Geometrical error compensation of machines with significant random errors

In this paper, we present a new statistical approach towards soft geometrical error compensation of machines with significant errors. The approach, based on an analysis of the probability of the random error recurring, can reduce the adverse influence of random errors on the compensation of systematic errors. The proposed methodology is made up of three steps. First, error classes are defined from the error bands obtained from calibration. Second, the probability of the magnitude of random error belonging to each of these classes is computed based on the density of the data set within the class. Based on these probabilities, the most probable systematic part of the error measurement can be statistically deduced. Finally, the geometrical error compensation is carried out based on this value. Experimental results are provided for the linear error compensation of a single-axis piezo-ceramic motion system.