The Implementation of Simultaneous Trilateration to Measure Dynamic Three-Dimensional Contours Using the Laser Ball Bar

Introduction In computer numerical control (CNC) machining, the desired trajectory of the tool is defined by the part program. The purpose of the part program is to place the tool tip at specific coordinates relative to the part at every instant in time, leaving behind surfaces which form a workpiece of proper dimensions. Errors in the machined part dimensions are determined by the accuracy with which the commanded tool trajectory is followed, combined with any deflections of the tool, part, or machine caused by cutting forces. The accuracy of the tool trajectory is dependent on the static machine geometry, the machine’s thermal state, and dynamic errors of the control system. Using current technology, it is possible to measure the quasi-static geometric errors of a machine tool and their thermally induced deviations. With this data, one can construct a thermal/geometric error model of the machine which predicts the static tool point positioning error anywhere in the workspace at any thermal state [1]. This machine error model can be used to predict tool position errors at discrete points along arbitrary CNC paths, and predict the dimensional errors of a machined part caused by the imperfect machine geometry. Comparisons of predicted and actual part dimensions show that the thermal/geometric error model obtained from static measurements is capable of predicting some, but not all, of the resulting part dimensional errors [1][2][3]. In order to improve the accuracy of models seeking to predict part dimensions, it is necessary to extend these models to include trajectory errors related to the controller, as well as errors induced by the cutting process. The purpose of this text is to demonstrate the use of an instrument capable of measuring arbitrary, dynamic tool paths through three-dimensional space with ±1 μm accuracy. The results of these dynamic path measurements can ultimately be used in two ways. First, differences between the measured dynamic path and the path predicted by the static thermal/geometric error model must be due to dynamic effects in the machine’s control system. The dynamic errors can then be separated from the thermal/geometric errors and used to evaluate, model, and optimize the contouring performance of NC systems. Second, differences between the dynamic path of the tool and the final part dimensions must be caused by cutting forces. These discrepancies between part dimensions and dynamic path errors may then be used to understand and model the cutting process dynamics. The instrument described here for the measurement of dynamic spatial paths is based on the laser ball bar (LBB), developed by Ziegert and Mize [4]. The laser ball bar uses sequential trilateration to measure the static spatial coordinates of the tool at arbitrary points throughout the work volume of a CNC machine tool. This new sensor uses three LBBs simultaneously (i.e., Simultaneous Trilateration Laser Ball Bar or STLBB system) to allow for dynamic path measurements. The design and testing of this instrument have been described previously [5]. Therefore, we will concentrate on the 3-D contour measurement results. Machining verification has also been completed, but will not be included here due to space limitations.