对心直动滚子从动件盘形凸轮机构精确解与近似解的比较

分析和比较了对心直动滚子从动件盘形凸轮机构顶杆运动方程的近似解和精确解。推导了理想状态下对心直动滚子从动件盘形凸轮机构顶杆运动方程的精确表达式,使用Taylor级数将精确表达式展开,通过数值算例,获得了顶杆的位移、速度和加速度表达式的精确解和分别对应的一阶、二阶、三阶近似解。结果表明:只有当凸轮转动中心到圆盘中心的距离与圆盘半径加上滚子半径之和的比值较小时,对心直动滚子从动件盘形凸轮机构近似解才接近精确解;比值较大时,近似解和精确解的差别较大。

Comparison between exact and approximate solutions of disk cam mechanism for center-following roller followers

The approximate solution and exact solution of disk cam mechanism ejector rod motion equation for center-following roller followers have been analyzed and compared in the text.The exact expression of motion equation has been derived under ideal status.Byuse of the Taylor series and numerical example,the exact solutions of the displacement,velocity and acceleration expressions for ejector rod have been obtained,as well as respectivecorresponding first order,second order and third order approximate solutions.The results show that the approximate solution is close to the exact solution only when the ratio of the distance from the camrotation centerto the disccenter and sum of disc radius and roller radius roller is small.While the differences between the approximate and exact solutionsare large when the ratio is big.