中文摘要：

在路径坐标系下,引入了恒定外部激励力二维库伦摩擦力系统滑移轨迹的精确解。当量纲一的外部激励力F〉1时,系统会最终进入黏滞状态,给出了对应的黏滞的位置和黏滞发生的时刻;当F〈1时,系统会保持滑移状态。当初始时刻外部激励力的方向与初始速度方向之间的夹角值较大时（接近于反向）,则在轨迹中存在一个滑移方向发生剧烈变化的拐点,特别的,当F〉1时,拐点接近于黏滞位置。传统积分算法不易求解含有转换及捌点的二维库伦摩擦力系统。假设在足够小的时间步长内,时变外载荷激励可以近似认为保持恒定不变,则利用上述解析解能够建立一种新的库伦摩擦力系统数值求解算法,进而分析粗糙接触表面多结点模型的微滑移以及微滑移诱发的磨损与能量损耗等。

英文摘要：

The closed form solutions for two-dimensional Coulomb frictional systems are proposed in path coordinated system. The system will stick when the dimensionless force ratio F1 and the position and time for sticking have also been presented, which could be utilized to predict the moment when stick commence accurately. There exist sharp bending corner, characterized by fierce slip direction variation, in the trajectory of system when F1 and the initial launch angle θ is very large, which denotes an opposite initial direction between external force and slip and this kind of sharp bending corner is very close to the slip/stick transition position. Numerical difficulties is introduced by slip/stick transitions and sharp bending corner on the trajectories when traditional numerical integration methods are employed to solve the responses of two-dimensional Coulomb frictional system. If the time step size is sufficient small, the time varying external excitation forces can be treat as constant and thus all those closed form solutions can be employed to propose a new numerical frictional algorithm, which can be utilized to analyze the microslip, wear and energy dissipation for rough contacting surfaces represented by multi-nodes model.