In order to solve the problem of annular belt corrugation in aspherical surface machining,an aspherical surface grinding and polishing machine tool was independently developed,the speed interpolation principle in the control system was expounded,and the key problems “the feed rate is not monotonic” existing in the application of the speed interpolation principle were analyzed mathematically,the root cause of the problem was “the initial velocity mismatch causes the adjacent segmental acceleration signs to be opposite” analyzed with the actual operation control parameters.Based on the genetic theory,the overall solution to the “feed rate non- monotonic” was proposed.The operation process and implementation steps of the speed optimization algorithm were refined,the effectiveness of the speed optimization algorithm to solve the problem of “non-monotonic feed speed” was proved by using the empirical data and fitting curves.The optimal initial speed of any subsection could be quickly matched,and the feed rate was constant monotonous during the machining process.So the practical problem is effectively solved,the surface machining accuracy can reach 14.130 0 μm and the surface roughness can reach 3.330 2 μm without any error compensation.