Research on Automatic Labeling of Contact Profiler Based on Big Data

This article mainly studies the problem of labeling various parameter values of the contact profiler. The contour size of the instrument is analyzed by the least square method for the mathematical theory, and the data analysis information of each line and arc is established based on the background of big data. As a result, the corresponding mathematical model is established to realize the labeling of outline dimensions. First, perform precision processing on the horizontal data of the workpiece, use Excel software to make a scatter diagram, use the difference method to quickly search and locate the special inflection point coordinates, borrow these feature points to obtain the dimension of each data in turn, and combine the equations of straight lines and circles Find out the width and radius of the notch, find out the various indicators in turn, and finally sort and summarize them through the table. Next, the tilt data and the original data given for the workpiece are represented by a scatter graph. Using coordinate rotation and translation, the tilt angle is 7°24’59” clockwise and the radian is -0.13017. Compare the two sets of data After the difference, finally use segmented fitting to carry out horizontal correction.


Introduction
The profiler is a two-coordinate measuring instrument, which consists of a working platform, a fixture, a workpiece to be measured, a probe, a sensor, and a servo drive. The working principle of the contact profiler is that the probe touches the surface of the workpiece to be measured and slides at a constant speed. The sensor senses the geometric changes of the measured surface, samples them in the X and Z directions, and converts them into electrical signals [1]. The electrical signal is amplified and processed, converted into a digital signal, and stored in a data file. In an ideal situation, the contour curve should be smooth, but due to the problems of probe contamination, probe defects, and inaccurate scanning position in the contact profiler, the detected contour curve is rough and uneven, which gives the workpiece shape Accurate labeling has an impact. In order to simplify the problem, it is assumed that the contour of the measured workpiece is a plane curve composed of straight lines and arcs (see Figure 1). Please establish a mathematical model and study the following questions based on the level and tilt measurement data of a certain workpiece. According to the measurement data provided by a workpiece in the horizontal state, its contour line is shown in Figure 1. Please mark the parameter values of the contour line: slot width (such as x1, x3, etc.), arc radius (such as R1, R2, etc.), the distance between the center of the circle (such as c1, c2, etc.), the length of the arc, the length of the horizontal line segment (such as x2, x4, etc.), the length of the diagonal line segment, the angle between the diagonal line and the horizontal line ( Such as ∠1, ∠2, etc.) and the height of the chevron line (z1). When the same workpiece is measured in different times, the calculated value of the contour parameters will also be different due to the different placement angle and position of the workpiece. The other set of data gives the measurement data of the contour of the workpiece 1 at an angle of inclination and some horizontal displacement. Please calculate the inclination angle of the workpiece according to the data and make horizontal correction. After the data is corrected, compare the difference between the calculated values of each parameter of Workpiece 1 in the two measurement states.

Preparation before solution
The contact profiler has high precision, and the provided workpiece data displays 12 decimal places. In order to simplify the problem, the contour line of the measured workpiece is regarded as a plane curve composed of straight lines and arcs. Therefore, the data is preprocessed before the modeling and analysis, and the X and Z coordinate data of the workpiece are reserved with 5 decimal places.

Draw contour map
Use Excel software to make a scatter plot of the preprocessed data and mark the special points. Denoted as i=1,2,...39; including the inflection point, as shown in Figure 2.

Summary of solution method
The first step is to calculate the included angle. First, calculate the difference between the processed data. The calculation formula is as follows: (2) Next, calculate the ratio of formula (3) on the result data, and find the slope: Finally, the angle formula obtained by using the inverse trigonometric function is: The second step is to calculate the distance between two points. According to the marked points, use the distance formula between two points to calculate the width of the notch and the length of the horizontal line segment: The third step is to calculate the arc radius. To calculate the arc radius, you need to determine the coordinates of three points and use the arc radius formula to find the radius, where the arc radius is: The fourth step is to calculate the arc length. Within the range of arc length, find two coordinates with approximately equal ordinates, find the chord length according to the coordinates, and finally use the arc length formula to calculate: 180 r nπ = I (7)  Figure 2, and use the least square method to mark the parameter values of the contour line according to the calculation formula 1-7. It can be found from that Table 1 is the slope and horizontal angle of the workpiece in Figure 1 obtained by formula 1-4.  It can be found that Table 2 and Table 3 are the results of using formula 5 to find the width of the notch and the length of the horizontal line. In this paper, Lingo software is used to quickly calculate the arc radius of the workpiece in Figure 1, and the calculation results are shown in Table 4. Next, use the formula 7 to quickly calculate the arc length of the workpiece in Figure 1 with Excel software. The calculation results are shown in Table 5.

Research on the marking results after the profiler is tilted
The common error of the contact profiler is the position error of the measuring object, and there is a certain angle between the coordinate of the measuring object and the measuring system. Therefore, the processing data is effective. The position points at equal intervals of 0.0005 are adopted, and the side head of the sensor is placed on the workbench and rises with the workbench at equal intervals, and the value of the sensor without compensation is recorded. According to the compensation formula, a higher-order equation is used to fit the actual displacement.
When the same workpiece is measured in different times, the placement angle and position will be different. Therefore, the tilt data of the workpiece is preprocessed before modeling and analysis. The X and Z coordinate data in the tilt data retain 5 decimal places. Since the data is different due to different angles and positions, compare the original data of the workpiece and the tilt data by drawing a scatter diagram in Excel, as shown in Figure 3.