4) Selection。 The inpiduals with stable fitness were selected as the new generation。

5) Crossover。 The partial chromosomes of 40 inpiduals selected will be exchanged at a certain probability and thus 40 new inpiduals were generated。 Crossover probability was set to be 0。9。

6) Mutation。 40 inpiduals selected were given a certain mutation probability to form a new generation。 The mutation probability was set to be 0。05。

7) Judgment。 It will be analyzed whether the new generation can meet the constraints。 If it didn’t meet the constraints, the optimization will stop。 Otherwise, the optimization will return to the third step to continue。

Fig。 9。 Optimization flow of suspension system

5。 Results and discussions

Optimized analysis was carried out on the suspension by genetic algorithm。 The change processes of the maximum dynamic load and the sum of the error square during optimization iteration process were shown in Fig。 10 and Fig。 11。

Fig。 10。 Iteration process of the dynamic load

Fig。 11。 Iteration process of the sum of the error square

According to the figures, with the progress of iteration, the dynamic load on the suspension gradually decreased, while the sum of the error square gradually increased。 It was shown that if the constraint for the sum of the error square was relaxed, the dynamic load on the suspension will be further reduced。 When the iteration reached the 13th step, the iteration converged。 The maximum value of the dynamic load became 258。53 MPa, and the sum of the error square was 29。80072。

Size of iterations should be as many as possible theoretically。 However, for the time-consuming optimization process in this paper, its further optimization space was very small after sufficient repeated iterations。 Therefore, the strategy of exchanging time for the limited optimization effect was unacceptable。 Generally, a group of satisfactory solutions was enough。

Fig。 12。 Dynamic load on the jounce bumper before optimization

Dynamic loads which acted on the jounce bumper before and after the optimization were

obtained through the mentioned analysis, as shown in Fig。 12 and Fig。 13。 It was shown in the figures that the maximum dynamic loads acting on the jounce bumper before optimization    was

263。5 MPa。 The value changed into 258。5 MPa after optimization。

Fig。 13。 Dynamic load on the jounce bumper after optimization

In order to further verify optimization effect, vibration isolation ratios of the suspension system after optimization were extracted, which were compared with results before optimization (shown in Fig。 7), as shown in Fig。 14。 It was shown in the figure that the vibration isolation ratio of the suspension system after optimization increased obviously when the frequency was over 30 Hz。 In this way, and the suspension could attenuate vibration transmitted from pavement to the vehicle body and could also improve ride comfort。

Fig。 14。 Comparison of vibration isolation ratios of the suspension system before and after optimization

Fig。 15。 Fatigue life of the jounce bumper before optimization

Dynamic loads in Fig。 12 and Fig。 13 were circulated with the circle of 4 s。 They were applied to the finite element model of the jounce bumper。 Therefore, fatigue lives of the jounce  bumper

before and after optimization could be respectively obtained, as shown in Fig。 15 and Fig。 16。

According to the nephogram of fatigue life, the position with the maximum fatigue life was improved at some extent。 However, the change at position with the minimum life was not significant。 Four elements on different places of the jounce bumper were taken from the exterior to interior to compare the fatigue life of these elements before and after optimization, as shown in Table 1。