8.6.1 Modeling of Dynamic Grinding Processes
A mathematical model of dynamic grinding process can be established taking the factors shown in Figure 8.6 into account. The characteristic parameters in grinding dynamics, which are not generally necessary to consider in cutting dynamics, are the contact stiffness of the grinding wheel and the grinding damping. A comprehensive block diagram for representing the dynamic grinding process becomes very complex. Therefore, the process is divided into two extreme cases: the dynamic grinding process model for work-regenerative chatter and the model for the wheel — regenerative chatter. This simplification can be made possible by taking the geometrical interference into account. When the condition ycr /y > 1 in Equation 8.1 is satisfied, only the work-regenerative effect need be considered and hence the grinding wheel regenerative effect can be ignored. This is due to the following two reasons:
1. The work-regenerative effect has a large effect on the process stability.
2. The development of grinding wheel regeneration is much slower than that of workpiece regeneration.
On the other hand, for the case of ycr / y«1, the workpiece regenerative effect can be ignored because the amplitude of waves generated on the workpiece surface is much smaller than the amplitude of the relative vibration. However, the regenerative effect on the grinding wheel surface must be considered in the stability analysis.
Based on the above simplification, the block diagrams for the dynamic grinding process are depicted as shown in Figure 8.7 and Figure 8.8 for the workpiece regenerative chatter and for the grinding wheel regenerative chatter, respectively [Inasaki 1977b].