A Generalized Geometric Error Model for Multi-Axis Machines

Virtual manufacturing: prediction of work piece geometric quality by considering machine and set-up accuracy

“…If we compare this work to other works dealing with the geometric error modelling for machine tools (Kyoung-Gee et al 2005, Ahn and Cho 1999, Eman and Wu 1987, Chen 2000, Yao and al. 2006), our aim is to predict by simulation (virtual machining) the work piece errors made by machine tool accuracy which are experimentally identified, and set -up errors of the machined part.…”

“…In fact the machine architecture has still some geometrical defect (perpendicularity, parallelism, position…), the machine presents uncertainties in kinematic movements (gaps, deformations, yaw, pitch or roll deviations) and the part presents set-up deviations. For the normal accuracy class N (over a range of 5 classes), 22 errors on the machined work pieces caused by deviations of main geometrical accuracy parameters of machine tools have been identified (Reshetov and Portman 1988 Works has been done to develop models for machine tool error (Reshetov and Portman 1988, Moon and Kota 2002, Tutenea-Fatan and Feng 2004, Ahn and Cho 1999, Eman and Wu 1987, for our purpose a model of machine tool deviations by homogeneous transformation matrix is used, so the same mathematical tool is used for modelling perfect and real machine. In the cases of small deviations a linearised expression of the displacement can be used and a small displacement matrix (equation 3) which describes the small displacement screw is used.…”

“…So equation 2 becomes: This procedure is an efficient framework for kinematic modelling and systematic design of re-configurable machine tools (D'Acunto et al 2007, Moon and Kota 2002, Tutenea-Fatan and Feng 2004 If we compare this work to others works dealing with the geometric error modelling for machine tools (Kyoung-Gee et al 2005, Ahn and Cho 1999, Eman and Wu 1987, Chen 2000, Yao and al. 2006), our aim is to predict by simulation (virtual machining) the work piece error made by machine tool accuracy which are experimentally identified, and set -up errors of the machined part.…”

“…Works have been done to develop models for machine tool error (Reshetov and Portman 1988, Moon and Kota 2002, Tutenea-Fatan and Feng 2004, Ahn and Cho 1999, Eman and Wu 1987, for our purpose a model of machine tool deviations by homogeneous transformation matrix is used, so the same mathematical tool is used for modelling perfect and real machine. In the cases of small deviations, a linearised expression of the displacement can be used and a small displacement matrix (equation 3) which describes the small displacement screw is used.…”

A method to analyze the machining accuracy reliability sensitivity of machine tools based on Fast Markov Chain simulation

“…Furthermore, the various methods for modeling the geometric errors from different perspectives have experienced a gradual development [7]. To describe the error of the cutter location and the tool orientation between the two kinematic chains, the error model is normally established using homogeneous transformation sciENcE aNd tEchNology matrices (HTM) [10,18,20], denavit-hartenberg (D-H) method [16], modified denavit-hartenberg (MD-H) method [19], or multi-body system (MBS) theory [31,32]. Among these different approaches, MBS theory, first proposed by Houston, has evolved into the best method for the modeling of geometric errors of machine tools because it provides for a simple and convenient method to describe the topological structure of an MBS [21].…”