Stability Judgment Method for Multi-tool Parallel Turning Based on Differential Quadrature Method

Abstract

The invention provides a multi-turning-tool parallel turning stability judgment method based on a differential quadrature method. The multi-turning-tool parallel turning stability judgment method comprises the steps that dynamics modeling is carried out on a multi-turning-tool parallel turning system, and a multi-delay second order differential equation is built; a normalized state space equation is built and obtained; the second kind of Chebyshev points is adopted as discrete points in adjacent unit intervals (0, 1) and (-1, 0); speed items are expressed by displacement items at the discrete points based on a Lagrange's interpolation function by using the differential quadrature method; the intervals where the discrete points of delay items are located are judged, and the delay items are expressed by the second kind of Chebyshev points of the intervals where the discrete points of the delay items are located; state transfer matrixes between the adjacent unit intervals are constructed, and the stability of an original system is judged based on the Floquet theory. Compared with traditional single-turning-tool turning, the dynamic characteristic of the multi-turning-tool parallel turning system is analyzed by adopting the differential quadrature method, optimized cutting parameters are obtained, and machining efficiency is greatly improved.

Description

technical field [0001] The present invention relates to a new method for judging the stability of multi-tool parallel turning, that is, differential quadrature method (Differential Quadrature Method). Affects high-efficiency and high-quality processing. Background technique [0002] In the field of machining, turning is one of the most common and commonly used processing methods. The research on traditional single turning tool machining has been very mature, but the processing method of parallel turning with multiple turning tools is a new concept proposed by the academic circle in recent years, especially the research on the stability of parallel turning with multiple turning tools is still in its infancy. In theory, the processing efficiency of parallel turning with multiple turning tools is much higher than that of traditional turning, but the processing mechanism of parallel turning with multiple turning tools is much more complicated than that of traditional turning. ...

AI Technical Summary

Problems solved by technology

[0009] The frequency domain method has simple steps and fast calculation speed, but it is not conducive to considering various complex working conditions

The results of the time-domain simulation method are intuitive, but the calculation speed is slow, and only the machining stability under the condition of a single cutting parameter combination can be obtained, which is not conducive to drawing the stability map of the machining parameter space

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