﻿ 基于连续接触力方法的接触碰撞问题研究 Study on Contact Impact Problem Based on Continuous Contact Force Method

International Journal of Mechanics Research
Vol.06 No.01(2017), Article ID:19954,7 pages
10.12677/IJM.2017.61003

Study on Contact Impact Problem Based on Continuous Contact Force Method

Yingxue Zhang 1, 2, Wenli Yao1

1School of Science, Qingdao Technological University, Qingdao Shandong

2Qingdao Kawasaki Vehicle Technology Co., Ltd., Qingdao Shandong

Received: Mar. 3rd, 2016; accepted: Mar. 17th, 2017; published: Mar. 23rd, 2017

ABSTRACT

For collision with friction, the change of the state of tangential motion of contact point may cause the change of direction and magnitude of the frictional force. The direct use of the traditional instantaneous collision hypothesis may cause the energy inconsistence. Contact-impact model is built based on continuous contact force method. In this model nonlinear damping spring model is used on normal and non-smooth Coulomb friction model is used on tangential. The classic example of oblique impact is a rigid body system consisted by a member bar and ground. Dynamics simulations are done in the process of impact for this classic example. Study the movement variation and the corresponding sliding mode of this system on different friction coefficients, different initial velocity and different initial configuration. With this model, the complex tangential sliding mode during the impact process is demonstrated, which provide the basis for the choice of the collision model.

Keywords:Continuous Contact Force, Collision, Friction Sliding Mode

1青岛理工大学理学院，山东 青岛

2青岛四方川崎车辆技术有限公司，山东 青岛

Copyright © 2017 by authors and Hans Publishers Inc.

This work is licensed under the Creative Commons Attribution International License (CC BY).

http://creativecommons.org/licenses/by/4.0/

1. 引言

2. 刚体平面运动接触碰撞模型

2.1. 法向接触力模型

(1)

2.2. 切向摩擦模型

(2)

3. 匀质杆件与地面接触碰撞模型

(3)

(4)

(5)

(6)

Figure 1. Sketch map of the collision between the uniform thin rod and the ground

1) 假设，则摩擦力可能为静摩擦力，切向的运动微分方程不满足，则得到新的平衡微分方程：

(7)

2) 当时，根据加速度的方向，可以判断摩擦力的方向，此时运动微分方程依然满足公式（6），但是其摩擦力的方向随速度的改变发生改变。

4. 数值算例

4.1. 初始位形及切向摩擦对法向接触力的影响

Figure 2. Curves of normal contact force under different initial configurations

Figure 3. Normal contact force curve of different friction coefficient method

4.2. 碰撞过程中切向滑动模式的验证

5. 数值算例

Figure 4. Tangential velocity of contact point in contact impact process

Figure 5. Actual friction and maximum static friction

Study on Contact Impact Problem Based on Continuous Contact Force Method[J]. 力学研究, 2017, 06(01): 17-23. http://dx.doi.org/10.12677/IJM.2017.61003

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