Non-linear Analysis In Boring Bar System Model With Time Delay

The main approach to cutting machining hole is boring.Flutter phenomenon will happen in the boring process.Flutter will reduce the processing precision of parts,making it difficult to meet the requirements of modern industry for machined parts quality.In addition,the flutter also can produce noise and damages to the cutting tool and machine tool,so it is necessary to do in-depth research of flutter phenomenon.Flutter due to many reasons,so to establish a mathematical model of the boring bar need to include all the main factors affecting vibration.This paper research a model of the boring bar system considering the time delay,this model is different from the boring bar system model before,in which joined the time delay.Then the model is studied from two aspects of the stability of system at the equilibrium point and hopf bifurcation nature,expectting to get a concrete relations between delay value and and the system nonlinear characteristics.In this paper,the concrete work contents are as follows:Through the simplified summary of boring bar system structure,and the analysis of the relationship between the Time-varying cutting force and real-time cutting thickness,real-time cutting thickness and the delay value,set up a kind of the mathematical model of the boring bar system which considering the effect of time delay.Considering the effect of time delay the stability of the mathematical model of the boring bar is studied,by studying the distribution of characteristic roots of the characteristic equation of the model,the results of the different parameter value system to keep stability of the time-delay value scope and system hopf bifurcation condition.Using simulation software simulation,get the vibration of the system time response curve,the simulation results support the analytical analysis conclusion.Using the center manifold theorem and specification method to consider the time delay of the boring bar system hopf bifurcation of the properties of the calculation and analysis,the results got a judgment formula from different parameter valuessystem hopf bifurcation direction and stability of periodic solutions.Give specific values of system parameters,and the use of Matlab software simulation,results under different time delay values of vibration time response curve,the conclusion is verified the correctness of the conclusions are obtained by analytic method.