# Optimization of the Control Algorithm for an Active Bearing Support
## 5 Statistical Analysis  
The graphs presented in Figures 11 and 12 may not provide a clear answer as to whether the proposed control system works properly and whether reducing the vibration amplitude of the spindle tip is significant. To check this relationship, the Statistica program was used to perform the calculations. The measured average values of the maximum displacement amplitudes for both rotational speeds (500 and 1000 rpm) and both bearing support spacings (154 and 204 mm) of the shaft were used as the input parameters. The statistical analysis was carried out based on a method called single-variant significance of differences, the so-called ANOVA (Analysis of Variance) method [27; 28]. It allows you to check whether the analyzed factors (active adjustment of bearing preload) influence specific results (amplitude of the vibration displacement of the front spindle tip). Based on the calculations, a probability level of 0.05 was determined for the Student's \(t\)-test value and the null hypothesis was rejected. Thanks to this, it was possible to start estimating the level of significance of differences. For this purpose, the measurements carried out after developing an active bearing support control algorithm were divided into eight groups, four for each bearing support spacing. Groups 1, 3, 11 and 33 concerned the speed of 500 rpm (measurements without and with control), and groups 2, 4, 22 and 44 concerned the speed of 1000 rpm (measurements without and with control). In both cases, the significance level of differences was set at \(p<\) 0.05 and testing was carried out using two types of post hoc test (NIR test and Tukey's test) [29]. Examples of statistical analysis results obtained on the basis of these tests are presented in Tables 2 and 3, and they concern a shaft with a support spacing of 154 mm. Due to the type of study, only the \(p\) values obtained for the comparison of groups 1, 3, 2 and 4 (marked in yellow in the table) were significant. advisable to use a signal processor in the control system. Another problem, when the rotational speed of the spindle shaft is significantly increased, may be the method of introducing force to the front end of the spindle, which in the event of a possible failure of the intermediate bearing between the replacement mass and the shaft may lead to damage to the test stand. In further research, it may be important to use high-voltage piezoactators, which are characterized by a higher stiffness and a shorter response time. You can also use the force measurement from each piezoactuator for control. An important element of the research may be carrying out machining tests with forces coming from the cutting process. This would enable checking the possibility of using active regulation of bearing preload to influence the level of self-excited vibrations. The main conclusions and observations resulting from this work can be presented in the following points:  
1. Based on experimental tests and numerical analyses, it was shown that changing the spacing of bearing supports has a small impact on the resonance frequency of the system as well as on the vibration level of the spindle tip. The values obtained for both shaft lengths are similar. 2. The bearing preload control algorithm allows for a statistically significant reduction of the spindle tip vibration displacements within the basic resonance frequency. 3. Changing the preload during spindle operation is possible and ensures a change in the frequency and form of resonant vibrations. Therefore, it can be used to actively regulate spindle vibrations. 4. The application in LabView proposed by the author had limitations in handling the control loop, so further work seems to be important to take into account a larger number of variable spindle operating parameters (e.g., temperature or rotational speed), which would enable more effective regulation of the bearing preload.