Trajectory Planning And Experimental Research Of Ellipsoid Surface Based On Micro Motion Tool System

After entering the 21 st century,optical components in the military,civil,medical,aerospace and other fields of application more and more,the accuracy of optical components constantly put forward higher requirements,manufacturing optical components of ultra-precision processing technology has been paid attention to by various countries.Although China’s ultra-precision machining technology has made great progress in decades of research,there is still a gap compared with the international top technology level.Therefore,further research and development has great value and significance.Deterministic polishing technology requires precise polishing removal of workpiece surface,which involves theoretical analysis of polishing removal,analysis of contact state,trajectory planning and other problems.In this paper,the surface quality improvement and quantitative removal problems involved in computercontrolled polishing technology are studied based on micro motion tool system,the polishing material removal model is established,and the trajectory planning method of space surface with controllable row spacing and bow height errors is proposed.The main contents of the study are as follows:1.A theoretical model of polishing material removal is established.Combination of contact mechanics is deduced polishing contact half axial length and accurate formula to calculate the pressure distribution,and head of polishing tool and workpiece surface contact geometry relationship is analyzed,by polishing the relative linear velocity distribution model of contact area,finally combined with Preston experience equation established a mathematical model for the theory of material removal rate.2.The variation law between the main curvature and the parameters of polishing contact surface is analyzed.The general calculation formula of principal curvature of ellipsoid is derived by differential geometry.The relation and variation range of the main curvatures of polishing contact surface are analyzed when the fluctuation of each parameter is relatively small and the contact surface is nearly round.Four types of ellipsoid surface are obtained,and the principal curvature and parameter variation of polishing contact surface are analyzed by practical examples.Through error calculation and analysis,a suitable formula for calculating approximate radius of contact surface is found,which provides a theoretical basis for trajectory planning.3.The influence of bow height error on ellipsoid polishing was analyzed,and the relationship between bow height error and step size was established.The relation between the radius of polishing contact surface and the line spacing of ellipsoid is established by defining the overlap quantity.According to the material removal model of fixed-point polishing,the model of average material removal rate per unit length is deduced.Through the function fitting of the average material removal rate model,the theoretical formula of approximate optimal line spacing and approximate optimal overlap is derived.An improved spiral trajectory planning algorithm and an improved scanning trajectory planning algorithm based on semicircle iteration are proposed,and the line spacing and bow height errors can be controlled according to the requirements to adjust the uniformity of trajectory point distribution.4.Through comparative experiments,it is verified that the improved spiral trajectory can greatly reduce the surface roughness of the ellipsoid surface,and the polishing effect is better than that of the spiral trajectory with equal row spacing.Experiments verify that the improved trajectory is not limited by the type of ellipsoid on the whole,and can greatly reduce the ellipsoid roughness,and the higher the consistency between the trajectory direction and the main curvature direction,the better the polishing removal effect.The experimental results show that the improved scanning trajectory is slightly better than the improved spiral trajectory.It is also verified by polishing experiments that the improved spiral trajectory can reduce the ellipsoid profile error slightly.