计及碰撞瞬态拓扑特征识别的落体系统运动机理完整性分析方法研究

doi:10.3901/JME.2025.05.214

摘要/Abstract

摘要： 准确识别涵盖法向嵌入深度、切向侧滑阻尼、碰撞相对位姿及相对速度、接触轮廓几何非线性等要素的正/斜碰撞瞬态拓扑特征，对冲击碰撞影响下系统的局部与整体运动响应分析具有重要意义。鉴于此，基于多体力学建模方法的系统性与普适性，首先提出一种关于落体正/斜碰撞时变性瞬态拓扑特征识别的有效方法，进而提出一种集合法向碰撞与切向侧滑于一体的单/双侧冲击碰撞广义力模型的通用性构建方法；其次针对落体碰撞事件后期系统的纯滚动运动状态需由落体转角与路面轮廓曲线上其接触点切线斜率共同决定的复杂性运动几何特征，通过向系统引入新型增广构型矢量，提出一种将上述纯滚动非完整运动约束转化为滚动体轮廓上一等效动点对路面轮廓轨迹实施跟踪的完整运动约束的研究方法；再次针对落体与路面形成的碰撞多体系统，提出一种涵盖碰撞前、中、后3个子事件的系统动力学综合模型的构建方法；最后通过圆环-谐波路面落体运动的数值仿真，有效揭示落体碰撞系统事件完整性运动机理及规律，同时验证分析方法的正确性与有效性。研究成果对冲击碰撞动力学与多体运动学的理论丰富与应用，具有重要的学术与应用价值。

关键词: 落体碰撞系统, 碰撞瞬态拓扑特征, 增广构型变量, 运动机理, 完整性

Abstract: Accurately recognizing the transient topological features of collisions is crucial for analyzing the local and global motion responses of a system upon impact. These features include the normal embedding depth, tangential sideslip damping, relative posture and velocity of collisions, and geometric nonlinearity of contacting contours, among others. To address this issue, a technique based on the systematic and universal principles of multi-body mechanics modelling, identifying time-varying transient topological features for normal/oblique collisions of falling-body systems is proposed. Additionally, a universal modelling technique is introduced for generalized force models of single and bilateral impact collisions, which can handle normal collisions and tangential sideslips. And then, a new augmented configuration vector is incorporated into a falling-body collision system to address the complex geometric characteristics of its pure rolling motion state. This state is should be determined by comprehensively considering its rotation angle and tangent slope at the contact point on the road contour. Building on this, the study goes on to propose a research method for converting the non-holonomic constraint of pure rolling into a holonomic constraint, enabling the tracking of the road contour trajectory by using an equivalent moving point on the rolling body contour. Furthermore, we propose a system modelling method for the comprehensive dynamics model that covers three sub-events: before, during, and after the collision of a multi-body system consisting of a falling body and a road contour. By conducting numerical simulations, the motion mechanism and laws governing the integrity of the collision event between a circular ring and a harmonic road contour are effectively elucidated. The results validate the accuracy and efficacy of the analysis method, thereby advancing theories and engineering practices in impact collision dynamics and multi-body kinematics.

Key words: falling-body collision system, transient topological features in collisions, augmented configuration vector, motion mechanism, integrity

中图分类号:

TH122

杨玉维, 李照童, 陈鹏宇, 龚健超, 王浩宇, 刘祺, 马跃. 计及碰撞瞬态拓扑特征识别的落体系统运动机理完整性分析方法研究[J]. 机械工程学报, 2025, 61(5): 214-227.

YANG Yuwei, LI Zhaotong, CHEN Pengyu, GONG Jianchao, WANG Haoyu, LIU Qi, MA Yue. Analysis Method for the Integrity of the Motion Mechanism in a Falling-body System with the Recognition of Transient Topological Features of Collisions[J]. Journal of Mechanical Engineering, 2025, 61(5): 214-227.

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