Parameter estimation and model verification of first order quasistatic error model for three-axis machining centers

Abstract

This paper is the second in a series of three papers addressing the problem of modeling and compensation of quasistatic machine-tool errors. In the first paper of this set, a general nth order model for the geometric errors of a machine was developed. The use of such a model as the basis of an on-line compensation scheme for a machine-tool requires that its parameters be known and changes in their magnitudes (due to mechanical and thermal changes) tracked during its operation. This paper presents a parameter estimation approach which requires observation of components of the volumetric error of the machine at certain points in the machine's work space. What is the minimal number of observations required? and What are the best locations for these observation points in a machine's work space? are questions answered in this paper. The estimation procedure is discussed for a first order model; however, it generalizes to any order error model. Experimental evidence of the effectiveness of the first order model error model in adequately representing the quasistatic errors of a machine-tool is presented. The effectiveness of the parameter estimation approach is also demonstrated. Finally, the use of the model and parameter estimation procedure as the basis of a compensation scheme that is practicable in a production environment is discussed.