A recursive algorithm for dynamics of planar multibody systems with frictional unilateral constraints

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling Pub Date : 2024-10-03 DOI:10.1016/j.apm.2024.115747

Yangyang Miao , Xiaoting Rui , Pingxin Wang , Yu Feng , Tang Li , Jianshu Zhang

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引用次数: 0

Abstract

The contact impact problem in planar multibody systems can be efficiently solved by formulating it as the linear complementarity problem, which requires a complex modeling process. To simplify the process, a recursive algorithm for the dynamics of planar multibody systems with frictional unilateral constraints is proposed based on the reduced multibody system transfer matrix method. Firstly, the contact forces of frictional unilateral constraints are integrated into the recurrence relations of system components using Lagrange multipliers. Subsequently, the relative motion equations of the contact positions are discretized in time, which are then utilized to describe the linear complementarity problem for systems. The dynamics of the system is solved by the Moreau time-stepping method with the recursive method. Finally, the proposed algorithm was validated using the woodpecker toy and used to model a slider-crank mechanism with clearance, which shows its characteristics of facilitating modeling, universal, and highly programmable. This recursive algorithm provides an effective tool for solving non-smooth planar multibody systems while extending the application of the multibody system transfer matrix method.

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具有摩擦单边约束的平面多体系统动力学递归算法

平面多体系统中的接触撞击问题可以通过将其表述为线性互补问题来有效解决，而线性互补问题需要复杂的建模过程。为了简化这一过程，基于还原多体系统传递矩阵法，提出了一种具有摩擦单边约束的平面多体系统动力学递归算法。首先，利用拉格朗日乘法器将摩擦单边约束的接触力整合到系统组件的递推关系中。随后，对接触位置的相对运动方程进行时间离散化，然后利用这些方程来描述系统的线性互补问题。利用莫罗时间步进法和递归法解决系统的动力学问题。最后，利用啄木鸟玩具对所提出的算法进行了验证，并将其用于模拟带间隙的滑块-曲柄机构，结果表明该算法具有建模方便、通用性强、可编程性高的特点。该递归算法为解决非光滑平面多体系统提供了有效工具，同时扩展了多体系统传递矩阵法的应用范围。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Mathematical Modelling 数学-工程：综合

CiteScore

9.80

自引率

8.00%

发文量

508

审稿时长

43 days

期刊介绍： Applied Mathematical Modelling focuses on research related to the mathematical modelling of engineering and environmental processes, manufacturing, and industrial systems. A significant emerging area of research activity involves multiphysics processes, and contributions in this area are particularly encouraged. This influential publication covers a wide spectrum of subjects including heat transfer, fluid mechanics, CFD, and transport phenomena; solid mechanics and mechanics of metals; electromagnets and MHD; reliability modelling and system optimization; finite volume, finite element, and boundary element procedures; modelling of inventory, industrial, manufacturing and logistics systems for viable decision making; civil engineering systems and structures; mineral and energy resources; relevant software engineering issues associated with CAD and CAE; and materials and metallurgical engineering. Applied Mathematical Modelling is primarily interested in papers developing increased insights into real-world problems through novel mathematical modelling, novel applications or a combination of these. Papers employing existing numerical techniques must demonstrate sufficient novelty in the solution of practical problems. Papers on fuzzy logic in decision-making or purely financial mathematics are normally not considered. Research on fractional differential equations, bifurcation, and numerical methods needs to include practical examples. Population dynamics must solve realistic scenarios. Papers in the area of logistics and business modelling should demonstrate meaningful managerial insight. Submissions with no real-world application will not be considered.