ARM_Target_Setting_Procedure

1

SAE Commercial Vehicle ConferenceOctober 27, 2004

A Target Setting Procedure for the Design A Target Setting Procedure for the Design of the Suspension System of a Tractor and of the Suspension System of a Tractor and

Semi-Trailer CombinationSemi-Trailer Combination

Ragnar LedesmaRagnar LedesmaCorporate Engineering

ArvinMeritor, Inc.

2


Background: Suspension Design Procedure (Target Cascading Process)

Vehicle-Level Targets

Subsystem-Level Targets

3


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


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


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


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


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


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


TruckSim Model Inputs

• Tractor front axle and suspensionFront 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



• 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



• 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



• 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


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


Automated Modeling and Simulation with LMS Optimus

15


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


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


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


Response Surface ModelingGenerate 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


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


Stochastic Optimization and Robust Design• Minimize variation in performance metrics

• Apply probabilistic constraints on design variables and responses ( constraints)

Performance Metric Mean Value

Standard Deviation

+ 6* Value

+ 6* Robust Constraint Equation

Understeer gradient (deg/g) 4.5562 0.073972 5.0 + 6* < 5.0 Yaw rate overshoot (%) 5.4080 0.27952 7.085 + 6* < 7.5 Rollover threshold Ay (g’s) 0.5685 0.00089031 0.5632 0.55 < - 6* Std. deviation of Az (g’s) 0.01973 0.00028036 0.021416 + 6* < 0.025

21


Stochastic Optimization and Robust Design

• The optimum solution is pulled back from the constraint boundaries

in order to satisfy the 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


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


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


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

ARM_Target_Setting_Procedure

Documents

Transcript of ARM_Target_Setting_Procedure