Self-calibration measurement method for workpiece straightness based on Fourier three-point method

Abstract

The present invention discloses a self-calibration measurement method for workpiece straightness based on Fourier three-point method. The method first installs three displacement sensors at different positions, measures the displacement signal of the workpiece surface, calculates the height difference between the second and third sensors, and compensates the third sensor signal. After that, the Fourier three-point method is used to calculate the Fourier estimation value and transfer determinant of each harmonic of the workpiece straightness. Then, the position of the first sensor is changed, and the Fourier three-point method measurement is performed multiple times. The optimal Fourier coefficient estimation value is selected according to the maximum value of the transfer determinant. Finally, the workpiece straightness is calculated from the optimal Fourier coefficient estimation value. The present invention can avoid manual adjustment that is time-consuming and cumbersome and difficult to ensure accuracy, reduce the adjustment cost, and has simple operation, high repeatability, and easy to implement operation method.

Description

Technical Field

[0001] The invention relates to measurement technology, and in particular to a workpiece straightness self-calibration measurement method based on Fourier three-point method. Background Art

[0002] For the sliding guide rail module, the straightness of the guide rail will directly affect the movement accuracy, friction and wear, and service life of the module. To ensure the yield of the chip, the silicon wafer needs to have almost perfect flatness / straightness. However, due to the errors of the processing machine tools themselves, these workpieces inevitably have straightness errors. Error compensation is one of the effective measures to improve the accuracy of straight / plane processing. In order to achieve this goal, first of all, the accurate measurement of the straightness of the workpiece must be completed.

[0003] In-situ measurement can effectively avoid the repeated disassembly and assembly required for offline measurement, as well as the clamping errors and lengthy installation and calibration time that are introduced. However, after in-situ measurement, the sensor signal not only contains the straightness error of the workpiece, but also couples the motion error of the machine tool table. Therefore, in order to achieve accurate in-situ measurement of the straightness of the workpiece, a self-calibration measurement method must be used: separating the motion error of the table from the straightness error of the workpiece.

[0004] At present, the commonly used straightness error separation methods are: continuous two-point method, continuous three-point method, Fourier two-point method and Fourier three-point method. Among them, the Fourier three-point method can solve the measurement problem caused by the non-periodicity of the contour curve in the straightness error separation, and therefore has a good application prospect. Figure 1 As shown, three displacement sensors are installed on the fixture, and the worktable moves randomly while measuring the displacement signal on the workpiece surface. The signal P3 of the third sensor is spliced ​​with the signal of the second sensor P2 to form a spliced ​​signal. The spliced ​​signal and the signal of the first sensor P1 are subtracted to eliminate the error motion of the machine tool worktable, and then the Fourier transform method is used to calculate the straightness of the workpiece.

[0005] However, the measurement accuracy of the existing Fourier three-point method is still restricted by the following two factors: First, the sensor height difference. When using the Fourier three-point method, the signals of the second and third sensors need to be spliced. However, the sensor height difference will cause a step deviation in the second half of the spliced ​​signal (the third sensor signal part), and ultimately cause a non-negligible deviation in the measurement result. Second, the problem of sensitive harmonics. In the Fourier three-point method, the measurement accuracy of individual harmonics is easily affected by sensor noise, that is, for these sensitive harmonics, very small sensor noise can cause a large harmonic measurement deviation. Summary of the invention

[0006] The purpose of the present invention is to overcome the shortcomings of the above prior art and provide a workpiece straightness self-calibration measurement method based on the Fourier three-point method. This workpiece straightness self-calibration measurement method based on the Fourier three-point method can eliminate the step deviation of the splicing signal caused by the sensor height difference and improve the measurement accuracy.

[0007] The purpose of the present invention is achieved through the following technical solution: The workpiece straightness self-calibration measurement method based on the Fourier three-point method comprises the following steps:

[0008] S1. Collect displacement signals: Let the three displacement sensors be P1, P2 and P3, P1, P2 and P3 are all installed in the same fixture, and P1 is between P2 and P3, where the distance between P1 and P2 is d, the distance between P2 and P3 is L, and the distance between P3 and P1 is Ld; in the coordinate system, let the positions of P1, P2 and P3 be 0, d and dL respectively, let P1 move from 0 to the X-axis direction in the coordinate system by a distance x, 0≤x≤L, then the displacement signals collected by the three displacement sensors are: m1(θ), m2(θ) and m3(θ):

[0009] m1(θ)=A1+f(θ)+g(θ), which is formula (1);

[0010]

[0011] Where θ is the equivalent angle of the P1 sensor moving coordinate x, Then 0≤θ<2π; f(θ) is the straightness of the workpiece; g(θ) is the error motion of the worktable; A1, A2, A3 are the initial readings of P1, P2, P3 respectively;

[0012] S2. Calculate the inclination slope of the workpiece: Taking the guide rail as the reference and parallel to the X-axis, g(0)=g(2π)=0, f(0)=0≠f(2π)=2πk, and then calculate the inclination slope of the workpiece using the displacement signal collected by P1:

[0013]

[0014] S3. Determine the sensor height difference: The difference between the signals of the two displacement sensors P2 and P3 at the joint is equal to the height difference Δ of the two displacement sensors h and 2πk, then:

[0015]

[0016] S4, Correction signal: Use the displacement signal of P3 plus Δ h , to compensate for the difference in sensor height between P2 and P3 to obtain a correction signal:

[0017] m′3(θ)=m3(θ)+Δ h , which is formula (6);

[0018] S5, splicing signal: After splicing the correction signal m′3(θ) to the displacement signal m2(θ) of P2, a splicing signal m is formed. r2 (θ):

[0019]

[0020] S6. Determine the straightness of the workpiece:

[0021] S6-1: For m1(θ) and m r2 (θ) is subtracted to eliminate the error motion of the worktable:

[0022]

[0023] Among them, m(θ) is the weight function;

[0024] S6-2: Perform Laplace transform on the weight function m(θ):

[0025]

[0026] Among them, F(s) and M(s) are the Laplace transforms of the workpiece straightness f(θ) and the weight function m(θ), respectively;

[0027] S6-3: Based on formula (9), the pull-type transformation of the workpiece straightness is obtained:

[0028]

[0029] S6-4: Let s = jω, and obtain the harmonic Fourier coefficient of the workpiece straightness:

[0030]

[0031] Among them, F(jω) and M(jω) are the Fourier coefficients of the workpiece straightness f(θ) and the weight function m(θ), ω is the harmonic order, j is the imaginary unit, and the transfer function is

[0032] S6-5. Perform inverse Fourier transform on formula (11) to obtain the straightness f(θ) of the workpiece:

[0033] f(θ)=F -1 [F(jω)], which is formula (12);

[0034] S7, repeat steps S1 to S6, and adjust the distance d between P1 and P2 each time, and calculate the transfer determinant and the Fourier coefficient of the workpiece straightness; according to the maximum value of the transfer determinant, select the optimal Fourier coefficient estimate for each harmonic, which is recorded as the hybrid Fourier coefficient F hybri (jω), and then the hybrid Fourier coefficient F hybrid (jω) performs inverse Fourier transform to calculate the final workpiece straightness.

[0035] Preferably, the specific process of step S7 is as follows:

[0036] S7-1. Repeat steps S1 to S6 n times, where n is a natural number. When the i-th measurement is repeated, the measurement number is recorded as i, and the distance between P1 and P2 is adjusted to d. i , and calculate the Fourier coefficient F of the workpiece straightness i (jω) and the transfer function T i (jω), where i = 1, 2, …, n;

[0037] S7-2 uses the transfer function T i (jω), calculate the determinant of the transfer matrix |W i (ω)|;

[0038] S7-3. Calculate the transfer determinant |W for each harmonic i The maximum value of (ω)| is obtained to obtain the corresponding measurement number m, and the Fourier coefficient calculated by the Fourier three-point method is used as the optimal Fourier coefficient estimate of the harmonic, which is recorded as the hybrid Fourier coefficient F hybrid (jω):

[0039] F hybr (jω)=F(jω) m

[0040] m=argmax{|W1(ω)|,|W2(ω)|,…,|W i (ω)|,…,|W n (ω)|}, this is formula (13);

[0041] S7-4, by the hybrid Fourier coefficient F hybrid (jω) performs inverse Fourier transform to calculate the final workpiece straightness.

[0042] Preferably, the specific steps of step S7-2 are as follows:

[0043] S7-2-1. According to the fact that the Fourier coefficient of the workpiece straightness has a real part and an imaginary part, the transfer function T can be obtained by using formula (10). i (jω) is rewritten as the transfer matrix Wi (ω):

[0044]

[0045] Among them, Re and Im are functions for finding the real part and imaginary part of the Fourier coefficient respectively.

[0046] S7-2-2. Substitute the Euler formula into formula (14) and calculate to obtain the determinant of the transfer matrix |W i (ω)|:

[0047]

[0048] Preferably, in step S1, when the three displacement sensors are installed on the same fixture, the three displacement sensors are arranged in a row and on the same plane.

[0049] The present invention has the following advantages over the prior art:

[0050] 1. The present invention can calculate the sensor height difference through the sensor signal and compensate the sensor height. Therefore, it can avoid time-consuming and cumbersome manual adjustment with difficult accuracy guarantee, reduce the adjustment cost, and has simple operation, high repeatability and easy implementation.

[0051] 2. The present invention improves the measurement accuracy of the workpiece straightness by calculating the most accurate Fourier coefficient estimation value of each harmonic through the transfer matrix |W(ω)| with the largest determinant. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 It is a schematic diagram of the layout of three displacement sensors in the existing Fourier three-point method test.

[0053] Figure 2 It is a schematic diagram of the Fourier three-point method test of the present invention.

[0054] Figure 3a It is the sensor signal before the displacement sensor height difference compensation.

[0055] Figure 3b It is the sensor signal after the height difference of the displacement sensor of the present invention is compensated.

[0056] Figure 4 It is the spatial domain measurement result of the displacement sensor of the present invention before and after height difference compensation.

[0057] Figure 5a It is the spatial domain measurement result after the height difference compensation of the displacement sensor of the present invention.

[0058] Figure 5b It is the frequency domain measurement result after the height difference compensation of the displacement sensor of the present invention.

[0059] Figure 6 It is the transfer determinant |W(ω)| at different values of the distance d between P1 and P2 of the present invention.

[0060] Figure 7a It is the measurement result in the spatial domain after frequency-domain hybridization of the present invention.

[0061] Figure 7b It is the measurement result in the frequency domain after frequency-domain hybridization of the present invention. Detailed implementation manners

[0062] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0063] As Figure 2 shown, the workpiece straightness self-calibration measurement method based on the Fourier three-point method includes the following steps:

[0064] S1. Collect displacement signals: Let the three displacement sensors be P1, P2, and P3 respectively. P1, P2, and P3 are all installed on the same fixture. The three displacement sensors are arranged in a row in the XOZ plane of the coordinate system. P1 is between P2 and P3. The distance between P1 and P2 is d. At this time, d = 34.10 mm, and the distance between P2 and P3 is L. Then, the distance between P3 and P1 is L - d, that is, 65.90 mm. In the coordinate system, let the positions of P1, P2, and P3 be the 0 position, the d position, and the d - L position respectively. Let P1 move x distance in the X-axis direction of the coordinate system from the 0 position, 0 ≤ x < L. In this embodiment, L = 100 mm, that is, as Figure 1 shown, P1 moves 100 mm in the X-axis direction in the coordinate axis, and P2 and P3 installed on the same fixture also move 100 mm in the X-axis direction at the same time.

[0065] Then the displacement signals collected by the three displacement sensors are respectively: m1(θ), m2(θ), and m3(θ):

[0066] m1(θ) = A1 + f(θ) + g(θ), this is Equation (1);

[0067]

[0068] Among them, θ is the equivalent angle of the moving coordinate x of the P1 sensor, then 0 ≤ θ < 2π; f(θ) is the straightness of the workpiece; g(θ) is the error motion of the workbench; A1, A2, and A3 are the initial readings of P1, P2, and P3 respectively;

[0069] S2. Calculate the inclination slope of the workpiece: Taking the guide rail as the reference and parallel to the X-axis, g(0)=g(2π)=0, f(0)=0≠f(2π)=2πk, and then calculate the inclination slope of the workpiece using the displacement signal collected by P1:

[0070]

[0071] S3, determine the sensor height difference: the signals of the two displacement sensors P2 and P3 are at the joint The difference is equal to the height difference Δ of the two displacement sensors h and 2πk, then:

[0072]

[0073] S4, Correction signal: Use the displacement signal of P3 plus Δ h , to compensate for the sensor height difference between P2 and P3, and obtain the correction signal:

[0074] m′3(θ)=m3(θ)+Δ h , which is formula (6);

[0075] S5, splicing signal: modify the corrected signal m′3(θ) Part of the displacement signal m2(θ) spliced ​​to P2 After the parts are combined, the spliced ​​signal m is formed. r2 (θ):

[0076]

[0077] At this time, the signal before the sensor height difference compensation is as follows Figure 3a As shown, the signal after the sensor height difference is compensated by the present invention is as follows Figure 3b As shown;

[0078] S6. Determine the straightness of the workpiece:

[0079] S6-1: For m1(θ) and m r2 (θ) is subtracted to eliminate the error motion of the worktable:

[0080]

[0081] Among them, m(θ) is the weight function;

[0082] S6-2: Perform Laplace transform on the weight function m(θ):

[0083]

[0084] Among them, F(s) and M(s) are the Laplace transforms of the workpiece straightness f(θ) and the weight function m(θ), respectively;

[0085] S6-3: Based on formula (9), the pull-type transformation of the workpiece straightness is obtained:

[0086]

[0087] S6-4: Let s = jω, and obtain the harmonic Fourier coefficient of the workpiece straightness:

[0088]

[0089] Among them, F(jω) and M(jω) are the Fourier coefficients of the workpiece straightness f(θ) and the weight function m(θ), ω is the harmonic order, j is the imaginary unit, and the transfer function is

[0090] S6-5. Perform inverse Fourier transform on formula (11) to obtain the straightness f(θ) of the workpiece:

[0091] f(θ)=F -1 [F(jω)], which is formula (12);

[0092] At this time, the traditional Fourier three-point method is used to calculate the workpiece straightness before compensating the sensor height difference. Figure 4 As shown by the dotted line in FIG. 1 , the embodiment of the present invention uses the traditional Fourier three-point method to calculate the straightness of the workpiece after compensating the height difference of the sensor, as shown in FIG. Figure 4 The thin solid line in

[0093] S7, repeat steps S1 to S6, and adjust the distance d between P1 and P2 each time, and calculate the transfer determinant and the Fourier coefficient of the workpiece straightness; according to the maximum value of the transfer determinant, select the optimal Fourier coefficient for each harmonic, which is recorded as the hybrid Fourier coefficient F hybrid (jω), and then the hybrid Fourier coefficient F hyb (jω) performs inverse Fourier transform to calculate the straightness of the workpiece after frequency domain hybridization.

[0094] The specific process of step S7 is as follows:

[0095] When repeating the i-th measurement, record the measurement number as i and adjust the distance between P1 and P2 to d i , and calculate the Fourier coefficient F of the workpiece straightness i (jω) and the transfer function T i (jω), where i = 1, 2, …, n;

[0096] S7-1. Repeat steps S1 to S6 n times, where n is a natural number, and when repeating for the i-th time, let the distance d between P1 and P2 be d i ; Specifically, in this embodiment, n=3, that is, the number of steps S1 to S6 is repeated 2 times; plus the embodiment of S1 to S6, the measurement mark of the current measurement is numbered as i, and the Fourier coefficient F of the straightness of the workpiece is calculated i (jω) and the transfer function T i (jω), where i = 1, 2, ..., n; when repeated twice, the distance d takes the values ​​of 48.50 mm and 78.60 mm respectively; at this time, the straightness of the workpiece calculated after compensating the height difference of the sensor in the embodiment of the present invention is as follows Figure 5a As shown by the thin line in the figure; the Fourier coefficient of the workpiece straightness is calculated after compensating the height difference of the sensor in the embodiment of the present invention as shown in Figure 5b As shown by the thin lines in

[0097] S7-2. Using the transfer function T i (jω), calculate the determinant of the transfer matrix |W i (ω)|:

[0098] The specific process of step S7-2 is as follows:

[0099] S7-2-1. According to the fact that the Fourier coefficient of the workpiece straightness has a real part and an imaginary part, the transfer function T can be obtained by using formula (10). i (jω) is rewritten as the transfer matrix W i (ω):

[0100]

[0101] Among them, Re and Im are functions for finding the real part and imaginary part of the Fourier coefficient respectively.

[0102] S7-2-2. Substitute the Euler formula into formula (13) and calculate to obtain the determinant of the transfer matrix |W i (ω)|:

[0103]

[0104] At this time, the transfer determinant |W(ω)| calculated by the embodiment of the present invention is as follows Figure 6 Shown by thin line.

[0105] S7-3. Calculate the transfer determinant |W for each harmonic i The maximum value of (ω)| is obtained to obtain the corresponding measurement number m, and the Fourier coefficient calculated by the Fourier three-point method is used as the optimal Fourier coefficient estimate of the harmonic, which is recorded as the hybrid Fourier coefficient F hybrid (jω):

[0106] F hybrid (jω)=F(jω) m

[0107] m=argmax{|W1(ω)|,|W2(ω)|,…,|W i (ω)|,…,|W n (ω)|}, this is formula (13);

[0108] S7-4, by the hybrid Fourier coefficient F hybrid (jω) performs inverse Fourier transform to calculate the final workpiece straightness. At this time, the workpiece straightness calculated by the present invention is as follows: Figure 7a As shown by the dotted line in FIG. 1 , the Fourier coefficients of each harmonic of the workpiece straightness calculated by the present invention are as follows: Figure 7b The midpoint is shown by the dashed line.

[0109] Depend on Figure 3a and 3b It can be seen that due to the height difference between the P2 and P3 sensors, before the sensor height difference is compensated, the splicing signal has a step deviation of 37.4 μm at the splicing point. After the height difference is compensated by the present invention, the step deviation of the splicing signal at the splicing point is reduced to 0 μm. Figure 4 It can be seen that after compensating for the height difference between the P2 and P3 sensors, the measurement accuracy of the Fourier three-point method is improved.

[0110] Depend on Figure 5a It can be seen that after compensating for the height difference of the sensor, the workpiece straightness calculated by the Fourier three-point method has a large measurement deviation of some sensitive harmonics, resulting in a large fluctuation error in the calculation result of the workpiece straightness. The present invention uses the maximum transfer function value ( Figure 6 The bold line shows the Fourier coefficients calculated by the Fourier three-point method (as shown in Figure 5b The best Fourier coefficient estimate is selected (shown by the thin line in the middle). The selected results are shown in Figure 7b As shown by the dotted line in the figure, the influence of sensitive harmonic error on the Fourier three-point method is eliminated, so the measurement accuracy of the workpiece straightness is improved (such as Figure 7b midpoint dashed line).

[0111] The above specific implementation modes are preferred embodiments of the present invention and cannot be used to limit the present invention. Any other changes or other equivalent replacement methods that do not deviate from the technical solution of the present invention are included in the protection scope of the present invention.

Claims

1. A self-calibration measurement method for workpiece straightness based on the Fourier three-point method, characterized in that: Including the following steps: S1. Collect displacement signals: Let the three displacement sensors be P1, P2, and P3 respectively. P1, P2, and P3 are all installed on the same fixture, and P1 is between P2 and P3. The distance between P1 and P2 is d, the distance between P2 and P3 is L, and the distance between P3 and P1 is L - d. In the coordinate system, let the positions of P1, P2, and P3 be the 0 position, the d position, and the d - L position respectively. Let P1 move x distance in the X-axis direction from the 0 position, where 0 ≤ x < L. Then the displacement signals collected by the three displacement sensors are: m1(θ), m2(θ), and m3(θ): m1(θ) = A1 + f(θ) + g(θ), this is Equation (1); Where θ is the equivalent angle of the P1 sensor moving coordinate x, 0≤θ<2π; f(θ) is the straightness of the workpiece; g(θ) is the error motion of the worktable; A1, A2, A3 are the initial readings of P1, P2, P3 respectively; S2. Calculate the inclination slope of the workpiece: Taking the guide rail as the reference and parallel to the X-axis direction, then g(0) = g(2π) = 0, f(0) = 0 ≠ f(2π) = 2πk. Then, based on the displacement signal collected by P1, calculate the inclination slope of the workpiece: S3. Calculate the sensor height difference: The difference between the signals of the two displacement sensors P2 and P3 at the joint is equal to the height difference Δ of the two displacement sensors h and 2πk, then: S4, Correction signal: Use the displacement signal of P3 plus Δ h , to compensate for the sensor height difference between P2 and P3, and obtain the correction signal: m′3(θ)=m3(θ)+Δ h , which is formula (6); S5, splicing signal: After splicing the correction signal m′3(θ) to the displacement signal m2(θ) of P2, a splicing signal m is formed. r2 (θ): S6. Determine the straightness of the workpiece: S6-1: For m1(θ) and m r2 (θ) is subtracted to eliminate the error motion of the worktable: where, m(θ) is the weight function; S6-2: Perform Laplace transform on the weight function m(θ): This is formula (9); where, F(s) and M(s) are the Laplace transforms of the workpiece straightness f(θ) and the weight function m(θ) respectively; S6-3: Based on Equation (9), obtain the Laplace transform formula of the workpiece straightness: This is formula (10); S6-4: Let s = jω to obtain the Fourier transform formula of the workpiece straightness: This is formula (11); Among them, F(jω) and M(jω) are the Fourier coefficients of the workpiece straightness f(θ) and the weight function m(θ), ω is the harmonic order, j is the imaginary unit, and the transfer function is S6-5. Perform inverse Fourier transform on Equation (11) to obtain the straightness f(θ) of the workpiece: f(θ)=F -1 [F(jω)], which is formula (12); S7, repeat steps S1 to S6, and adjust the distance d between P1 and P2 each time, and calculate the transfer determinant and the Fourier coefficient of the workpiece straightness; according to the maximum value of the transfer determinant, select the optimal Fourier coefficient for each harmonic, which is recorded as the hybrid Fourier coefficient F hybrid (jω), and then the hybrid Fourier coefficient F hybri (jω) performs inverse Fourier transform to calculate the straightness of the workpiece in the frequency domain hybridization.

2. The workpiece straightness self-calibration measurement method based on the Fourier three-point method according to claim 1 is characterized in that: The specific process of step S7 is as follows: S7-1. Repeat steps S1 to S6 n times, where n is a natural number. When the i-th measurement is repeated, the measurement number is recorded as i, and the distance between P1 and P2 is adjusted to d. i , and calculate the Fourier coefficient F of the workpiece straightness i (jω) and the transfer function T i (jω), where i = 1, 2, …, n; S7-2. According to the transfer function T i (jω), and calculate the determinant of the transfer matrix |W i (ω)|: S7-3. Calculate the transfer determinant |W for each harmonic i The maximum value of (ω)| is used to obtain the corresponding measurement number i, and the Fourier coefficient calculated by the Fourier three-point method is used as the optimal Fourier coefficient estimate of the harmonic, which is recorded as the hybrid Fourier coefficient F hybrid (jω): F hybri (jω)=F(jω) m m=argmax{|W1(ω)|,|W2(ω)|,…,|W i (ω)|,…,|W n (ω)|}, this is formula (13); S7-4, by the hybrid Fourier coefficient F hybrid (jω) performs inverse Fourier transform to calculate the final workpiece straightness.

3. The workpiece straightness self-calibration measurement method based on the Fourier three-point method according to claim 2 is characterized in that: The specific steps of S7-2 are as follows: S7-2-1. According to the fact that the Fourier coefficient of the workpiece straightness has a real part and an imaginary part, the transfer function T can be obtained by using formula (10). i (jω) is rewritten as the transfer matrix W i (ω): where, Re and Im are the functions for finding the real part and the imaginary part of the Fourier coefficients respectively; S7-2-2. Substitute the Euler formula into formula (14) and calculate to obtain the determinant of the transfer matrix |W i (ω)|:

4. The method for self-calibration of workpiece straightness based on Fourier three-point method according to claim 1 is characterized in that: In step S1, when the three displacement sensors are installed on the same fixture, the three displacement sensors are arranged in a row and in the same plane.

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