模拟有间隙的无摩擦空间关节的非平滑动力学框架

IF 2.6 2区 工程技术 Q2 MECHANICS
Ekansh Chaturvedi, Corina Sandu, Adrian Sandu
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引用次数: 0

摘要

现实世界中的多体系统并没有理想的关节;大多数关节都有一定的间隙。间隙允许连接体发生错位,由此产生的动力学受由此形成的接触控制。处理接触的方法通常有两种:常用的连续动力学方法假定接触的赫兹性质由非线性单边弹簧-阻尼元件建模;而非平稳动力学方法则导致互补性问题。本文采用非平滑动力学方法,为模拟具有间隙的无摩擦关节的多体系统建立了一个连贯的框架。由于间隙相对于机械部件的尺寸很小,因此假定关节中接触的性质是非弹性的。利用这一假设和一般非光滑动力学框架,推导出了有间隙的圆柱形、棱柱形和外旋形关节的参数公式。制定了运动方程,并将其时间具体化为非线性编程问题。与最先进的方法相比,所提出的方案还对欧拉参数实施了归一化约束,这有利于在适当的步长范围内保持解的稳定性。此外,还引入了一种可变时间步进方案,将步长作为优化过程中的一个额外变量,并讨论了其稳定性能。通过数值实验证明了所提框架的多功能性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

A nonsmooth dynamics framework for simulating frictionless spatial joints with clearances

A nonsmooth dynamics framework for simulating frictionless spatial joints with clearances

Real-world multibody systems do not have ideal joints; most joints have some clearance. The clearance allows the connected bodies to undergo a misalignment, and the resulting dynamics is governed by the contacts thus formed. Two approaches are typically taken to deal with contacts: the commonly used continuous dynamics approaches assume the Hertzian nature of the contact modeled by nonlinear unilateral spring-damper elements; while the nonsmooth dynamics approach results in a complementarity problem. This paper employs a nonsmooth dynamics approach to develop a coherent framework for the simulation of multibody systems having frictionless joints with clearances. Because clearances are of small magnitude relative to the dimensions of the mechanical components, the nature of the contact in the joints is assumed to be inelastic. Using this assumption and the general nonsmooth dynamics framework, the parametric formulations for cylindrical, prismatic, and revolute joints with clearances are derived. The equations of motion are formulated, and their time-discretized counterparts are cast as a nonlinear programming problem. The proposed scheme also enforces normalization constraint on Euler parameters in contrast to state-of-the-art methods that is conducive to stability of the solution for a suitable range of step sizes. In addition, a variable time-stepping scheme that includes the step size as an extra variable in the optimization is introduced and its stability properties are discussed. The versatility of the proposed framework is demonstrated through numerical experiments.

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来源期刊
CiteScore
6.00
自引率
17.60%
发文量
46
审稿时长
12 months
期刊介绍: The journal Multibody System Dynamics treats theoretical and computational methods in rigid and flexible multibody systems, their application, and the experimental procedures used to validate the theoretical foundations. The research reported addresses computational and experimental aspects and their application to classical and emerging fields in science and technology. Both development and application aspects of multibody dynamics are relevant, in particular in the fields of control, optimization, real-time simulation, parallel computation, workspace and path planning, reliability, and durability. The journal also publishes articles covering application fields such as vehicle dynamics, aerospace technology, robotics and mechatronics, machine dynamics, crashworthiness, biomechanics, artificial intelligence, and system identification if they involve or contribute to the field of Multibody System Dynamics.
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