# Simulation Model for Correction and Modeling of Probe Head Errors in Five-Axis Coordinate Systems
## 4 Discussion  
The primary conclusion of the presented experiments is that the developed simulation model allows for faithful reproduction of the error field for probe heads used in five-axis coordinate systems. In the case of the two presented positions used during verification measurements, the percentage of properly simulated error values was 95.31% and 100%, respectively. Such high numbers prove the effectiveness of the presented model and suggest its possible application as a module for probe head error simulation in virtual models of five-axis CMMs. The developed model may also be helpful during the correction of probe head errors. As was shown in Table 2, the precision of the roundness deviation measurements has noticeably improved following the implementation of the correction using the methodology presented in Section 2.4. It should be noted that the effectiveness of probe head error correction is more pronounced in the case of a smaller number of measuring points used for the calculation of geometrical features. In this paper, example measurements were carried out on a circle, but the authors' previous research suggests similar relationships in the case of other features. This phenomenon is connected with the averaging tendency of the least squares method, usually utilized for calculating features. The results presented in Figure 5 indicate good stability of probe head error characteristics. It can be concluded from this that irrespective of the usage of the developed model, the initial measurements aimed at gathering input data for the model would not have to be repeated very frequently. The ideal interval for the re-identification of probe head errors should be investigated for different probe head types, but the authors suppose that it could be expressed in months. As for future research directions, the most important goal is to develop a fully functional virtual model of a five-axis coordinate system. The research presented in this paper marks the first step in this direction. The simulative model discussed here should be connected to a model responsible for simulating kinematic system errors of the machine. Such a combined virtual model would reduce the time spent on the determination of the uncertainty of measurements performed on the five-axis coordinate system. Seeing as numerous systems of this type are presently used in industrial conditions, this would be likely to significantly reduce costs associated with quality control, and as a natural consequence, the total production costs would also drop down. The model presented in this paper was checked for the measurements of regular rotary features for which the probes such as the one discussed here are usually applied in practice. In case of features such as cylinders, circles, spheres, cones, _etc._, the measurements may be easily performed using only the movements of the probe head, which significantly reduces their total time (in relation to the standard three-axis CMM). The measurements of more complicated shapes are also possible but the reduction of the measurement duration is not that meaningful as in the case of regular features. So it may be concluded that the model works properly for the majority of practical usages of the discussed probes. However, in the future, it will be advisable to also include in it the possibility of simulating the measurements of more complicated geometries, when the stylus has to move on complex trajectories and the \(\alpha\) angle cannot be easily defined on the plane perpendicular to the probe when it is oriented using A and B angular positions. The next important possibility of improving the presented model is to reduce the number of orientations and points used during identification measurements. It should be possible to minimize