Low-cost high-precision centroid measuring device and method

Abstract

The invention discloses a low-cost high-precision mass center measuring device and method. The device comprises a fixed base, a weighing sensor assembly, a movable frame, a front bracket, a rear bracket, a driving roller assembly, a front driven roller, a rear driven roller, a front hoop and a rear hoop. The fixed base is fixed on the ground; the weighing sensor assembly is mounted on the fixed base; the movable frame is arranged on the weighing sensor assembly; the front bracket and the rear bracket are mounted on the movable frame; the front and rear driven rollers are mounted at the tops of the front and rear brackets; the driving roller assembly is mounted on the front bracket and the rear bracket; and the front and rear hoops are arranged on the front and rear brackets. The method comprises five parts of coordinate system establishment, sensor reading, mass calculation, centroid calculation and centroid fitting. According to the invention, mass center measurement of a large-scale rotary body product is realized, and the method has the advantages of high measurement precision, low cost and the like.

Description

Technical Field

[0001] This invention belongs to the field of centroid measurement technology, and particularly relates to a low-cost, high-precision centroid measurement device and method. Background Technology

[0002] The research and development of large rotating products requires the measurement of the center of mass. These products are characterized by large size, heavy weight, small batch size, and many specifications.

[0003] In measuring the center of mass of rotating products, the product under test needs to rotate under the drive of two sets of rollers, one at the front and one at the back. For rotating products of standard sizes, the requirement for the synchronization of the front and rear roller rotations is not very high. However, when measuring large rotating products with a diameter exceeding 1 meter and a length exceeding 5 meters, even slight asynchrony in the rotation of the front and rear rollers can cause significant and visible interference to the measurement results. Furthermore, due to the small batch size and diverse specifications of large rotating products, there are certain requirements for cost control of the measuring equipment.

[0004] Currently common centroid measurement devices, such as the high-precision centroid measurement device for large-mass eccentric workpieces disclosed in Chinese patent CN106908199B, are designed for rotating products of standard dimensions. However, this solution fails to address the synchronization issue of the front and rear rollers, making it unsuitable for large rotating products. Furthermore, this approach uses multiple sets of sensors with different ranges for repeated measurements to improve accuracy, making it relatively expensive for measuring large rotating products with small batches and diverse specifications. Another example is the split-type measurement mechanism disclosed in Chinese patent CN101846542B for measuring the mass and three-dimensional centroid of an object. This split-type structure cannot solve the problem of front-to-back synchronization during the rotation of the measured object. Additionally, Chinese patent CN104792464B discloses a method for testing the centroid of a rotating body, and Chinese patent CN105136099B discloses a method for inspecting the eccentricity of a rotating body. All of these solutions rely on calibration to improve the accuracy of the measurement results, which is costly and generally impractical for engineering applications, and they do not achieve the separation of systematic and random errors. Summary of the Invention

[0005] The technical problem solved by the present invention is to overcome the shortcomings of the prior art and provide a low-cost, high-precision centroid measurement device and method, which aims to realize the centroid measurement of large rotating products and has the advantages of high measurement accuracy and low cost.

[0006] To solve the above-mentioned technical problems, the present invention discloses a low-cost, high-precision centroid measuring device, comprising: a fixed base, a weighing sensor assembly, a movable frame, a front bracket, a rear bracket, an active roller assembly, a front driven roller, a rear driven roller, a front clamp, and a rear clamp.

[0007] The fixed base is fixed to the ground;

[0008] The weighing sensor assembly is mounted on a fixed base;

[0009] The active frame is placed on the weighing sensor assembly;

[0010] The front and rear brackets are mounted on the movable frame;

[0011] A front driven roller is provided on one side of the top of the front bracket, and a rear driven roller is provided on one side of the top of the rear bracket; the front driven roller and the rear driven roller are coaxially arranged.

[0012] The active roller assembly is connected to the other side of the top of the front bracket and the other side of the top of the rear bracket, respectively;

[0013] The front clamp is placed on the front bracket, and the rear clamp is placed on the rear bracket.

[0014] In the aforementioned low-cost, high-precision centroid measurement device, the fixed base includes: a welded substrate, adjusting shims, chemical anchors, a front mounting plate, and a rear mounting plate; wherein, the adjusting shims are evenly distributed on both sides of the welded substrate; the upper surface of the welded substrate is leveled using the adjusting shims; after the upper surface of the welded substrate is leveled, the welded substrate is fixed to the ground using chemical anchors; the front mounting plate and the rear mounting plate are respectively set at the front and rear ends of the upper surface of the welded substrate; the number of adjusting shims and chemical anchors is the same, denoted as N, where N≥2.

[0015] In the aforementioned low-cost, high-precision centroid measurement device, the weighing sensor assembly includes: four weighing sensor units; the four weighing sensor units are arranged in a rectangular layout and mounted on a fixed base.

[0016] In the aforementioned low-cost, high-precision centroid measurement device, the four weighing sensor units are: a first weighing sensor unit, a second weighing sensor unit, a third weighing sensor unit, and a fourth weighing sensor unit; wherein, the first and second weighing sensor units form one group and are mounted on the front mounting plate; the third and fourth weighing sensor units form another group and are mounted on the rear mounting plate.

[0017] In the aforementioned low-cost, high-precision centroid measurement device, the weighing sensor unit includes: a weighing sensor, an extension block, and a nut; wherein, the weighing sensor is mounted on a fixed base by screws; the extension block is connected to the weighing sensor by threads and secured by a nut; the height of the upper surface of the extension block is adjusted by the threads, and after the upper surfaces of the four extension blocks of the four weighing sensor units are at the same horizontal plane, the nut is tightened to fix the position of the extension block and to prevent loosening.

[0018] In the aforementioned low-cost, high-precision centroid measurement device, the movable frame includes: a square steel skeleton, ball joints, a linear guide rail, and a sliding plate. The bottom of the square steel skeleton has four ball joints, each corresponding to one of the four weighing sensor units. When the movable frame is placed on the weighing sensor assembly, the four ball joints contact the upper surfaces of the four extended supports of each weighing sensor unit. The upper surface of the square steel skeleton includes a fixed section and a sliding section. The front support is connected to the fixed section of the square steel skeleton, and its position on the movable frame is fixed. The linear guide rail is installed on the sliding section of the square steel skeleton, and the sliding plate is installed on the linear guide rail. The rear support is installed on the sliding plate and can move along the linear guide rail with the sliding plate, allowing adjustment of the distance between the rear support and the front support to accommodate different sizes of the measured object.

[0019] In the aforementioned low-cost, high-precision centroid measuring device, the active roller assembly includes: a solid roller, a coupling, a ball spline shaft, a non-flanged splined sleeve, a hollow roller, a sleeve with a flanged splined sleeve, a front roller mounting base, a reducer, a handle, and a rear roller mounting base. The solid roller is mounted on the other side of the top of the rear bracket via the rear roller mounting base. One end of the solid roller is connected to the reducer, and the other end is connected to one end of the ball splined shaft via the coupling. The handle is connected to the reducer. The hollow roller is mounted on the front roller mounting base. The mounting base is installed on the other side of the top of the front bracket; the non-flanged spline sleeve is installed at both ends inside the hollow roller, and the splined sleeve is installed at both ends inside the front roller mounting base. The other end of the ball spline shaft passes through the hollow roller front roller mounting base, which can drive the hollow roller and the solid roller to rotate synchronously, thereby driving the measured object to rotate; when the rear bracket moves along the linear guide with the slide plate, the other end of the ball spline shaft can freely extend and retract through the hollow roller, realizing the synchronous rotation of the hollow roller and the solid roller at any position.

[0020] Accordingly, the present invention also discloses a centroid measurement method based on the above-mentioned low-cost, high-precision centroid measurement device, comprising:

[0021] Establish a spatial rectangular coordinate system O A -X A Y A Z A and spatial rectangular coordinate system O B -X B Y B Z B Among them, the spatial rectangular coordinate system O A -X A Y A Z A The space is stationary relative to the ground, in a rectangular coordinate system O. A -X A Y A Z A OriginA Coinciding with the theoretical center of the front clamp, X A The axis points from the theoretical center of the front clamp to the theoretical center of the rear clamp, Z. A The axis is vertically upward, Y A Axis and X A Axis and Z A The axes satisfy the right-hand rule; spatial rectangular coordinate system O B -X B Y B Z B The object is stationary relative to the object being measured, but rotates with the object during the measurement process, in a spatial rectangular coordinate system O. B -X B Y B Z B Origin B The center of the object being measured is aligned with the center of the front clamp; ideally, during the first measurement, the spatial rectangular coordinate system O... B -X B Y B Z B The initial state and the spatial rectangular coordinate system O A -X A Y A Z A coincide;

[0022] The average mass of the object being measured is calculated based on the readings of the weighing sensor assembly obtained from n measurements.

[0023] Based on the calculated average mass of the object being measured, centroid fitting is performed to determine the centroid of the object being measured.

[0024] In the above centroid measurement method, the average mass of the measured object is calculated based on the readings of the weighing sensor assembly obtained from n measurements, including:

[0025] Place the front and rear clamps on the front and rear brackets respectively, and rotate the handle of the drive roller assembly to make the drive roller assembly rotate clockwise. Each rotation of the clamp... The readings of the four load cell units of the weighing sensor assembly are collected once; among them, the readings of the four load cell units collected when the center of mass measuring device is unloaded are recorded as: A 1i A 2i A 3i A 4i , i = 1, 2, ..., n;

[0026] The object to be measured is mounted on the centroid measuring device using front and rear clamps, so that the spatial rectangular coordinate system O... B -X B Y B Z Band spatial rectangular coordinate system O A -X A Y A Z A Overlap; rotate the handle to make the active roller assembly rotate clockwise, and the measured object rotates for each revolution. The readings of the four load cell units of the weighing sensor assembly are collected once; among them, the readings of the four load cell units collected when the center of mass measuring device is under load are recorded as: B 1i B 2i B 3i B 4i ;

[0027] The tare reading m of each weighing sensor unit was calculated for each measurement. 1i m 2i m 3i m 4i :

[0028]

[0029] Then, the average mass M of the measured object is:

[0030]

[0031] In the above centroid measurement method, based on the calculated average mass of the object being measured, centroid fitting is performed to determine the centroid of the object, including:

[0032] In X A Axial direction, relative to the origin O A Establish the first torque equilibrium equation:

[0033] m 1i ·X s1 +m 2i ·X s2 +m 3i ·X s3 +m 4i ·X s4 =M·X i

[0034] Among them, X i This indicates that during the i-th measurement, the centroid of the measured object lies in the Cartesian coordinate system O. A -X A Y A Z A X in A Axis coordinates; X s1 X s1 X s3 and X s4 These represent the four weighing sensor units in the spatial rectangular coordinate system O. A -XA Y A Z A X in A Axis coordinates, X s1 =X s2 =0,X s3 =X s4 =L, where L represents the distance between the theoretical center of the front clamp and the theoretical center of the rear clamp;

[0035] Solving the first torque equilibrium equation, we get:

[0036]

[0037] Then, the centroid of the measured object lies in the spatial rectangular coordinate system O. A -X A Y A Z A X in A The average value of the axis coordinates X is:

[0038]

[0039] In Y A Axial direction, relative to the origin O A Establish the second torque equilibrium equation:

[0040] m 1i ·Y s1 +m 2i ·Y s2 +m 3i ·Y s3 +m 4i ·Y s4 =M·Y i

[0041] Among them, Y i This indicates that during the i-th measurement, the centroid of the measured object lies in the Cartesian coordinate system O. A -X A Y A Z A Y in A Y-axis coordinates; s1 Y s1 Y s3 and Y s4 These represent the four weighing sensor units in the spatial rectangular coordinate system O. A -X A Y A Z A Y in A Y-axis coordinates s1 =Y s3 =K / 2, Y s2 =Y s4=-K / 2, where K represents the distance between the first weighing sensor unit and the second weighing sensor unit;

[0042] Solving the second torque equilibrium equation, we get:

[0043]

[0044] According to Y i Determine Z i :

[0045] Z i =Y i+n / 4

[0046] Among them, Z i This indicates that during the i-th measurement, the centroid of the measured object lies in the Cartesian coordinate system O. A -X A Y A Z A Z in A Axis coordinates;

[0047] In the spatial rectangular coordinate system O A -X A Y A Z A Y A O A Z A In a plane, the center of mass of the measured object approximately forms a circle after n rotations. The equation of this circle is denoted as:

[0048] (yA) 2 +(zB) 2 =R 2

[0049] Where y and z represent any point on the circle in the spatial rectangular coordinate system O. A -X A Y A Z A In the coordinate system O, the vertical coordinates are ordinates and inverted coordinates, R represents the radius of the circle; A and B represent the coordinates of the circle's center in the Cartesian coordinate system O. A -X A Y A Z A The vertical and ordinates in the graph;

[0050] Take three intermediate parameters: a, b, c, and let:

[0051] a = -2A, b = -2B, c = A 2 +B 2 -R 2

[0052] Then we have:

[0053] y 2 +z 2 +ay+bz+c=0

[0054] The distance d between the measured object and the center of the circle obtained from the i-th measurement is calculated. i :

[0055]

[0056] The i-th measurement d is calculated. i Deviation from R:

[0057]

[0058] Then, the total deviation Q(a,b,c) of n measurements is:

[0059]

[0060] The values ​​of the three intermediate parameters that minimize Q(a,b,c) are obtained by solving the problem. in, This represents the values ​​of a, b, and c when Q(a,b,c) is minimized.

[0061] Then, the optimal radius of the circle for:

[0062]

[0063] Determine the spatial rectangular coordinate system O A -X A Y A Z A To the spatial rectangular coordinate system O B -X B Y B Z B Transformation coefficient ρ:

[0064]

[0065] Then, the centroid of the measured object lies in the spatial rectangular coordinate system O. B -X B Y B Z B The coordinates in the image are: (X, ρY1, ρY) 1+n / 4 ).

[0066] The present invention has the following advantages:

[0067] (1) This invention discloses a low-cost, high-precision centroid measurement scheme, which can realize the centroid measurement of large rotating products with a diameter of more than 1 meter and a length of more than 5 meters. The measurement is highly accurate, low-cost, and simple to install, use and maintain.

[0068] (2) This invention discloses a low-cost and high-precision centroid measurement scheme. The pure structural design of ball spline knot solves the problem of asynchronous rotation of front and rear rollers during the centroid measurement of large rotating products, and realizes zero backlash synchronous rotation of front and rear rollers at any distance.

[0069] (3) This invention discloses a low-cost, high-precision centroid measurement scheme. Based on the systematic error separation design of data point fitting, the systematic error is separated from the measurement data by multiple acquisitions and multiple data point fitting, which effectively improves the accuracy of centroid measurement in principle. Attached Figure Description

[0070] Figure 1 This is a three-dimensional view of a low-cost, high-precision centroid measuring device according to an embodiment of the present invention;

[0071] Figure 2 This is a front view of a low-cost, high-precision centroid measuring device according to an embodiment of the present invention;

[0072] Figure 3 This is a schematic diagram of the motion state of a low-cost, high-precision centroid measuring device according to an embodiment of the present invention;

[0073] Figure 4 This is a schematic diagram of a fixed base in an embodiment of the present invention;

[0074] Figure 5 This is a schematic diagram of the structure of a weighing sensor unit in an embodiment of the present invention;

[0075] Figure 6 This is a three-dimensional view of an active frame in an embodiment of the present invention;

[0076] Figure 7 This is a front view of an active frame in an embodiment of the present invention;

[0077] Figure 8 This is a three-dimensional view of an active roller assembly according to an embodiment of the present invention;

[0078] Figure 9 This is a front view of an active roller assembly according to an embodiment of the present invention;

[0079] Figure 10 yes Figure 9 A magnified view of a portion of the image;

[0080] Figure 11This is a schematic diagram of error separation in an embodiment of the present invention;

[0081] Figure 12 This is a schematic diagram of a coordinate system in an embodiment of the present invention. Detailed Implementation

[0082] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments disclosed in the present invention will be described in further detail below with reference to the accompanying drawings.

[0083] Reference Figures 1-3 In this embodiment, the low-cost, high-precision centroid measuring device includes: a fixed base 1, a weighing sensor assembly 2, a movable frame 3, a front bracket 41, a rear bracket 42, an active roller assembly 5, a front driven roller 61, a rear driven roller 62, a front clamp 71, and a rear clamp 72. The fixed base 1 is fixed to the ground; the weighing sensor assembly 2 is mounted on the fixed base 1; the movable frame 3 is placed on the weighing sensor assembly 2; the front bracket 41 and the rear bracket 42 are mounted on the movable frame 3; a front driven roller 61 is provided on one side of the top of the front bracket 41, and a rear driven roller 62 is provided on one side of the top of the rear bracket 42; the front driven roller 61 and the rear driven roller 62 are coaxial; the active roller assembly 5 is connected to the other side of the top of the front bracket 41 and the other side of the top of the rear bracket 42, respectively; the front clamp 71 is placed on the front bracket 41, and the rear clamp 72 is placed on the rear bracket 42.

[0084] In this embodiment, as Figure 4 As shown, the fixed base 1 mainly includes: a welding base 101, adjusting shims 102, chemical anchors 103, a front mounting plate 104, and a rear mounting plate 105. The welding base 101 is straightened and annealed after welding to remove residual stress, and then its upper and lower surfaces are machined to ensure good flatness and parallelism. Adjusting shims 102 are evenly distributed on both sides of the welding base 101; the upper surface of the welding base 101 is leveled using the adjusting shims 102; after the upper surface of the welding base 101 is leveled, it is fixed to the ground using chemical anchors 103. The front mounting plate 104 and the rear mounting plate 105 are respectively located at the front and rear ends of the upper surface of the welding base 101. The number of adjusting shims 102 and chemical anchors 103 is the same, denoted as N, where N≥2.

[0085] In this embodiment, the weighing sensor assembly 2 includes four weighing sensor units: a first weighing sensor unit 21, a second weighing sensor unit 22, a third weighing sensor unit 23, and a fourth weighing sensor unit 24. The four weighing sensor units are arranged in a rectangular layout and mounted on the fixed base 1. Specifically, the first weighing sensor unit 21 and the second weighing sensor unit 22 form one group, mounted on the front mounting plate 104; the projection of the theoretical center of the front clamp 71 onto the horizontal ground coincides with the projection of the midpoint of the line connecting the first weighing sensor unit 21 and the second weighing sensor unit 22 onto the horizontal ground. The third weighing sensor unit 23 and the fourth weighing sensor unit 24 form another group, mounted on the rear mounting plate 105; the projection of the theoretical center of the rear clamp 72 onto the horizontal ground coincides with the projection of the midpoint of the line connecting the third weighing sensor unit 23 and the fourth weighing sensor unit 24 onto the horizontal ground.

[0086] Each weighing sensor unit has the same structure, such as Figure 5 As shown, the weighing sensor unit mainly includes: a weighing sensor 201, an extension block 202, and a nut 203. The weighing sensor 201 is mounted on the fixed base 1 with screws (the weighing sensors in the first and second weighing sensor units are mounted on the front mounting plate of the fixed base with screws; the weighing sensors in the third and fourth weighing sensor units are mounted on the rear mounting plate of the fixed base with screws). The extension block 202 is threaded to the weighing sensor 201 and secured with the nut 203. The height of the upper surface of the extension block 202 is adjusted by the thread. After the upper surfaces of the four extension blocks of the four weighing sensor units are at the same horizontal plane, the nut is tightened to fix the position of the extension block and prevent loosening.

[0087] In this embodiment, as Figures 6-7As shown, the movable frame 3 mainly includes: a square steel frame 301, ball joints 302, a linear guide rail 303, and a sliding plate 304. The upper and lower surfaces of the square steel frame 301 are machined to achieve good precision. Four ball joints 302 are located at the bottom of the square steel frame 301, and their positions correspond to the positions of the four weighing sensor units. When the movable frame 3 is placed on the weighing sensor assembly 2, the four ball joints 302 contact the upper surfaces of the four extended supports of the four weighing sensor units. The upper surface of the square steel frame 301 includes a fixed section and a sliding section; the front bracket 41 is connected to the fixed section of the square steel frame 301, and the position of the front bracket 41 on the movable frame 3 is fixed; the linear guide rail 303 is installed on the sliding section of the square steel frame 301, and the slide plate 304 is installed on the linear guide rail 303; the rear bracket 42 is installed on the slide plate 304 and can move along the linear guide rail 303 with the slide plate 304 to realize the adjustment of the distance between the rear bracket 42 and the front bracket 41 to adapt to the test objects of different specifications. In this embodiment, the test objects mainly refer to large rotating products with a diameter of more than 1 meter and a length of more than 5 meters.

[0088] In this embodiment, as Figures 8-10 As shown, the active roller assembly 5 mainly includes: a solid roller 501, a coupling 502, a ball spline shaft 503, a non-flanged splined sleeve 504, a hollow roller 505, a sleeve with a flanged splined sleeve 506, a front roller mounting base 507, a reducer 508, a handle 509, and a rear roller mounting base 510. The solid roller 501 and the hollow roller 505 need to rotate synchronously to drive the measured object to rotate; if they are not synchronized, it will significantly affect the measurement results. The solid roller 501 is mounted on the other side of the top of the rear bracket 42 via the rear roller mounting base 510; one end of the solid roller 501 is connected to the reducer 508, and the other end is connected to one end of the ball splined shaft 503 via the coupling 502; the handle 509 is connected to the reducer 508. Hollow roller 505 is mounted on the other side of the top of front bracket 41 via front roller mounting base 507; non-flanged spline sleeve 504 is mounted at both ends inside hollow roller 505, and splined sleeve 506 is mounted at both ends inside front roller mounting base 507. The other end of ball spline shaft 503 passes through front roller mounting base 507 of hollow roller 505, which can drive hollow roller 505 and solid roller 501 to rotate synchronously, thereby driving the measured object to rotate. When rear bracket 42 moves along linear guide rail 303 with slide plate 304, the other end of ball spline shaft 503 can freely extend and retract through hollow roller 505, realizing synchronous rotation of hollow roller 505 and solid roller 501 at any position, such as... Figure 3 As shown.

[0089] In this embodiment, the active roller assembly 5, the front driven roller 61, and the rear driven roller 62 are installed at designated positions on the front bracket 41 and the rear bracket 42 to support the front clamp 71, the rear clamp 72, and the object under test, and drive the front clamp 71, the rear clamp 72, and the object under test to rotate through friction.

[0090] In this embodiment, the centroid measurement method based on the aforementioned low-cost, high-precision centroid measurement device includes the following steps:

[0091] S1, Establish a spatial rectangular coordinate system O A -X A Y A Z A and spatial rectangular coordinate system O B -X B Y B Z B .

[0092] In this embodiment, as Figure 12 As shown, the spatial rectangular coordinate system O A -X A Y A Z A Stationary relative to the ground; spatial rectangular coordinate system O A -X A Y A Z A Origin A The theoretical center of the front clamp 71 coincides with the origin O. A The projections on the horizontal ground coincide with the projections of the midpoints of the lines connecting the first weighing sensor unit 21 and the second weighing sensor unit 22 onto the horizontal ground; X A The axis is the theoretical center of the front clamp 71 pointing to the theoretical center of the rear clamp 72, Z. A The axis is vertically upward, Y A Axis and X A Axis and Z A The axes satisfy the right-hand rule. Spatial rectangular coordinate system O B -X B Y B Z B Origin B The center of the object being measured is coincident with the center of the front clamp 71, i.e., the origin O. B The projections on the horizontal ground coincide with the projections of the midpoints of the lines connecting the third and fourth weighing sensor units 23 and 24 onto the horizontal ground; spatial rectangular coordinate system O B -X B Y B Z B It is stationary relative to the object being measured, but rotates with the object during the measurement process; ideally, in the first measurement, the spatial rectangular coordinate system O...B -X B Y B Z B The initial state and the spatial rectangular coordinate system O A -X A Y A Z A coincide.

[0093] S2, calculate the average mass of the object being measured based on the readings of the weighing sensor assembly 2 obtained from n measurements.

[0094] In this embodiment, the readings of the weighing sensor assembly 2 include: the readings of the weighing sensor assembly 2 when the center of mass measuring device is unloaded and the readings of the weighing sensor assembly 2 when the center of mass measuring device is loaded.

[0095] Acquisition of load cell assembly readings under no-load conditions: Place the front clamp 71 and rear clamp 72 on the front bracket 41 and rear bracket 72 respectively, and rotate the handle 509 of the drive roller assembly 5 to make the drive roller assembly 5 rotate clockwise. Each rotation of the clamp... The readings of the four load cell units of the weighing sensor assembly 2 are collected once. The readings of the four load cell units collected when the center of mass measuring device is unloaded are recorded as follows: A 1i A 2i A 3i A 4i , i = 1, 2, ..., n.

[0096] Acquisition of load cell assembly readings under load: The object to be measured is mounted on the center of mass measuring device via the front clamp 71 and the rear clamp 72, so that the spatial rectangular coordinate system O B -X B Y B Z B and spatial rectangular coordinate system O A -X A Y A Z A Overlap; rotate handle 509 to make the active roller assembly 5 rotate clockwise, and the measured object rotates 1 / 2 of each rotation. The readings of the four load cell units of the weighing sensor assembly 2 are collected once. The readings of the four load cell units collected under load by the center of mass measuring device are recorded as follows: B 1i B 2i B 3i B 4i .

[0097] The tare reading m of each weighing sensor unit was calculated for each measurement. 1i m 2i m 3i m4i :

[0098]

[0099] Then, the average mass M of the measured object is:

[0100]

[0101] S3. Based on the calculated average mass of the object being measured, perform centroid fitting to determine the centroid of the object being measured.

[0102] In this embodiment, step S3 is implemented as follows:

[0103] In X A Axial direction, relative to the origin O A Establish the first torque equilibrium equation:

[0104] m 1i ·X s1 +m 2i ·X s2 +m 3i ·X s3 +m 4i ·X s4 =M·X i

[0105] Among them, X i This indicates that during the i-th measurement, the centroid of the measured object lies in the Cartesian coordinate system O. A -X A Y A Z A X in A Axis coordinates; X s1 X s1 X s3 and X s4 These represent the four weighing sensor units in the spatial rectangular coordinate system O. A -X A Y A Z A X in A Axis coordinates, X s1 =X s2 =0,X s3 =X s4 =L, where L represents the distance between the theoretical center of the front clamp 71 and the theoretical center of the rear clamp 72.

[0106] Solving the first torque equilibrium equation, we get:

[0107]

[0108] Then, the centroid of the measured object lies in the spatial rectangular coordinate system O.A -X A Y A Z A X in A The average value of the axis coordinates X is:

[0109]

[0110] In Y A Axial direction, relative to the origin O A Establish the second torque equilibrium equation:

[0111] m 1i ·Y s1 +m 2i ·Y s2 +m 3i ·Y s3 +m 4i ·Y s4 =M·Y i

[0112] Among them, Y i This indicates that during the i-th measurement, the centroid of the measured object lies in the Cartesian coordinate system O. A -X A Y A Z A Y in A Y-axis coordinates; s1 Y s1 Y s3 and Y s4 These represent the four weighing sensor units in the spatial rectangular coordinate system O. A -X A Y A Z A Y in A Y-axis coordinates s1 =Y s3 =K / 2, Y s2 =Y s4 =-K / 2, where K represents the distance between the first weighing sensor unit and the second weighing sensor unit;

[0113] Solving the second torque equilibrium equation, we get:

[0114]

[0115] Rotate the object under test by 90°. The calculated ordinate of the centroid at this point is numerically equal to the initial ordinate of the centroid, i.e., Z1 = Y4. Similarly, we can obtain: Z i =Y i+n / 4 Among them, Z i This indicates that during the i-th measurement, the centroid of the measured object lies in the Cartesian coordinate system O. A -XA Y A Z A Z in A Axis coordinates.

[0116] Therefore, after the object being measured completes one full rotation, the centroid of the object in the Cartesian coordinate system O can be obtained. A -X A Y A Z A The n measurement results are as follows: (X1,Y1,Y 1+n / 4 (X2,Y2,Y) 2+n / 4 ), ..., (X) i ,Y i ,Y i+n / 4 ), ..., (X) n ,Y n ,Y n+n / 4 ).

[0117] In the spatial rectangular coordinate system O A -X A Y A Z A Y A O A Z A In a plane, the center of mass of the measured object approximately forms a circle after n rotations. The equation of this circle is denoted as:

[0118] (yA) 2 +(zB) 2 =R 2

[0119] Where y and z represent any point on the circle in the spatial rectangular coordinate system O. A -X A Y A Z A In the coordinate system O, the vertical coordinates are ordinates and inverted coordinates, R represents the radius of the circle; A and B represent the coordinates of the circle's center in the Cartesian coordinate system O. A -X A Y A Z A The vertical and ordinates in the graph.

[0120] Take three intermediate parameters: a, b, c, and let:

[0121] a = -2A, b = -2B, c = A 2 +B 2 -R 2

[0122] Then we have:

[0123] y 2 +z 2 +ay+bz+c=0

[0124] The distance d between the measured object and the center of the circle obtained from the i-th measurement is calculated. i :

[0125]

[0126] The i-th measurement d is calculated. i Deviation from R:

[0127]

[0128] Then, the total deviation Q(a,b,c) of n measurements is:

[0129]

[0130] Find the values ​​of the three intermediate parameters that minimize Q(a,b,c): in, This represents the values ​​of a, b, and c when Q(a,b,c) is minimized.

[0131] Then, the optimal center of the circle and optimal radius They are respectively:

[0132]

[0133] Spatial rectangular coordinate system O A -X A Y A Z A Origin A The vector to the center of the fitted circle is the systematic error of the centroid measuring device, and the optimal radius is... The distance between the centroid of the measured object and the theoretical axis is used to separate systematic errors from random errors, such as... Figure 11 As shown.

[0134] As mentioned earlier, under ideal conditions, the spatial rectangular coordinate system O is used for the first measurement. B -X B Y B Z B The initial state and the spatial rectangular coordinate system O A -X A Y A Z A Coincident; at this point, the spatial rectangular coordinate system O can be determined. A -X A Y A Z A To the spatial rectangular coordinate system O B -X B Y B ZB The transformation coefficient ρ is:

[0135]

[0136] Then, the centroid of the measured object lies in the spatial rectangular coordinate system O. B -X B Y B Z B The coordinates in the image are: (X, ρY1, ρY) 1+n / 4 ).

[0137] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention by utilizing the methods and techniques disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.

[0138] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A low-cost, high-precision centroid measuring device, characterized in that, include: Fixed base (1), load cell assembly (2), movable frame (3), front bracket (41), rear bracket (42), active roller assembly (5), front driven roller (61), rear driven roller (62), front clamp (71) and rear clamp (72); The fixed base (1) is fixed to the ground; The weighing sensor assembly (2) is mounted on the fixed base (1); The active frame (3) is placed on the weighing sensor assembly (2); The front bracket (41) and the rear bracket (42) are mounted on the movable frame (3); A front driven roller (61) is provided on one side of the top of the front bracket (41), and a rear driven roller (62) is provided on one side of the top of the rear bracket (42); the front driven roller (61) and the rear driven roller (62) are coaxially arranged. The active roller assembly (5) is connected to the other side of the top of the front bracket (41) and the other side of the top of the rear bracket (42), respectively; The front clamp (71) is placed on the front bracket (41), and the rear clamp (72) is placed on the rear bracket (42).

2. The low-cost, high-precision centroid measuring device according to claim 1, characterized in that, The fixed base (1) includes: a welding base (101), adjusting shims (102), chemical anchors (103), a front mounting plate (104), and a rear mounting plate (105); wherein, the adjusting shims (102) are evenly distributed on both sides of the welding base (101); the upper surface of the welding base (101) is leveled by adjusting shims (102); after the upper surface of the welding base (101) is leveled, the welding base (101) is fixed to the ground by chemical anchors (103); the front mounting plate (104) and the rear mounting plate (105) are respectively set at the front and rear ends of the upper surface of the welding base (101); the number of adjusting shims (102) and chemical anchors (103) is the same, denoted as N, N≥2.

3. The low-cost, high-precision centroid measuring device according to claim 2, characterized in that, The weighing sensor assembly (2) includes: four weighing sensor units; the four weighing sensor units are arranged in a rectangular layout and mounted on a fixed base (1).

4. The low-cost, high-precision centroid measuring device according to claim 3, characterized in that, The four weighing sensor units are: the first weighing sensor unit (21), the second weighing sensor unit (22), the third weighing sensor unit (23), and the fourth weighing sensor unit (24); wherein the first weighing sensor unit (21) and the second weighing sensor unit (22) are a group and are mounted on the front mounting plate (104); the third weighing sensor unit (23) and the fourth weighing sensor unit (24) are another group and are mounted on the rear mounting plate (105).

5. The low-cost, high-precision centroid measuring device according to claim 4, characterized in that, The weighing sensor unit includes: a weighing sensor (201), an extension block (202), and a nut (203); wherein, the weighing sensor (201) is mounted on the fixed base (1) by screws; the extension block (202) is connected to the weighing sensor (201) by threads and is fastened by the nut (203); the height of the upper surface of the extension block (202) is adjusted by the threads, and after the upper surfaces of the four extension blocks of the four weighing sensor units are at the same level, the nut is tightened to fix the position of the extension block and to prevent loosening.

6. The low-cost, high-precision centroid measuring device according to claim 5, characterized in that, The movable frame (3) includes: a square steel frame (301), ball joints (302), a linear guide rail (303), and a sliding plate (304); wherein, the bottom of the square steel frame (301) is provided with four ball joints (302), the positions of the four ball joints (302) correspond to the positions of the four weighing sensor units respectively; when the movable frame (3) is placed on the weighing sensor assembly (2), the four ball joints (302) contact the upper surfaces of the four extended supports of the four weighing sensor units respectively; the upper surface of the square steel frame (301) The surface includes: a fixed section and a sliding section; the front bracket (41) is connected to the fixed section of the square steel frame (301), and the position of the front bracket (41) on the movable frame (3) is fixed; the linear guide rail (303) is installed on the sliding section of the square steel frame (301), and the slide plate (304) is installed on the linear guide rail (303); the rear bracket (42) is installed on the slide plate (304), and can move along the linear guide rail (303) with the slide plate (304) to realize the adjustment of the distance between the rear bracket (42) and the front bracket (41) to adapt to different specifications of the measured object.

7. The low-cost, high-precision centroid measuring device according to claim 6, characterized in that, The active roller assembly (5) includes: a solid roller (501), a coupling (502), a ball spline shaft (503), a non-flanged spline sleeve (504), a hollow roller (505), a spline sleeve with a flanged spline (506), a front roller mounting base (507), a reducer (508), a handle (509), and a rear roller mounting base (510); wherein, the solid roller (501) is mounted on the other side of the top of the rear bracket (42) via the rear roller mounting base (510); one end of the solid roller (501) is connected to the reducer (508), and the other end is connected to one end of the ball spline shaft (503) via the coupling (502); the handle (509) is connected to the reducer (508); the hollow roller (505) is mounted on the other side of the top of the rear bracket (42) via the front roller mounting base (510); one end of the solid roller (501) is connected to the reducer (508), and the other end is connected to one end of the ball spline shaft (503) via the coupling (502); the handle (509) is connected to the reducer (508); the hollow roller (505) is mounted on the other side of the rear bracket (42) via the front roller mounting base (510). The seat (507) is installed on the other side of the top of the front bracket (41); the non-flanged spline sleeve (504) is installed at both ends inside the hollow roller (505), and the spline sleeve (506) is installed at both ends inside the front roller mounting seat (507). The other end of the ball spline shaft (503) passes through the hollow roller (505) and the front roller mounting seat (507), which can drive the hollow roller (505) and the solid roller (501) to rotate synchronously, so as to drive the measured object to rotate; when the rear bracket (42) moves along the linear guide (303) with the slide plate (304), the other end of the ball spline shaft (503) can freely extend and retract through the hollow roller (505), so as to realize the synchronous rotation of the hollow roller (505) and the solid roller (501) at any position.

8. A method for measuring the centroid based on the low-cost, high-precision centroid measuring device according to claim 1, characterized in that, include: Establish a spatial rectangular coordinate system O A -X A Y A Z A and spatial rectangular coordinate system O B -X B Y B Z B ; Among them, the spatial rectangular coordinate system O A -X A Y A Z A The space is stationary relative to the ground, in a rectangular coordinate system O. A -X A Y A Z A Origin A Coinciding with the theoretical center of the front clamp (71), X A The axis is the theoretical center of the front clamp (71) pointing to the theoretical center of the rear clamp (72), Z A The axis is perpendicular to the vertical and points upward, Y A Axis and X A Axis and Z A The axes satisfy the right-hand rule; spatial rectangular coordinate system O B -X B Y B Z B The object is stationary relative to the object being measured, but rotates with the object during the measurement process, in a spatial rectangular coordinate system O. B -X B Y B Z B Origin B The center of the object being measured is coincident with the center of the front clamp (71) that holds the object; ideally, during the first measurement, the spatial rectangular coordinate system O B -X B Y B Z B The initial state and the spatial rectangular coordinate system O A -X A Y A Z A coincide; The average mass of the object being measured is calculated based on the readings of the weighing sensor assembly (2) obtained from n measurements. Based on the calculated average mass of the object being measured, centroid fitting is performed to determine the centroid of the object being measured.

9. The centroid measurement method according to claim 8, characterized in that, Based on the readings of the weighing sensor assembly (2) obtained from n measurements, the average mass of the measured object is calculated, including: Place the front clamp (71) and rear clamp (72) on the front bracket (41) and rear bracket (42) respectively, and rotate the handle (509) of the drive roller assembly (5) to make the drive roller assembly (5) rotate clockwise. Each rotation of the clamp... The readings of the four weighing sensor units of the weighing sensor assembly (2) are collected once; among them, the readings of the four weighing sensor units collected when the centroid measuring device is unloaded are recorded as: A 1i A 2i A 3i A 4i , i = 1, 2, ..., n; The object to be measured is mounted on the centroid measuring device using the front clamp (71) and the rear clamp (72), so that the spatial rectangular coordinate system O B -X B Y B Z B and spatial rectangular coordinate system O A -X A Y A Z A Overlap; rotate the handle (509) to make the active roller assembly (5) rotate clockwise, and the measured object rotates for each revolution. The readings of the four weighing sensor units of the weighing sensor assembly (2) are collected once; among them, the readings of the four weighing sensor units collected when the center of mass measuring device is under load are recorded as: B 1i B 2i B 3i B 4i ; The tare reading m of each weighing sensor unit was calculated for each measurement. 1i m 2i m 3i m 4i : Then, the average mass M of the measured object is:

10. The centroid measurement method according to claim 9, characterized in that, Based on the calculated average mass of the object under test, centroid fitting is performed to determine the centroid of the object under test, including: In X A Axial direction, relative to the origin O A Establish the first torque equilibrium equation: m 1i ·X s1 +m 2i ·X s2 +m 3i ·X s3 +m 4i ·X s4 =M·X i Among them, X i This indicates that during the i-th measurement, the centroid of the measured object lies in the Cartesian coordinate system O. A -X A Y A Z A X in A Axis coordinates; X s1 X s1 X s3 and X s4 These represent the four weighing sensor units in the spatial rectangular coordinate system O. A -X A Y A Z A X in A Axis coordinates, X s1 =X s2 =0,X s3 =X s4 =L, where L represents the distance between the theoretical center of the front clamp (71) and the theoretical center of the rear clamp (72); Solving the first torque equilibrium equation, we get: Then, the centroid of the measured object lies in the spatial rectangular coordinate system O. A -X A Y A Z A X in A The average value of the axis coordinates X is: In Y A Axial direction, relative to the origin O A Establish the second torque equilibrium equation: m 1i ·Y s1 +m 2i ·Y s2 +m 3i ·Y s3 +m 4i ·Y s4 =M·Y i Among them, Y i This indicates that during the i-th measurement, the centroid of the measured object lies in the Cartesian coordinate system O. A -X A Y A Z A Y in A Y-axis coordinates; s1 Y s1 Y s3 and Y s4 These represent the four weighing sensor units in the spatial rectangular coordinate system O. A -X A Y A Z A Y in A Y-axis coordinates s1 =Y s3 =K / 2, Y s2 =Y s4 =-K / 2, where K represents the distance between the first weighing sensor unit and the second weighing sensor unit; Solving the second torque equilibrium equation, we get: According to Y i Determine Z i : Z i =Y i+n4 Among them, Z i This indicates that during the i-th measurement, the centroid of the measured object lies in the Cartesian coordinate system O. A -X A Y A Z A Z in A Axis coordinates; In the spatial rectangular coordinate system O A -X A Y A Z A Y A O A Z A In a plane, the center of mass of the measured object approximately forms a circle after n rotations. The equation of this circle is denoted as: (y-A) 2 +(z-B) 2 =R 2 Where y and z represent any point on the circle in the spatial rectangular coordinate system O. A -X A Y A Z A In the coordinate system O, the vertical coordinates are ordinates and inverted coordinates, R represents the radius of the circle; A and B represent the coordinates of the circle's center in the Cartesian coordinate system O. A -X A Y A Z A The vertical and ordinates in the graph; Take three intermediate parameters: a, b, c, and let: a=-2A,b=-2B,c=A 2 +B 2 -R 2 Then we have: y 2 +z 2 +ay+bz+c=0 The distance d between the measured object and the center of the circle obtained from the i-th measurement is calculated. i : The i-th measurement d is calculated. i Deviation from R: Then, the total deviation Q(a,b,c) of n measurements is: The values ​​of the three intermediate parameters that minimize Q(a,b,c) are obtained by solving the problem. in, This represents the values ​​of a, b, and c when Q(a,b,c) is minimized. Then, the optimal radius of the circle for: Determine the spatial rectangular coordinate system O A -X A Y A Z A To the spatial rectangular coordinate system O B -X B Y B Z B Transformation coefficient ρ: Then, the centroid of the measured object lies in the spatial rectangular coordinate system O. B -X B Y B Z B The coordinates in the image are: (X, ρY1, ρY) 1+n4 ).

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