Dynamic Parameters Online Identification And Accurate Stability Prediction Of Thin-wall Milling System

Milling occupies an important position in the aerospace industry and is widely used for milling low stiffness and large deformation workpieces such as aero-engine blades,cassettes,impellers and impeller discs.However,chattering is an important factor affecting machining accuracy,machining efficiency and surface integrity in milling.Therefore,it is necessary to study the cutting mechanism of thin-walled workpieces in the milling process and establish a kinetic model to meet the requirements of high machining quality and high machining efficiency of thin-walled parts in actual machining.In this paper,we analyze the tool-workpiece time-lagged time-varying system in milling machining,establish the mapping relationship between the eigenvalues of the discrete system matrix and the eigenvalues of the time-lagged system,and form an online identification method based on the approximate projection recursive subspace modal parameters through the research.A Sample-Newton full discrete algorithm for fast prediction of stability leaflet diagram is proposed and verified by experiments.The main research contents and results of the paper are as follows.(1)Dynamic cutting force model for thin-walled parts milling processing is established.Firstly,based on the micro-element cutting theory of tool milling,the mechanical cutting force calculated expression and cutting differential disc angle under different helix angle working conditions are given.Then,based on the instantaneous undeformed dynamic chip thickness,the dynamic milling force model is further established and the transformation relationship between the dynamic milling force in the tool-workpiece coordinate system and the modal space coordinate system is given.Finally,based on the constant milling force coefficient identification method,a time-varying milling force coefficient identification strategy combined with the dynamic undeformed chip thickness is given.(2)An equivalent linear model of the state space equations of the nonlinear time-lagged time-varying system is constructed.For the time-varying dynamics of thin-walled parts milling,the collected response acceleration signals are processed by the stochastic subspace method,and the input vector signals in the signal subspace containing the current state information are obtained by combining the projection matrix theorem.The corresponding output data at each moment are symmetrized so that the input vector signal at each moment in the signal subspace is updated to satisfy the subspace recursive identification,and then an equivalent linear system for subspace identification is established.(3)An online identification method for the stochastic subspace of the system modal parameters is developed.Based on the stochastic subspace theory,the recurrence law between the updated data and the incremental observable matrix is revealed by tracking the incremental observable matrix of the system at the next moment through the input data.The system matrix mapping relationship between the augmented discrete system and the continuous system is given,and the system modal parameters are solved based on the state transfer matrix.The effectiveness of the online identification algorithm proposed in this paper is verified through milling machining experiments.(4)A milling stability prediction method with high accuracy is proposed.The method uses a cubic spline interpolation formula to approximate the state term of the Duham integral and a cubic Newton interpolation formula to approximate the time lag term of the Duham integral to obtain a more accurate equivalent ordinary differential equation model for the state response of the system;for the large number of integral matrices and polynomial functions generated in the calculation process,a fine integration method is used to solve the equation efficiently.Through the simulation of two standard cases,the algorithm has a more accurate convergence accuracy and faster computational efficiency than the previous methods proposed in the literature,especially when the tool immersion is relatively small.Meanwhile,the experimental results show that the stability prediction results of the method are in good agreement with the experimental results.