kg Includes axle, wheel ends, leaf springs, 2 tires
Unsprung mass roll & yaw inertia 400 kg-m^2
Tire and wheel spin inertia 13.5 kg-m^2 1 wheel/drum and 1 tire
Suspension spring rate 200 N/mm Wheel rate
Spring travel ratio 1.0 Ratio of spring travel to vertical wheel travel
Shock absorber damping rate 5000 N-s/m Per shock
Shock travel ratio 1.135 Ratio of shock travel to vertical wheel travel
Auxiliary roll stiffness 2000 N-m/deg
Axle roll steer coefficient -0.20 Understeer effect
Kingpin offset at wheel center 133 mm Lateral distance from KP axis to wheel center
Kingpin inclination angle 6.25 deg
Kingpin caster angle 3.0 deg

10. 10
SAE Commercial Vehicle Conference
October 27, 2004
TruckSim Model Inputs
• Tractor tandem-rear axle and suspension
Forward-Rear Drive Axle:
Roll center height 837 mm Height from ground (327 mm above wheel center)
Spring spacing 755 mm
Shock spacing 1020 mm
Track width 1797 mm Average of dual tires
Wheel spacing 310 mm Lateral spacing of dual tires
Unsprung mass 1042 kg Includes axle, carrier, trailing arm, wheel ends, 4 tires
Unsprung mass roll & yaw inertia 543 kg-m^2
Tire and wheel spin inertia 27.0 kg-m^2 1 wheel/drum and 2 tires
Suspension spring rate 300 N/mm Wheel rate
Spring travel ratio 1.0 Ratio of spring travel to vertical wheel travel
Shock absorber damping rate 10,000 N-s/m Per shock
Shock travel ratio 1.217 Ratio of shock travel to vertical wheel travel
Auxiliary roll stiffness 11,000 N-m/deg
Axle roll steer coefficient 0.05 Understeer effect
Rearward-Rear Drive Axle:
Unsprung mass 933 kg Includes axle, trailing arm, wheel ends, 4 tires
Unsprung mass roll & yaw inertia 535 kg-m^2

11. 11
SAE Commercial Vehicle Conference
October 27, 2004
TruckSim Model Inputs
• Trailer sprung mass and payload
Trailer:
Wheelbase 10,554 mm From 5th
wheel hitch to trailer tandem center
Tandem trailer axle spacing 1245 mm
Sprung mass c.g. x-coordinate 5280 mm From 5th
wheel hitch to trailer sprung mass c.g.
Sprung mass c.g. z-location 1661 mm From ground to trailer sprung mass c.g
Trailer sprung mass 4,490 kg
Sprung mass roll inertia 9,960 kg-m^2
Sprung mass pitch inertia 171,300 kg-m^2
Sprung mass yaw inertia 180,000 kg-m^2
Trailer Payload:
Payload c.g. x-coordinate 5275 mm From 5th
wheel hitch to payload c.g.
Payload c.g. z-location 1750 mm From ground to payload c.g
Payload mass 20,620 kg
Payload roll inertia 8,266 kg-m^2
Payload pitch inertia 173,250 kg-m^2
Payload yaw inertia 178,730 kg-m^2

12. 12
SAE Commercial Vehicle Conference
October 27, 2004
TruckSim Model Inputs
• Trailer tandem-axle suspension
Forward and Rearward Trailer
Axles:
Roll center height 700 mm Height from ground (190 mm above wheel center)
Spring spacing 1143 mm
Shock spacing 762 mm
Track width 1968 mm Average of dual tires
Wheel spacing 337 mm Lateral spacing of dual tires
Unsprung mass 735 kg 1 Trailer axle with 4 tires
Unsprung mass roll & yaw inertia 590 kg-m^2 1 Trailer axle with 4 tires
Tire and wheel spin inertia 27.0 kg-m^2 1 wheel/drum and 2 tires
Suspension spring rate 420 N/mm Wheel rate
Spring travel ratio 1.0 Ratio of spring travel to vertical wheel travel
Shock absorber damping rate 10,000 N-s/m Per shock
Shock travel ratio 1.0 Ratio of shock travel to vertical wheel travel
Auxiliary roll stiffness 25,000 N-m/deg
Axle roll steer coefficient 0.05 Understeer effect

13. 13
SAE Commercial Vehicle Conference
October 27, 2004
Ride and Handling Events and Vehicle-
Level Performance Metrics
• Vehicle Ride
• Event: cross-slope sinusoidal bumps with increasing frequency
• Metrics: truck frame vertical acceleration (standard deviation,
SAE-filtered RMS value, ISO-filtered 1/3-octave peak, absorbed
power value)
• Vehicle Handling
• Events: constant-steer-angle test, step-steer test (transient)
• Metrics: understeer grad, Ay percent overshoot, response time
• Rollover Safety
• Event: swept-steer test
• Metrics: rollover threshold lateral acceleration

14. 14
SAE Commercial Vehicle Conference
October 27, 2004
Automated Modeling and Simulation with
LMS Optimus

15. 15
SAE Commercial Vehicle Conference
October 27, 2004
Analytical Target Setting Procedure
• Define the design variables
• Design of experiments (screening DOE)
• Response surface modeling (generate surrogate model)
• Deterministic multi-objective optimization
• Stochastic optimization and robust design
• Source model verification of candidate optimum design
• Target cascading (top-down) and design validation
(bottom-up)

16. 16
SAE Commercial Vehicle Conference
October 27, 2004
Define the Design Variables
Design Variables (Factors) Nominal
Value
Lower
Bound
Upper
Bound
Front axle roll center height (mm) 488 388 588
Front axle roll steer coefficient (deg/deg) -0.20 -0.25 -0.15
Front axle wheel rate (N/m) 200,000 150,000 250,000
Front axle damping rate (N-s/m) 5,000 3,750 6,250
Front axle auxiliary roll stiffness (N-m/deg) 2,000 1,500 2,500
Rear axle roll center height (mm) 837 737 937
Rear axle roll steer coefficient (deg/deg) 0.05 0.0 0.1
Rear axle wheel rate (N/m) 300,000 225,000 375,000
Rear axle damping rate (N-s/m) 10,000 7,500 12,500
Rear axle auxiliary roll stiffness (N-m/deg) 11,000 8,250 13,750
Trailer axle roll center height (mm) 700 600 800
Trailer axle roll steer coefficient (deg/deg) 0.05 0.0 0.1
Trailer axle wheel rate (N/m) 420,000 315,000 525,000
Trailer axle damping rate (N-s/m) 10,000 7,500 12,500
Trailer axle auxiliary roll stiffness (N-m/deg) 25,000 18,750 31,250
5 factors are selected from each suspension system

17. 17
SAE Commercial Vehicle Conference
October 27, 2004
Resolution V Fractional-Factorial
Screening DOE
Design Variables (Factors) Percent
Contribution
Front axle roll center height 17.0 %
Front axle roll steer coefficient 14.7 %
Front axle wheel rate 1.1 %
Front axle auxiliary roll stiffness 2.1 %
Rear axle roll center height 23.5 %
Rear axle roll steer coefficient 10.6 %
Rear axle wheel rate 1.0 %
Rear axle auxiliary roll stiffness 26.2 %
Other main effects and 2-factor interactions 3.8 %
Results of Screening DOE: Percent Contribution
to the Variation in Understeer Gradient

18. 18
SAE Commercial Vehicle Conference
October 27, 2004
Response Surface Modeling
Generate the Surrogate Model
• Perform a higher-order
(3 levels or more) DOE
• Central composite
designs or 3-level full
factorial designs
• Express each response
(performance metric) as
a polynomial function of
the design variables

19. 19
SAE Commercial Vehicle Conference
October 27, 2004
Deterministic Multiple Objective
Optimization
• Sequential quadratic programming, genetic algorithms,
random search methods
Design Variables (Factors) Minimize
Understeer
Gradient
Minimize
Yaw Rate
Overshoot
Maximize
Rollover
Threshol
d
Minimize
Ride
Metrics
Combined
Objectives
(Weighted
)
Front axle roll center height (mm) 388 388 588 588 388
Front axle roll steer coeff. (deg/deg) -0.15 -0.15 -0.15 -0.15 -0.15
Front axle wheel rate (N/m) 150,000 150,000 250,000 250,000 150,000
Front axle damping rate (N-s/m) 5,000 6,250 4,760 6,038 6,176
Front axle aux. roll stiffness (N-m/deg) 1,500 1,500 2,500 2,500 1,500
Rear axle roll center height (mm) 937 937 937 937 937
Rear axle roll steer coeff. (deg/deg) 0.0 0.0 0.024 0.10 0.0
Rear axle wheel rate (N/m) 352,000 375,000 225,000 225,000 366,820
Rear axle damping rate (N-s/m) 9,973 12,500 9,910 12,500 9,010
Rear axle aux. roll stiffness (N-m/deg) 13,750 13,750 13,750 13,750 13,750
Trailer axle roll center height (mm) 619 800 600 600 662
Trailer axle roll steer coeff. (deg/deg) 0.037 0.0 0.051 0.10 0.0
Trailer axle wheel rate (N/m) 371,000 525,000 315,000 315,000 315,000
Trailer axle damping rate (N-s/m) 10,000 7,500 9,990 9,986 12,500
Trailer aux. roll stiffness (N-m/deg) 18,750 18,750 18,750 18,750 21,179

20. 20
SAE Commercial Vehicle Conference
October 27, 2004
Stochastic Optimization and Robust
Design
• Minimize variation in performance metrics
• Apply probabilistic constraints on design variables and
responses (µ+6σ constraints)
Performance Metric Mean
Value
Standard
Deviation
µ + 6*σ
Value
µ + 6*σ Robust
Constraint
Equation
Understeer gradient (deg/g) 4.5562 0.073972 5.0 µ + 6*σ < 5.0
Yaw rate overshoot (%) 5.4080 0.27952 7.085 µ + 6*σ < 7.5
Rollover threshold Ay (g’s) 0.5685 0.00089031 0.5632 0.55 < µ - 6*σ
Std. deviation of Az (g’s) 0.01973 0.00028036 0.021416 µ + 6*σ < 0.025

21. 21
SAE Commercial Vehicle Conference
October 27, 2004
Stochastic Optimization and Robust
Design
• The optimum solution is pulled back from the constraint boundaries
in order to satisfy the µ+6σ constraints on the design variables.
Design Variables (Factors) Nominal
Values
Standard
Deviation
Robust
Design
Front axle roll center height (mm) 488 10 448
Front axle roll steer coefficient (deg/deg) -0.20 0.005 -0.18
Front axle wheel rate (N/m) 200,000 5,000 180,000
Front axle damping rate (N-s/m) 5,000 125 5,500
Front axle auxiliary roll stiffness (N-m/deg) 2,000 50 1,800
Rear axle roll center height (mm) 837 10 877
Rear axle roll steer coefficient (deg/deg) 0.05 0.005 0.03
Rear axle wheel rate (N/m) 300,000 5,000 333,160
Rear axle damping rate (N-s/m) 10,000 250 9,284
Rear axle auxiliary roll stiffness (N-m/deg) 11,000 250 12,250
Trailer axle roll center height (mm) 700 10 740
Trailer axle roll steer coefficient (deg/deg) 0.05 0.005 0.03
Trailer axle wheel rate (N/m) 420,000 5,000 345,000
Trailer axle damping rate (N-s/m) 10,000 250 11,000
Trailer axle auxiliary roll stiffness (N-m/deg) 25,000 250 25,777

22. 22
SAE Commercial Vehicle Conference
October 27, 2004
Source Model Verification of Candidate
Optimum Design
• Use TruckSim (source model) to verify that the results of
the deterministic/stochastic optimization results are
accurate
• Required if the optimization was performed with the
surrogate model used as the function evaluation routine

23. 23
SAE Commercial Vehicle Conference
October 27, 2004
Target Cascading and Subsystem
Design Validation
• Target cascading (top-down process): use the optimum
values of the design variables as the response targets in
the design of the next (lower) subsystem
• Subsystem design validation (bottom-up process):
evaluate the effect of not achieving the design targets on
higher-level system models
• An iterative procedure of going top-down and bottom-up
along the modeling hierarchy is required in order to
converge to an overall optimal solution

24. 24
SAE Commercial Vehicle Conference
October 27, 2004
Summary
• Benefits of analytical target cascading
• Mimics the experimental procedure of vehicle benchmarking
• Leverages the advantages of CAE in up-front design and
optimization of complete vehicle systems
• Reveals the sources of conflicts or incompatibilities between
subsystems
• Allows the concurrent design of large-scale, multi-disciplinary
design problems
• Reduce design iterations late in the development process
• Overall reduction in the design cycle time