Rapid mapping of volumetric machine errors using distance measurements

Abstract

This paper describes a relatively inexpensive, fast, and easy to execute approach to maping the volumetric errors of a machine tool, coordinate measuring machine, or robot. An error map is used to characterize a machine or to improve its accuracy by compensating for the systematic errors. The method consists of three steps: (1) models the relationship between volumetric error and the current state of the machine, (2) acquiring error data based on distance measurements throughout the work volume; and (3)fitting the error model using the nonlinear equation for the distance. The error model is formulated from the kinematic relationship among the six degrees of freedom of error an each moving axis. Expressing each parametric error as function of position each is combined to predict the error between the functional point and workpiece, also as a function of position. A series of distances between several fixed base locations and various functional points in the work volume is measured using a Laser Ball Bar (LBB). Each measured distance is a non-linear function dependent on the commanded location of the machine, the machine error, and the location of the base locations. Using the error model, the non-linear equation is solved producing a fit for the error model Also note that, given approximate distances between each pair of base locations, the exact base locations in the machine coordinate system determined during the non-linear filling procedure. Furthermore, with the use of 2048 more than three base locations, bias error in the measuring instrument can be removed The volumetric errors of three-axis commercial machining center have been mapped using this procedure. In this study, only errors associated with the nominal position of the machine were considered Other errors such as thermally induced and load induced errors were not considered although the mathematical model has the ability to account for these errors. Due to the proprietary nature of the projects we are not able to report actual error measurements. instead, we have scaled the work volume to 5OOx5OOx5OOmm and proportionally scaled the errors. The fitted model was able to predict independently measured laser body diagonals to within 3.{mu}m peak-to-valley throughout @ scaled 500 x 500 x 500 mm` volume. or approximately 88% of the total error. Furthermore, this approach performed as well as, if not better than the parametric methods, but required only four hours to collect data for calibration.