Reduction of synchronous errors in rigid tapping by iterative learning control

In this study, an iterative learning control (ILC) algorithm is proposed to improve the synchronous errors in rigid tapping. In rigid tapping, it is essential that the displacements of z-axis and spindle are synchronous; otherwise the tool will be damaged easily. The learning control is used to provide better commands for both the z-axis and spindle dynamics so that the output responses of z-axis and spindle can be as synchronous as possible. The algorithm of the leaning control makes use of the synchronous error at all time steps in the previous cycle of tapping to modify the current position commands of both z-axis and spindle. It is found that the lower triangular learning gain matrix can lead to an ILC that guarantees monotonic convergence of synchronous errors. Numerical simulations of an actual tapping center verify the theoretical analysis.