Centerless grinding as an affine profile transformation: Physics-based and data-driven approaches

Material removal processes are industrially adopted to transform a given initial workpiece geometry into a final one with desired properties in terms of shape and accuracy. This paper analyses the modelling of the centerless grinding process as a direct mathematical transformation between the initial and final workpiece profiles. By modelling the grinding process as a discrete linear dynamical system, each stage of the operation (e.g., roughing and finishing) can be described as an affine transformation operated by a constant transition matrix that embeds the linearized discrete process dynamics, and an offset component that reproduces the nominal material removal due to axis feed. Relying on an opportune state augmentation, the affine transformation includes a linear-phase low pass filter that reproduces the contact filtering effect due to wheel and workpiece engagement. The affine transformation can be built starting from the static physics-based model of the process but also identified from grinding experiments, following a purely data-driven approach, by solving an over-determined linear system on the measured initial and final profiles. For this latter case, the identification accuracy is analysed relying on “virtual experiments” provided by a high-fidelity non-linear process model that allows the effect of all involved phenomena, like structural dynamics and grinding wheel-workpiece detachment, to be investigated. The proposed affine model, in addition to allowing a rapid estimation of the final profile quality, provides interesting insight into the properties of the process in terms of profile transformation.