Regenerative chatter in self-interrupted plunge grinding

This paper investigates dynamics of regenerative chatter in self-interrupted plunge grinding with delayed differential equations (DDEs) and partial differential equations (PDEs). The DDEBIFTOOL, a numerical simulation tool and the method of multiple scales are used to analyse stability and construct bifurcation diagrams. It was found out that in majority of cases, chatter is accompanied by a loss of contact. The loss of contact leaves uncut surface during the pass of grinding wheels, and thus the regeneration mechanism does not play a role. In that case, the delay used to represent the time span between two successive cuts should be multiple (double, triple, quadruple or higher). As a consequence, the chatter with losing contact cannot be accurately described by the DDEs with a fixed time delay. To address this problem, the PDEs are introduced to record the variation of workpiece profile. The PDEs are transformed into the ODEs by a Galerkin projection, and then the grinding dynamics is studied numerically. Solutions obtained from the DDEs and the PDEs are in a good agreement for a continuous grinding but there is a discrepancy for a self-interrupted cutting.