# Spindle Error Movements and Their Measurement
## 4 Commercial Systems for Testing Error Movements of High-Speed Spindles
### Set for Measuring Spindle Error Movements--by Optodyne  
For the measurement of spindle error movements, the Optodyne company, known for its laser measuring devices and the selection of CNC machine tools, recommends using the MCV-500 (Compact Linear Machine Calibration System) set with DI-500 (Non-contact Laser Dial-Indicator) [23].  
The company records state that measurements with a laser system are easier than with capacitive sensors. With higher accuracy, resolution and range do not require such precise patterns (sphere, target, and artefact) subject to periodic calibration and mounted in the spindle. In addition to the above, it is possible to make a polar diagram by measuring only one axis.  
A unique feature of the LDDM (Laser Doppler Displacement Meter) system used is the use of a single optical element, both for sending and receiving the laser beam. For this reason, the reflecting surface can be a polished flat or spherical surface. In the case of a spherical one, in order to strengthen the reflected ray, additional focus lenses are used. The idea of the measurement is presented in Figure 16.  
Figure 16: Diagram of the laser system and the ball standard [23].  
Figure 15: Program menu with available tests.  
Details of the devices used to build the test stand can be found in [24]. Figure 17 shows a photograph taken during the measurements.  
One laser head measures in the X direction, and the other measures in the Y direction. As shown in Figure 18, first, a ball standard is set at the axis of rotation of the spindle with 4 fine-pitch screws, and then, the spindle is rotated 180 degrees.  
Figure 17: Optodyne set for the measurement of error movements [24].  
Figure 18: Spindle, holder, and ball standard [24].  
After rotating the spindle 180 degrees, as shown in Figure 19, the offset is twice as large as before rotation. The maximum difference in the X direction is marked \(\Delta\)X\({}_{\text{M}}\), and that in the Y direction is marked \(\Delta\)Y\({}_{\text{M}}\). The shift between the axis of rotation of the spindle and the centre of the sphere 0 can be determined from the following formula:  
\[\Delta=0.25\ ^{*}\text{SQRT}[\Delta\text{X}_{\text{M}}\ ^{*}\Delta\text{X}_{ \text{M}}+\Delta\text{Y}_{\text{M}}\ ^{*}\Delta\text{Y}_{\text{M}}] \tag{2}\]  
\[\Phi=\text{Arctan}\ [\text{Y}_{\text{M}}/\Delta\text{X}_{\text{M}}] \tag{3}\]  
The uncertainty of measurement depends on the execution error of the ball standard (typically 0.5 \(\upmu\)m). To measure the total spindle error movement, the spindle is rotated and the readings of the laser system \(\Delta\)X(t) i \(\Delta\)Y(t) are recorded for several dozen revolutions.  
As Optodyne performs the measurement of spindle error movements by combining two commercially available, independent devices, the software for calculating the values of error movements is not provided. It is true that a technical article [23] provides formulas according to which the error value can be calculated based on the indications of laser systems, but the calculation algorithms and polar diagrams recommended in the standards must be programmed by the user. A spreadsheet (e.g., Excel) can be used for this purpose.