确定凸轮廓线曲率半径的数值微分法

应用数值微分法计算凸轮廓线坐标的一、二阶导数,代入微积分学中曲率半径公式,即得凸轮廓线的曲率半径。用两次计算曲率半径值的办法给出了计算误差的估计式。计算表明该方法在计算精度上足以满足工程上的需要,并能避免烦琐的公式推导。当凸轮廓线由离散值给出时,各种解析法不便应用,采用本法更有其独特的优点。该方法不但适用于推杆为直动、摆动、平底等各种情形,且便于编制各种情况下统一的计算程序。

Determination of Curvature Radius of Cam Profiles Using Numerical Differentiation

The first and second derivatives of the coordinates of a cam profile are calculated using numerical differentiation method, and substituted with curvature radius formulas in calculus, thus obtaining its curvature radius. Computing the curvature radius twice, we establish error estimation formulas. Computation results demonstrate that this method produces accurate computation, meets the engineering needs, and the troublesome equation derivation is avoided. When the cam profile is given in discrete values, other analysis methods are not suitable, but the proposed method has its unique strengths. The method has a universal character and can be applied to any types of cam mechanism and to the development of uniform computation programs for any cam mechanisms.