Journal of Jilin University(Engineering and Technology Edition) ›› 2023, Vol. 53 ›› Issue (8): 2227-2235.doi: 10.13229/j.cnki.jdxbgxb.20211166

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Impact dynamic modeling and simulation for ball joint with clearance considering nonlinear stiffness

Shu-pei ZHANG(),Ming-yue XIA,Wei ZHANG,Zhao CHEN,Yi-xiang CHEN   

  1. School of Automotive and Traffic Engineering，Jiangsu University，Zhenjiang 212013，China
  • Received:2021-11-08 Online:2023-08-01 Published:2023-08-21

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Abstract:

In order to improve the accuracy of analysis of ball joint with clearance， the coupling characteristics between the non-linear contact stiffness of the contact bodies and the mechanism in the impact were considered， and the contact-impact characteristics of the ball joint was studied under the conditions of different restitution coefficients and initial impact speed. The results show that the contact stiffness and hysteresis damping coefficient avoid the situation that remains constant during the real contact process； the improved model describes the impact characteristics of the spherical joint more currently； the peak contact force and deformation is greater with increase of coefficient of restitution， the longer time it takes to reach the peak and shorter time to complete an impact； the contact-impact force and deformation increase rapidly with the increase of initial velocity， and the time to complete the impact decreases. The accuracy of obtaining the impact characteristics of the spherical joint provides a mechanical basis for the precise control of vehicle handling stability.

Key words: vehicle engineering, clearance, spherical joint, contact-impact, finite element

CLC Number: 

  • U463.46

Fig.1

Geometric constraint model of spherical joint"

Fig.2

Impact process of ball pin and ball socket"

Fig.3

Relationship between spherical joint contact deformation coefficient and clearance"

Fig.4

Variation law of contact deformation coefficient with the change of clearance and deformation"

Fig.5

Fitting results of contact deformation coefficient"

Table 1

Simulation parameters"

参数数值参数数值
球销半径/mm14球铰间隙/mm0.1
球窝内表面半径14.1初始速度/（mm·s-1）1 000
球销弹性模量/GPa206球窝弹性模量/GPa2.6
球销泊松比0.3泊松比0.2
球销密度/（g·cm-3）7.82球销密度/（g·cm-3）0.139

Fig.6

Points selection of spherical joint"

Fig.7

Displacement and time curve of the contact point of contact surface between the ball pin and the ball socket"

Fig.8

Relationship curve of contact force and time"

Fig.9

Relationship curve of contact force and deformation"

Fig.10

Relationship curve of contact force，deformation and time during an impact"

Fig.11

Influence of different restitution coefficients on impact characteristics"

Fig.12

Influence of different initial velocities on impact characteristics"

Fig.13

Simulation results of three models with different clearance"

1 赵洪志,杨刚,孟庆海,等.转向球铰球面加工机床及误差分析[J].吉林大学学报:工学版,2008,38(3):548-551.
Zhao Hong-zhi, Yang Gang, Meng Qing-hai, et al. Design of machine tool for surface of spherical hinge and error analysis[J]. Journal of Jilin University (Engineering and Technology Edition), 2008,38(3): 548-551.
2 李研彪,徐涛涛,郑航,等. 含球面副间隙的空间并联机构动态特性[J]. 浙江大学学报:工学版,2020,54(2):348-356.
Li Yan-biao, Xu Tao-tao, Zheng Hang, et al. Dynamic characteristics of spatial parallel mechanism with spherical joint clearance[J]. Journal of Zhejiang University (Engineering Science),2020,54(2):348-356.
3 Askari E. Mathematical models for characterizing non-Hertzian contacts[J]. Applied Mathematical Modelling, 2021, 90 : 432-447.
4 Lankarani H M, Nikravesh P E. A contact force model with hysteresis damping for impact analysis of multibody systems[J]. Journal of Mechanical Design, 1990,112(3):369-376.
5 韩雪艳,李富娟,高振辉,等. 考虑摩擦与刚度的空间机构动力学特性[J].机械工程学报, 2020, 56(15): 170-180.
Han Xue-yan, Li Fu-juan, Gao Zhen-hui, et al. Dynamic characteristics of space mechanism considering friction and stiffness[J]. Journal of Mechanical Engineering, 2020, 56(15):170-180.
6 Flores P, Machado M, Silva M T, et al. On the continuous contact force models for soft materials in multibody dynamics[J]. Multibody System Dynamics, 2011,25(3): 357-375.
7 王庚祥,刘宏昭. 考虑球面副间隙的4-SPS/CU并联机构动力学分析[J].机械工程学报,2015,51(1):43-51.
Wang Geng-xiang, Liu Hong-zhao. Dynamics analysis of 4-SPS /CU parallel mechanism with spherical joint clearance[J]. Journal of Mechanical Engineering,2015,51(1):43-51.
8 Wang G, Liu H, Deng P. Dynamics analysis of spatial multibody system with spherical joint wear[J]. Journal of Tribology, 2015, 137(2):021605.
9 Chen X, Jia Y. Wear analysis of spatial parallel mechanisms with multiple 3D spherical clearance joints[J]. Journal of Tribology, 2019, 141(10):4044295.
10 Liu C S, Zhang K, Yang L. Normal force-displacement relationship of spherical joints with clearances[J]. Journal of Computational & Non-linear Dynamics, 2006, 1(2):160-167.
11 王旭鹏,刘更,马尚君.含间隙运动副机构的动力学特性研究[J]. 振动与冲击,2016,35(7):110-115.
Wang Xu-peng, Liu Geng, Ma Shang-jun. Dynamic characteristics of mechanisms with revolute clearance joints[J]. Vibration and Shock, 2016,35(7):110-115.
12 Tian Q, Flores P, Lankarani H M. A comprehensive survey of the analytical, numerical and experimental methodologies for dynamics of multibody mechanical systems with clearance or imperfect joints[J]. Mechanism & Machine Theory, 2018, 122:1-57.
13 张静. 铰链及含铰折展桁架非线性动力学建模与分析[D]. 哈尔滨:哈尔滨工业大学机电工程学院,2014.
Zhang Jing. Modeling and analysis of nonlinear dynamics for joint and deployable structure[D]. Harbin:School of Mechatronics Engineering, Harbin Institute of Technology, 2014.
14 李忠洪. 考虑铰链间隙的空气舵传动机构动力学建模及分析[D]. 哈尔滨:哈尔滨工业大学机电工程学院,2015.
Li Zhong-hong. Dynamic modeling and analysis of transmission mechanism with joint clearances for air rudder[D]. Harbin:School of Mechatronics Engineering, Harbin Institute of Technology, 2015.
15 迟华瑞. 考虑涂层的间隙转动副接触碰撞力模型及其应用[D].秦皇岛:燕山大学机械工程学院,2019.
Chi Hua-rui. The contact-impact force model of coated revolute joints with clearance and its application[D]. Qinhuangdao:School of Mechanical Engineering, Yanshan University, 2019.
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