The document discusses wheel shimmy in heavy duty trucks, which was observed during testing of a prototype vehicle. A simulation model was developed and numerical experiments were conducted to understand the shimmy phenomenon and identify design changes. The analysis found that increased kingpin friction, stiffer steering components and tires, and reduced caster angle could eliminate shimmy by increasing damping. The recommended design modifications were implemented and resolved the issue.

1. Wheel Shimmy in Heavy Duty Trucks:Wheel Shimmy in Heavy Duty Trucks:
Using Designed Numerical ExperimentsUsing Designed Numerical Experiments
to Determine a Robust Solutionto Determine a Robust Solution
Ragnar LedesmaRagnar Ledesma
Principal EngineerPrincipal Engineer
Commercial Vehicle SystemsCommercial Vehicle Systems
ArvinMeritor, Inc.ArvinMeritor, Inc.

2. 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.

3. Presentation OutlinePresentation Outline
•Introduction
•Vehicle Description and Field Test Observations
•Model Description
•Designed Numerical Experiments
•Analysis of Simulation Results
•Concluding Remarks

4. 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

5. 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

6. 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

7. 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

8. 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

9. Truck Frame Vibration ModesTruck Frame Vibration Modes
First Lateral Bending Mode

10. Truck Frame Vibration ModesTruck Frame Vibration Modes
Second Lateral Bending Mode

11. Truck Frame Vibration ModesTruck Frame Vibration Modes
Combined Lateral Bending and Frame Twist Mode

12. Model Verification: Natural FrequenciesModel Verification: Natural Frequencies
vertical acceleration response lateral acceleration response

13. Model Verification: Shimmy SimulationModel Verification: Shimmy Simulation
knuckle rotation: time history knuckle rotation: frequency spectrum

14. Model Verification: Shimmy SimulationModel Verification: Shimmy Simulation
frame lateral acceleration: time
history
frame lateral acceleration: frequency
spectrum

15. 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)

16. 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

17. 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

18. Response Surface: Knuckle RotationResponse Surface: Knuckle Rotation
Effect of vehicle speed and tire relaxation length on wheel shimmy
0.939374
1.50165
2.06393
2.62621
3.18849
KingpinRotation
500.00
625.00
750.00
875.00
1000.00
30.00
37.50
45.00
52.50
60.00
A: tire relaxation leng th
E: vehicle speed

19. Response Surface: Knuckle RotationResponse Surface: Knuckle Rotation
Effect of kingpin friction and steering arm length on wheel
shimmy
0.0883032
0.840693
1.59308
2.34547
3.09786
KingpinRotation
0.00
0.03
0.05
0.08
0.10
280.20
286.55
292.90
299.25
305.60
B: king pin frictionC : steering arm leng th

20. Response Surface: Frame Lateral AccelerationResponse Surface: Frame Lateral Acceleration
Effect of vehicle speed and tire relaxation length on wheel shimmy
0.0950708
0.169451
0.243832
0.318212
0.392593
FrameLateralAccel
500.00
625.00
750.00
875.00
1000.00
30.00
37.50
45.00
52.50
60.00
A: tire relaxation leng th
E: vehicle speed

21. Response Surface: Frame Lateral AccelerationResponse Surface: Frame Lateral Acceleration
Effect of kingpin friction and steering arm length on wheel
shimmy
0.0230786
0.110925
0.198771
0.286617
0.374463
FrameLateralAccel
0.00
0.03
0.05
0.08
0.10
280.20
286.55
292.90
299.25
305.60
B: king pin friction
C : steering arm leng th

22. 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

23. 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

24. Design ModificationDesign Modification
Initial Design of Front Axle and Suspension

25. Design ModificationDesign Modification
Final Design of Front Axle and Suspension

26. 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