Sensor Reconstructed Nonlinear Stochastic Modeling for Monitoring Precision Grinding Processes

Much of the complexity in grinding and other abrasive finishing processes emerges from nonlinear stochastic dynamics of the underlying processes. Earlier attempts to consistently monitor surface quality using conventional, largely statistical and linear dynamic, approaches have had limited success. In this paper, the analytical derivation and experimental validation of an approach for real-time monitoring of surface finish (R_a < 50nm) in precision grinding are presented. The approach is based on reconstructing customized multi-scale representations (CMR) and low-order nonlinear stochastic differential equation (n-SDE) models from an array of vibration sensors. The experiments were conducted on an instrumented surface grinder (Proth PSGS 3060BH) and a cylindrical grinder (Browne and Sharpe 1024). Vibration sensor features extracted based on the models were used to estimate R_a under various wheel degradation levels and in-feed settings. The results show that model correctly captures the dimensionality of the dynamics underlying the measured vibration signals. The features were able to accurately estimate R_a values below 50 nm, and improve surface roughness predictability by∼30% over commonly used static mappings between the features and quality states.