# Optimization of the Control Algorithm for an Active Bearing Support
## 1 Introduction
An example dependency graph is shown in Figure 1.  
Adjusting the spindle stiffness depending on the current operating conditions is a problem widely discussed in the modern scientific literature. Various authors have conducted various tests to change the stiffness of the machine tool's spindle system [9; 10; 11; 12; 13; 14] and have proposed various solutions, both active and passive [15; 16], allowing for its change during spindle operation. The author presents a more extensive description of this issue in one of his earlier articles, which he wrote when he was dealing with the topic of active regulation of bearing preload [17]. These types of structures are intended to maintain the stiffness of the spindle system at a sufficient, but as low as possible, level of bearing preload, so as to ensure minimal resistance to movement and negligible wear of the bearings while maintaining their stable operation. In this article, the author presents his own design of a machine tool spindle equipped with an active bearing support, which allows the preload of the bearings to be changed during its operation. This change is made using piezoelectric elements in the full range of preload values for the B7206-CT-PS4-UM bearings from FAG [18]. For this type of bearing, the preload value is in the range of 60-430 N and is selected automatically using  
Figure 1: Dependence of the relative axial movement of the rings of an angular contact bearing on the axial load for bearings with different nominal contact angles [8]. a dedicated control algorithm. This type of solution can be called fully active. To build the active support, three PSt 150/10/40 VS15 piezoactuators from Piezomechanik GmbH, Munchen Germany [19] were used, placed parallel to the spindle axis and spaced at an angle of 120 degrees to each other. The piezoactuators were equipped with a strain gauge system that allowed for monitoring their load during operation and they were powered using a three channel SVR 150/3 power supply from Piezomechanik GmbH. Additionally, the active support had three built-in MDKa-F1 displacement sensors from VIS with an accuracy of 0.4 \(\upmu\)m. The detailed construction of the complete test stand along with the description of preliminary tests and model tests was presented in articles [20; 21]. Previous works have published preliminary tests for the station presented in the work with a model machine tool spindle equipped with an active bearing support. They only showed the structural correctness of the station and its correct operation under the influence of external forces. In none of these works did the author present a specific solution on how and on the basis of what parameters the control of the active support could be implemented. The aim of this article is to present the results of the process of selecting and optimizing the settings of the PID controller implemented in the LabView program that controls the preload of bearings in a model machine tool spindle. The process of checking its correct functioning was carried out for spindles with different spacings of bearing supports (154 mm--shaft A and 204 mm--shaft B). The value of the amplitude of forced vibrations of the front spindle tip, which was monitored continuously, was used as a control parameter for the correct operation of the control system. The most important novelty of this article is the developed control algorithm and the selection of its optimal operating parameters. After applying this algorithm, it is possible to actively reduce the vibration amplitude of the front spindle tip based on its actual measurement. The control algorithm adjusts the bearing preload values thanks to the use of piezoelectric actuators. When such a need arises (due to an excessive increase in the vibration amplitude), the control system changes the output value of the PID controller, which results in a change in the bearing preload value and at the same time limits the vibrations of the spindle tip.