| This project is funded by the national natural science funds( Based on the nonlineardynamic theory, to study critical type chatter in power ultrasonic honing (50975265)),mainly to analyse nonlinear dynamic characteristics of chatter in ultrasonic honing.Throughthe analysis the surface properties of oil-stone and the cutting mechanism in ultrasonic honing,using tribological theory, established the mathematical model of dynamic honing force byfriction in ultrasonic honing. Based on vibration theory of continuous elastomer in structuraldynamics, combined with the structural characteristics of ulstrasonic honing device andulstrasonic honing cutting mechanism, estabished dynamic model of ulstrasonic honingchatter consisting of workpiece and flexible pole-oil stone elastic subsystem, and set upnonlinear vibration differential equations. Applying the Runge-Kutta method in numericalanalysis method, to solve the nonlinear dynamic vibration equation of ultrasonic honingchatter system. Using the Matlab software to simulate the vibration equation, got the wavetime history and phase track chart when chatter system occur one-to-two, one-to-four internalresonance, and analyze the charts. Due to the limitation of numerical analysis, the paper solvethe nonlinear vibration equation of ultrasonic honing chatter on analytical solution. Based onthe average method in nonlinear vibration analysis method, to approximately analysize thenonlinear vibration equation of ultrasonic honing chatter.This paper’s main research and achievement are:1. First introduced some simple mathematical model of friction, and according to theultrasonic honing cutting characteristic, established the mathematical model of honing forcecaused by the friction. Based on vibration theory of continuous elastomer in structuraldynamics, combined with the structural characteristics of ulstrasonic honing device and ulstrasonic honing cutting mechanism, estabished dynamic model of ulstrasonic honingchatter consisting of workpiece and flexible pole-oil stone elastic subsystem, and set upnonlinear vibration differential equations.2. Through analyzed the advantages and characteristics of numerical analysis methodand simulation in solving the nonlinear differential equations, then have got the equationsdimensionless transform to get ready to next work. Then, it briefly introduced the solutionprocedure of Runge-Kutta method and Matlab simulation. Based on Runge-Kutta method, tosolve the nonlinear dynamic vibration equation of ultrasonic honing chatter system, and usedthe Matlab software to simulate the vibration equation, got the wave time history and phasetrack chart when chatter system occur one-to-two, one-to-four internal resonance, and analyzethe charts.3. First, it expounded the importance of analytical method in solving nonlinear vibrationdifferential equations, and then introduced the basic ideas and solution steps of averagemethod. Then, to solve the nonlinear vibration equations of ultrasonic honing chatter system.It approximately analysized the nonlinear vibration equation of ultrasonic honing chatter inone-to-two internal resonance. |
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