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<p>To address contact-impact problems across the full range of restitution coefficients, this paper proposes a novel compliant contact force model with enhanced adaptability. Distinguished from existing formulations, the proposed model introduces a nonlinear coefficient function rather than conventional constant coefficients to determine the hysteresis damping factor, thereby achieving superior characterization of collision dynamics throughout the entire restitution coefficient spectrum. Furthermore, this study establishes rigorous mathematical foundations for nonlinear parameter fitting by deriving the upper and lower bounds of the nonlinear coefficient function through analytical solutions of high-precision numerical formulations. This theoretical breakthrough ensures precise fitting characteristics of the hysteresis damping factor across all restitution scenarios, guaranteeing the model’s mathematical robustness and physical validity. The resultant contact force formulation demonstrates significant improvements in applicability and prediction accuracy. Comprehensive validation is performed through four numerical benchmarks: fitting performance tests, bouncing ball dynamics, shaft-bearing impact analysis, and crank-slider mechanism simulations. Systematic comparisons with classical contact force models confirm the proposed model’s superior accuracy in energy dissipation prediction, dynamic response characterization, and numerical stability across diverse impact scenarios.</p>

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A new compliant contact force model for impact analysis

  • 期刊论文

  • 发表日期：

    2025年4月7日

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  • Maosheng Zheng,
  • Mingbo Tong,
  • Yuening Li,
  • Xiong Pan,
  • Qiang Dong

摘要

To address contact-impact problems across the full range of restitution coefficients, this paper proposes a novel compliant contact force model with enhanced adaptability. Distinguished from existing formulations, the proposed model introduces a nonlinear coefficient function rather than conventional constant coefficients to determine the hysteresis damping factor, thereby achieving superior characterization of collision dynamics throughout the entire restitution coefficient spectrum. Furthermore, this study establishes rigorous mathematical foundations for nonlinear parameter fitting by deriving the upper and lower bounds of the nonlinear coefficient function through analytical solutions of high-precision numerical formulations. This theoretical breakthrough ensures precise fitting characteristics of the hysteresis damping factor across all restitution scenarios, guaranteeing the model’s mathematical robustness and physical validity. The resultant contact force formulation demonstrates significant improvements in applicability and prediction accuracy. Comprehensive validation is performed through four numerical benchmarks: fitting performance tests, bouncing ball dynamics, shaft-bearing impact analysis, and crank-slider mechanism simulations. Systematic comparisons with classical contact force models confirm the proposed model’s superior accuracy in energy dissipation prediction, dynamic response characterization, and numerical stability across diverse impact scenarios.