圆盘滚动的动力学分析

Dynamic analysis of disc rolling

圆盘按质量是否均匀分布可分为均质圆盘和偏心圆盘,对这2种圆盘在水平面和斜面的运动进行了简单分析.均质圆盘在接触面上做纯滚动时,摩擦力的方向与外力F的大小以及作用线到质心的距离有关;偏心圆盘在水平面和斜面滚动时会出现跳滚现象,偏心圆盘发生跳滚的角速度临界条件为√gcosφ/e,只与偏心距e和接触面倾斜角度φ有关.当偏心圆盘离开接触面时,先做加速上升运动,再做减速上升运动,最后做加速下降运动.计算了偏心圆盘离开斜面后圆心运动方程和第一次与斜面的碰撞点坐标.

Absract:Discs can be divided into homogeneous discs and eccentric discs according to whether the mass is evenly distributed.The motion of these two kinds of disks in horizontal plane and inclined plane is analyzed simply.When the homogeneous disc does pure rolling on the contact surface,the direction of the friction is related to the size of the external force and the distance from the action line to the center of mass.When the eccentric disk rolls on the horizontal plane and the inclined plane,the phenomenon of jumping roll occurs.The critical condition of angular velocity of the eccentric disk is √gcosφ/e that it is only related to the eccentricity e and the inclination angle φ of the contact surface.When the eccentric disc leaves the contact surface,the first accelerated ascending motion,then decelerated ascending motion,and finally accelerated descending motion.The motion equation of the center of the eccentric disc after leaving the slope and the coordinates of the first collision point with the slope are calculated.