Abstract

Tire wear cost accounts for a large proportion of the total cost of heavy mining dump trucks (HMDTs), and the shimmy of the steering system aggravates the tire wear severely. This study proposes a model-based approach to avoid the shimmy of the steering system for such trucks without replacement or destruction of steering structure. First, a five degrees-of-freedom (DOF) shimmy dynamic model of the steering system is established considering the tire lateral dynamics and the nonlinearity of the hydro-pneumatic suspension (HPS). Second, the unstable parameter range of the dynamic model is obtained based on the Lyapunov’s first approximation theorem and Hopf bifurcation theory. The stability analysis results show that the steering system of heavy mining dump trucks is a self-excited vibration system because of the Hopf bifurcation in the unstable parameter range, and this unstable parameter range is greatly affected by the load and the initial pneumatic volume of hydro-pneumatic suspension. In addition, the accuracy of the dynamic is verified by a field test. Therefore, how the load and initial pneumatic volume affect the shimming is analyzed numerically. In other words, how to match the load and initial pneumatic volume is uncovered to avoid the shimmy. For instance, it shows that the shimmy at full load can be avoided at the speed of 30 km/h by charging the initial pneumatic volume of hydro-pneumatic suspension to 14.5 l.

References

1.
Zhou
J.
,
Hall
,
R. A.
,
Fowler
G.
, and
Huntingford
K.
,
2008
, “
Evaluation of the Effect of Off-the-Road Tire Air Pressure Setting on Tire Performance
,”
Int. J. Min. Reclam. Environ.
,
22
(
3
), pp.
237
244
.10.1080/17480930701679459
2.
Zhang
,
N.
,
Yin
,
G. D.
,
Chen
,
N.
,
Mi
,
T.
, and
Li
,
P.
,
2017
, “
A State-of-the-Art Survey on Shimmy Problem in Vehicle Dynamics
,”
J. Mech. Eng.
,
53
(
14
), pp.
16
28
. 10.3901/JME.2017.14.016
3.
Orlando
,
C.
, and
Alaimo
,
A.
,
2017
, “
A Robust Active Control System for Shimmy Damping in the Presence of Free Play and Uncertainties
,”
Mech. Syst. Sig. Process.
,
84
(
1
), pp.
551
569
. 10.1016/j.ymssp.2016.07.038
4.
Mi
,
T.
,
Chen
,
N.
,
Stepan
,
G.
, and
Takacs
,
D.
,
2018
, “
Energy Distribution of a Vehicle Shimmy System With the Delayed Tyre Model
,”
IFAC-PapersOnLine
,
51
(
14
), pp.
7
12
. 10.1016/j.ifacol.2018.07.190
5.
Thota
,
P.
,
Krauskopf
,
B.
, and
Lowenberg
,
M.
,
2013
, “
Multi-Parameter Bifurcation Study of Shimmy Oscillations in a Dual-Wheel Aircraft Nose Landing Gear
,”
Nonlinear Dyn.
,
2
(
70
), pp.
1675
1688
. 10.1007/s11071-012-0565-1
6.
Kadoi
K.
,
Inoue
T.
,
Kawano
J.
, and
Kondo
M.
,
2018
, “
Nonlinear Analysis of a Torsional Vibration of a Multidegrees-of-Freedom System With Centrifugal Pendulum Vibration Absorbers and Its Suppression
,”
ASME J. Vib. Acoust.
,
140
(
6
), p.
061008
.10.1115/1.4040042
7.
Lu
,
J. W.
,
Chen
,
H.
,
Xin
,
J. Y.
, and
Liu
,
M. J.
,
2015
, “
Influence of Steering Linkage Clearance on Dynamic Behaviour of Vehicle Shimmy System
,”
J. Vib. Shock
,
3
(
16
), pp.
171
175
.
8.
Lu
,
J. W.
,
Gu
,
J.
, and
Liu
,
M.
,
2010
, “
Modeling of the Vehicle Shimmy System With Consideration of Clearance of the Steering Linkage Mechanism
,”
Meccanica
,
45
(
1
), pp.
53
61
. 10.1007/s11012-009-9223-1
9.
Lu
,
J. W.
,
Xu
,
Y.
,
Wang
,
X.
, and
Stephanos
,
T.
,
2013
, “
Analysis of Shimmy Characteristic Based on Temperature Effects and Steering Linkage Clearance for Vehicle
,”
Trans. Chin. Soc. Agric. Eng.
,
29
(
14
), pp.
74
81
. 10.3969/j.issn.1002-6819.2013.14.010
10.
Zhang
,
L.
,
Lu
,
J. W.
,
Jiang
,
J. Z.
,
Yan
,
P. L.
, and
Li
,
L.
,
2016
, “
Dynamics Modelling and Analysis on Shimmy in Independent Suspension Vehicle With Consideration of Clearances in Kinematic Pairs
,”
Automot. Eng.
,
38
(
12
), pp.
1477
1482
.
11.
Wei
,
D. G.
,
Wang
,
Y.
,
Jiang
,
T.
,
Zheng
,
S. F.
,
Zhao
,
W. J.
, and
Pan
,
Z. J.
,
2017
, “
Chaos Vibration of Pinion and Rack Steering Trapezoidal Mechanism Containing Two Clearances
,”
Mech. Syst. Sig. Process.
,
92
(
1
), pp.
146
155
. 10.1016/j.ymssp.2017.01.019
12.
Wang
,
W.
,
Song
,
Y.
, and
Li
,
K.
,
2011
, “
Influence of Independent Suspension Automotive Steering Clearance and Coulomb Friction on Hopf Bifurcation Characteristic
,”
Chin. J. Mech. Eng.
,
47
(
2
), pp.
130
135
. 10.3901/JME.2011.02.130
13.
Zhuravlev
,
V. P.
,
Klimov
,
D. M.
, and
Plotnikov
,
P. K.
,
2013
, “
A New Model of Shimmy
,”
Mech. Solids
,
48
(
5
), pp.
490
499
.10.3103/S0025654413050026
14.
Kireenkov
,
A. A.
,
2018
, “
Improved Friction Model of the Aviation Tyre Contact With the Landing Strip
,”
IFAC-PapersOnLine
,
51
(
2
), pp.
890
894
. 10.1016/j.ifacol.2018.04.027
15.
Wei
,
D. G.
,
Xu
,
K.
,
Jiang
,
Y. B.
,
Chen
,
C. H.
,
Zhao
,
W. J.
, and
Zhou
,
F. G.
,
2015
, “
Hopf Bifurcation Characteristics of Dual-Front Axle Self-Excited Shimmy System for Heavy Truck Considering Dry Friction
,”
Shock Vib.
,
25
(
1
), pp.
1
20
. 10.1155/2015/839801
16.
Wang
,
W.
,
Chen
,
J.
, and
Song
,
Y.
,
2013
, “
Coupled Dynamic Characteristics of Car Steering System and Front Suspension System
,”
Trans. Chin. Soc. Agric. Mach.
,
44
(
12
), pp.
17
21
. 10.6041/j.issn.1000-1298.2013.12.004
17.
Mi
,
T.
,
Stepan
,
G.
,
Takacs
,
D.
,
Chen
,
N.
, and
Zhang
,
N.
,
2017
, “
Model Establishment and Parameter Analysis on Shimmy of Electric Vehicle With Independent Suspensions
,”
Procedia IUTAM
,
22
(
1
), pp.
259
266
. 10.1016/j.piutam.2017.08.034
18.
Guo
,
K. H.
,
1995
, “
Influence of Tire Dynamic Cornering Characteristics on Vehicle Shimmy
,”
Automob. Technol.
,
4
(
1
), pp.
1
6
.
19.
Zuo
,
S.
,
Su
,
H.
, and
Wang
,
J.
,
2012
, “
Simulation of Self-Excited Vibration of a Rolling Tire and Its Influencing Factors Analysis
,”
J. Vib. Shock
,
31
(
4
), pp.
18
24
. 10.13465/j.cnki.jvs.2012.04.027
20.
Wang
,
D.
,
Jiang
,
R.
,
Liu
,
H.
, and
Xu
,
C.
,
2015
, “
A Study on the Effect of Wheel Unbalance on the Ride Comfort of Dump Truck
,”
Automot. Eng.
,
2
(
1
), pp.
219
223
.
21.
Ran
,
S.
,
Besselink
,
I.
, and
Nijmeijer
,
H.
,
2015
, “
Energy Analysis of the Von Schlippe Tyre Model With Application to Shimmy
,”
Veh. Syst. Dyn.
,
53
(
12
), pp.
1795
1810
.10.1080/00423114.2015.1093151
22.
Beregi
,
S.
,
Takács
,
D.
, and
Hos
,
C.
,
2017
, “
Nonlinear Analysis of a Shimmying Wheel With Contact-Force Characteristics Featuring Higher-Order Discontinuities
,”
Nonlinear Dyn.
,
90
(
4
), pp.
1
12
. 10.1007/s11071-017-3699-3
23.
Wang
,
W.
,
2012
, “
Nonlinear Vibration Semi-Active Control of Automotive Steering Using Magneto-Rheological Damper
,”
Meccanica
,
47
(
8
), pp.
2027
2039
.10.1007/s11012-012-9572-z
24.
Dutta
,
S.
, and
Choi
,
S. B.
,
2016
, “
Control of a Shimmy Vibration in Vehicle Steering System Using a Magneto-Rheological Damper
,”
J. Vib. Control
,
24
(
4
), pp.
797
807
. 10.1177/1077546316652786
25.
Zhao
,
J.
,
Gu
,
Z.
,
Zhang
,
S.
,
Ma
,
X. K.
,
Zhu
,
Y. F.
, and
Hu
,
K.
,
2015
, “
Research and Optimization on the Mechanical Property of Mining Dump Truck’s Hydro-Pneumatic Suspension
,”
J. Mech. Eng.
,
51
(
10
), pp.
112
118
. 10.3901/JME.2015.10.112
26.
Frimpong
,
S.
,
Changirwa
,
R.
, and
Szymanski
,
J.
,
2003
, “
Simulation of Automated Dump Trucks for Large Scale Surface Mining Operations
,”
Int. J. Surf. Min. Reclam. Environ.
,
17
(
3
), pp.
183
195
. 10.1076/ijsm.17.3.183.14770
27.
Aouad
,
N.
, and
Frimpong
,
S.
,
2014
, “
Lagrangian Formulation and Numerical Solutions to Dump Truck Vibrations Under HISLO Conditions
,”
ASME J. Vib. Acoust.
,
136
(
2
), p.
021020
. 10.1115/1.4026479
28.
Ali
,
D.
, and
Frimpong
,
S.
,
2018
, “
Artificial Intelligence Models for Predicting the Performance of Hydro-Pneumatic Suspension Struts in Large Capacity Dump Trucks
,”
Int. J. Ind. Ergon.
,
67
(
1
), pp.
283
295
. 10.1016/j.ergon.2018.06.005
29.
Nyaaba
,
W.
,
Frimpong
,
S.
, and
Anani
,
A.
,
2019
, “
Fatigue Damage Investigation of Ultra-Large Tire Components
,”
Int. J. Fatigue
,
119
(
1
), pp.
247
260
. 10.1016/j.ijfatigue.2018.07.009
30.
Arzanpour
,
S.
, and
Golnaraghi
,
M. F.
,
2010
, “
Development of an Active Compliance Chamber to Enhance the Performance of Hydraulic Bushings
,”
ASME J. Vib. Acoust.
,
132
(
4
), p.
041012
.10.1115/1.4001500
31.
Lu
C.-Y.
, and
Shih
M.-C.
,
2004
, “
Application of the Pacejka Magic Formula Tyre Model on a Study of a Hydraulic Anti-Lock Braking System for a Light Motorcycle
,”
Veh. Syst. Dyn.
,
41
(
6
), pp.
431
448
. 10.1080/00423110512331383848
32.
Liang
,
C. Y.
,
Allen
,
R. W.
,
Rosenthal
,
T. J.
,
Chrstos
,
J. P.
, and
Nunez
,
P.
,
2004
, “
Tire Modeling for Off-Road Vehicle Simulation
,”
SAE Trans.
,
113
(
6
), pp.
1063
1073
.
33.
Mi
,
T.
,
Stepan
,
G.
,
Takacs
,
D.
, and
Chen
,
N.
,
2017
, “
Shimmy Model for Electric Vehicle With Independent Suspensions
,”
Proc. Inst. Mech. Eng. Part D J. Automob. Eng.
,
232
(
3
), pp.
1
11
.
34.
Ding
,
W.
,
2011
,
Self-Excited Vibration
,
Tsinghua University Press
,
Beijing, China
.
35.
Feng
,
Z. P.
,
Lin
,
X.
, and
Zuo
,
M. J.
,
2016
, “
Joint Amplitude and Frequency Demodulation Analysis Based on Intrinsic Time-Scale Decomposition for Planetary Gearbox Fault Diagnosis
,”
Mech. Syst. Sig. Process.
,
72–73
(
1
), pp.
223
240
. 10.1016/j.ymssp.2015.11.024
36.
Hoyle
,
J. B.
,
2004
, “
Modelling the Static Stiffness and Dynamic Frequency Response Characteristics of a Leaf Spring Truck Suspension
,”
Proc. Inst. Mech. Eng. Part D: J. Automob. Eng.
,
218
(
3
), pp.
259
278
. 10.1243/095440704322955795
You do not currently have access to this content.