Modeling and analysis for time-varying dynamics of thin-walled workpieces in mirror milling considering material removal

To reduce the vibration and deformation of large thin-walled workpieces during the milling process,mirror milling is widely used due to its point-to-point support and strong applicability.The influence of the support head on the workpiece’s dynamic characteristics is crucial in determining whether the mirror milling process is reliable and effective.Therefore,this study establishes a time-varying dynamic model for mirror milling of thin-walled workpieces with various boundary conditions to accurately analyze and predict the dynamic characteristics and response of the workpiece.First,a new analytical method for material removal with extensive applicability and high precision is proposed.In this method,the Ritz mode shape is used to approximate the workpiece’s mode shape as it changes during material removal.Next,the Hertz contact theory is adopted to establish a tool-workpiece-support head coupling model,which considers the jump-off phenomenon between them.Subsequently,the dynamic model is solved using the Newmark-β numerical integration method to obtain the workpiece’s time-domain acceleration and displacement responses under the forced vibration.Finally,the measured frequency response function(FRF)and vibration signals of workpieces verify the correctness of the proposed mirror milling model for thin-walled workpieces considering material removal.In addition,this paper analyzes the dynamic characteristics and forced vibration law of workpieces in mirror milling,which lays the foundation for high precision mirror milling.

Dynamic synchronous motion accuracy measurement and estimation for a five-axis mirror milling system

A mirror milling system(MMS)comprises two face-to-face five-axis machine tools,one for the cutting spindle and the other for the support tool.Since it is essential to maintain the cutter and support coaxial during the cutting process,synchronous motion accuracy is the key index of the MMS.This paper proposed a novel method for measuring and estimating the synchronous motion accuracy of the dual five-axis machine tools.The method simultaneously detects errors in the tool center point(TCP)and tool axis direction(TAD)during synchronous motion.To implement the suggested method,a measurement device,with five high-precision displacement sensors was developed.A kinematic model was then developed to estimate the synchronous motion accuracy from the displacement sensor output.The screw theory was used to obtain the analytical expression of the inverse kinematic model,and the synchronous motion error was compensated and adjusted based on the inverse kinematic model of the dual five-axis machine tools.TCP and TAD quasi-static errors,such as geometric and backlash errors,were first compensated.By adjusting the servo parameters,the dynamic TCP and TAD errors,such as gain mismatch and reversal spike,were also reduced.The proposed method and device were tested in a large MMS,and the measured quasi-static and dynamic errors were all reduced when the compensation and adjustment method was used.Monte Carlo simulations were also used to estimate the uncertainty of the proposed scheme.