磨削加工具有复杂母线的旋转体的微分模型

An ODE Based Mathematical Model for Grinding Surfaces with Sophisticated Meridia

综合运用微分几何、坐标变换、分段二次Hermite插值及微分方程等数学工具,将磨削加工具有复杂母线的旋转体的问题,通过建立微分模型,然后根据求出的解,设计出了具体的加工方案.对于具有抛物线母线的工件,给出了一个在上台电机进给速度恒定的条件下,加工时间尽可能短的加工方案.对于具有一般母线的工件,利用分段二次Hermite插值,转化为抛物线的情形,也得到了很好的解决.还编写了一系列Matlab程序,作为解决过程中的产品,它们的输出可以直接用于控制磨床,加工具有任意母线的工件.此外,在使得砂轮表面的磨损尽量均匀的问题上,做了富有创造性的探索,并且给出了一个使得圆柱形砂轮磨损比较均匀的加工方案.总体而言,模型具有适用范围广、加工精度高等优点.

To solve the problem of grinding surfaces of revolution,which meridians,or generating curves are highly sophisticated,mathematical tools deduced from differential geometry~coordinate shift~spline interpolation and differential equation are widely used to develop a strategy for processing.The main idea of the strategy is to establish an ODE deduced from the problem and solve it.For workpiece with parabola generating curve,our strategy is proved to has the quickest processing speed while preserving the smoothness of upper workbench's motion.Generalized situation are solved by applying the tools of spline interpolation,which shifts the problem into parabola meridian case.As a by-product of our work,a series of Matlab files are programmed,which can be taken into application.Further more,to improve the uniform of grinding wheel's abrasion,we did a creative research and improved the strategy for cylinder shaped grinding wheels.The main advantages of our strategy is high accuracy and wide application.