Multi-point calibration method based on three-coordinate scanning probe

Abstract

The invention relates to the technical field of precision measurement, and particularly discloses a multi-point calibration method based on a three-coordinate scanning probe, which comprises the following steps: acquiring a theoretical measurement position of the three-coordinate scanning probe; constructing a measuring head deflection semi-linear model based on output signals of the three-axis linear displacement sensor; calibrating the measuring head deflection semi-linear model based on the output signal of the three-axis linear displacement sensor through a 25-point calibration method to obtain a calibrated measuring head deflection semi-linear model; inputting the current signals respectively output by the three-axis linear displacement sensor into the calibrated measuring head deflection semi-linear model for deflection calculation to obtain the current deflection of the three-coordinate scanning measuring head; and calculating the actual measurement position of the three-coordinate scanning probe according to the theoretical measurement position and the current deflection of the three-coordinate scanning probe. The whole calibration process can be completed only by detecting 25 points on the sphere, the calibration process is simpler and more convenient, and the calibration efficiency is improved.

Description

Technical Field

[0001] The present invention relates to the field of precision measurement technology, and more specifically, to a multi-point calibration method based on a coordinate measuring machine (CMM) scanning probe. Background Art

[0002] There are various methods for detecting the surface shape tolerance of industrial parts. Among them, the contact measurement of a coordinate measuring machine (CMM) has been widely used. In a CMM, one of the key components affecting the measurement accuracy is the performance of the probe system. According to different triggering principles, contact probe systems can be divided into two types, namely, trigger probes and scanning probes.

[0003] The trigger probe is binary during its movement, outputting an on or off signal. Due to the movement of the machine, this binary operation introduces a pre-travel error. Compared with the trigger probe, the scanning probe has significant advantages in terms of accuracy and efficiency. On the one hand, the scanning probe can continuously measure on the surface, avoiding a large number of inefficient sampling points during probing. On the other hand, the scanning probe can continuously output a voltage signal corresponding to the current deflection, thereby eliminating the inherent pre-travel error of the trigger probe. The scanning probe is a very promising coordinate measurement method, and a large number of studies have been conducted on the sampling strategy and path planning of scanning measurement. However, the scanning probe needs to calibrate more parameters. The current commercial calibration methods require designing complex scanning paths for calibration, which takes a long time. For example, Renishaw uses the SP25 scanning probe for scanning calibration. Since the SP25 scanning probe is a non-linear probe, this means that a high-order polynomial is required to represent the relationship between the deflection of the probe and the signal. The complexity of the model leads to a complex calibration process. The standard calibration procedure provided by Renishaw requires using two different deflection amounts to scan multiple latitudes and longitudes on a standard sphere, including forward and reverse, which is a key factor leading to low calibration efficiency of the scanning probe. Summary of the Invention

[0004] The present invention aims to overcome the above defects and provide a multi-point calibration method based on a CMM scanning probe to solve the problems of complex and time-consuming calibration process in the existing CMM.

[0005] As a first aspect of the present invention, there is provided a multi-point calibration method based on a CMM scanning probe. The CMM scanning probe is installed at the end of the Z-axis column of the CMM. A three-axis linear displacement sensor is provided in the CMM scanning probe. The three-axis linear displacement sensors are an X-axis linear displacement sensor, a Y-axis linear displacement sensor, and a Z-axis linear displacement sensor respectively. When the CMM scanning probe contacts the object to be measured, a certain deflection occurs in the actual measurement position of the CMM scanning probe relative to the theoretical measurement position. The theoretical measurement position of the CMM scanning probe is expressed as [Xp , Y p , Z p T , the actual measurement position of the three - coordinate scanning probe is expressed as [x p , y p , z p T , the deflection of the three - coordinate scanning probe is expressed as [d x , d y , d z T ;

[0006] The multi - point calibration method based on the three - coordinate scanning probe includes the following steps:

[0007] Step S1: Obtain the theoretical measurement position [X p , Y p , Z p of the three - coordinate scanning probe through the coordinate measuring machine; T ;

[0008] Step S2: Construct a semi - linear model of the probe deflection based on the output signals of the three - axis linear displacement sensors;

[0009] Step S3: Calibrate the semi - linear model of the probe deflection based on the output signals of the three - axis linear displacement sensors through the 25 - point calibration method to obtain the calibrated semi - linear model of the probe deflection;

[0010] Step S4: Input the current signals output by the X - axis linear displacement sensor, Y - axis linear displacement sensor, and Z - axis linear displacement sensor respectively into the calibrated semi - linear model of the probe deflection for deflection calculation to obtain the current deflection of the three - coordinate scanning probe;

[0011] Step S5: Calculate the actual measurement position [x p , Y p , Z p of the three - coordinate scanning probe according to the theoretical measurement position [X T and the current deflection [d x , d y , d z of the three - coordinate scanning probe; T to obtain [x p , y p , z p T .

[0012] ​​​​Further, parallel leaf springs are also provided in the three - coordinate scanning probe. The parallel leaf springs are respectively an X - axis parallel leaf spring, a Y - axis parallel leaf spring, and a Z - axis parallel leaf spring. Cores are provided on the X - axis linear displacement sensor, the Y - axis linear displacement sensor, and the Z - axis linear displacement sensor. The X - axis parallel leaf spring is connected to the core on the X - axis linear displacement sensor, the Y - axis parallel leaf spring is connected to the core on the Y - axis linear displacement sensor, and the Z - axis parallel leaf spring is connected to the core on the Z - axis linear displacement sensor. After the three - coordinate scanning probe contacts the object to be measured, it will move. The three - coordinate scanning probe can drive the X - axis parallel leaf spring, the Y - axis parallel leaf spring, and the Z - axis parallel leaf spring to move. The movement of the X - axis parallel leaf spring, the Y - axis parallel leaf spring, and the Z - axis parallel leaf spring can drive the cores connected thereto to move. At this time, the X - axis linear displacement sensor, the Y - axis linear displacement sensor, and the Z - axis linear displacement sensor will output displacement signals. The displacement signals output by the X - axis linear displacement sensor, the Y - axis linear displacement sensor, and the Z - axis linear displacement sensor are proportional to the displacements of their respective cores.

[0013] Further, constructing a semi - linear model of the probe deflection based on the output signals of the three - axis linear displacement sensors further includes:

[0014] The semi - linear model of the probe deflection based on the output signals of the three - axis linear displacement sensors is expressed as:

[0015]

[0016] where p, q, and r are respectively the displacement signals output by the X - axis linear displacement sensor, the Y - axis linear displacement sensor, and the Z - axis linear displacement sensor, and k px 、k qy and k rz are all linear terms, h p 、h q and h r are all quadratic terms, and k qx 、k rx 、k py 、k ry 、k pz and k qz are all cross - coupling terms.

[0017] Further, calibrating the semi - linear model of the probe deflection based on the output signals of the three - axis linear displacement sensors by the 25 - point calibration method to obtain the calibrated semi - linear model of the probe deflection further includes:

[0018] Determining the parameters k px 、k qy 、krz , h p , h q , h r , k qx , k rx , k py , k ry , k pz and k qz , to obtain the calibrated semi - linear model of the probe deflection;

[0019] The process of the 25 - point calibration method is as follows:

[0020] Select 25 points on the standard sphere, each point having a different normal direction. Measure the 25 points on the standard sphere with a coordinate measuring probe. The deflections generated when the coordinate measuring probe measures the 25 points are different. When the coordinate measuring probe measures each point, it goes through three stages: approaching, stabilizing, and retracting. During the calibration process, data from the three stages of approaching, stabilizing, and retracting are used. Select 10 samples from each of the three stages of approaching, stabilizing, and retracting. 750 sample points are generated during the measurement of the 25 points. All 750 sample points are located on a sphere with a radius equal to the radius of the standard sphere plus the radius of the probe tip. When the coordinate measuring probe measures the i - th sample point, use the coordinate measuring machine to obtain the theoretical measurement position P of the coordinate measuring probe i = [X i , Y i , Z i . At this time, the X - axis linear displacement sensor, Y - axis linear displacement sensor, and Z - axis linear displacement sensor respectively output displacement signals p, q, r. Solve Equation (1) through the LM algorithm to obtain the parameter k in the semi - linear model of the probe deflection based on the output signals of the three - axis linear displacement sensors px , k qy , k rz , h p , h q , h r , k qx , k rx , k py , k ry , k pz and k qz ;

[0021]

[0022] where, [X c , Y c , Z c is the center coordinate of the standard sphere, R is the radius of the standard sphere, r is the radius of the tip of the coordinate measuring probe, [X i , Y i , Zi is the theoretical measurement position of the three - coordinate scanning probe when measuring the i - th sample point.

[0023] Further, based on the theoretical measurement position [X p , Y p , Z p T and the current deflection [d x , d y , d z T of the three - coordinate scanning probe, the actual measurement position [x p , y p , z p T is calculated, and further includes:

[0024] The calculation formula of the actual measurement position [x p , y p , z p T is as follows:

[0025]

[0026] A multi - point calibration method based on a three - coordinate scanning probe provided by the present invention has the following beneficial effects: only 25 points on the spherical workpiece need to be detected to complete the entire calibration process, and the calibration process is more convenient; when the accuracy of the MWU probe adopted in the present invention is equivalent to that of the Renishaw probe, the proposed 25 - point calibration method has the same or even higher measurement accuracy than the Renishaw calibration method, but the calibration time is greatly reduced, improving the calibration efficiency. Brief Description of the Drawings

[0027] The drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the following specific embodiments, they are used to explain the present invention, but do not constitute a limitation to the present invention.

[0028] Figure 1 is a flowchart of the multi - point calibration method based on a three - coordinate scanning probe provided by the present invention.

[0029] Figure 2 is a schematic structural diagram of a coordinate measuring machine provided by the present invention.

[0030] Figure 3 is a working principle diagram of a three - coordinate scanning probe provided by the present invention.

[0031] Figure 4 is a schematic structural diagram of a three - coordinate scanning probe provided by the present invention.

[0032] Figure 5 This is the schematic diagram of the axial displacement movement of the three-coordinate scanning probe provided by the present invention.

[0033] Figure 6 This is the 25-point distribution diagram of the standard sphere provided by the present invention.

[0034] Figure 7 This is the diagram of the probe signal changing with the movement of the machine provided by the present invention.

[0035] Figure 8 This is the schematic diagram of the measurement accuracy verification result of the 25-point calibration method provided by the present invention. Detailed implementation manners

[0036] To further elaborate on the technical means and effects adopted by the present invention to achieve the predetermined invention purpose, the following, in combination with the drawings and preferred embodiments, details the specific implementation manners, structures, features and effects of a multi-point calibration method based on a three-coordinate scanning probe according to the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0037] It should be noted that the terms "first", "second", etc. in the description and claims of the present invention and the above drawings are used to distinguish similar objects, and do not necessarily need to describe a specific order or sequence. It should be understood that such data can be interchanged under appropriate circumstances for the embodiments of the present invention described herein. In addition, the terms "comprising" and "having" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device comprising a series of steps or units does not necessarily have to be limited to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products or devices.

[0038] In this embodiment, a multi-point calibration method based on a three-coordinate scanning probe is provided. As Figure 2-4 shown, the three-coordinate scanning probe 2 is installed at the end of the Z-axis column of the three-coordinate measuring machine 1. A three-axis linear displacement sensor 7 is provided in the three-coordinate scanning probe 2. The three-axis linear displacement sensor 7 is respectively an X-axis linear displacement sensor, a Y-axis linear displacement sensor and a Z-axis linear displacement sensor. When the three-coordinate scanning probe 2 contacts the object to be measured 3, a certain deflection 6 is generated between the actual measurement position 5 and the theoretical measurement position 4 of the three-coordinate scanning probe. The theoretical measurement position 4 of the three-coordinate scanning probe is expressed as [X p , Y p , Zp T The actual measurement position 5 of the three - coordinate scanning probe is expressed as [x p , y p , z p T , that is, the center of the probe tip. The deflection 6 of the three - coordinate scanning probe is expressed as [d x , d y , d z T ;

[0039] As Figure 1 shown, the multi - point calibration method based on the three - coordinate scanning probe includes the following steps:

[0040] Step S1: Obtain the theoretical measurement position [X p , Y p , Z p of the three - coordinate scanning probe through the coordinate measuring machine T ;

[0041] It should be noted that the controller of the coordinate measuring machine obtains the theoretical measurement position [X p , Y p , Z p according to the motion values of the X - axis, Y - axis and Z - axis motors T . Therefore, in order to obtain the final actual measurement position [x p , y p , z p , it is necessary to accurately obtain the probe deflection [d T , d x , d y , d z T .

[0042] It should be understood that, as Figure 4 shown, the structure of the entire scanning probe can be regarded as an institution composed of three independent structures of the X - axis, Y - axis and Z - axis orthogonally. Among them, the respective linear displacement sensors LVDT are installed along the axis. The signals output by the X - axis linear displacement sensor, Y - axis linear displacement sensor and Z - axis linear displacement sensor are respectively expressed as p, q, r. Calibration is to find the relationship between the signals p, q, r output by the linear displacement sensors and the probe deflection [d x , d y , d z T .

[0043] Step S2: Construct a semi - linear model of the probe deflection based on the output signals of the three - axis linear displacement sensors;

[0044] ​​​​​Preferably, the construction of the semi-linear model of the probe deflection based on the output signals of the three-axis linear displacement sensors further includes:

[0045] Establish the mathematical motion relationship between the linear variable differential transformer (LVDT) and the displacement of the probe tip: Both the parallel leaf spring and the LVDT exhibit good linear characteristics within a small displacement range. The relationship between them should be expressed as a linear model. Due to manufacturing and assembly errors, the three LVDTs cannot be perfectly aligned with the X, Y, and Z axes. Corresponding cross-coupling terms are introduced, and quadratic terms are added to improve the robustness of the model, thereby dealing with the non-linearity and large displacements of the probe. The semi-linear model of the probe deflection based on the output signals of the three-axis linear displacement sensors is expressed as:

[0046]

[0047] where p, q, and r are the displacement signals output by the X-axis linear displacement sensor, the Y-axis linear displacement sensor, and the Z-axis linear displacement sensor, respectively, and k px , k qy and k rz are all linear terms, h p , h q and h r are all quadratic terms, and k qx , k rx , k py , k ry , k pz and k qz are all cross-coupling terms. This semi-linear model of the probe deflection simplifies the model parameters, avoids the problem of overfitting, and reduces the need for a large amount of calibration data.

[0048] Step S3: Calibrate the semi-linear model of the probe deflection based on the output signals of the three-axis linear displacement sensors through a 25-point calibration method to obtain the calibrated semi-linear model of the probe deflection;

[0049] Preferably, the calibration of the semi-linear model of the probe deflection based on the output signals of the three-axis linear displacement sensors through a 25-point calibration method to obtain the calibrated semi-linear model of the probe deflection further includes:

[0050] Determine the parameters k px , k qy , k rz , h p , h q , h r , k qx , k rx, k py , k ry , k pz and k qz , so as to obtain the calibrated semi-linear model of the probe deflection

[0051] The process of the 25-point calibration method is as follows:

[0052] To determine the above model parameters k px , k qy , k rz , h p , h q , h r , k qx , k rx , k py , k ry , k pz and k qz , 25 points are selected on the standard sphere for calibration. As Figure 6 shown, the distribution of the 25 points refers to the ISO 10360-5 standard. Each point has a different normal direction. The 25 points on the standard sphere are measured by a coordinate measuring probe. The deflections generated when the coordinate measuring probe measures the 25 points are different; when the coordinate measuring probe measures each point, it has to go through three stages: approaching, stable, and retracting. As Figure 7 shown, there is an obvious relationship between the movement in the X-axis direction and the p signal. The movement relationships in the Y-axis and Z-axis directions are similar to that in the X-axis. Each detection starts from the approaching point. Therefore, in the first half S1-1 of S1, the tip of the probe does not touch the spherical surface, and the detection signal remains unchanged. After the tip of the probe touches the spherical surface, the signal gradually increases as the deflection of the probe increases. The retracting stage is similar. S3-1 represents the stage when the tip of the probe still touches the surface of the standard sphere during the retracting process, while S3-2 represents the stage when the tip of the probe leaves the surface of the standard sphere; during the calibration process, the data in the S1-2, S2, and S3-1 stages are used. 10 samples are selected from each of the S1-2, S2, and S3-1 stages, and 750 sample points are generated in the measurement of 25 points. The 750 sample points are all located on a sphere with a radius equal to the radius of the standard sphere plus the radius of the probe tip. When the coordinate measuring probe measures the i-th sample point, the controller of the coordinate measuring machine is used to obtain the theoretical measurement position P of the coordinate measuring probe at a sampling rate of 1000HZ i = [X i , Y i , Z i, at this time, the X-axis linear displacement sensor, Y-axis linear displacement sensor, and Z-axis linear displacement sensor respectively output displacement signals p, q, and r, and the parameters k in the probe deflection semi-linear model based on the output signals of the three-axis linear displacement sensor are obtained by solving Equation (1) through the LM algorithm (Levenberg-Marquardt). px , k qy , k rz , h p , h q , h r , k qx , k rx , k py , k ry , k pz and k qz ;

[0053]

[0054] Among them, [X c , Y c , Z c is the center coordinate of the standard sphere, R is the radius of the standard sphere, r is the radius of the tip of the three-coordinate scanning probe, and [X i , Y i , Z i is the theoretical measurement position of the three-coordinate scanning probe when measuring the i-th sample point.

[0055] It should be noted that 25 points distributed on the standard sphere are measured, and in the three stages of approaching, stabilizing, and retracting during the detection by the three-coordinate measuring machine, the point set is reasonably taken, and based on the data of the taken point set and the formula, the relevant parameters in the probe deflection semi-linear model based on the output signals of the three-axis linear displacement sensor are solved.

[0056] Step S4: Input the current signals respectively output by the X-axis linear displacement sensor, Y-axis linear displacement sensor, and Z-axis linear displacement sensor into the calibrated probe deflection semi-linear model for deflection calculation to obtain the current deflection of the three-coordinate scanning probe;

[0057] Step S5: Calculate the actual measurement position [x p , y p , z p of the three-coordinate scanning probe according to the theoretical measurement position [X T and the current deflection [d x , d y , d z of the three-coordinate scanning probe T p , y p , z​p T 。

[0058] Specifically, the actual measurement position [x p , y p , z p T of the three - coordinate scanning probe has the following calculation formula:

[0059]

[0060] Preferably, as Figure 5 shown, a parallel leaf spring 8 is also provided in the three - coordinate scanning probe 2, which can perform approximate linear motion within a relatively short distance. During its precise displacement process, the linear displacement sensor can accurately detect the change of the motion. The parallel leaf springs 8 are respectively an X - axis parallel leaf spring, a Y - axis parallel leaf spring, and a Z - axis parallel leaf spring. A magnetic core 9 is provided on each of the X - axis linear displacement sensor, the Y - axis linear displacement sensor, and the Z - axis linear displacement sensor. The X - axis parallel leaf spring is connected to the magnetic core 9 on the X - axis linear displacement sensor, the Y - axis parallel leaf spring is connected to the magnetic core 9 on the Y - axis linear displacement sensor, and the Z - axis parallel leaf spring is connected to the magnetic core 9 on the Z - axis linear displacement sensor. After the three - coordinate scanning probe 2 contacts the object to be measured 3, it will move. The three - coordinate scanning probe 2 can drive the X - axis parallel leaf spring, the Y - axis parallel leaf spring, and the Z - axis parallel leaf spring to move. The movement of the X - axis parallel leaf spring, the Y - axis parallel leaf spring, and the Z - axis parallel leaf spring can drive the respective connected magnetic cores 9 to move. At this time, the X - axis linear displacement sensor, the Y - axis linear displacement sensor, and the Z - axis linear displacement sensor will output displacement signals, and the displacement signals output by the X - axis linear displacement sensor, the Y - axis linear displacement sensor, and the Z - axis linear displacement sensor are proportional to the displacements of their respective magnetic cores 9.

[0061] ​​Verification of measurement accuracy method: In a constant temperature room at 20°C, using the same coordinate measuring machine, successively equipped with a scanning probe (here, the self-designed MWU probe) and a Renishaw SP25 probe, the accuracy comparison verification was carried out in sequence. As shown in Table 1, the three groups of verification objects were named MWU_p, MWU_r, and SP_r respectively. MWU_p represents the calibration by the 25-point method using the MWU probe, MWU_r represents the calibration by the Renishaw method using the MWU probe, and SP_r represents the calibration by the Renishaw method using the Renishaw SP25 probe. And the three objects were verified according to the order of the three groups of experiments. First, the performance verification of the probe system was carried out. As shown in Table 2, 25 points were measured on the hemisphere of a standard ball, and the deviation of each point from the center of the least squares sphere was calculated. The maximum deviation minus the minimum deviation (abbreviation "PForm") was used to represent the overall performance of the probe. In the entire measurement range, different deflections of the probe were selected for calibration, and the calibration time and the PForm of the standard ball were recorded. Second, the effectiveness verification of the probe in scanning measurement was carried out. As shown in Table 3, another standard ball was selected to perform scanning measurement along a spiral path on its surface, and the radius error and shape error (abbreviation "RMS") of the standard ball were obtained through measurement. In the entire measurement range, different deflections of the probe were selected for calibration and scanning measurement for verification. Third, the verification of the probe length measurement accuracy was carried out. As shown in Table 4, a 30-mm long standard gauge block was selected to perform length measurement along the X-axis, Y-axis, and the XY diagonal axis of the coordinate measuring machine respectively. In the entire measurement range, different deflections of the probe were selected for calibration and the length measurement of the gauge block for verification. The experimental results of the above methods are shown in Figure 8 , it can be seen that when the accuracy of the MWU probe adopted in the present invention is equivalent to that of the Renishaw probe, the proposed 25-point calibration method has the same or even higher measurement accuracy than the Renishaw calibration method, but the calibration time is greatly reduced, improving the calibration efficiency.

[0062] The multi-point calibration method based on a three-coordinate scanning probe provided by the present invention enables good calibration effect of the scanning probe that generates displacement based on a parallel leaf spring, requires fewer parameters, avoids the problem of overfitting in calibration, reduces the amount of data required for calibration, and greatly improves the efficiency of the calibration process while ensuring the calibration accuracy.

[0063] The above are only the preferred embodiments of the present invention, and do not impose any form of limitation on the present invention. Although the present invention has been disclosed above with the preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some changes or modifications to equivalent embodiments of equivalent changes within the scope of the technical solution of the present invention by using the technical content disclosed above. However, as long as it does not depart from the content of the technical solution of the present invention, any simple modification, equivalent change and modification made to the above embodiments based on the technical essence of the present invention still fall within the scope of the technical solution of the present invention.

Claims

1. A multi-point calibration method based on a three-coordinate scanning probe, characterized in that, The three - coordinate scanning probe (2) is installed at the end of the Z - axis column of the three - coordinate measuring machine (1). A three - axis linear displacement sensor (7) is arranged in the three - coordinate scanning probe (2). The three - axis linear displacement sensor (7) is respectively an X - axis linear displacement sensor, a Y - axis linear displacement sensor and a Z - axis linear displacement sensor. When the three - coordinate scanning probe (2) contacts the object to be measured (3), a certain deflection (6) occurs between the actual measurement position (5) and the theoretical measurement position (4) of the three - coordinate scanning probe. The theoretical measurement position (4) of the three - coordinate scanning probe is expressed as [X p , Y p , Z p T , and the actual measurement position (5) of the three - coordinate scanning probe is expressed as [x p , y p , z p T . The deflection (6) of the three - coordinate scanning probe is expressed as [d x , d y , d z T ;​​​ the multi-point calibration method based on a three-coordinate scanning probe comprises the following steps: Step S1: Obtain the theoretical measurement position [X p , Y p , Z p T ; Step S2: Construct a semi-linear model of the probe deflection based on the output signals of the three-axis linear displacement sensors; Step S3: Calibrate the semi-linear model of the probe deflection based on the output signals of the three-axis linear displacement sensors by a 25-point calibration method to obtain a calibrated semi-linear model of the probe deflection; Step S4: Input the current signals output by the X-axis linear displacement sensor, the Y-axis linear displacement sensor, and the Z-axis linear displacement sensor respectively into the calibrated semi-linear model of the probe deflection for deflection calculation to obtain the current deflection of the three-coordinate scanning probe; Step S5: According to the theoretical measurement position [X p , Y p , Z p T of the coordinate measuring probe and the current deflection [d x , d y , d z T of the coordinate measuring probe, calculate the actual measurement position [x p , y p , z p T .

2. The multi-point calibration method based on a three-coordinate scanning probe according to claim 1, characterized in that, a parallel leaf spring (8) is further provided in the three-coordinate scanning probe (2), the parallel leaf springs (8) are respectively an X-axis parallel leaf spring, a Y-axis parallel leaf spring, and a Z-axis parallel leaf spring, magnetic cores (9) are provided on the X-axis linear displacement sensor, the Y-axis linear displacement sensor, and the Z-axis linear displacement sensor, the X-axis parallel leaf spring is connected to the magnetic core (9) on the X-axis linear displacement sensor, the Y-axis parallel leaf spring is connected to the magnetic core (9) on the Y-axis linear displacement sensor, the Z-axis parallel leaf spring is connected to the magnetic core (9) on the Z-axis linear displacement sensor, after the three-coordinate scanning probe (2) contacts the object to be measured (3), it will move, the three-coordinate scanning probe (2) can drive the X-axis parallel leaf spring, the Y-axis parallel leaf spring, and the Z-axis parallel leaf spring to move, the movement of the X-axis parallel leaf spring, the Y-axis parallel leaf spring, and the Z-axis parallel leaf spring can drive the respective connected magnetic cores (9) to move, at this time, the X-axis linear displacement sensor, the Y-axis linear displacement sensor, and the Z-axis linear displacement sensor will output displacement signals, and the displacement signals output by the X-axis linear displacement sensor, the Y-axis linear displacement sensor, and the Z-axis linear displacement sensor respectively are proportional to the displacements of their respective magnetic cores (9).

3. The multi-point calibration method based on a three-coordinate scanning probe according to claim 1, characterized in that, the construction of the semi-linear model of the probe deflection based on the output signals of the three-axis linear displacement sensors further comprises: the semi-linear model of the probe deflection based on the output signals of the three-axis linear displacement sensors is expressed as: where p, q, and r are the displacement signals output by the X-axis linear displacement sensor, Y-axis linear displacement sensor, and Z-axis linear displacement sensor, respectively, and k px , k qy and k rz are all linear terms, h p , h q and h r are all quadratic terms, k qx , k rx , k py , k ry , k pz and k qz are all cross-coupling terms.

4. The multi-point calibration method based on a three-coordinate scanning probe according to claim 3, characterized in that, the calibration of the semi-linear model of the probe deflection based on the output signals of the three-axis linear displacement sensors by a 25-point calibration method to obtain a calibrated semi-linear model of the probe deflection further comprises: The parameters k in the semi-linear model of the probe deflection based on the output signal of the three-axis linear displacement sensor are determined by the 25-point calibration method px 、k qy 、k rz 、h p 、h q 、h r 、k qx 、k rx 、k py 、k ry 、k pz and k qz , so as to obtain the calibrated semi-linear model of the probe deflection; the process of the 25-point calibration method is as follows: Select 25 points on a standard sphere, each point having a different normal direction. Measure the 25 points on the standard sphere with a coordinate measuring probe. The deflections generated by the coordinate measuring probe when measuring the 25 points are different. When the coordinate measuring probe measures each point, it has to go through three stages: approaching, stabilizing, and retracting. During the calibration process, use the data from the three stages of approaching, stabilizing, and retracting. Select 10 samples from each of the three stages of approaching, stabilizing, and retracting. 750 sample points are generated during the measurement of the 25 points. All 750 sample points are located on a sphere with a radius equal to the radius of the standard sphere plus the radius of the probe tip. When the coordinate measuring probe measures the i-th sample point, use the coordinate measuring machine to obtain the theoretical measurement position P i =[X i ,Y i ,Z i . At this time, the X-axis linear displacement sensor, Y-axis linear displacement sensor, and Z-axis linear displacement sensor respectively output displacement signals p, q, and r. Solve Equation (1) through the LM algorithm to obtain the parameters k px 、k qy 、k rz 、h p 、h q 、h r 、k qx 、k rx 、k py 、k ry 、k pz and k qz ; Among them, [X c , Y c , Z c are the center coordinates of the standard sphere, R is the radius of the standard sphere, r is the radius of the tip of the three-coordinate scanning probe, and [X i , Y i , Z i are the theoretical measurement positions of the three-coordinate scanning probe when measuring the i-th sample point.

5. The multi-point calibration method based on a three-coordinate scanning probe according to claim 4, characterized in that, The theoretical measurement position [X p , Y p , Z p T of the three - coordinate scanning probe and the current deflection [d x , d y , d z T are used to calculate the actual measurement position [x p , y p , z p T , further comprising: The actual measurement position [x p , y p , z p T has the following calculation formula:

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