Real-time compensation of backlash positional errors in CNC machines by localized feedrate modulation

A methodology for analyzing the influence of gear backlash in the axis drive systems of a Cartesian CNC machine on positional accuracy is developed. The approach is based on solving the machine dynamical equations in the context of an angular dead-zone backlash model and an osculating circle approximation of smooth paths in a neighborhood each path turning point, which admit an essentially exact solution for a P controller. This methodology is the basis for schemes to minimize backlash degradation of positional accuracy through feedrate or path geometry modifications, rather than hardware or controller upgrades (that may be expensive or disruptive for CNC machines in continuous production use). As a preliminary demonstration of the methodology, results are presented from the use of smooth feedrate reductions about each path turning point as a means to suppress positional inaccuracies incurred by gear backlash in CNC machine axis drive systems.