Shafting measurement device and shafting profile online reconstruction method based on hybrid four-point method

Abstract

The shaft system measurement device based on the hybrid four-point method and the shaft system profile online reconstruction method disclosed in the present invention use an improved four-point error separation technology to perform on multiple axial sections of the shaft to be measured through a directional and equidistant mobile fixed frame, extract the relative change of the center of each measured section, and then fit the spatial midline according to the center position of each section, and use the extracted spatial midline as the reference axis to combine the roundness errors separated from each section onto the axis, thereby realizing the profile reconstruction of the rotary shaft system, and further performing shape error assessment. The present invention can accurately separate the radial error motion and the tilt error motion of the rotary shaft system during the measurement process, thereby ensuring the accuracy of the reconstructed shaft system profile.

Description

Technical Field

[0001] The present invention belongs to the field of precision shaft system testing technology and online measurement equipment detection technology, and specifically relates to a shaft system measuring device based on a hybrid four-point method and a shaft system profile online reconstruction method. Background Art

[0002] As the core of high-precision machine tools, the operating state of precision rotating shaft systems directly affects the accuracy of mechanical processing. To study precision rotating shaft systems, we must first have a clear understanding and description of their spatial motion state. For machine tools, the deviation of the machine tool shaft will have an important impact on the processing accuracy, which will directly determine the shape and roughness of the processed parts. Therefore, the rotation accuracy has a direct impact on the operation of precision rotating shaft systems. It is a very important research method to accurately measure and extract the rotation error of precision shaft systems. Among the many form and position error detection items specified by the national standard, the detection of the cylindrical error of cylindrical workpieces is a very important component. At present, the main instruments used to measure cylindricality in my country are roundness meters, three-coordinate measuring machines, etc. These precision measuring instruments are relatively expensive, have high requirements for the measurement environment, and are difficult to meet online measurement needs.

[0003] In order to achieve precise measurement of the shape error of the precision rotating shaft system, it is almost impossible to continue to improve the accuracy of the measuring instrument. Therefore, many scholars at home and abroad have taken a different approach and studied higher-precision measurement methods. Cylindrical parts can be regarded as the superposition of countless cross-section circles along the axial direction. In theory, the cross-section method can be used to achieve online reconstruction of the cylinder, and the roundness errors on a limited number of cross sections are used to combine the error shape of the cylinder [Li Shengyi, Dai Yifan, etc. Precision and ultra-precision machining on-site detection and error separation technology [M]. National University of Defense Technology Press, 2007]. Error Separation Techniques (EST) is a basic method for precision measurement. Its basic idea is as follows: using the unique feature of the contour surface of the workpiece to be measured, multiple probes are used to measure the surface of the measured part. The measured signal will also contain the shape error of the measured part and the motion error of the measuring mechanism. A certain mathematical algorithm is used to separate the shape error of the measured part and the motion error of the measuring mechanism. Then, the shape error of the measured workpiece and the motion error of the measuring mechanism are obtained, thereby realizing the precise measurement of the shape error of the measured part [Gou Fuhua, Li Jishun, Zhang Luoping, etc. Design of high-precision cylindrical measurement system [J]. Journal of Luoyang Institute of Technology (Natural Science Edition), 2002, (1): 46-48]. The traditional three-point method has an inherent first-order harmonic suppression problem [Li Shengyi, Dai Yifan, etc. In-situ detection and error separation technology for precision and ultra-precision machining [M]. National University of Defense Technology Press, 2007], which makes it difficult to accurately separate the first-order harmonic components of the shaft system rotation error and shape error. Although it does not affect the evaluation of the cross-sectional roundness error, it implies the bending of the central axis of the cylinder, which makes it difficult to reconstruct the cylinder online and also affects the evaluation of the cylindricity. Therefore, this is also the key to the measurement of the shape error of shaft system parts. Summary of the invention

[0004] In order to solve the above technical problems, the present invention provides an axis system measurement device and an axis system profile online reconstruction method based on the hybrid four-point method, which can separate and remove the guide rail error, axis system motion error and tilt error introduced by the measurement system from the measured signal, thereby obtaining the accurate signal to be measured and ensuring the accuracy of the reconstructed cylinder.

[0005] The shaft system measuring device based on the hybrid four-point method of the present invention comprises: a motor, a guide rail mechanism, a sliding frame, a fixed frame, a first displacement sensor, a second displacement sensor, a third displacement sensor and a fourth displacement sensor; the guide rail mechanism comprises two parallel guide rails, the sliding frame is straddled on the two guide rails and can move along the guide rails, the fixed frame is installed on the top of the sliding frame, and a circular arc through hole is provided on the fixed frame; the output shaft of the motor is connected to one end of the shaft to be measured, and the other end of the shaft to be measured is penetrated in the through hole; the first displacement sensor, the second displacement sensor and the third displacement sensor are installed on the fixed frame and are located on a first plane, and the first plane is perpendicular to the axis of the shaft to be measured; the probes of the first displacement sensor, the second displacement sensor and the third displacement sensor are located in the through hole and on the same circumference concentric with the shaft to be measured, and the fourth displacement sensor is installed on the fixed frame, and the probe of the fourth displacement sensor and the probe of the first displacement sensor are located on a straight line parallel to the axis of the shaft to be measured.

[0006] The shafting profile online reconstruction method based on the hybrid four-point method of the present invention uses the shafting measurement device based on the hybrid four-point method described in claim 1 to collect data, and comprises:

[0007] Step 1: Divide the axis to be measured into L measurement sections with a spacing of d along the axial direction, move the sliding frame so that the first plane is aligned with the L sections respectively, and when the moving frame is positioned at the corresponding measurement section, the axis to be measured rotates one circle and the distance between the probe head and the axis surface is collected as measurement data by the first displacement sensor, the second displacement sensor, the third displacement sensor and the fourth displacement sensor:

[0008] Step 2: Perform discrete Fourier transform on the measurement data collected in step 1, and obtain the s-order harmonic component of the roundness profile of the measurement section aligned with the first plane by the cross-sectional three-point roundness error separation method, where s=0, 2, 3, ..., N-2, and N represents the total number of measurement points of each sensor; obtain the first-order harmonic component of the radial error separation result by the axial two-point method;

[0009] Step 3: Calculate the first-order harmonic component of the roundness profile of the L measurement sections on the measured axis:

[0010] Step 4: Fit the spatial centerline according to the first-order harmonic component of the roundness profile of the L measured sections, combine the profile shapes of each section onto the spatial centerline, and reconstruct the cylindrical profile of the shaft to be measured.

[0011] The shaft system measurement device based on the hybrid four-point method and the shaft system profile online reconstruction method of the present invention have at least the following beneficial effects:

[0012] 1. The online reconstruction method of the shafting profile based on the hybrid four-point method proposed in the present invention cooperates with the shafting measurement device to perform data measurement: specifically, four displacement sensors are used to measure the two axial sections and perform error separation, and the relative change of the centers of the two section circles is extracted. Since this relative change is an inherent characteristic between the two sections and will not change with the rotation of the shafting, the centers of the sections of the measured object are fitted to obtain the spatial centerline of the reconstructed cylinder. This technical theory is an innovation in the concept of error separation based on three-dimensional reconstruction of the cylinder.

[0013] 2. The present invention believes that the radial rotation error is not repeatable under the condition of one weekly rotation of the shaft system. By combining the three-point roundness error separation method with the axial two-point method, the cross-sectional roundness error, the radial error and tilt error caused by the shaft system rotation motion, and the guide rail error motion can be accurately separated during the error separation process. This is one of the innovations of the hybrid four-point method that distinguishes it from existing error separation methods.

[0014] 3. In the present invention, since the error motion caused by the rotation of the shaft system and the error motion of the guide rail can be accurately separated during the error separation process, there is no excessively high precision requirement for the guide rail in the measurement system, which greatly reduces the cost of online measurement of the shaft system. This is also the application value of the present invention.

[0015] 4. The measuring method of the present invention uses the roundness error on each cross section to combine the error shape of the cylinder based on the fitted space midline. Therefore, the cylinder shape error can be evaluated more comprehensively, including errors such as roundness, cylindricity, and generatrix straightness, and thus has a wider application.

[0016] In summary, the present invention obtains the roundness error of each section through the cross-sectional three-point roundness error separation method, extracts the relative change of the center of the two cross-sectional circles through the axial two-point method, and fits the center of each cross-sectional circle as the reference axis for reconstructing the cylinder, which solves the problem that the change of the cross-sectional circle center cannot be extracted due to first-order harmonic suppression. The roundness profiles of each section are combined with the fitted midline as the reference axis, realizing the innovation from evaluating the change of the roundness error of a single section to evaluating the change of the entire cylindrical profile error, and providing a more comprehensive shape error evaluation method. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 is a schematic diagram of a shaft system measurement device based on a hybrid four-point method according to an embodiment of the present invention;

[0018] Figure 2 is a top view of a shaft system measurement device based on a hybrid four-point method according to an embodiment of the present invention;

[0019] Figure 3 It is a flow chart of the method for online reconstruction of shafting profile based on the hybrid four-point method of the present invention;

[0020] Figure 4 The measurement principle diagram of the shaft system measurement device based on the hybrid four-point method of the present invention;

[0021] Figure 5 This is a schematic diagram of the impact of guide error motion and axis error motion on the measurement process. DETAILED DESCRIPTION

[0022] The shaft system measuring device based on the hybrid four-point method of the present invention comprises: a motor, a guide rail mechanism, a sliding frame 9, a fixed frame 8, a first displacement sensor 1, a second displacement sensor 2, a third displacement sensor 3 and a fourth displacement sensor 4. The guide rail mechanism comprises two parallel guide rails 10, the sliding frame 9 is straddled on the two guide rails 10 and can move along the guide rails 10, the fixed frame 8 is mounted on the top of the sliding frame 9, and a circular arc through hole is provided on the fixed frame 8. The output shaft of the motor is connected to one end of the shaft 5 to be measured, and the other end of the shaft 5 to be measured is penetrated in the through hole. The first displacement sensor 1, the second displacement sensor 2 and the third displacement sensor 3 are mounted on the fixed frame 8 and are located on a first plane, and the first plane is perpendicular to the axis of the shaft to be measured; the probes of the first displacement sensor 1, the second displacement sensor 2 and the third displacement sensor 3 are located in the through hole and on the same circumference concentric with the shaft to be measured, and the fourth displacement sensor 4 is mounted on the fixed frame 8, and the probe of the fourth displacement sensor 4 and the probe of the first displacement sensor 1 are located on a straight line parallel to the axis of the shaft to be measured. The guide rail 10 is provided with scale lines. The fixing frame 8 is provided with four sensor positioning holes, and the first displacement sensor 1, the second displacement sensor 2, the third displacement sensor 3 and the fourth displacement sensor 4 are arranged in the corresponding sensor positioning holes and fixed by set screws. The four sensors are located within 25 μm of the measured shaft surface. The angle between the first displacement sensor 1 and the second displacement sensor 2 is 60°, and the angle between the first displacement sensor 1 and the third displacement sensor 3 is 120°.

[0023] like Figure 1 and 2 As shown, in this embodiment, the rotary axis system of the electric spindle 7 is taken as an example. Due to the complex structure of the rotary axis system of the electric spindle, its rotary axis cannot be directly measured. In this embodiment, a connecting rod 6 is provided to respectively connect the electric spindle 7 and the axis to be measured 5, and the roundness error of the rotating axis of the electric spindle is detected by online reconstruction of the axis to be measured 5.

[0024] The fixed frame 8 can move in the Z direction along the guide rail 10 with the support of the sliding frame 9. The electric spindle 7 is connected to the axis 5 to be measured through the connecting rod 6 and drives the axis 5 to be measured to rotate. The guide rail 10 is parallel to the axis 5 to be measured. At the beginning of the measurement, the fixed frame 8 moves along the guide rail 10 in the Z direction to the axial end of the connecting rod 6 with the support of the sliding frame 9, so that the fixed frame 8 is located in the first measurement position, and the sliding frame 9 moves a distance d each time along the Z direction. In the specific implementation, the online reconstruction method of the shaft system profile based on the hybrid four-point method is used to obtain the roundness error of each section through the section three-point roundness error separation method, and the axial two-point method is used to extract the relative change of the center of the two sections, and the center of each section circle is fitted as the reference axis of the reconstructed cylinder, which solves the problem that the change of the center of the section circle cannot be extracted due to the first-order harmonic suppression, and the roundness error of each section is combined with the fitted midline as the reference axis, realizing the innovation from the change of the roundness of a single section to the change of the entire cylindrical profile, providing a more comprehensive shape error assessment method.

[0025] like Figure 3 The flowchart of the online reconstruction method of the shafting profile based on the hybrid four-point method is shown. The method uses the shafting measurement device based on the hybrid four-point method to collect data, and specifically includes:

[0026] Step 1: the measured shaft is divided into L measurement sections with a spacing of d along the axial direction, and the sliding frame is moved to align the first plane with the L sections respectively. When the moving frame is positioned at the corresponding section, the measured shaft rotates one circle and the distance between the probe and the shaft surface is collected as measurement data by the first displacement sensor, the second displacement sensor, the third displacement sensor and the fourth displacement sensor. Step 1 includes:

[0027] Step 1.1, arrange the first displacement sensor, the second displacement sensor and the third displacement sensor on the fixed frame according to the three-point roundness error separation method, so that the three sensors are located on the first plane, the fourth displacement sensor is located on the second plane, the first plane and the second plane are parallel and the distance is d,

[0028] Step 1.2, define the length direction of the guide rail as the Z-axis direction, the vertical direction as the Y-axis direction, the direction perpendicular to the Y-axis in the end face of the axis to be measured as the X-axis direction, the angle between the first displacement sensor and the X-axis is 0, the angle between the second displacement sensor and the first displacement sensor is β1, and the angle between the third displacement sensor and the first displacement sensor is β2, such as Figure 4 As shown;

[0029] Step 1.3, the measured shaft is divided into L measuring sections with a spacing of d along the axial direction; a positioning sequence P=1, 2, ..., L is defined; the positioning refers to the measuring section aligned with the first plane after the fixed frame moves a distance d from the end of the measured shaft along the Z-axis direction;

[0030] Step 1.4, initialize P=1;

[0031] Step 1.5, move the fixing frame along the Z-axis direction so that the first plane of the fixing frame is aligned with the Pth measuring section of the axis to be measured;

[0032] Step 1.6, the motor drives the axis to be measured to rotate one circle, and the first displacement sensor, the second displacement sensor and the third displacement sensor collect the measurement data of the axis to be measured rotating one circle on the Pth measurement section; the fourth displacement sensor collects the measurement data of the axis to be measured rotating one circle on the P+1th measurement section, and the measurement of the Pth position is completed;

[0033] Step 1.7, repeat steps 1.5 and 1.6 to perform the measurement of the P+1 position until the data measurement of the Lth position is completed, and the measurement data of L positions are obtained.

[0034] Step 2: Perform discrete Fourier transform on the measurement data collected in step 1, and obtain the s-order harmonic component of the roundness profile of the measurement section aligned with the first plane by the cross-sectional three-point roundness error separation method, where s=0, 2, 3, ..., N-2, and N represents the total number of measurement points of each sensor; obtain the first-order harmonic component of the radial error separation result by the axial two-point method. Step 2 includes:

[0035] Step 2.1: During the Pth position measurement, the measurement data collected by the first displacement sensor, the second displacement sensor and the third displacement sensor are m i (l P ,k), where i = 1, 2, 3, k = 0, 1, ..., N-1; N represents the total number of measurement points of each sensor, and the sampling angular interval is α = 2π / N, l P =P×d represents the axial positioning of the Pth measurement position of the axis to be measured; k represents the measurement point number of each sensor;

[0036] Step 2.2: Use the three-point roundness error separation method to extract the s-order harmonic component R(l P ,s),s=0,2,3...,N-2 represents the order of harmonic components;

[0037] The three-point roundness error separation method is used to perform weighted combination calculation on the measurement data collected by the first displacement sensor, the second displacement sensor, and the third displacement sensor as follows:

[0038]

[0039] Since the angle β1 between the first displacement sensor 1 and the X-axis is 0, the weighting coefficients of the outputs of the first displacement sensor 1, the second displacement sensor 2 and the third displacement sensor 3 are respectively: a1=1, a2=-sinβ2 / sin(β2-β1), a3=sinβ1 / sin(β2-β1), so that the radial motion error of the shaft system and the linear motion error of the guide rail in the weighted signal are removed to achieve the separation of the roundness error;

[0040] By performing discrete Fourier transform on equation (1), when the harmonic order s≠1, N-1, all s satisfy the condition of G(l,s)≠0, the roundness error of the measured section can be obtained by performing discrete Fourier inverse transform on the harmonic component R(l,s) of the roundness of the measured section, and applying the time delay and phase shift properties of Fourier transform, we can obtain:

[0041]

[0042] The transfer function is:

[0043]

[0044] In the formula, s (s = 0, 1, ..., N-1) is the order of the harmonic, G (l, s) is the transfer function of the three-point roundness error separation method; R (l, s) = DFT [r (l, k)] represents the s-order harmonic component of the roundness of the measured section. Substituting the weighted function coefficients into the error separation transfer function formula (3), its discrete form is:

[0045]

[0046] By selecting appropriate p1, p2 so that the greatest common divisor of p1, p2 and N is 1, except for s=1, N-1, the transfer function G(s)≠0 (s=0,2,…,N-2), the harmonic component r(l,k)=IFFT[R(l,s)] of the roundness profile of the measured section can be calculated.

[0047] Studies have confirmed that when the harmonic order s = 1 and s = N-1, the transfer function G(s) = 0, G(s-1) = 0, and the three-point error separation technology cannot effectively obtain the harmonic component R(l, s) of the roundness profile of the measured section, and thus cannot accurately obtain the roundness error r(l, k) of the measured section, which makes it difficult to separate the roundness error and rotation error of the shaft system. This is the so-called "first harmonic suppression". Therefore, the three-point roundness error separation method has an inherent first-order harmonic suppression problem. Although it has no effect on the error separation process, it has a very important impact on the evaluation of the bending change of the central axis of the cylinder, and also makes it difficult to reconstruct the cylinder online. Since the first-order harmonic component of the roundness profile of the measured section is the eccentricity error of the least squares center of the measured section, the eccentric coordinates of the measured section are calculated next, and then the eccentric vector of the roundness profile of the measured section, that is, the first-order harmonic component, is obtained.

[0048] Step 2.3: Perform discrete Fourier transform on the data collected by the first displacement sensor and the fourth displacement sensor in the measurement data of the Pth position, and obtain the first-order harmonic component of the radial error separation result by the axial two-point method, specifically:

[0049] At the Pth measurement position, the axis to be measured is rotated one circle, and the first displacement sensor and the fourth displacement sensor respectively collect data of the measurement section P and P+1 rotating one circle:

[0050]

[0051]

[0052] Where: r(l p ,k),r(l p+1 ,k)k=0,2,3…,N-2 are the roundness profiles of the Pth and P+1th positions of the axis to be measured respectively; ε x (l p , k) is the jitter caused by the X-direction error motion of the first displacement sensor at the Pth position without tilt error at the shaft end; d×β(l p , k) is the runout caused by the X-direction error motion of the first displacement sensor at the shaft end caused by the tilt error at the P+1th position; are the displacements in the X direction of the fixed frame caused by the axis to be measured at the Pth and P+1th measurement positions during the linear motion of the sliding frame; m1(l p ,k),m4(l p , k) respectively represent the measurement data collected by the first displacement sensor and the fourth displacement sensor at the Pth position when the measured shaft rotates one circle. Figure 5 The figure shows the influence of guide rail error motion and axis error motion on the measurement process.

[0053] It is necessary to explain here that, firstly, the first displacement sensor 1 is repeatedly used, which is respectively applied to the three-point roundness error separation method of the measured section and the two-point method of the axial direction, thereby reducing the number of sensors to alleviate the uncertainty effect caused by the large number of sensors in the error separation process; secondly, the first displacement sensor 1 is located at the shaft end, and the tilt error at the shaft end is zero, see Figure 2 .

[0054] By performing discrete Fourier transform on both sides of equations (5.1) and (5.2), the first-order harmonic component of the cross-sectional radial error separation result can be obtained:

[0055] M1(l p ,1)=R(l p ,1)+E x (l p ,1) (6.1)

[0056] M4(l p ,1)=R(l p+1 ,1)+E x (l p ,1)+d×Φ(1) (6.2)

[0057] In the formula, R(l p ,1)=DFT[r(l p ,1)] is the first-order harmonic component of the profile of the measurement section at the Pth position; E x (l p ,1)=DFT[ε x (l p ,1)] is the first-order harmonic component of the radial motion error of the measured section at the Pth position; d×Φ(1)=DFT[d×β(l p ,1)] is the first-order harmonic component of the X-axis motion error caused by the axis tilt error.

[0058] Since the offset signal of the fixed frame 8 in the X-axis direction caused by the axis 5 to be measured at the Pth and P+1th measurement positions during the linear motion of the guide rail 10 is a constant within one cycle, the first-order harmonic component of the constant is zero after discrete Fourier transformation, that is, Therefore, the linear motion error of the guide rail 10 is eliminated in equations (6.1) and (6.2).

[0059] Step 3: Calculate the first-order harmonic component of the roundness profile of L measurement sections on the measured axis. Step 3 includes:

[0060] Step 3.1, initialize P=1;

[0061] Step 3.2: The Fourier series form of the roundness profile of the measuring section of the measured axis at the Pth position can be expressed as formula (7):

[0062]

[0063] Where r0(α) is the DC harmonic component of the roundness profile of the measured cross section, which is also the radius of the measured cross section profile; r1=a1cosα+b1sinα is the first-order harmonic component R(l P ,1), (a1, b1) represents the eccentric coordinates of the center of the measured cross-sectional profile and the center of the least squares circle; is the harmonic component of the roundness profile of the measured section, that is, the roundness profile error of each section;

[0064] make Represents the known harmonic components, equation (7) can be written as:

[0065] r(α)=r1(α)+r2(α) (8)

[0066] Step 3.3, the measurement data of the first displacement sensor and the second displacement sensor are as follows:

[0067] m1(l,k)=r(l,k)+ε x (l,k) (9.1)

[0068] m2(l,k)=r(l,k+p1)+ε x (l,k)×cosβ1+ε y (l,k)×sinβ1 (9.2)

[0069] Its discrete form is as follows:

[0070]

[0071]

[0072] Wherein, k=0,1,...,N-1 represents the sample point of each sensor, N represents the total number of measurement points; α=2π / N is the sampling interval, which is the number of interval points between the first displacement sensor and the X-axis, that is, p1α is the angle between the first displacement sensor and the X-axis; p2=β2 / α(p2=0,1,...,N-1) is the number of interval points between the second displacement sensor and the X-axis;

[0073] Step 3.4: According to equations (10.1) and (10.2), we can get:

[0074] a1 cos(kα)+b1 sin(kα)+ε x (k) = m1(k) - r2(k) = h1 (11.1)

[0075]

[0076] In the formula, m1(k), m2(k) are the output signals of the first displacement sensor and the second displacement sensor after removing the 1st order harmonic component and the N-1th order harmonic component, which are known discrete sequences; r2(k), r2(k+p1) are the roundness error sequences of the three-point roundness errors of the first displacement sensor and the second displacement sensor after removing the 1st order harmonic component and the N-1th order harmonic component; the right sides of the equations are all known quantities, let the right side of equation (11.1) be h1, and the right side of equation (11.2) be h2;

[0077] The radial rotation error of the shaft system is represented by ε(k), and the components of the radial rotation error of the shaft system on the X and Y axes [ε x (k),ε y (k)] can be expressed as:

[0078] ε x (k)=ε(k)×cos(kα) (12.1)

[0079] ε y (k)=ε(k)×sin(kα) (12.2)

[0080] By combining equations (11.1), (11.2), (12.1) and (12.2) to eliminate the components of the radial rotation error of the shaft system on the XY axis in equations (12.1) and (12.2), we can obtain:

[0081] h2(k)cos(kα)-h1sin(kα)=b1cos(2kα)-a1sin(2kα) (13)

[0082] Step 3.5: To obtain the eccentric coordinates (a1, b1) between the center of the circle of the measured cross-sectional profile and the center of the least squares circle, multiply both sides of equation (13) by the trigonometric functions sin(2kα) and cos(2kα), respectively, and sum them within one measurement cycle. According to the orthogonality of trigonometric functions, we can obtain:

[0083]

[0084]

[0085] Step 3.6: The first-order harmonic component R(l) of the roundness profile of the measured section at the Pth position on the measured shaft 5 can be obtained according to the following formula: P ,1):

[0086] R(l P ,1)=r1(α)=a1cosα+b1cosα (15)

[0087] Step 3.7, move the sliding frame 9 so that the fixed frame 8 is located at the P+1 position of the axis to be measured 5, and repeat step 3.2 to obtain the first-order harmonic component R (l P+1 ,1);

[0088] Step 3.8, obtain the first-order harmonic component of the cylinder tilt error at the right section of the Pth position on the measured axis using the following formula:

[0089] d×Φ(1)=M4(l P ,1)-M1(l P ,1)-R(l P+1 ,1)+R(l P ,1) (16)

[0090] Step 3.9: When the measured body position 5 is measured at the P+1th position, the first-order harmonic component R(l) of the roundness profile of the measured cross section at the P+2th position is obtained according to formula (17). P+2 ,1):

[0091] R(l P+2 ,1)=M4(l P+1 ,1)-M1(l P+1 ,1)-d×Φ(1)+R(l P+1 ,1) (17)

[0092] Step 3.10: According to the N-1th order harmonic component R(l P+1 ,N-1) is the first-order harmonic component R(l P+1 , the conjugate complex number of 1) can obtain the N-1 order harmonic component of the roundness profile of the measured section of the measured axis 5 at the Pth position;

[0093] Step 3.11, assign P+1 to P, and repeat step 3.9 until the first-order harmonic component and the N-1th-order harmonic component of the roundness profile of the L measured cross-section are obtained.

[0094] It is worth noting here that it is only necessary to calculate the first-order harmonic component of the roundness profile of the measured cross-section at the Pth and P+1th measurements. Starting from the P+2th measurement, the first-order harmonic component of the roundness profile of the measured cross-section can be iteratively calculated according to formula (17).

[0095] Step 4: Fit the spatial center line according to the first-order harmonic components of the roundness profiles of the L measured cross-sections, combine the shapes of the cross-section profiles onto the spatial center line, and reconstruct the cylindrical profile. Step 4 includes:

[0096] Step 4.1: Use equation (18) to calculate the s-order harmonic component R(l P,s)(s=0,1,2,…,N-1) to perform inverse discrete Fourier transform and obtain the contour shape r(l P ,k):

[0097] r(l P ,k)=IDFT[R(l P ,s)],k=0,1,2,…,N-1 (18)

[0098] Step 4.2, after obtaining the harmonic components of the measured cross-sectional shapes of the L measured positions, repeat step 4.1 to obtain the cross-sectional contour shapes of the L measured positions;

[0099] Step 4.3: The center vector 2R(l P ,1) / N,P=1,2,…,L is fitted into a spatial centerline as the reference axis of the L measured sections, and the contour of the measured axis 5 is reconstructed, thereby realizing the shape error evaluation of the measured axis 5.

[0100] The above description is only a preferred embodiment of the present invention and is not intended to limit the concept of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. The online reconstruction method of shaft system profile based on the hybrid four-point method is characterized by: The following shaft system measurement device based on the hybrid four-point method is used for data acquisition, and the shaft system measurement device based on the hybrid four-point method includes: a motor, a guide rail mechanism, a sliding frame, a fixed frame, a first displacement sensor, a second displacement sensor, a third displacement sensor and a fourth displacement sensor; the guide rail mechanism includes two parallel guide rails, the sliding frame is straddled on the two guide rails and can move along the guide rails, the fixed frame is installed on the top of the sliding frame, and an arc-shaped through hole is provided on the fixed frame; the output shaft of the motor is connected to one end of the shaft to be measured, and the other end of the shaft to be measured is passed through the through hole; the first displacement sensor, the second displacement sensor and the third displacement sensor are installed on the fixed frame and Located on a first plane, the first plane is perpendicular to the axis of the shaft to be measured; the probes of the first displacement sensor, the second displacement sensor and the third displacement sensor are located in the through hole and on the same circumference concentric with the shaft to be measured, the fourth displacement sensor is installed on a fixing frame, and the probe of the fourth displacement sensor and the probe of the first displacement sensor are located on a straight line parallel to the axis of the shaft to be measured; the fixing frame is provided with 4 sensor positioning holes, the first displacement sensor, the second displacement sensor, the third displacement sensor and the fourth displacement sensor are arranged in the corresponding sensor positioning holes and fixed by a stop screw; the guide rail is provided with scale lines; the shaft system profile online reconstruction method comprises: Step 1: The shaft to be measured is divided into L measurement sections with a spacing of d along the axial direction, and the sliding frame is moved to align the first plane with the L sections respectively. When the moving frame is positioned at the corresponding measurement section, the shaft to be measured rotates one circle and the distance between the probe and the shaft surface is collected as measurement data by the first displacement sensor, the second displacement sensor, the third displacement sensor and the fourth displacement sensor; Step 2: Perform discrete Fourier transform on the measurement data collected in step 1, and obtain the s-order harmonic component of the roundness profile of the measurement section aligned with the first plane by the cross-sectional three-point roundness error separation method, where s=0, 2, 3, ..., N-2, and N represents the total number of measurement points of each sensor; obtain the first-order harmonic component of the radial error separation result by the axial two-point method; Step 3: Calculate the first-order harmonic component of the roundness profile of L measurement sections on the measured axis; Step 4: Fit the spatial centerline according to the first-order harmonic component of the roundness profile of the L measured sections, combine the profile shapes of each section onto the spatial centerline, and reconstruct the cylindrical profile of the shaft to be measured.

2. The method for online reconstruction of shafting profile based on the hybrid four-point method according to claim 1, characterized in that: Step 1 includes: Step 1.1, arranging the first displacement sensor, the second displacement sensor and the third displacement sensor on the fixed frame according to the three-point roundness error separation method, so that the three sensors are located on the first plane, the fourth displacement sensor is located on the second plane, the first plane and the second plane are parallel and the distance between them is d; Step 1.2, define the length direction of the guide rail as the Z-axis direction, the vertical direction as the Y-axis direction, the direction perpendicular to the Y-axis direction in the end face of the axis to be measured as the X-axis direction, the angle between the first displacement sensor and the X-axis is 0, the angle between the second displacement sensor and the first displacement sensor is β1, and the angle between the third displacement sensor and the first displacement sensor is β2; Step 1.3, the measured shaft is divided into L measuring sections with a spacing of d along the axial direction; a positioning sequence P=1, 2, ..., L is defined; the positioning refers to the measuring section aligned with the first plane after the fixed frame moves a distance d from the end of the measured shaft along the Z-axis direction; Step 1.4, initialize P=1; Step 1.5, move the fixing frame along the Z-axis direction so that the first plane of the fixing frame is aligned with the Pth measuring section of the axis to be measured; Step 1.6, the motor drives the axis to be measured to rotate one circle, and the first displacement sensor, the second displacement sensor and the third displacement sensor collect the measurement data of the axis to be measured rotating one circle on the Pth measurement section; the fourth displacement sensor collects the measurement data of the axis to be measured rotating one circle on the P+1th measurement section, and the measurement of the Pth position is completed; Step 1.7, repeat steps 1.5 and 1.6 to perform the measurement of the P+1 position until the data measurement of the Lth position is completed, and the measurement data of L positions are obtained.

3. The method for online reconstruction of shafting profile based on the hybrid four-point method according to claim 1, characterized in that: Step 2 includes: Step 2.1: During the Pth position measurement, the measurement data collected by the first displacement sensor, the second displacement sensor and the third displacement sensor are m i (l P ,k), where i = 1, 2, 3, k = 0, 1, ..., N-1; N represents the total number of measurement points of each sensor, and the sampling angular interval is α = 2π / N, l P =P×d represents the axial positioning of the Pth measurement position of the axis to be measured; k represents the measurement point number of each sensor; Step 2.2: Use the three-point roundness error separation method to extract the s-order harmonic component R(l P ,s),s=0,2,3K,N-2 represents the order of harmonic components; Step 2.3: Perform discrete Fourier transform on the data collected by the first displacement sensor and the fourth displacement sensor in the measurement data of the Pth position, and obtain the first-order harmonic component M1(l p ,1) and M4(l P ,1).

4. The method for online reconstruction of shafting profile based on the hybrid four-point method according to claim 3, characterized in that: The step 2.3 is specifically as follows: At the Pth measurement position, the axis to be measured is rotated one circle, and the first displacement sensor and the fourth displacement sensor respectively collect data of the measurement section P and P+1 rotating one circle: By performing discrete Fourier transform on both sides of equations (5.1) and (5.2), the first-order harmonic component of the cross-sectional radial error separation result can be obtained: M1(l p ,1)=R(l p ,1)+E x (l p ,1) (6.1) M4 (l p ,1)=R(l p+1 ,1)+Ε x (l p ,1)+d×Φ(1) (6.2) In the formula, R(l p ,1)=DFT[r(l p ,1)] is the first-order harmonic component of the profile of the measurement section at the Pth position; E x (l p ,1)=DFT[ε x (l p ,1)] is the first-order harmonic component of the radial motion error of the measured section at the Pth position; d×Φ(1)=DFT[d×β(l p ,1)] is the first-order harmonic component of the X-axis motion error caused by the axis tilt error.

5. The method for online reconstruction of shafting profile based on hybrid four-point method according to claim 1, characterized in that: Step 3 includes: Step 3.1, initialize P=1; Step 3.2: The Fourier series form of the roundness profile of the measuring section of the measured axis at the Pth position can be expressed as formula (7): Where r0(α) is the DC harmonic component of the roundness profile of the measured cross section, which is also the radius of the measured cross section profile; r1=a1cosα+b1sinα is the first-order harmonic component R(l P ,1), (a1, b1) represents the eccentric coordinates of the center of the measured cross-sectional profile and the center of the least squares circle; is the harmonic component of the roundness profile of the measured section, that is, the roundness profile error of each section; make Representing the known harmonic components, equation (7) can be written as: r(α)＝r1(α)+r2(α) (8) Step 3.3, the measurement data of the first displacement sensor and the second displacement sensor are as follows: m1(l,k)=r(l,k)+ε x (l,k) (9.1) m2(l,k)=r(l,k+p1)+ε x (l,k)×cosβ1+ε y (l,k)×sinβ1 (9.2) Its discrete form is as follows: Wherein, k = 0, 1, K, N-1 represents the sampling point of each sensor, N represents the total number of measurement points; α = 2π / N is the sampling interval, p1 = β1 / α (p1 = 0, 1, K, N-1) is the number of interval points between the first displacement sensor and the X-axis, that is, p1α is the angle between the first displacement sensor and the X-axis; p2 = β2 / α (p2 = 0, 1, K, N-1) is the number of interval points between the second displacement sensor and the X-axis; Step 3.4: According to equations (10.1) and (10.2), transform and name the right sides of equations (11.1) and (11.2) as h1 and h2, we can know: a1cos(ka)+b1 sin(ka)+e x (k)=m1(k)-r2(k)=h1 (11.1) Step 3.5: The eccentric coordinates (a1, b1) of the center of the circle of the measured cross-sectional profile and the center of the least squares circle can be obtained by calculation: Step 3.6: The first-order harmonic component R(l) of the roundness profile of the measuring section at the Pth position on the axis to be measured can be obtained according to the following formula: P ,1): R(l P ,1)=r1(α)=a1cosα+b1cosα (15) Step 3.7, move the sliding frame so that the first plane is located at the P+1th measurement position of the axis to be measured, and repeat step 3.2 to obtain the first-order harmonic component R(l P+1 ,1); Step 3.8, combine formulas 6.1 and 6.2 to obtain the first-order harmonic component of the cylinder tilt error at the second plane of the Pth position on the measured axis: d×Φ(1)=M4(l P ,1)-M1(l P ,1)-R(l P+1 ,1)+R(l P ,1) (16) Step 3.9: When the axis to be measured is measured at the P+1 position, the first-order harmonic component R(l) of the roundness profile of the measured section at the P+2 position is obtained according to formula (17). P+2 ,1): R(l P+2 ,1)=M4(l P+1 ,1)-M1(l P+1 ,1)-d×Φ(1)+R(l P+1 ,1) (17) Step 3.10: According to the N-1th order harmonic component R(l P+1 ,N-1) is the first-order harmonic component R(l P+1 , the conjugate complex number of 1) can obtain the N-1 order harmonic component of the roundness profile of the measuring section at the Pth measuring position of the axis to be measured; Step 3.11, assign P+1 to P, and repeat step 3.9 until the 1st-order harmonic component and the N-1th-order harmonic component of the roundness profile of the measurement section at L positions are obtained.

6. The method for online reconstruction of shafting profile based on the hybrid four-point method according to claim 1, characterized in that: Step 4 includes: Step 4.1: Use equation (18) to calculate the s-order harmonic component R(l P ,s)(s=0,1,2,L,N-1) to perform inverse discrete Fourier transform and obtain the contour shape r(l P ,k): r(l P ,k)=IDFT[R(l P ,s)],k=0,1,2,L,N-1 (18) Step 4.2, after obtaining the harmonic components of the measured cross-sectional shapes of the L measured positions, repeat step 4.1 to obtain the cross-sectional contour shapes of the L measured positions; Step 4.3: The center vector 2R(l P ,1) / N,P=1,2,L,L is fitted into a spatial centerline as the reference axis of L measurement sections to reconstruct the contour of the axis to be measured, thereby realizing the shape error evaluation of the axis to be measured.

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