Determination of Stability Regions of Wheel and Workpiece in Plunge Grinding Process Using a 3-D Workpiece Model

The chatter phenomenon is a kind of unstable self-excited vibration which occurs in most machining processes including grinding. A 3-D nonlinear model of chatter vibrations in grinding process has been presented in this paper. The workpiece has been modeled as a continuous rotating shaft with transverse vibrations and wheel is regarded as a one degree of freedom damped spring–mass system. The equations of motion have been dimensionless by π-Buckingham theory. Then using assumed modes method, partial differential equations of workpiece changed to ordinary differential equations and then the method of multiple scales is adopted for the approximate solution. Stability regions for workpiece and wheel in various workpiece rotary speeds and various wheel positions drawed and then the effect of various parameters such as rotational speed of the wheel,and the radius of the workpiece have been investigated. Results showed that vibrations in workpiece and in wheel are quite different from each other. When grinding occurs in the middle of the workpiece the possibility of chatter phenomenon is more, while the position of wheel has no effect on the vibration of the wheel.