Modeling of residual stress distribution in D2 steel via grinding dynamics using a second-order damping system

A second-order system is proposed to model residual stress distributions in D2 tool steel under various heat treatment procedures and grinding dynamics. The study was motivated to predict the magnitude of the residual stress, tensile peak location, and to establish the nonlinear superposition relationship in the residual stress distribution due to the number of grinding passes. The grinding dynamics was represented as a lumped system composed of a spring-mass-damper of the grinding machine and a damper-stiffness of the workpiece. A nested factorial experiment of 18 conditions with 3 levels of tempering, 2 levels of grinding conditions and 3 multipass grinding levels was used for the model development and validation. The parameters of each condition were then optimized by using auto-regressive system identification. The proposed model depicts changes of the complex experimental treatment conditions and estimates in a precise and parsimonious way the corresponding change in the subsurface residual stress distribution. With only one parameter involved, the model facilitates conceptual progress in the residual stress superposition; the prediction elucidates grinding dynamics and supports a theory of the heat treatment and grinding effects on the material characteristics.