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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.
By using mathematical tools such as differential geometry, coordinate transformation, piecewise quadratic Hermite interpolation and differential equations, the problem of grinding and machining a rotating body with complicated busbars is established. The differential model is established and then the specific solution is designed .For the workpiece with parabolic busbar, a machining program with the shortest processing time under the condition of constant feed speed of the motor is given. For the workpiece with common busbar, by using the piecewise quadratic Hermite interpolation, Converted to a parabolic situation, has also been a good solution.Also written a series of Matlab program, as the process of solving the product, their output can be directly used to control the grinding machine, processing with any busbar workpiece.In addition, Grinding wheel surface as uniform as possible on the issue, made a creative exploration, and gives a cylindrical grinding wheel wear more uniform processing program.In general, the model has a wide range of applications, the advantages of high precision.