Analysis Method for the Integrity of the Motion Mechanism in a Falling-body System with the Recognition of Transient Topological Features of Collisions

doi:10.3901/JME.2025.05.214

Abstract

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

CLC Number:

TH122

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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