## 3 Experiment  
### Experimental Device  
In this experiment, the digital grating probe is selected, the model is 7130-10, the baud rate is 9600, and the absolute coded grating can still save the last measurement data after power failure. Digital signal output is adopted, so there is no need to match an amplifier. The measuring range of the probe is 0-12.7 mm, the accuracy is 1.6 \(\upmu\)m, the resolution is 0.1 \(\upmu\)m, the lateral outgoing line is 0.5 \(\upmu\)m, and the force is 1.5 N.  
The line laser sensor is a laser profile scanner from Micro-Epsilon Company, Ortenburg, Germany. The model is 3002-50. The measuring range is 50 mm, and it has high resolution in the \(X\)-axis and \(Z\)-axis directions, which can realize accurate profile measurements. The measuring frequency is up to 10 kHz, which can realize dynamic detection and provide the highest measuring calibration data of 7.37 million points per second. The starting point and ending point of the standard measuring range of the \(Z\) axis are 105 mm, the measuring range height is 40 mm, the midpoint is 125 mm, the maximum deviation of a single point is 0.08%, and the linearity of the contour line is 3 \(\upmu\)m. The standard measuring range of the \(X\) axis starts at 43.3 mm and ends at 56.5 mm, the measuring range midpoint is 50 mm, and the resolution is 2048 points per profile.  
As shown in Figure 12, the experimental platform is mainly divided into a clamping device and a measuring device.  
The clamping device consists of a chuck and a thimble. One end of the workpiece to be tested is fixed on the rotary chuck, and the other end is fixed by the thimble. The control cabinet is responsible for controlling the rotation of the chuck and its rotating speed so that the workpiece can be scanned all around.  
The six grating probes are displaced in the same plane, and the detection plane intersects with the left end face of the workpiece. The line laser sensor is fixed on the linear guide rail of the lead screw and can move back and forth along the guide rail with the slider, and the laser light band irradiates the surface of the workpiece.  
Before the measuring system starts measuring, it should be calibrated according to the calibration method described in Section 2. The grating probes are numbered and named in the software system. The experimental data include data collected by a line laser sensor and the data collected by digital grating probes. In order to meet the experimental requirements, the experimental platform was built.  
The measured workpiece is a camshaft, for example, which is a typical SW. The camshaft is tested, and the corresponding error parameters are obtained and compared with the measured values of CMM to verify whether it meets the actual requirements. The camshaft for detection is shown in Figure 13.  
Figure 12: Experimental platform.  
Figure 13: Diagram of the measured workpiece.  
Through the above points, the ellipse equation of the section is solved by fitting. The coordinate of the center of the ellipse is (0, 1.1276, \(-\)1.8054), and the direction vector of the axis is (1.63, \(-\)0.59, \(-\)0.08), so the equation of the axis is  
\[\frac{x}{1.63}=\frac{y-1.1276}{-0.59}=\frac{z+1.8054}{-0.08} \tag{29}\]  
After calibrating the line laser sensor, check the experimental data. It is known that the geometrical surface of the line laser sensor is a cylindrical surface, and the coordinates of the detection point in space can be determined according to the measurement data. The deviation between the calculated point-to-axis distance in the spatial data table and the theoretical value of 30 mm is very small, meeting the experimental requirements.