Modeling And Experimental Research On The Removal Function Of Two-dimensional Vibration Polishing For Optical Small Surfaces

Small-surface optical components with high precision and high surface integrity requirements are increasingly needed in the important fields of mobile communications,medical diagnosis,scientific instruments,military and other important fields.The small surface optical element currently in the optical industry mainly refers to an optical element with a small aperture,such as,the aperture is several millimeters or more than ten centimeters,but there is no unified definition at present.Whether it is a small surface optical element or a small surface optical mold,due to the changing characteristics of the curvature of the curved surface,in order to achieve the desired machining accuracy and surface quality,it is often necessary to use sub-aperture computer controlled polishing process.Although the optical manufacturing academia and industry have proposed some sub-aperture CCP methods,the polishing methods that can be applied to small-diameter surfaces are still very limited.At present,it mainly involves two methods to obtain small surface optical elements that meet the processing requirements,one is based on jet or energy beam,the other is the mechanical polishing method based on the small tools.Compared with the polishing process method based on jet or energy beam,the vibration-assisted polishing process method based on small tool has the advantages of high polishing efficiency,low cost of polishing tool system,easy control of polishing scope,easy suppression of polishing mid-spatial frequency error,etc.It has more obvious advantages in the polishing process of small surface optical components or molds.In the existing mechanical polishing methods based on small tools,in oder to solve the problem of periodic polishing marks on the surface which caused by the small polishing tools,a polishing method using two-dimensional vibration driving tool for Lissajous motion is proposed,but there are still the following problems to be solved.First,in order to generate the random-like Lissajous motion with a desired frequency ratio,the vibration-assisted polishing tool system must have the ability to actively adjust the vibration frequency and amplitude.The existing resonant polishing system is difficult to accurately control the vibration frequency and obtain the desired frequency ratio.Therefore,it is necessary to use a non-resonant polishing system to drive the small polishing tool,which is conducive to generating random-like Lissajous motion with the desired frequency ratio;Second,the action mechanism of the grid-like polishing trajectory parameters formed by the random-like Lissajous motion of the small tool on the removal function in a polishing cycle has not been revealed,which is the key to the deterministic polishing of small surfaces;Third,the effect mechanism of the polishing process parameters on the surface quality of the workpiece has not been effectively revealed in the study of two-dimensional vibration polishing.In order to solve the above three problems,this paper mainly carried out the following research work.(1)Driven by two-dimensional vibration,the polishing motion trajectory of the small tool,the polishing scope formed by motion trajectory envelope and the variation of the relative velocity are studied.The influence of two-dimensional vibration parameters(vibration amplitude,vibration frequency,frequency ratio,phase difference)on the polishing motion trajectory of the small tool,the scope formed by the motion trajectory envelope and the relative velocity change law between the polishing tool and workpiece are analyzed;The conditions for the small polishing tool to perform closed-loop random-like lissajous motion are obtained;The influence of frequency ratio on the variation of relative velocity between polishing tool and workpiece along the polishing trajectory is analyzed.(2)A non-resonant polishing system is developed,which can actively adjust the vibration frequency and amplitude,and the small tool can be driven to generate random-like Lissajous motion with the desired frequency ratio.Using the double parallelogram flexure hinge mechanism as the motion mechanism and two piezoelectric stacks as the driver,a polishing motion generating mechanism which can decouple the mutual interaction between two-dimensional vibrations is developed;The statics and dynamics characteristics of the double parallelogram hinge mechanism are investigated by finite element analysis and performance test;Two-dimensional vibration decoupling test of the double parallelogram hinge mechanism is carried out.(3)The mechanism of the grid-like polishing trajectory parameters formed by the random-like Lissajous motion of the small tool on the removal function in a polishing cycle has been studied and revealed.A theoretical model of the removal function of the small tool in the polishing scope is established under the two-dimensional vibration drive.The effect of the two-dimensional vibration parameters on the relative velocity between the polishing tool and the workpiece along the polishing motion trajectory is analyzed,The influence of different polishing motion trajectories on the distribution characteristics of removal function is analyzed;The influence of polishing process parameters(polishing force,vibration amplitude,vibration frequency,frequency ratio,feed rate)on the maximum removal depth are studied theoretically and experimentally;The surface processing experiments are carried out by using the random-like Lissajous polishing trajectory and the circular polishing trajectory respectively.In addition,the surface roughness Ra value and surface shape accuracy PV value are compared to verify that the random-like Lissajous polishing trajectory is more conducive to removing the periodic trajectory.(4)The effect mechanism of two-dimensional vibration polishing process parameters on workpiece surface quality is studied.Under the condition that the workpiece is processed by reciprocating linear motion,the effects of polishing force,vibration amplitude,vibration frequency and frequency ratio on the surface roughness are studied by orthogonal experiments.The Taguchi methodology and the analysis of variance method are used to optimize the main polishing process parameters.In addition,the significance of the influence of different process parameters on the surface roughness is analyzed;The surface roughness prediction model is established based on multiple linear regression,and the regression equation and its coefficients are tested for significance;The surface roughness prediction model is verified through single factor polishing experiments.The study carried out in this paper will provide an effective solution for obtaining the random-like Lissajous polishing motion trajectory with adjustable two-dimensional frequency ratio,thereby suppressing the mid-spatial frequency error caused by the polishing of the small polishing tool;The obtained removal function will provide a theoretical basis for the optimization design of two-dimensional vibration polishing tools and the surface geometry simulation of two-dimensional vibration polishing.