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Approximation Solution for the Zener Impact Theory

Author

Listed:
  • Ping-Kun Tsai

    (Department of Bio-Industrial Mechatronics Engineering, National Chung Hsing University, Taichung 402, Taiwan)

  • Cheng-Han Li

    (Department of Bio-Industrial Mechatronics Engineering, National Chung Hsing University, Taichung 402, Taiwan)

  • Chia-Chun Lai

    (Department of Bio-Industrial Mechatronics Engineering, National Chung Hsing University, Taichung 402, Taiwan)

  • Ko-Jung Huang

    (Department of Bio-Industrial Mechatronics Engineering, National Chung Hsing University, Taichung 402, Taiwan)

  • Ching-Wei Cheng

    (College of Intelligence, National Taichung University of Science and Technology, Taichung 404, Taiwan)

Abstract

Collisions can be classified as completely elastic or inelastic. Collision mechanics theory has gradually developed from elastic to inelastic collision theories. Based on the Hertz elastic collision contact theory and Zener inelastic collision theory model, we derive and explain the Hertz and Zener collision theory model equations in detail in this study and establish the Zener inelastic collision theory, which is a simple and fast calculation of the approximate solution to the nonlinear differential equations of motion. We propose an approximate formula to obtain the Zener nonlinear differential equation of motion in a simple manner. The approximate solution determines the relevant values of the collision force, material displacement, velocity, and contact time.

Suggested Citation

  • Ping-Kun Tsai & Cheng-Han Li & Chia-Chun Lai & Ko-Jung Huang & Ching-Wei Cheng, 2021. "Approximation Solution for the Zener Impact Theory," Mathematics, MDPI, vol. 9(18), pages 1-12, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:18:p:2222-:d:632812
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