Cutting Force Control in Machining: Bayesian Update of Mechanistic Force Model

For closed loop control of machining forces in the turning process, it is well established that identification of the mechanistic force model is necessary to ensure stable operation of the process. This work proposes a novel approach to update the mechanistic force model by incorporating uncertainty in the deterministic framework. Force coefficient values reported in literature are based on wide spectrum of machining conditions and so cause difficulty in predicting the machining force using the mechanistic force model. This variability stems from variation in material workpiece input quality variation. This work proposes to treat force coefficient and process variables (shear stress and friction angles) as random variables and use Bayesian Statistical techniques to infer true distribution of force coefficients via observing cutting force and feed force values and updating shear stress and friction angle joint probability distribution. A numerical analysis is performed for calculating force coefficients for Titanium alloy (Ti6-Al4V) Markov Chain Monte Carlo (MCMC) simulation is performed to sample from the posterior distribution of the force coefficient. A single update cycle shows high reduction in the variability of the force coefficient. Numerical simulations presented indicate that it is possible to implement Bayesian update scheme in a closed loop control of cutting force for online identification of force coefficients and shear stress and friction angle distributions with few required update cycles and efficiently rejects the disturbance caused by changing machining parameters.