The Smoothing Theory And Experimental Research Of Small Tool Numerical Control Polishing On Intermediate Frequency Error

In the past few decades,computer-controlled optical surfacing has been widely and successfully applied to the manufacture of optical components.In typical extreme optical manufacturing projects such as large aperture telescope system,nanoscale lithography system and high power laser system,the surface error of the optical components plays a key role in affecting the imaging and operation quality of the whole system.Among them,the theory and technology of suppressing mid-spatial frequency errors(MSFE)are the most difficult.In this paper,the smoothing theory of the surface error with NC tool polishing is studied.According to the existing theoretical model,a smoothing evolution model which combining various process parameters has been established.And through the design and implementation of specific experiments,the accuracy and feasibility of the theoretical model are verified.The specific contents of the article are listed as follow:(1)Based on Presston equation,the tool influence function of the NC polishing pad has been modeled,and the theoretical expression of removal function has been obtained.The relationship between the volume removal rate as well as the the shape of the TIF and the rotation,eccentricity,radius of the polishing pad are simulated.At the same time,the shape change of the TIF under a non-uniform pressure distribution is analyzed.(2)Based on the theory of parametric smoothing model,an exponential convergence smoothing evolution model has been established with the actual parameters of the polishing progress.In order to numerically represent smoothing efficiency,an error decreasing factor(EDF)is defined in the model.The smoothing efficiency of MSFE is decomposed into a material influence factor and a process influence factor which contains polishing pressure,the size of polishing pad and the volume removal rate.(3)The smoothing curve of the theoretical model is simulated.By changing some parameters of EDF,the theoretical comparison of smoothing efficiency under different technological conditions is realized.In the smoothing process of different polishing pad,the greater the material influence factor ?totol,the higher the overall smoothing efficiency.Similarly,the greater the process influence factor,the higher the smoothing efficiency.(4)A set of smoothing experiment on the surface error with spatial periods of 3 mm,5 mm and 7 mm were performed.The results show that under the same polishing parameters,the smoothing efficiency with larger spatial frequency will be higher and the convergence curve will decline faster.The material influencing factor ?totol at those three spatial frequencies were 108.045 Pa nm-1,77.357 Pa nm-1 and 29.465 Pa nm-1,respectively.The curve prediction of the smoothing model was validated on a 150 mm diameter workpieace.It was found that the predicted curve of the theoretical model was very close to the actual smoothing convergence curve.The relative error of the factor EDF was less than 5%,which proved the accuracy of the theoretical model.The overall research shows that the smoothing evolution model is accurate in predicting the smoothing of MSFE,and the smoothing prediction of the whole surface is close to the actual measured data,which shows that the model has preliminary guiding role in practical engineering.