Application of Kaczmarz method for solving inverse modelling problems of magnetic-abrasive finishing process of planar surfaces

The article considers the solution technique for inverse modelling problems of magnetic-abrasive finishing of planar surfaces. The solution of the problem enables the determination of control law of the pressure exerted onto the workpiece needed for realization of material removal according to the prescribed function. The problem is posed in matrix form on the basis of Preston’s equation, and the corresponding linear system of equations is solved using iterative Kaczmarz method. On the basis of numerical examples it is shown that pressure control during machining enables sufficiently precise (with deviation no more than 2.2 as the removal function providing compensation of initial shape errors of the workpiece.