# Spindle Error Movements and Their Measurement
## 5 Publications Related to the Measurement of Spindle Error Movements
### Measurement of the Spindle Error Movements under a Simulated Load  
An interesting idea of the test stand that enables load simulation during dynamic spindle tests was described in [43; 44]. The proposed test method assumes the use of a specially designed device that allows the hydraulic application of a load to a rotating spindle through a bearing mounted in a tool holder, as shown in Figure 59.  
The test stand was assembled on a three-axis CNC milling machine, as shown in Figure 60, and then a series of measurements of displacement of a spindle loaded with a force perpendicular to its axis (radial force) with a value in the range of 0-500 N started. Before starting the actual tests, the influence of errors generated by the rotating bearing was first checked, which was assessed as small (which was probably influenced by the high accuracy class of the bearing used and the damping of some vibrations by the hydraulic system that applied the load). A series of measurements of the displacement of a spindle was carried out under a simulated load for various rotational speeds in the range of 50-1550 rpm. The obtained results were plotted on appropriate graphs showing changes in asynchronous error (Figure 61), synchronous error (Figure 62), and total error (Figure 63) of the spindle position as a function of its load and rotation. Figure 59: The experimental unit used to apply test load during spindle errors measurements: the external force acts over a precise ball bearing (**1**). The force of the load unit (**6**) can be controlled through the pressure exciter (**4**). The load unit is directly linked with a tensor unit (**5**) and a contact pin (**7**). Displacement in the X, Y, and Z axes is measured on a high precision double-ball artefact (**2**) by proximity sensors (**3**) [43]  
Figure 60: The load unit used on a machine tool [43]. As a result of the research, the team of scientists came to the following conclusions:  
* The increase in the force loading the spindle had the greatest impact on the value of the total error movement up to 950 rpm. * In case of revolutions higher than 950 rpm, the value of error movement increased slightly with the given load. The authors of this study do not agree with the interpretation given for the results. We believe that the presented graphs clearly show the influence of the load on the change in value of asynchronous, synchronous and total error, e.g., for the 650 rpm speed, the smallest measured total error is about 3 \(\upmu\)m and the largest is about 7 \(\upmu\)m, so it is over 2.3 times higher. Despite the differences in interpretation, the proposed research method is very interesting because it allows you to check the accuracy of the spindle's work under load, i.e., in conditions simulating at least roughly real working conditions. Figure 61: Dependency of asynchronous error on spindle speed and load [43]. Figure 62: Dependency of synchronous error on spindle speed and load [43]. Propagation of Measurement Uncertainty in Spindle Error Separation Techniques--Research with the Stochastic Spectral Method  
In the article of [45], the authors described a method investigating the uncertainty propagation of error separation techniques during the measurement of error movements. In order to perform the study, the authors built a special test stand (shown in Figure 64) consisting of a DC motor (Maxon DC motor 201018). A gauge plunger was attached to the motor spindle, the displacements of which were tested by three sensors I, II, and III, which were used to determine the spindle rotation angle and to collect the superposition signal consisting of spindle error, spindle roundness error, and noise generated by the probe. The data collected by the measuring sensors were processed by a control system using algorithms based on the systems theory and the stochastic spectral method. Using a specially constructed test stand with the use of systems theory and the stochastic spectral method, the law of propagation of measurement uncertainty of the measuring probe was formulated.