Wheel Shimmy in Heavy Duty Trucks: Wheel Shimmy in Heavy Duty Trucks: Using Designed Numerical Experiments Using Designed Numerical Experiments

to Determine a Robust Solutionto Determine a Robust Solution

Ragnar LedesmaRagnar LedesmaPrincipal EngineerPrincipal Engineer

Commercial Vehicle SystemsCommercial Vehicle SystemsArvinMeritor, Inc.ArvinMeritor, Inc.

AbstractAbstract

This presentation addresses the wheel shimmy phenomenon commonly encountered in heavy-duty trucks with dependent (solid beam) front axle suspensions. A MSC.ADAMS model of a class-8 tractor-semi-trailer combination has been developed to study the front wheel shimmy observed during road testing of a prototype vehicle. The MSC.ADAMS model was able to reproduce the shimmy event at the observed frequency and vehicle speed. The unstable shimmy mode comprised a coalescence of different vibration modes at the shimmy frequency. These vibration modes include the frame twist mode, frame lateral bending mode, axle roll mode, axle lateral mode, and steering system vibration mode. The solution strategy adopted in this study is to use designed numerical experiments in order to find the optimum combination of possible design changes to the front axle suspension for a given set of design constraints. Possible solutions to the shimmy problem include a combination of the following: increased kingpin friction damping, changing the location of the steering arm ball joint, changing the caster angle, increasing the lateral stiffness of the suspension by various means, and increasing the lateral stiffness of the tires. The DOE/sensitivity study results showed that tire relaxation (lag in the tire response), which results in a negative damping effect, plays a dominant role in wheel shimmy propensity. The sensitivity study identifies kingpin friction damping as the most effective means of controlling wheel shimmy.

Presentation OutlinePresentation Outline

•Introduction•Vehicle Description and Field Test Observations•Model Description

•Designed Numerical Experiments

•Analysis of Simulation Results•Concluding Remarks

IntroductionIntroduction

•ArvinMeritor is the system supplier of the front axle and suspension for a new series of Class-8 tractors

•A prototype vehicle was tested on public roads and proving grounds

•A front wheel shimmy problem was observed at specific vehicle speeds and road conditions

•Vehicle dynamics simulation and analysis were requested in order to understand the shimmy phenomenon and seek acceptable modifications to the design of the front axle and suspension

Vehicle DescriptionVehicle Description

•Axle Loads: Front: 10,760 lbm Rear: 8,350 lbm (bobtail)

•Wheelbase: 230 inches•Front axle beam: tubular•Front axle suspension: hybrid air spring and mechanical leaf spring•Tandem rear axle suspension: trailing arm and air spring•Truck frame: 5/16” C-channels•Cab: day-cab or sleeper variants

Field Test: ObservationsField Test: Observations

•Front wheel shimmy occurs at 6-7 Hz, and sustained at vehicle speeds greater than 30 mph•Running modes analysis shows that shimmy is a coalescence of frame twist mode, frame lateral bending mode, engine yaw mode, axle roll mode, axle lateral mode, and steering system vibration mode

Modeling and Simulation ObjectivesModeling and Simulation Objectives

•Reproduce shimmy phenomenon observed in the field•Develop an understanding of the shimmy phenomenon•Determine the sensitivity of shimmy propensity to various front axle and suspension design parameters

•Recommend modifications to the design of the front axle and suspension

MSC.ADAMS Model DescriptionMSC.ADAMS Model Description

Truck frame: modal neutral file from MSC.NASTRAN

Front suspension: mechanical leaf spring (beam elements), air spring (nonlinear force-deflection curve), and shock absorbers (nonlinear force-velocity curves)

Rear suspension: trailing arm (beam elements) and air springs

Steering system: pitman arm, drag link, steering arm, tie rod arms, cross tube

Cab, engine, transmission: rigid bodies

Tires: Pacejka magic formula tire model

Truck Frame Vibration ModesTruck Frame Vibration Modes

First Lateral Bending Mode

Truck Frame Vibration ModesTruck Frame Vibration Modes

Second Lateral Bending Mode

Truck Frame Vibration ModesTruck Frame Vibration Modes

Combined Lateral Bending and Frame Twist Mode

Model Verification: Natural FrequenciesModel Verification: Natural Frequencies

vertical acceleration response lateral acceleration response

Model Verification: Shimmy SimulationModel Verification: Shimmy Simulation

knuckle rotation: time history knuckle rotation: frequency spectrum

Model Verification: Shimmy SimulationModel Verification: Shimmy Simulation

frame lateral acceleration: time history

frame lateral acceleration: frequency spectrum

Designed Numerical ExperimentsDesigned Numerical Experiments

•Factors: Tire relaxation length (tire characteristic) Kingpin friction (steering system damping) Steering arm length (steering geometry) Kingpin caster angle (axle geometry) Vehicle speed (operational parameter) Front axle suspension lateral stiffness (suspension characteristic)

•Responses: Knuckle rotation about kingpin axis (standard deviation value) Truck frame lateral acceleration (standard deviation value)

ANOVA Table: Knuckle RotationANOVA Table: Knuckle Rotation Sum of Mean F Source Squares DF Square Value Prob > F Model 49.83 14 3.56 436.45 < 0.0001 B 16.57 1 16.57 2031.95 < 0.0001 C 7.43 1 7.43 910.62 < 0.0001 D 0.64 1 0.64 78.11 < 0.0001 AE 5.26 1 5.26 644.54 < 0.0001 BC 7.39 1 7.39 905.63 < 0.0001 BD 0.63 1 0.63 76.85 < 0.0001 BE 0.13 1 0.13 16.11 0.0002 CD 0.26 1 0.26 31.91 < 0.0001 ABE 5.16 1 5.16 632.47 < 0.0001 ACE 2.96 1 2.96 362.97 < 0.0001 ADE 0.10 1 0.10 12.31 0.0010 BCD 0.26 1 0.26 31.68 < 0.0001 ABCE 2.96 1 2.96 363.30 < 0.0001 ABDE 0.097 1 0.097 11.90 0.0012 Residual 0.40 49 8.155E-003 Cor Total 50.23 63

ANOVA Table: Frame Lateral AccelerationANOVA Table: Frame Lateral Acceleration Sum of Mean F Source Squares DF Square Value Prob > F Model 0.72 18 0.040 313.99 < 0.0001 A 4.470E-003 1 4.470E-003 35.17 < 0.0001 B 0.22 1 0.22 1766.13 < 0.0001 C 0.11 1 0.11 829.25 < 0.0001 D 7.787E-003 1 7.787E-003 61.29 < 0.0001 E 3.517E-003 1 3.517E-003 27.68 < 0.0001 F 1.444E-003 1 1.444E-003 11.37 0.0015 AB 4.221E-003 1 4.221E-003 33.22 < 0.0001 AE 0.076 1 0.076 600.86 < 0.0001 BC 0.11 1 0.11 827.49 < 0.0001 BD 7.614E-003 1 7.614E-003 59.92 < 0.0001 BF 1.942E-003 1 1.942E-003 15.28 0.0003 CD 3.045E-003 1 3.045E-003 23.96 < 0.0001 ABE 0.077 1 0.077 603.25 < 0.0001 ACE 0.045 1 0.045 354.47 < 0.0001 ADE 1.630E-003 1 1.630E-003 12.83 0.0008 BCD 2.989E-003 1 2.989E-003 23.53 < 0.0001 ABCE 0.045 1 0.045 353.18 < 0.0001 ABDE 1.651E-003 1 1.651E-003 12.99 0.0008 Residual 5.718E-003 45 1.271E-004 Cor Total 0.72 63

Response Surface: Knuckle RotationResponse Surface: Knuckle Rotation

Effect of vehicle speed and tire relaxation length on wheel shimmy

DESIGN-EXPERT Plot

Kingpin Rotation

X = A: tire relaxation length

Y = E: v ehicle speed

Actual Factors

B: kingpin f riction = 0.00

C: steering arm length = 280.20

D: caster angle = 5.50

F: susp lateral stif f ness = 26250.00

0 .9 3 9 3 74

1 .5 0 16 5

2 .06 3 9 3

2 .6 2 6 2 1

3 .1 8 8 49

Kin

gpin

Rot

atio

n

5 0 0 .0 0

62 5 .0 0

7 5 0 .0 0

8 75 .0 0

1 0 0 0 .0 0

3 0 .0 0

3 7 .5 0

4 5 .0 0

52 .5 0

6 0 .0 0

A : tir e r elaxation leng th

E: vehic le speed

Response Surface: Knuckle RotationResponse Surface: Knuckle Rotation

Effect of kingpin friction and steering arm length on wheel shimmy

DESIGN-EXPERT Plot

Kingpin Rotation

X = B: kingpin f riction

Y = C: steering arm length

Actual Factors

A: tire relaxation length = 1000.00

D: caster angle = 5.50

E: v ehicle speed = 60.00

F: susp lateral stif f ness = 26250.00

0 .0 8 8 3 0 3 2

0 .8 4 0 6 9 3

1 .5 9 3 0 8

2 .3 4 5 4 7

3 .0 9 7 86

Kin

gpin

Rot

atio

n

0 .0 0

0 .0 3

0 .0 5

0 .08

0 .1 0

2 8 0 .20

28 6 .5 5

2 9 2 .9 0

2 9 9 .25

3 0 5 .6 0

B : king pin fr ic tion C : s teer ing ar m leng th

Response Surface: Frame Lateral AccelerationResponse Surface: Frame Lateral Acceleration

Effect of vehicle speed and tire relaxation length on wheel shimmy

DESIGN-EXPERT Plot

Frame Lateral Accel

X = A: tire relaxation length

Y = E: v ehicle speed

Actual Factors

B: kingpin f riction = 0.00

C: steering arm length = 280.20

D: caster angle = 5.50

F: susp lateral stif f ness = 26250.00

0 .0 95 0 7 0 8

0 .1 6 9 45 1

0 .2 4 3 8 3 2

0 .31 8 2 1 2

0 .3 9 2 59 3

Fra

me

Late

ral A

ccel

5 0 0 .0 0

6 2 5 .0 0

7 5 0 .0 0

87 5 .0 0

10 0 0 .0 0

30 .0 0

3 7 .50

4 5 .0 0

5 2 .50

6 0 .0 0

A : ti r e r elaxation leng th

E: vehic le speed

Response Surface: Frame Lateral AccelerationResponse Surface: Frame Lateral Acceleration

Effect of kingpin friction and steering arm length on wheel shimmy

DESIGN-EXPERT Plot

Frame Lateral Accel

X = B: kingpin f riction

Y = C: steering arm length

Actual Factors

A: tire relaxation length = 1000.00

D: caster angle = 5.50

E: v ehicle speed = 60.00

F: susp lateral stif f ness = 26250.00

0 .0 2 3 0 7 8 6

0 .1 1 0 9 2 5

0 .1 9 8 77 1

0 .2 8 6 6 1 7

0 .3 7 4 4 6 3

Fra

me

Late

ral A

ccel

0 .0 0

0 .0 3

0 .0 5

0 .0 8

0 .1 0

2 80 .2 0

28 6 .5 5

2 9 2 .90

2 9 9 .2 5

3 0 5 .6 0 B : king pin fr ic tion

C : s teer ing arm leng th

DOE ResultsDOE Results

•All factors were found to be significant to wheel shimmy propensity

•Kingpin friction was the most significant factor – increasing kingpin friction helps reduce wheel shimmy propensity

•Interaction between vehicle speed and tire relaxation length (negative damping effect) was a dominant contributor to wheel shimmy

•2, 3, and 4-factor interactions were present – it is difficult to make general statements regarding the effect of any one specific factor on shimmy propensity

Design RecommendationsDesign Recommendations

•These recommendations are specific to the prototype vehicle: Increase kingpin friction Increase length of steering arm Use tires with higher lateral stiffness (bias ply tires) Reduce caster angle Increase suspension lateral stiffness

Design ModificationDesign Modification

Initial Design of Front Axle and Suspension

Design ModificationDesign Modification

Final Design of Front Axle and Suspension

Summary and ConclusionSummary and Conclusion

•A MSC.ADAMS model was used in simulating the front wheel shimmy phenomenon

•Using designed numerical experiments, the model was utilized in determining a robust solution to the shimmy problem

•Design modifications were made based on the findings of the DOE/sensitivity study

•Vehicle tests confirmed that the shimmy issue has been eliminated