Research Papers

A Comparative Study of the Dissipative Contact Force Models for Collision Under External Spring Forces

[+] Author and Article Information
Dong Xiang

Department of Mechanical Engineering,
Tsinghua University,
Beijing 100084, China
e-mail: xd@mail.tsinghua.edu.cn

Yinhua Shen

Department of Mechanical Engineering,
Tsinghua University,
Beijing 100084, China
e-mail: syhua_2001@163.com

Yaozhong Wei

Department of Mechanical Engineering,
Tsinghua University,
Beijing 100084, China
e-mail: weiyz12@163.com

Mengxing You

Department of Mechanical Engineering,
Tsinghua University,
Beijing 100084, China
e-mail: ymx2016qy@163.com

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received April 19, 2018; final manuscript received July 20, 2018; published online August 22, 2018. Assoc. Editor: Javier Cuadrado.

J. Comput. Nonlinear Dynam 13(10), 101009 (Aug 22, 2018) (13 pages) Paper No: CND-18-1177; doi: 10.1115/1.4041031 History: Received April 19, 2018; Revised July 20, 2018

The dissipative contact force model plays a key role in predicting the response of multibody mechanical systems. Contact-impact event can frequently take place in multibody systems and the impact pair is often affected by supporting forces which are treated as external spring forces. However, the external spring forces are ignored during the derivation process of existing dissipative contact force models. Considering the influences of external spring forces, the fact is discussed that the crucial issues, including relative velocity and energy loss, in modeling dissipative contact force are different compared to the same issues analyzed in existing literatures. These differences can result in obvious errors in describing the collision response in multibody systems. Thus, a comparative study is carried out for examining the performances of several popular dissipative contact force models in multibody dynamics. For this comparison, a method associated with Newton's method is proposed to calculate the contact force that meets the Strong's law of energy loss and this force is used as reference. The comparative results show that the models suitable for both hard and soft contact exhibit good accuracy when contact equivalent stiffness is far larger than external spring stiffness by two orders of magnitude. Conversely, these models can cause varying degree and obvious errors in contact force, number of collisions, etc., especially when the difference in stiffness is close to or less than one order of magnitude.

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Fig. 1

One-dimensional direct central collision process between two solid spheres

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Fig. 2

Relation between εpost and εpre for different contact models

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Fig. 3

Example of single steel ball supported by spring impacts on wall

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Fig. 4

Dynamic response of the ball when k = 1.4 × 106 N/m and ε = 0.9

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Fig. 5

Comparison of hysteresis loop when k = 1.4 × 104 N/m and ε = 0.3

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Fig. 6

Comparison of hysteresis loop when k = 1.4 × 104 N/m and ε = 0.5

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Fig. 7

Comparison of hysteresis loop when k = 1.4 × 104 N/m and ε = 0.7

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Fig. 8

Comparison of hysteresis loop when k = 1.4 × 104 N/m and ε = 0.9

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Fig. 9

Comparison of hysteresis loop when k = 1.4 × 106 N/m and ε = 0.3

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Fig. 10

Comparison of hysteresis loop when k = 1.4 × 106 N/m and ε = 0.5

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Fig. 11

Comparison of hysteresis loop when k = 1.4 × 106 N/m and ε = 0.7

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Fig. 12

Comparison of hysteresis loop when k = 1.4 × 106 N/m and ε = 0.9

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Fig. 13

Comparison of hysteresis loop when k = 1.4 × 107 N/m and ε = 0.3

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Fig. 14

Comparison of hysteresis loop when k = 1.4 × 107 N/m and ε = 0.5

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Fig. 15

Comparison of hysteresis loop when k = 1.4 × 107 N/m and ε = 0.7

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Fig. 16

Comparison of hysteresis loop when k = 1.4 × 107 N/m and ε = 0.9



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