# Spindle Error Movements and Their Measurement
## 5 Publications Related to the Measurement of Spindle Error Movements
### Measurement of Spindle Error Movements Using Vision Methods  
The papers [31; 32] describe an experimental method measuring error movements of a lathe spindle thanks to the use of a specially constructed vision system (machine vision), tracking the displacements of the edge of the cylindrical spindle face (master cylinder) mounted in the three-jaw self-centring chuck of the machine spindle. The vision system consisted of a complementary metal-oxide semiconductor (CMOS) camera mounted in a tool holder and an image acquisition system implemented on a PC. An important element of the stand was a properly selected and set strong light source, which allowed for even illumination of the front surface of the gauge plunger and for reductions in unwanted shadows and in adverse influence of ambient light. Figure 30 shows a general view of the described test stand. The research team proposed its own methodology for measuring spindle error movements. Figure 29: The prototype design and coordinate definition of the developed test device: (**a**) the schematic plot and coordinate definition, (**b**) the 3D prototype design [29]. Before starting the tests, the camera were calibrated, the purpose of which was to determine the so-called conversion coefficient to convert dimensions from pixels to millimetres. For this step, photos of the gauge slip or a specially prepared board with a pattern representing a chessboard (Figures 31 and 32) with known field sizes were used. After taking pictures of these objects, their size expressed in pixels was compared to the actual size expressed in millimetres, which made it possible to calculate the conversion coefficient. It should be emphasized that the use of a board with a chessboard pattern additionally allows you to check the level of distortions generated by the objective lens. Figure 30: The experimental arrangement for spindle radial error measurement using the vision system in a lathe [32]. Figure 31: Scaling factor from calibrated camera [32]  
After setting the light source and calibrating the camera, the main phase in investigating error movements began for the next selected rotational speeds of the lathe spindle. For this purpose, a gauge plunger was attached to its holder, the rotation of which was recorded by the CMOS AVT Marlin F-131b camera, and changes in its angular position were saved on a PC in the form of a sequence of consecutive shots (Figure 33) using the so-called IEEE-1394A frame grabber cards and LABVIEW Image software. In further data processing, the software controlling the measurement system automatically analysed the collected shots and performed the next steps of the research algorithm to detect edges based on the so-called Canny operator (Figure 34). Figure 33: A sequence of master cylinder images acquired at a spindle speed of 25 rpm [32]. Figure 32: Photography of check pattern board used for CMOS camera calibration [32]. The next step was to determine the position of specific subpixels that best match the images of the previously detected edge position--for this purpose, the control program performed calculations based on the Circular Hough Transform (CHT). The results of these calculations were then subjected to further transformations, among others based on the least squares method and the Fourier transformation, which led to determination of the instantaneous positions of the axis of rotation (Figure 35) and then to separation of the synchronous and asynchronous components and finally gave the value of the error movement of the tested spindle (Figure 36). Figure 34: Application of the canny edge detection for identifying edge pixels: a grey-scale image of the master cylinder (**a**) Canny edge detected pixels (**b**) [32]. Figure 35: Fourier series analysis of the circle centre data in X direction [32]. Extraction of periodic components using the least squares fitting of the Fourier curve [32]  
The repeatability of the results was assessed, and satisfactory results were obtained.