## Abstract  
Improving volumetric error compensation is one of the machine tool user's key objectives. Smart compensation is bound to calibration accuracy. Calibration quality depends largely on its setup factors. An evaluation criterion is thus required to test the quality of the compensation deduced from these setup factors. The residual error map, which characterizes post-compensation machine errors, is therefore chosen and then needs to be evaluated. In this study, the translation axes of a machine tool were calibrated with a multilateration tracking laser interferometer. In order to optimize such measurements, the residual error map was then characterized by two appliances: a laser interferometer and the tracking laser already employed for the calibration, using for that purpose the sequential multilateration technique. This research work thus aimed to obtain a smart setup of parameters of machine tool calibration analyzing these two residual error maps through the Design Of Experiment (DOE) method. To achieve this goal, the first step was to define the setup parameters for calibrating a compact machine tool with a multilateration tracking laser. The second step was to define both of the measurement processes that are employed to estimate the residual error map. The third step was to obtain the optimized setup parameters using the DOE method.  
machine tool; calibration; compensation; tracking laser; sequential multilateration; error map +
Footnote †: journal: Medical  
The aim is to numerically change tool trajectory to minimize the locating error between the real tool trajectory and the ideal toolpath. Several techniques and appliances are used to estimate this error in the whole discretized working volume: telescopic ball-bar [10; 11], 3D probe-ball [12], R-test [13], laser technology [14; 15; 16], etc. Laser techniques are the most widespread appliances in the research field and the tracking laser is the most reliable instrument used [15; 16]. Its advantages are the submicron measurement resolution and the high number of data that may be collected. Afterwards, the computed compensation matrix is combined with a mathematical model based on the machine structure to generate a compensated toolpath. For this purpose, homogenous transformation matrices are widely used [17; 18]. Improving volumetric error compensation is one of the machine tool users' key objectives. Smart compensation is bound to calibration accuracy. Calibration quality depends largely on its setup factors. An evaluation criterion is thus required to test the quality of the compensation deduced from these setup factors. The residual error map, which characterizes post-compensation machine error, is therefore chosen and then needs to be evaluated. The appliance used for the evaluation usually has to be different from the one used to determine the calibration. In this study, the translation axes of a five-axis machine tool are calibrated with a multilateration tracking laser (TL). The residual error map is then characterized by two different appliances: a classical laser interferometer (LI) and the TL already used for the calibration.  
This research work aimed to provide optimized setup parameters for machine tool calibration using a design of experiment (DOE) method. To achieve this objective, the first step was to present the setup parameters for calibrating a compact five-axis Computer Numerical Control (CNC) machine tool with a TL. The second step was to define the measurement processes employed with both instruments (TL and LI) to estimate the residual error map. The third step was to introduce the methodology applied to obtain optimized setup parameters. A DOE was used for that purpose. Finally, the results obtained with the two appliances were compared, and the best practice for implementing machine tool calibration is here proposed.