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Journal of Testing
and Evaluation
Wenguang Wu,
1
Lin Hu,
1
and Zhiyong Zhang
2
DOI: 10.1520/JTE20180506
Collaborative Optimization of
Nonlinear Hydropneumatic
Suspension Dynamic
Characteristics
Copyright by ASTM Int'l (all rights reserved); Wed Jun 12 21:43:27 EDT 2019
Downloaded/printed by
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Wenguang Wu,
1
Lin Hu,
1
and Zhiyong Zhang
2
Collaborative Optimization of Nonlinear
Hydropneumatic Suspension Dynamic
Characteristics
Reference
W. Wu, L. Hu, and Z. Zhang, “Collaborative Optimization of Nonlinear Hydropneumatic
Suspension Dynamic Characteristics,”Journal of Testing and Evaluation
https://doi.org/10.1520/JTE20180506
ABSTRACT
Vehicle handling stability and ride comfort play important roles in a vehicle’s performance. This
article proposes a new concept for vehicle handling and ride optimization. The proposed method
combines the handling optimization object and design variables with the ride optimization ob-
ject and design variables. This optimization is based on a rigid-flexible model of a dump truck
used for mining and equipped with nonlinear hydropneumatic suspension. The truck model is a
composite of a flexible main-chassis and other rigid parts. Optimization is realized using the
response surface model because it is based on the design of experiment (DOE) method,
and then the DOE results are calculated in the rigid-flexible model. The proximate model is then
optimized using Isight software. The optimized results are compared with the numerical results
that are calculated in the dynamic model in the ADAMS software, the results of which indicate
that the optimized dynamic performance is enhanced, including the handling and ride character-
istics. The proposed method can provide a balance for vehicle performance optimization.
Keywords
hydropneumatic suspension, collaborative optimization, dump truck, running test
Nomenclature
Z
n
=system optimization object function
Z=system optimization platform design variable
x
i
=design variable coupled with every subsystem
¯
xi=subsystem partial design variable
y
i
=subsystem output state variable
z
j
=design variable sent by the system
Manuscript received July 27, 2018;
accepted for publication February
1, 2019; published online April 5,
2019.
1
Changsha University of Science
and Technology, No. 960 South
Wanjiali Rd., Changsha, Hunan
Province 410114, China,
http://orcid.org/0000-0002-
1081-293X (W.W.)
2
Changsha University of Science
and Technology, No. 960 South
Wanjiali Rd., Changsha, Hunan
Province 410114, China
(Corresponding author), e-mail:
zzy04@163.com
Journal of Testing and Evaluation
Copyright © 2019 by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959
doi:10.1520/JTE20180506 available online at www.astm.org
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c
i
=system partial constraint function
N
W
=truck’s handling stability score of steady static circular test
N
H
=truck’s handling stability score of return ability test
N
S
=truck’s handling stability score of the pylon course slalom
N
R
=ride comfort score of the rough road
N
VDV
=ride comfort score of the bumpy road
Introduction
Mining dump trucks operate throughout their service life on unpaved roads that are in terrible condition. As
handling and ride are the most important performance indexes, they are vital in ensuring the driving safety and
reliable running of the truck. The hydropneumatic suspensions of the trucks significantly influence their handling
and ride optimization. However, it is difficult to optimize the handling and ride of the trucks at the same time in
an engineering project using the traditional methods.
A number of research groups have studied the optimization of passive hydropneumatic suspension, and
these studies optimized the vehicle’s performance. For instance, a passive suspension setting method that could
set the suspension performance for either the ride mode or handling mode was developed, but the suspension was
unable to work in a combined ride and handling mode.
1
The handling stability and steering maneuverability can
also be improved by coupling the steering control force and displacement.
2
The ride comfort of a truck was
optimized using the Genetic Algorithm,
3
but it appears that it is difficult to apply to an engineering project.
In the author’s previous articles,
4,5
the handling and ride performance optimization showed that the proximate
model method was successful as a method for solving nonlinear optimization problems, but in this research,
optimizing the handling always leads to a reduction in the ride performance, and optimizing the ride always
leads to a reduction in handling performance. Few of the research papers introduced a method to solve the
handling and ride decoupling problem. Increasing numbers of research papers have paid attention to active
or interconnected hydropneumatic suspension, but it appears that it is hard to equip a mining dump truck with
controlled hydropneumatic suspension because of its huge size. Therefore, it looks as if passive hydropneumatic
suspension optimization is still a feasible way to ensure the driving safety and reliability of a dump truck.
A collaborative optimization method was proposed in the 1990s to fill the gap between different courses.
6
Nowadays, this method is used to solve complicated optimization problems in engineering projects. An optimal
design for aerodynamics and structural mechanics was presented in the literature
7
; to achieve this design, three
different subsystems relating to weight, noise, and emissions of oxides of nitrogen were built and optimized by the
use of the Genetic Algorithm. The results showed that the collaborative optimization produced an improvement
for the multiple objectives. A collaborative optimization method was used to match the power system of the
mining dump truck; the results showed that the emissions of the truck were reduced.
8
The train schedules
and circulation plans were transformed in the literature into a mixed-integer linear programming problem;
the problem was optimized by the Collaborative Optimization method, and the results of the study were incor-
porated into the data of Beijing’s Yizhuang Line.
9
A brand-new chassis system for an electric-wheel vehicle com-
prising a semi-active suspension is presented and optimized by using a bilevel integrated system collaborative
optimization method. It shows impressive performance of handling, ride comfort, and economic efficiency.
10
Although the collaborative method has been used in many areas of research, the problems of a complex opti-
mization model and an uncertain objective should be solved to optimize nonlinear hydropneumatic suspension.
Vehicle Dynamics Model
MODELING
To accurately optimize the dynamics performance of the hydropneumatic suspension, the rigid-flexible coupled
multidynamics model was built in the ADAMS software and verified by carrying out a vehicle vibration test. The
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coupled model consisted of 40 rigid parts and 1 flexible mainframe, the parts were connected by 62 joints and 4
contact points, and the model has been shown in figure 1.
VERIFICATION
In order to verify the accuracy of the coupled model, a vehicle vibration test was carried out in an open pit main in
the west of China as shown in figure 2. The vibration data, such as the acceleration of the center of the wheel, the
upper and lower suspension points, and the deck and the seat, were collected.
As shown in figure 3, the rigid dynamic model and coupled model were very accurate compared
with the rigid dynamic model, and approximately a 5 % precision improvement was achieved by the coupled
model.
Collaborative Optimization Method
OVERVIEW
The collaborative optimization method was introduced to solve complex and interdisciplinary design problems.
As shown in figure 4, the method consists of a system optimization platform (SOP) and many sub-SOPs that
run respectively; the SOP harmonizes every sub-SOP that runs independently, and they do not influence each
other.
To harmonize the inconsistent characteristic of every sub-SOP and return the system information, it is nec-
essary to make sure every sub-SOP returns the same desired value for the same design variable; many iterations
will probably be required to complete the optimization as shown in figure 5.
FIG. 1
Coupled dynamics
model of the dump truck.
FIG. 2
Experimental
environment and sensor.
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Mathematic Model of the Collaborative Optimization
MATHEMATIC MODEL OF THE SOP
In the collaborative optimization, the purpose of the SOP is to harmonize every subsystem and to ensure the
integrity of the entire assignment. The mathematic model can be written as follows:
FIG. 3 Results of the model verification: (A) Root Mean Square of the wheel center acceleration and (B) RMS of the deck
acceleration.
FIG. 4
Collaborative
optimization method.
FIG. 5
The information transfer
of the optimization.
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8
<
:
min Zn
w:r:t:Z=fz1,z2,···,zng
s:t:JiðZÞ=0∀subspacei
(1)
where Z
n
is the system optimization object function, which corresponds to the subsystem output; Zis the SOP design
variable, consisting of the sub-SOP sharing design variables and coupled design variables; J
I
is the integrity restraint,
corresponding to the sub-SOP design restraint, the value of which can be calculated by the corresponding sub-SOP.
MATHEMATIC MODEL OF THE SOP
For the subsystem i, the mathematic model can be written as follows:
8
>
>
>
>
>
>
<
>
>
>
>
>
>
:
min Jiðxi,¯
xiÞ=Pm
j=1ðzj−xjÞ2+Pm+k
j=m+1ðzj−xjÞ2
w:r:t:xi,¯
xi
s:t:ciðxi,yi,¯
xiÞ
xi=fxi1,xi2,···,ximg
yi=fyi1,yi2, ··· ,yikg
¯
xi=f¯
xi1,¯
xi2,···,
¯
xilg
(2)
where x
i
is the design variable coupled with every subsystem; ¯
xiis the subsystem partial design variable; y
i
is the
subsystem output state variable; z
j
is the design variable sent by the system, in the subsystem, it is defined as a
fixed parameter; and c
i
is the system partial constraint function.
Design Objectives and Variables
DESIGN OBJECT
Objects of Handling Stability
To completely evaluate the handling, the Chinese standard GBT 6323, Controllability and Stability Test Procedure
for Automobile, was used to evaluate vehicle handling stability performance. The standard includes many projects:
the typical items, such as transient steering response test, pylon course slalom test, return ability test, steering
effort test procedure and steady static circular test procedure, are included. According to the operating condition
of the dump truck, the steady static circular test, return ability test and the pylon course slalom test are chosen to
evaluate the truck’s handling stability.
According to the testing method standard (Chinese standard GBT 6323.1, GBT6323.4, and GBT6323.6) and
the evaluation method standard (QC/T-480, Griterion Thresholde and Evaluation of Controllability and Stability
for Automobiles), the mathematic optimization model can be written as follows:
8
>
>
<
>
>
:
min fðNcÞ=P3
i=1Nci=3
s:t:fðNc,N*Þ=P3
i=1ðNci −N*
iÞ2≅0
−100 ≤Nci ≤−60, i=1, 2, 3
(3)
where N
c1
=−N
W
,N
c2
=−N
H
, and N
c3
=−N
S
; and N
W
,N
H
, and N
S
are the truck’s handling stability score of
steady static circular test, return ability test, and the pylon course slalom test, respectively, that were evaluated by
the truck’s dynamics model.
Objects of Ride Comfort
In order to enhance the vehicle’s ride comfort in both empty and loaded conditions, the ride comfort of the two
conditions with a vehicle speed of 20–40 km/h was taken into account. The vehicle ride comfort was evaluated
through the use of ISO 2631, Mechanical Vibration and Shock—Evaluation of Human Exposure to Whole-Body
Vibration, and the mathematic model for ride comfort optimization can be written as follows:
Journal of Testing and Evaluation
WENGUANG ET AL. ON DUMP TRUCK DRIVING TEST AND OPTIMIZATION
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8
>
>
<
>
>
:
min gðNpÞ=P5
j=4Npj=2
s:t:fðNpj,N*
jÞ=P5
j=4ðNpj −N*
jÞ2≅0
−100 ≤Npj ≤−60, j=4, 5
(4)
where the N
p4
=−N
R
,N
p5
=−N
VDV
;N
R
and N
VDV
are the truck’s ride comfort scores. N
R
is the ride comfort score
of the seat when truck is running on the rough road in the loaded and empty conditions, the truck speed is from
20–40 km/h. It can be shown as follows:
NR=0.15*ðNL20 +NE20 +NL40 +NE40Þ+0.2*ðNL30 +NE30 Þ(5)
where N
L20
,N
L30
, and N
L40
are the scores of truck in a loaded condition from a speed of 20–40 km/h, and where
N
E20
,N
E30
, and N
E40
are the ride comfort scores of the truck in an empty condition at a speed of 20–40 km/h. The
scores can be calculated by the following function:
N=60 +40
a60 −a100
ða60 −awÞ(6)
where a
60
=0.8 m/s
2
is the lower limitation of the seat’s weighted acceleration RMS; a
100
=0.315 m/s
2
is the upper
limitation of the seat’s weighted acceleration RMS; and a
w
is the measured value that was simulated by the
dynamics model.
N
VDV
is the ride comfort score of the seat when the truck is running on the bumpy road at a speed of 30 km/h.
NVDV =60 +40
m60 −m100
ðm60 −mÞ(7)
where m
60
=31.44 m/s
2
is the lower limitation of the seat’s instantaneous acceleration and m
100
=0m/s
2
is the
upper limitation of the seat’s instantaneous acceleration; mis the measured value that was simulated by the dy-
namics model.
SYSTEM OPTIMIZATION MODEL
The system optimization platform only harmonizes the two subsystem’s optimization; its mathematic model can
be written as follows:
8
<
:
min WðNÞ=λ1fðNcÞ+λ2gðNpÞ
s:t:bcðN,N*
cÞ=P3
i=1ðNi−N*
ciÞ2≅0
bpðN,N*
pÞ=P5
j=4ðNj−N*
jÞ2≅0
(8)
where Wis the system optimization objective function, which represents the comprehensive dynamics ability;
λ
1
and λ
2
are the weighted coefficients; N=(N
1
,N
2
,N
3
,N
4
,N
5
) corresponds to the subsystem objects; N*
c=
ðN*
c1,N*
c2,N*
c3Þare the inputs corresponding to the handling stability optimization subsystem outputs respectively;
N*
p=ðN*
p4,N*
p5Þare the inputs corresponding to the ride comfort optimization subsystem outputs respectively; b
c
and b
p
are the system constraints.
DEFINING THE DESIGN VARIABLES
It is very important to choose the correct variables for combined handling and ride comfort optimization. In
engineering design, every design variable will influence the object in a different way, and choosing the most
effective design variables to optimize will clearly enhance the optimization efficiency the most.
DESIGN VARIABLES
According to the design appearance, combined with the vehicle structure, the front suspension damping and
stiffness, rear suspension damping and stiffness, front and rear antiroll bar stiffness, and the front suspension
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fixed upper point coordinates (front and lateral direction, fs
z
,fs
x
) are chosen as design variables. Where the
suspension stiffness is decided by the gas height (h
1
,h
2
) and the suspension damping is decided by the damping
hole diameter (d
1
,d
2
); the front and rear antiroll bar stiffness is decided by the gas pressure (Prod
1
,Prod
2
). The
design variables have been defined in Table 1.
For the purpose of convenient optimization, X
i
(i=1, 2, 3, 4, 5, 6, 7, 8) were defined to normalize every
design variable.
−1<X1=h1−100
20 <1
−1<X2=h2−40
8<1
−1<X3=c1−8
1.6 <1
−1<X4=c2−8
1.6 <1
−1<X5=prod1−2
1<1
−1<X6=prod2−1
1<1
−1<X7=fsz
100 <1
−1<X8=fsx −1, 928
100 <1(9)
In order to build an approximate optimization model,the center composite design method was used in a design
of experiment (DOE). According to the DOE method theory and the numberof design variables, in order to build the
approximate model, it should simulate the dynamic model 93 times using the given DOE design variables. The
detailed calculation process has been abbreviated, and theapproximate model of the DOE has been shown as follows:
Yf=−79.5601 +1.3761X1+3.0710X2+0.5200X3+0.9689X4−1.5058X5
−1.4418X6−0.2238X7−0.1487X8+0.3119X2
1−1.2797X2
2+0.3975X2
3+0.9431X2
4
−0.1578X2
5+0.2072X2
6+0.2141X2
7+0.2366X2
8+0.2656X1X2+0.2550X1X3
−0.5962X1X4+0.2891X1X5−0.0297X1X7+0.2737X2X3−0.1956X2X4−0.0087X2X5
+0.0606X2X6−0.0194X2X7−0.2350X2X8+0.2612X3X4+0.1995X3X5+0.3575X3X6
+0.1863X3X7+0.0675X3X8+0.2675X4X5+0.2103X4X6−0.0797X4X7+0.0603X4X8
+0.2869X5X6+0.3503X5X7+0.2594X6X7−0.0041X6X8+0.2494X7X8
TABLE 1
Design variables
Design Variable Value MinValue MaxValue
h
1
/mm 100 80 120
h
2
/mm 40 32 48
d
1
/mm 8 6.4 9.6
d
1
/mm 8 6.4 9.6
Prod
1
/MPa 2 1 3
Prod
2
/MPa 2 1 3
fs
z
/mm 0 −100 100
fs
x
/mm 1,928 1,828 2,028
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FIG. 6 Main effect of the design variables: (A) main effect on handling stability and (B) main effect on ride comfort .
FIG. 7 Interactive effect of the design variables on handling stability: (A) rear suspension and front suspension and
(B) front and rear antiroll bar stiffness.
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Yg=−66.1600 −1.6952X1−0.2698X2+0.7857X3+0.4088X4+0.0062X5
+0.0553X6+0.0466X7+0.0333X8+0.4290X2
1+0.5666X2
2+0.3144X2
3
+0.2381X2
4−0.1313X2
5+0.0778X2
6+0.0122X2
7−0.0178X2
8
+0.2421X1X2+0.0131X1X3−0.0706X1X4−0.1494X1X5−0.1084X1X7
+0.2802X2X3−0.4484X2X4+0.0428X2X5+0.0112X2X6+0.0663X2X7
−0.1081X2X8+0.2809X3X4+0.0559X3X5+0.1075X3X6−0287X3X7
+0.0156X3X8+0.2940X4X5+0.0069X4X6−0.0225X4X7+0.0644X4X8
+0.2671X5X6+0.0097X5X7+0.2740X6X7+0.1047X6X8+0.2765X7X8
DOE DESIGN RESULTS AND DISCUSSION
Main Effect of the Design Variables
According to the DOE table simulation results, the influence of each design variable on every optimization object
has been analyzed. As shown in figure 6, the variables that had the maximum influence on the handling stability
and ride comfort were the front and rear suspension stiffness; next were the front and rear suspension damping.
The influence of the upper front fixed suspension point on the objects was not apparent; the stiffness of the
suspension caused the handling stability and ride comfort to increase and decrease, respectively.
FIG. 8 Interactive effect of design variables on ride comfort: (A) rear suspension and front suspension and (B) front and
rear antiroll bar stiffness for front suspension.
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Interactive Effect of the Design Variables on Handling Stability
As shown in figure 7A, when the rear suspension stiffness was low (a high X3 value indicates low suspension
stiffness), an interactive effect between the front and rear suspension stiffness was not evident, but if the stiffness
of the rear suspension was high (a low X3 indicates a high suspension stiffness), the effect was evident. The same
held true for the rear suspension damping. It can be concluded that when the rear suspension stiffness and damp-
ing had a low value, the handling stability will be affected by the front suspension characteristics. As shown in
figure 7B, no matter what the value of the stiffness of the front and rear antiroll bar, the interactive effect between
the front suspension stiffness and damping was not evident. This has shown that coordinating the front suspen-
sion and antiroll bar stiffness is of great importance.
Interactive Effect of the Design Variables on Ride Comfort
As shown in figure 8A, whether the rear suspension stiffness was low or high, its interactive effect on the front
suspension was not evident, but the contrary was the case for damping. The results showed that suspension
stiffness was a sensitive factor for vehicle comfort, but that damping was not so sensitive. From figure 8B,
it can be concluded that the stiffness of the antiroll bar does not clearly affect the ride comfort of the vehicle,
but the stiffness of the front antiroll bar affects the ride comfort of the vehicle significantly more than the stiffness
of the rear antiroll bar.
Optimization
OPTIMIZATION PROCEDURE
According to figure 9, the collaborative optimization procedure is as follows:
(1) The SOP transmitted the expectation object N
*
to the handling optimization subsystem and the ride op-
timization subsystem; the first expectation object could be chosen arbitrarily.
FIG. 9
Optimization procedure.
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(2) The handling optimization subsystem and the ride optimization subsystem started to optimize the pro-
gram after receiving the given expectation object. The results N*
cand N*
pwere often very close to the
object. The results were then transmitted to the SOP. After getting the results, the SOP started the opti-
mization program.
(3) The assignment of the SOP was to harmonize the design variable transmitted by the two subsystems, to
ensure all the values of the common design variable coincided. The constraints of the system usually
defined the variance of the expected design variable and optimized the design variable to zero.
FIG. 10 Results of the design variables: (A) front suspension stiffness and damping, (B) rear suspe nsion stiffness and
damping, and (C) front and rear antiroll bar stiffness.
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(4) The system platform then transmitted a new expectation object N
*
to the two subsystems, and then the
next time, the subsystem started the optimization.
(5) The process repeated until the program obtained the expectation object and satisfied all the constraints.
For the procedure in this article, the program obtained the object after about 20,000 iterative steps.
OPTIMIZATION RESULTS AND DISCUSSIONS
Results of Design Variables
The optimized results have been shown in figure 10. It can be concluded that after optimization the front sus-
pension stiffness and damping were decreased and thus the front suspension was “softer”; additionally, when the
rear suspension stiffness and damping increased, the rear suspension became “harder.”These characteristics of
the suspension dynamics always have the advantage of enhancing the vehicle ride and roll ability but are detri-
mental to the cornering characteristics.
From figure 10Cit can be concluded that the stiffness of the front and rear antiroll bar was increased, which
may reduce the vehicle roll angle and angular velocity. The handling stability of the vehicle was optimized but, as
previously mentioned, the stiffness of the antiroll bar inefficiently influenced the ride of the vehicle.
The optimized design variables have been shown in Table 2. It can be concluded from the table that the
suspension stiffness and the antiroll bar stiffness both decreased, and the front and rear suspension damping
increased. Therefore, the handling stability and ride comfort testing score increased.
Objects
Taking all the design variables and entering them into the dynamic model, the vehicle stability and ride comfort
score can be obtained, as shown in Table 3. It can be concluded from the table that the handling stability and ride
TABLE 2
Comparison of the design variables
No. Design Variable Optimization Result Original Value
1X1 0.483293202474911 110 mm
2X2−0.939392110989184 33 mm
3X3 0.360651018896621 8.6 mm
4X4−0.754394613845847 6.8 mm
5X5 0.57287298320881 2.6 MPa
6X6 0.329490848129054 2.3 MPa
7X7 0.30114032534828 30 mm
8X8 0.124779102288688 1,940 mm
9f−85.3115 85.31
10 g−76.2766 76.28
11 W−80.79 80.79
TABLE 3
Comparison of the optimization objects
Item Original
Optimized(Handling Only) Optimized(Ride Only) Collaborative Optimization Method
Score Diff. Score Diff. Score Diff.
Steady state circular test procedure 87.78 92.66 4.88 81.20 −6.58 90.53 2.75
Steering effort test procedure 79.56 88.72 9.16 72.14 −7.42 86.11 6.55
Pylon course slalom test 71.33 78.41 7.08 65.42 −5.91 75.98 4.65
Ride (rough road) 48.70 44.31 −4.39 67.85 19.15 60.07 11.37
Ride (bumpy road) 83.61 75.61 −8 88.21 4.6 87.82 4.21
Comprehensive score 72.86 73.28 0.42 75.48 2.62 79.20 6.34
Journal of Testing and Evaluation
WENGUANG ET AL. ON DUMP TRUCK DRIVING TEST AND OPTIMIZATION
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comfort are increased, and every item of the vehicle’s performance was optimized. Comparing this with the simple
optimization of handling stability or ride comfort, the collaborative optimization not only improved the vehicle’s
handling stability but also increased the truck’s ride comfort, and the comprehensive score of the truck is im-
proved by 8.70 %.
Conclusion
A collaborative optimization method was used to optimize the dynamic performance of nonlinear hydropneu-
matic suspension. Through the combination of multibody dynamic analysis, driving tests, and the collaborative
optimization method, the ride and handling optimization problems were successfully solved. From the optimi-
zation process of vehicle handling and ride, the following conclusions could be drawn:
(1) The rigid-flexible coupled modeling method provided a way to increase the accuracy of the model analysis,
and choosing the appropriate part would not decrease the efficiency of the model analysis.
(2) Combining the multibody dynamic analysis method with the approximate model method provided a
novel method for solving complicated nonlinear problems.
(3) The use of the collaborative optimization method to solve the problem of the contradictory ride and
handling characteristics, which suspension requires, has produced an excellent result.
ACKNOWLEDGMENTS
Special thanks to the National Natural Science Foundation of China (51705035), the Natural Science Foundation
of Hunan Province (2017JJ3336), and the Science Research Foundation of the Education Department of Hunan
province (16C0062).
References
1. P. E. Uys, P. S. Els, and M. Thoresson, “Suspension Settings for Optimal Ride Comfort of Off-Road Vehicles Travelling on
Roads with Different Roughness and Speeds,”Journal of Terramechanics 44, no. 2 (April 2007): 163–175, https://doi.org/
10.1016/j.jterra.2006.05.002
2. W. Zhao and H. Zhang, “Coupling Control Strategy of Force and Displacement for Electric Differential Power Steering
System of Electric Vehicle with Motorized Wheels,”IEEE Transactions on Vehicular Technology 67, no. 9 (June 2018):
8118–8128, https://doi.org/10.1109/TVT.2018.2850154
3. L.-L. Tian, Z.-Q. Gu, and W.-P. Li, “Ride Comfort Simulation and Parameters Optimization Design of Nonlinear Hydro-
Pneumatic Suspension System,”Journal of Central South University 42, no. 12 (December 2011): 3715–3721.
4. W. Wu and Z. Gu, “Handling Stability Optimization of Mining Dump Truck Based on Parameter Identification,”in SAE
2013 World Congress & Exhibition (Warrendale, PA: SAE International, 2013), https://doi.org/10.4271/2013-01-0702
5. W. Wu and Z. Gu, “Ride Comfort Optimization of Electric Wheel Dump Truck Based on a Vehicle Test,”in SAE 2013
World Congress & Exhibition (Warrendale, PA: SAE International, 2013), https://doi.org/10.4271/2013-01-1354
6. B. Roth and I. Kroo, “Enhanced Collaborative Optimization: Application to an Analytic Test Problem and Aircraft
Design,”in 12th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference (Reston, VA: American
Institute of Aeronautics and Astronautics), 1–14, https://doi.org/10.2514/6.2008-5841
7. C. Yan, Z. Yin, F. Guo, X. Shen, J. Fan, and J. Luo, “A Newly Improved Collaborative Optimization Strategy: Application
to Conceptual Multidisciplinary Design Optimization of a Civil Aero-Engine,”in ASME Turbo Expo 2017:
Turbomachinery Technical Conference and Exposition (New York, NY: American Society of Mechanical Engineers,
2017), https://doi.org/10.1115/GT2017-64177
8. J. Dai, “Optimization Design of Power-Train System in Mining Dump Truck Based on Collaborative Optimization,”
Mechanical Design and Manufacturing 6 (July 2017): 10–14.
9. Y. Luo, Y. Wang, F. Cao, M. Zhang, and T. Tang, “Collaborative Optimization of Train Schedule and Circulation Plan,”in
2017 Chinese Automation Congress (CAC) (Piscataway, NJ: Institute of Electrical and Electronics Engineers, 2017), 4447–
4452, https://doi.org/10.1109/CAC.2017.8243563
10. W. Zhao, Y. Wang, and C. Wang, “Multidisciplinary Optimization of Electric-Wheel Vehicle Integrated Chassis System
Based on Steady Endurance Performance,”Journal of Cleaner Production 186 (June 2018): 640–651, https://doi.org/10.
1016/j.jclepro.2018.03.157
Journal of Testing and Evaluation
WENGUANG ET AL. ON DUMP TRUCK DRIVING TEST AND OPTIMIZATION
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