**1. Introduction**

Machine tools with three, five or more axes are now equipped with touch trigger probes to accomplish metrology tasks such as tool path re-planning [1] or setup location and finishing path correction for the workpieces and even to evaluate the conformity of the finished machined parts [2]. The machine tool accuracy directly affects its ability to be used for such tasks. Accuracy is defined in the VIM (International Vocabulary of Metrology) as "closeness of agreement between a measured quantity value and a true quantity value of a measurand" [3] thus that it includes both systematic and so-called non-repeatable effects. A similar approach is used in the ISO (International Organization for Standardization) standard on machine tool accuracy [4].

On coordinate measuring machines, a probe head with two rotary axes is used to gain access to features on complex parts. The resulting change in the position of the stylus tip with respect to the machine foundation is handled by calibrating the change in this position through the probing of a reference ball at a fixed position in the machine base frame. A similar approach could be adopted on a five-axis machine, but it is not probably due to the limited available space on the workpiece table. Instead, the approach here is to rely on the measured angular positions of the rotary axes to perform the computation of the stylus tip in the workpiece table frame. Performing such calculation using a nominal, error free machine model will likely result in coordinates of a similar level of accuracy as the machine tool itself. Improvement in the computed coordinates, as was done on coordinate measuring

machines [5,6], is possible through the use of a rigid body kinematic model incorporating known machine errors. Using the mathematical models to simulate the machine tool geometry is the main concept to compensate the error parameters.

A variety of approaches have been proposed to acquire the machine error parameters [7,8], using touch trigger probes [9], scanning probes, ball bars [10], laser interferometers, and laser trackers are some methods which have been applied to this task. A pseudo 3D grid configured from a kinematically relocated calibrated 2D ball plate [11] was proposed for testing and calibrating machine tools but it was used for a 3-axis vertical machine. By increasing the number of machine axes, with rotary axes, the machine geometry becomes more complex and the number of error sources increases. Assessing the out of sphericity by probing 25 points on a precise ball mounted on the machine tool table, for various rotary axes indexations was used to assess the coordinate measurement accuracy of a five-axes machine tool before and after considering the machine's error parameters [12]. However, no traceability is provided to the meter. The ball dome artefact, proposed by Mayer and Hashemi [13] is made of Invar, to eliminate the thermal effects deformation, was developed to estimate a five-axis machine tool metrology performance. Calibrating the coordinates of the balls to obtain reference values provides this traceability.

Machining a part and then measuring it by a coordinate measuring machine (CMM) is a common industrial method to check the accuracy of a machine but it is not only an expensive and time consuming method but also it is just applicable to the machining mode and it is not useful for machine evaluation in the coordinate measuring mode [14,15].

In this paper, an alternative calibration verification method is defined for a five-axis machine center when all five axes contribute to the measurement. First, the SAMBA method for machine calibration [16] is briefly explained. Then the mathematical model used to compensate the machine readings using its topology and error parameters is presented. It is followed by the SAMBA experimental probing procedure, which produces the calibrated machine stylus tip offsets. Finally, the newly designed ball dome artefact is used to validate the SAMBA calibrated model for a five-axis machine tool used as a five-axis coordinate measuring machine.
