Chatter modeling, analysis and control for CNC machining systems.

In this research, based on a machining chatter model of nonlinear differential-difference equation (NLDDE), a systematic approach from stability analysis to analytical design of chatter control methods is presented. Utilizing the equivalent linearization method to present the nonlinearities in the dynamic cutting force, the characteristic equation of the equivalently linearized NLDDE is obtained. Based on this characteristic equation, Hopf bifurcation analyses on the depth of cut, the feed, the damping ratio, and the stiffness of the elastic structure of machine tool are performed and the stability of the NLDDE is investigated in the cases of constant time delay and periodically varying time delay. The stability theory of the NLDDE with geriodically varying time delay is applied to the spindle speed variation (SSV) method, which is valuable for industrial applications, yet still under development due to inadequacy in analyses. In this work, a systematic analysis on the SSV method is developed, and verified by numerical simulations and experiments. Some important results are achieved: the stability region of the SSV cutting is found and compared with that of the constant speed cutting, and the stability increment index (SII) is derived. The mechanism of machining stability increment by SSV cutting is revealed by employing internal energy analysis on the machining chatter system. Also proposed is a formula for selecting the SSV amplitude based on the internal energy analysis of the SSV cutting and the instantaneous sideband effect, which is meaningful for practical application of SSV cutting and leads to the possibility of a closed loop SSV cutting system. Due to difficulties of differential-difference equations, theoretical design of the adaptive control laws is a challenge. In this work, a theoretical design of model reference adaptive control for a class of n-dimensional linear autonomous differential-difference systems is presented. As its application, the design is applied to the linearized 2-dimensional differential-difference machining chatter model. The adaptive control laws of adjusting the spindle speed and feed for chatter suppression are determined. The effectiveness of the adaptive laws is verified by numerical simulations.PhDApplied SciencesMathematicsMechanical engineeringMechanicsPure SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/130179/2/9712137.pd