A new continuous contact force model for contacting problems with regular or irregular contacting surfaces and energy dissipations in multibody systems is presented and discussed in this work. The model is developed according to Hertz law and a hysteresis damping force is introduced for modeling the energy dissipation during the contact process. As it is almost impossible to obtain an analytical solution based on the system dynamic equation, an approximate dynamic equation for the collision system is proposed, achieving a good approximation of the system dynamic equation. An approximate function between deformation velocity and deformation is founded on the approximate dynamic equation, then it is utilized to calculate the energy loss due to the damping force. The model is established through modifying the original formula of the hysteresis damping parameter derived by combining the energy balance and the law of conservation of linear momentum. Numerical results of five different continuous contact models reveal the capability of our new model as well as the effect of the geometry of the contacting surfaces on the dynamic system response.

中文翻译：

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用于多体动力学冲击分析的连续接触力模型

在这项工作中，提出并讨论了一种新的连续接触力模型，用于处理多体系统中规则或不规则接触表面和能量耗散的接触问题。该模型是根据赫兹定律开发的，并引入了滞后阻尼力来模拟接触过程中的能量耗散。由于基于系统动力学方程几乎不可能得到解析解，因此提出了碰撞系统的近似动力学方程，实现了对系统动力学方程的良好逼近。在近似动力学方程的基础上建立了变形速度与变形之间的近似函数，然后利用它来计算阻尼力引起的能量损失。该模型是通过修正结合能量平衡和线性动量守恒定律推导出的滞后阻尼参数的原始公式建立的。五个不同的连续接触模型的数值结果揭示了我们新模型的能力以及接触表面的几何形状对动态系统响应的影响。