## 2 Challenges for Modeling of Five-Axis Coordinate Measuring Systems
### Determination and Modeling of Other Sources of Errors
#### 2.3.2 Probe Head Hysteresis  
Hysteresis is a term used to describe the fact that system response to certain input depends on the order of proceeding inputs. It can be observed for various measuring systems also for the number of probe heads used in coordinate metrology. Probe head hysteresis can be assessed, for example, by measuring specially mounted gauge blocks. Three standards are pushed together, the central one extends in front of the two gauges on the sides. The two equal distances can be measured, first between the planes of the central standard block and second between the planes of the side gauges that adhere to the planes of the central block. The absolute difference between measured lengths is treated as hysteresis error. The gauge block of 14 mm nominal length was used, with two additional flatness standards on the sides. The experiment results show that mean hysteresis error in the case  
Figure 2: The probe error (PE) values depending on the angle of probe approach \(\alpha\), obtained for different styli lengths.  
of measurements performed using only rotational movements of the head equals to 0.5 \(\upmu\)m. In turn, the same experiment repeated for typical three-axis measurements gives result that is five times bigger. Hysteresis can be also estimated by measurements of standard ring. Three procedures were included in appropriate research and they are shown on Figure 3.  
The first procedure was generated by metrological software and it was treated as a reference. The other two were designed to include the influence of two rotations of the head, however each time the same points were measured and what changed was, in fact, the measuring strategy. Then the hysteresis was calculated as absolute difference between PE obtained for corresponding points of reference and tested procedure. The results show that the biggest mean hysteresis error was obtained for the second procedure and it equaled about 1.5 \(\upmu\)m. The influence of hysteresis on the overall result is hard to estimate. It occurs only in certain conditions so it cannot be included in each measurement. Generally, hysteresis should not be a case for unidirectional measurements--for example, flatness measurements--or basically when the probing path is guided without changing the head rotation direction. However, in cases of manual programming of the machine, it becomes a bigger problem because different criteria like operator convenience or the tendency to minimize program duration are taken into account much more frequently than avoiding the effect of hysteresis. It is hard then to include the influence of the hysteresis directly in virtual machine software. In the case when hysteresis should be included in overall uncertainty, its influence may be added to this value using the propagation of the uncertainty rule, where the result of the simulation performed using virtual CMM methodology is one of the uncertainty contributors and hysteresis along with other similar influences (if applicable) are other contributors.  
However, the hysteresis changes depending on the measurement task. Research conducted in LCM shows that hysteresis variability in the case of probe head used in five-axis measuring systems is small (standard deviations do not exceed 0.3 \(\upmu\)m) so it should not disturb the simulation process performed by the virtual machine.