Geometric Error Measurement And Compensation Method Of Freeform Optics Multi-axis Precision Machine Tool

Due to the advantages in focusing,imagine and composing optical systems,the freeform optical surface has been widely used in many fields.For the complexity of the surface and the high accuracy demand,the freeform surface is often processed by multi-axis precision machine tool.The motion accuracy of machine tool is the key element for the machining accuray of freeform optics and the geometric errors are the main error sources of the machine tool.Thus,accurate measurement and compensation of geometric errors of machine tool can effectively improve the machining accuracy of machine tool.However,during the identification of geometric errors,the identified results which are identified by the traditional identification method,that sensitive to measurement errors and location errors,would be concealed by the affection of measurement errors.In order to solve the problem,this paper proceed to the geometric errors measurement and identification of translational axis and rotational axis,the geometric errors compensation strategy,microlens array machining and compensation experiment.The main achievements are listed as below:(1)Take the RTTTR type five-axis machine tool as an example,established the geometric error model of the machine tool based on the multi-body theory with the analysis of the topology structure,the tool chain and the workpiece chain.For doing that,provide the basis for the identification and compensation of machine tool,with the analysis of main errors distribution and error items.(2)Analyzing the influence of identification results affected by the measurement and location errors,the identification method of geometric errors of translational axis is proposed based on the multi-body theory.The method can identify the geometric errors of translational axis with redundancy measurement.And then,with the analyzing the influence of location errors and the application of two norm,the optimum installation positions,which is insensitive to location errors,are obtained.The simulations demonstrate that the method proposed in this article is more robust than the traditional three points method.The experiment show the maximum deviations between the actual measurement and estimate of positioning errors of axis Z can be reduced from 5.94μm to 0.18μm within the measuring range of 120mm.The effectiveness of this method is accordinglly verified.(3)For the large amount of geometric errors of rotational axis,which are sensitivity to measurement errors,the method based on kinematic analysis using double ball bar is proposed.A decoupled formulation for ball bar measurement is derived from kinematic analysis to reveal the relationship between sensitivity direction and setup position of ball bar,and identify the geometric errors including both angular errors and displacement errors.For doing that,lower the condition number and improve the accuracy of identification.In addition,According to the sensitivity characteristics,a method,which reduce the influence of measurement errors with double ball bar,is presented to correct the position dependent geometric errors.The experiments show the absolute maximum deviation values between the actual measurement and estimate of distance errors of double ball bar can be reduced from 26.4μm to 3.3μm.The effectiveness of this method is proved.(4)In order to further simplify the process of identification of geometric errors of rotational axis,the position-dependent geometric errors identification method for rotary axis is proposed based on the condition that the rotary axis has high precision.First,a minimum position,which is required for indentification of geometric error of rotational axis,using double ball bar have been demonstrated to reduce the procedure of accurate adjustment.Then,the position dependent geometric errors have been fitted as an nth B-spline cure,on the account of its being smooth and continuous.For doing that,transform the identification of geometric errors into the calculation of the control point of the error curve and reduce the measurement process.Finally,to identify the position dependent geometric errors,an optimization method by computing the suitable values of control points of nth B-spline curve of errors is proposed.The experiment show,compared to the traditional method,the measurement points reduce from 36 to 18,which improve about 50%efficiency.The maximum deviation between the actual measurement and estimate of distance errors of double ball bar can be reduced from 14.1μm to 2μm.The feasibility of this method is proved.(5)An improved compensation strategy is proposed to solve the problem that the compensation values will cause additional geometric errors during the compensation process.By setting the evaluation function,the method have compesated the error items in turn to reduce the errors caused by the compensation value.Finally,combining the above error measurement and compensation technique,the machining experiment of microlens array,with the machining radius of 5.7mm,is carried out.The experiment results show that the Depth of microlens array(ideal value 5μm)decrease from 5.116μm to 4.968μm,and the radius of sphere(ideal value 15mm)decrease from 15.233mm to 15.063mm after geometric errrors compensation.The effectiveness of the compensation strategy proposed in this article have been proved.