Published: 19 October 2020

Optimal design parameters of air suspension systems for semi-trailer truck. Part 2: results and discussion

Nguyen Van Tuan1
Le Van Quynh2
Vi Thi Phuong Thao3
Le Quang Duy4
1, 2, 4Faculty of Automotive and Power Machinery Engineering, Thai Nguyen University of Technology, Thai Nguyen, Vietnam
3Faculty of International Training, Thai Nguyen University of Technology, Thai Nguyen, Vietnam
Corresponding Author:
Le Van Quynh
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Abstract

Based on the results of model and algorithm in Part1 for searching the optimal design parameters of vehicle suspensions using genetic algorithm, in Part 2, the simulation results with MATLAB Simulink combined with an optimal program are written to search the optimal design parameters of vehicle air suspension systems in two optimal conditions. The optimal results indicate that the DLC values at all axles of vehicle respectively reduce by 9.09 %, 10.71 %, 11.11%, 10.81 %, 8.82 % (in Case 1) and 14.29 %, 19.23 %, 20.00 %, 17.14 %, 12.12 % (in Case 2) in comparison with the original air suspension systems when vehicle moves on the ISO class C road surface at v= 20 m/s and full load. All these things indicate that using the genetic algorithm optimization method does not only reduce the tire dynamic loads acting on road surface but also improves the ride comfort. Finally, the optimum performance of vehicle suspension systems is considered and reassessed under different operating conditions. The evaluation results indicate that the optimum performance of the air suspension systems has better potential to improve the road friendliness which provides a ride comfort for road surfaces and vehicle.

Optimal design parameters of air suspension systems for semi-trailer truck. Part 2: results and discussion

Highlights

  • The geometric parameters of the air springs of suspension systems are optimized by genetic algorithm.
  • The design parameters of the air suspension systems are optimized by genetic algorithm.
  • The simulation results with MATLAB Simulink combined with an optimal program are written to search the optimal design parameters of vehicle air suspension systems in two optimal conditions.

1. Introduction

In order to improve the performance of the air suspension system for reducing the negative impact on the road surface, the control and optimization methods for air suspension systems are discussed in some of the following studies such as the control methods: the genetic LQG and PID control were used to control an air suspension system [1], the performance of the air suspension system of heavy trucks was analyzed with semi-active fuzzy control [2] and the two-bag air suspension system for heavy-duty vehicles was analyzed using the multi-body vehicle model [3], the optimization technique available in OptiY with SIMULINK simulation was used to search the optimal parameters of air spring of suspension system using vehicle dynamic model with 2 d.o.f [4], The air suspension system with independent height and stiffness tuning was analyzed and the geometric parameters of air spring were optimized [5], the glowworm swarm optimization proportional-integral-derivative controlling algorithm was designed to optimize magnetorheological damper for air suspensions [6], the vehicle suspension parameters of non-linear air spring was analyzed and optimized by using the multi-objective optimization method [7], and the optimization of suspension geometric parameters was analyzed and optimized using a double-loop multi-objective particle swarm optimization algorithm (DL-MOPSO) when the vehicle operates under various driving conditions [8]. The optimal parameters of the suspension systems as well as drum’s isolation system were found out using genetic algorithm (GA) [9, 10]. Based on the results of model and algorithm in Part 1, the rest of this paper of Part 2 is organized as follows: Optimization of suspension parameters and discussion are presented in Section 2. Section 3 presents the efficiency of the optimal design parameters compared with the original design parameters of air suspension systems under the different vehicle operating conditions and the conclusions are given in Section 4.

2. Optimization of suspension parameters and discussion

In order to find the optimal design parameters for the air suspension systems of the articulated truck semi-trailer, Matlab/Simulink software is used to simulate the half-vehicle dynamic model with a set of parameters of the articulated truck semi-trailer in Table 1 when the vehicle moves on the ISO class C road surface at v= 20 m/s and full load.

Table 1Parameters of the 5-axle semi-trailer truck

Parameters
Values
Parameters
Value
Parameters
Values
kt1 / (N.m-1)
647500
kk / (N.m-1)
2000000
Ic / kg.m2
2056
kt2 / (N.m-1)
1185000
ks / (N.m-1)
28500
l1 / m
2.741
kt3 / (N.m-1)
1185000
ck / (N.s.m-1)
200000
l2 / m
2.229
kt4 / (N.m-1)
1185000
cs / (N.s.m-1)
9200
l3 / m
3.334
kt5 / (N.m-1)
1185000
ma1 / kg
584
l4 / m
1.330
ct1 / (N.s.m-1)
258.50
ma2 / kg
735
l5 / m
2.960
ct2 / (N.s.m-2)
325.00
ma3 / kg
735
l6 / m
5.620
ct3 / (N.s.m-1)
325.00
ma4 / kg
735
l7 / m
2.685
ct4 / (N.s.m-1)
325.00
ma5 / kg
735
l8 / m
1.115
ct5 / (N.s.m-1)
325.00
mb1 / kg
3783
l9 / m
0.235
c1 / (N.s.m-1)
11270
mb2 / kg
24800
l10 / m
1.200
kc1 / (N.m-1)
33860
mc / kg
1208
α2,3
0.0708
kc2 / (N.m-1)
33860
ms / kg
116
α4,5
0.0481
cc1 / (N.s.m-1)
3650
Ib1 / kg.m2
45819
β2,3
0.0223
cc2 / (N.s.m-1)
3650
Ib2 / kg.m2
195820
β4,5
0.0399

Operation parameters of genetic algorithm as follows: The population size is 100; The number of generations is 200; Elitism: best seven individuals from each generation were chosen for creation of next population; Mutation: random and adaptive mutations were used; Crossover: just neighboring individuals were crossed; and selection: random [9]. A genetic algorithm program in Matlab are called by Simulink module function using the sim function, the simulation results are calculated after the calculation of the population of the objective function value. The optimal values of the parameters of air suspension systems are obtained by genetic algorithms method in comparison with the original design parameters of air suspension systems with two cases, as shown in Table 2 and Table 3.

Table 2GA optimization results in Case 1

Air spring suspension parameters
Initial design parameters
GA optimization
Case 1 Optimal design of geometrical parameters of air spring suspension systems
A02 / m2
0.085
0.010
A03 / m2
0.085
0.016
V02 / m3
0.028
0.003
V03 / m3
0.028
0.005
p02 / MPa
0.692
0.428
p03 / MPa
0.692
0.528
A04 / m2
0.092
0.041
A05 / m2
0.092
0.032
V04 / m3
0.03
0.014
V05 / m3
0.03
0.011
p04 / MPa
0.492
0.254
p05 / MPa
0.492
0.260

Table 3GA optimization results in Case 2

Case 2 Optimal design of parameters of air suspension systems
A02 / m2
0.085
0.013
A03 / m2
0.085
0.021
V02 / m3
0.028
0.004
V03 / m3
0.028
0.007
p02 / MPa
0.692
0.243
p03 / MPa
0.692
0.304
A04 / m2
0.092
0.069
A05 / m2
0.092
0.032
V04 / m3
0.03
0.023
V05 / m3
0.03
0.011
p04 / MPa
0.492
0.287
p05 / MPa
0.492
0.337
c2 / (N.s.m-1)
26500
53000
c3 / (N.s.m-1)
26500
66300
c4 / (N.s.m-1)
38000
24700
c5 / (N.s.m-1)
38000
20900

The optimal results of the DLC values at 1st, 2nd, 3rd, 4th and 5th axles of vehicle in comparison with those original results with two cases are shown in Table 4. It is indicated from Table 4 that the DLC values of the optimal design parameters of air suspension systems at all axles of vehicle respectively reduce by 9.09 %, 10.71 %, 11.11 %, 10.81 %, 8.82 % (in Case 1) and 14.29 %, 19.31 %, 20.00 %, 17.14 %, 12.12 % (in Case 2) in comparison with the original air suspension systems.

All these things indicate that using this genetic algorithm optimization method does not only reduce the tire dynamic loads acting on road surface but also improves the ride comfort.

Table 4Comparison of optimized results

Parameters and indexes
DLCt1
DLCt2
DLCt3
DLC4
DLCt5
Case 1 Optimal design of geometrical parameters of air spring suspension systems
Before optimization
0.024
0.031
0.030
0.041
0.037
After optimization
0.022
0.028
0.027
0.037
0.034
Decrease %
9.09
10.71
11.11
10.81
8.82
Case 2 Optimal design of parameters of air suspension systems
Before optimization
0.024
0.031
0.030
0.041
0.037
After optimization
0.021
0.026
0.025
0.035
0.033
Decrease %
14.29
19.23
20.00
17.14
12.12

The comparison of optimized results of the vertical dynamic tire loads acting on road surface in time domain response at 2nd axle in case 1 and 4th axle in case 2 are show Fig. 1 and Fig. 2. The results from Fig. 1 and Fig. 2 show that the performance optimization of the air suspension systems with two cases is better than the original air suspension systems for reducing the negative impact on road surface, especially when the optimum design parameters of the air suspension systems in case 2.

3. Different operating conditions of vehicle

To evaluate the performance of the optimal design parameters of the air suspension systems on road surface friendliness, the different operating conditions such as road surface roughness, vehicle speed and vehicle load [11-15] are analyzed respectively in this paper.

Fig. 1Comparison of the vertical dynamic tire loads acting on road surface at 2nd axle in case 1 between before and after optimization

Comparison of the vertical dynamic tire loads acting on road surface  at 2nd axle in case 1 between before and after optimization

Fig. 2Comparison of the vertical dynamic tire loads acting on road surface at 4th axle in case 2 between before and after optimization

Comparison of the vertical dynamic tire loads acting on road surface  at 4th axle in case 2 between before and after optimization

3.1. Effect of road surface roughness

To evaluate the performance of the optimal design parameters of the air suspension systems in comparing with the original design parameters for reducing the negative impact on road surface with two cases, five road conditions from ISO class A (very good) to ISO class E (very poor) are used when vehicle moves at the vehicle speed of 20 m/s and full load. The DLC values at 2nd and 4th axles of vehicle with three cases are shown in Fig. 3(a). Fig. 3(a) shows that the DLC values at 2nd and 4th axles of vehicle with the optimal design parameters of air suspension system in case 1 respectively reduce by 10.96 %, 10.83 %, 10.71 %, 9.92 %, 9.31 % and 10.92 %, 10.95 %, 10.81 %, 9.35 %, 9.31 % in comparison with the original air suspension systems of vehicle. Similarly, the DLC values at 2ndand 4th axles of vehicle significantly reduce by 19.19 %, 20.00 %, 19.23 %, 19.91 %, 20.38 % and 17.26 %, 17.34 %, 17.14 %, 19.67%, 20.00 %, respectively in Case 2.

3.2. Effect of vehicle speed

The vehicle speeds of 5 m/s, 10 m/s, 15 m/s, 20 m/s and 25 m/s are considered to evaluate the performance of the optimal design parameters of the air suspension systems with two cases for a 5- axle semi-trailer truck when vehicle moves on the road surface condition of the ISO class C and full loaded. The DLC values at 2nd and 4th axles of vehicle with three cases are shown in Fig. 3(b), indicating that the optimal results have a significant improvement in road-friendly level in comparison with the original air suspension systems of vehicle at all vehicle speeds. Moreover, the DLC values at 2ndand 4th axles of vehicle with the optimal design parameters of air suspension system in the optimal results in case 2 are reduced by 6.14 %, 9.23 %, 7.95 % and 4.12 %, 2.31 %, 6.33 %, respectively in comparison with Case 1 when the vehicle speed increases from 10 to 15 m/s, and then to 20 m/s. The DLC values increase or decrease in abnormal manner in each of the vehicle speed because the vehicle speed affects the product of vehicle speed and the cutoff values of the roughness spatial frequency [16].

Fig. 3Comparing of the DLC values at 2nd and 4th axles of vehicle with three cases

Comparing of the DLC values at 2nd and 4th axles of vehicle with three cases

a) Effect of road surface roughness

Comparing of the DLC values at 2nd and 4th axles of vehicle with three cases

b) Effect of vehicle speed

Comparing of the DLC values at 2nd and 4th axles of vehicle with three cases

c) Effect of vehicle load

3.3. Effect of vehicle load

To continue evaluating the optimal design parameters of the air suspension systems in comparing with the original design parameters for reducing the negative impact on road surface with two cases, seven load conditions of vehicle from 0 % (empty load) to 150 % (over 150 %) are used when vehicle moves on the road surface condition of the ISO class C and the vehicle speed of 20 m/s. The DLC values at 2nd and 4th axles of vehicle with three cases are shown in Fig. 3(c). Fig. 3(c) shows that the DLC values at 2nd and 4th axles of vehicle with the optimal design parameters of air suspension system in case 2 significantly reduce by 14.10 %, 15.13 %, 19.29 %, 18.52 %, 18.31 %, 19.33 %, 20.25 % and 14.71 %, 13.88 %, 16.49 %, 16.69 %, 17.14 %, 18.86 %, 19.41 %, respectively in comparison with the original air suspension systems of vehicle. Moreover, the values of DLC at 2nd and 4th axles of vehicle increase the fastest when vehicle move under 50 % load condition and this problem has a negatively effect on road surface. However, when the vehicle's load increases over 75 % vehicle load, the values of DLC at 2nd and 4th axles of vehicle reduce gradually, which has a benefit effect on road surface. However, it has no benefit on the durability of the part of vehicle and the safe movement of vehicle [17].

4. Conclusions

In part 2 of this study, the simulation results by using MATLAB Simulink combined with an optimal program is written to solve the optimization problem of nonlinear air suspension parameters in two optimal conditions. The obtained the optimization results show that the DLC values of the optimal design parameters of air suspension systems at all axles of vehicle reduce in comparison with the initial air suspension systems of vehicle when vehicle moves on the ISO class C road surface at v= 20 m/s and full load. Especially, the DLC values of the optimal design parameters of air suspension systems at 1st, 2nd, 3rd 4th and 5th axles of vehicle considering case 2 respectively reduce by 4.76 %, 7.69 %, 8.00 %, 5.71 % and 3.03 % in comparison in Case 1. Finally, the optimum performance of vehicle suspension systems is considered and evaluated again under different operating conditions and the obtained optimization results indicated that the optimum performance is the significant reduction the tire loads and road surface damage. The study results can be used for the searchers, vehicle manufacturers and traffic managers for further considerations during design as well as perfect design in the design of vehicle air suspension systems.

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About this article

Received
25 June 2020
Accepted
09 August 2020
Published
19 October 2020
SUBJECTS
Mathematical models in engineering
Keywords
semi-trailer truck
air suspension system
dynamic load coefficient
genetic algorithm
optimal parameters
road friendliness
Acknowledgements

This research was supported financially by Thai Nguyen University of Technology, TNUT, Viet Nam.