An improved implicit method for mechanical systems with set-valued friction
An improved implicit method for mechanical systems with set-valued friction
复制标题
具有定值摩擦的机械系统的改进隐式方法
DOI：
10.1007/s11044-019-09713-0
复制
发表时间：
2020
影响因子：
3.4
通讯作者：
Wang Qingyun
中科院分区：
文献类型：
--
作者：
Zhang Runsen;Yu Yang;Wang Qi;Wang Qingyun
本文给出了摩擦力机械系统高阶隐式积分的计算方法。采用增广拉格朗日公式建立了动力学方程，用投影函数描述了集值摩擦力。为了减少事件转移引起的精度损失和消除加速度中的杂散振荡，提出了一种新的鲁棒事件驱动方案，该方案能够准确检测事件转移并校正开关点的摩擦力和加速度。通过对几个基准问题的求解，验证了该方案的数值性能。数值结果表明，该格式可以近似地达到二阶精度，在严密的计算下，其精度高于经典的Moreau时间步进格式。最后，对一个曲柄滑块系统进行了仿真，验证了该方法对非线性摩擦机械系统的有效性。
The computational procedures of higher-order implicit integrators for mechanical systems with friction are provided in this paper. The dynamic equations are established using the augmented Lagrangian formulation, and set-valued friction forces are described by projection functions. To reduce the accuracy loss caused by event transitions and to eliminate spurious oscillations in the acceleration, a new robust event-driven scheme, which accurately detects event transitions and corrects the friction forces and accelerations at switching points, is proposed. The numerical performance of the proposed scheme is demonstrated by solving several benchmark problems. Numerical results show that the newly developed scheme can approximately achieve second-order accuracy, and they are more accurate than the classical Moreau time-stepping scheme under close computational efforts. Finally, a slider-crank system is simulated to prove the validity of the developed method for nonlinear mechanical systems with friction.