Method and device for measuring the moment of inertia of an irregularly shaped product

Abstract

The application provides a method for measuring the rotational inertia of an irregularly shaped product, comprising: collecting point cloud information of a torsion pendulum measurement system's stage and the irregularly shaped product by a depth camera; preprocessing the point cloud information; calculating the coordinate axes of the stage's torsion pendulum center axis and the measured irregularly shaped product in the camera coordinate system; calculating the included angle between each axis of the measured irregularly shaped product and the stage's torsion pendulum center axis, and the distance from the irregularly shaped product's mass center to the stage's torsion pendulum center axis in the camera coordinate system; performing no less than 6 different pose measurements on the irregularly shaped product, and calculating the rotational inertia and the inertia product of the irregularly shaped product around its own coordinate axis by using the parallel axis theorem and the rotation axis theorem.

Description

Technical Field

[0001] This invention relates to the field of rotational inertia measurement technology, specifically to a method and apparatus for measuring the rotational inertia of irregularly shaped products. Background Technology

[0002] Research on moment of inertia measurement technology mainly focuses on the damping effect of torsional vibration and its compensation technology, and multi-parameter fusion measurement methods for mass characteristics. The torsional pendulum method is currently the most mainstream method for measuring moment of inertia. When using the torsional pendulum method to measure the moment of inertia of a product along a certain axis, it is necessary to adjust the product's posture so that the axis of the product being measured is completely aligned with the central axis of the torsional pendulum stage. The axes of regular products such as cylinders and cubes are easy to obtain, but the coordinate axes of irregularly shaped products are usually not directly available. This makes the torsional pendulum method unsuitable for directly measuring the moment of inertia of a certain axis of irregular products, reducing its practicality. Summary of the Invention

[0003] (a) Technical problems to be solved

[0004] To address the shortcomings of existing technologies, this invention provides a method and apparatus for measuring the moment of inertia of irregularly shaped products. This solves the problem mentioned in the background art that the coordinate axes of irregularly shaped products are usually not directly obtainable, which makes the torsion pendulum method unsuitable for measuring the moment of inertia of a certain axis of irregular products, thus reducing the practicality of the torsion pendulum method.

[0005] (II) Technical Solution

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] This invention provides a method for measuring the moment of inertia of an irregularly shaped product, comprising: acquiring point cloud information of the stage of a torsion measurement system and the irregularly shaped product using a depth camera; and preprocessing the point cloud information.

[0008] Calculate the axis of the stage torsion center in the camera coordinate system and the coordinate axis of the irregularly shaped product being measured;

[0009] Calculate the angles between each axis of the irregularly shaped product and the axis of the torsion center of the stage in the camera coordinate system, and the distance from the center of mass of the irregularly shaped product to the axis of the torsion stage.

[0010] For products with irregular shapes, perform at least 6 different pose measurements and calculate the moment of inertia and product of inertia about their own coordinate axes using the parallel axis theorem and the rotation axis theorem.

[0011] Preferably, the step of acquiring point cloud information of the stage and irregularly shaped product of the torsion measurement system using a depth camera includes: acquiring three-dimensional point clouds of the stage and irregularly shaped product using a TOF depth camera. The TOF depth camera first actively emits light pulses onto the stage and irregularly shaped product model, then receives the light pulses reflected back from the stage and irregularly shaped product through a sensor, and finally calculates the distance of each point on the surface of the stage and irregularly shaped product from the camera based on the round-trip time of the detected light pulses, thereby obtaining the three-dimensional point cloud information of the stage and irregularly shaped product.

[0012] Preferably, the calculation of the torsion center axis of the stage in the camera coordinate system and the coordinate axis of the irregularly shaped product being measured includes: point cloud registration with the CAD model;

[0013] The point cloud and CAD model registration includes: CAD model acquisition, coarse point cloud matching, and precise point cloud matching;

[0014] After obtaining the 3D point cloud information of the stage and the irregularly shaped product, the 3D CAD model is extracted by triangular mesh model.

[0015] The transformation matrix of the product coordinate system is obtained by matching point cloud information with the CAD model;

[0016] Finally, multiplying the product coordinate system with the transformation matrix yields the representation of the product coordinate system in the measuring camera coordinates.

[0017] Preferably, the step of obtaining the transformation matrix of the product coordinate system by matching point cloud information with the CAD model includes:

[0018] PCA decomposition is performed on the covariance matrix of the object point cloud. The eigenvectors corresponding to its three eigenvalues ​​form the product coordinate system. This product coordinate system is basically consistent with the CAD product coordinate system and can be used as the initial pose of the object's CAD product coordinate system relative to the camera coordinate system.

[0019] PCA decomposition is used to map the original 3D point cloud into a new 3D orthogonal feature space, and the newly constructed feature vectors are used to construct the object coordinate system.

[0020] Preferably, the step of mapping the original 3D point cloud to a new 3D orthogonal feature space using PCA decomposition, and constructing an object coordinate system using the newly constructed feature vectors, includes:

[0021] The three coordinate axes of the product coordinate system are represented by a set of unit vectors:

[0022]

[0023] The covariance matrix of a planar point cloud is calculated using the following formula:

[0024]

[0025]

[0026] In the formula r i represents a point in the point cloud; m is the number of points in the point cloud.

[0027] PCA decomposition of the covariance matrix yields the eigenvectors as shown in the formula:

[0028]

[0029] In the formula, Ni is the eigenvector corresponding to the eigenvalues ​​after PCA decomposition of the point cloud covariance matrix;

[0030] The rotation matrix of the product coordinate system relative to the camera coordinate system can be composed of eigenvectors:

[0031]

[0032] By calculating the centroid of the point cloud, the translation matrix of the product coordinate system relative to the camera coordinate system can be obtained:

[0033]

[0034] The transformation matrix of the product coordinate system relative to the camera coordinate system is:

[0035]

[0036] Finally, we obtain the representation of the three coordinate axes of the product coordinate system in the camera coordinate system:

[0037]

[0038] Preferably, the calculation of the torsional axis of the stage and the coordinate axis of the irregularly shaped product under the camera coordinate system further includes: a point cloud cylindrical axis fitting algorithm based on the least squares method to unify the coordinate axis of the irregularly shaped object with the axis of the torsional stage.

[0039] Preferably, the point cloud cylindrical axis fitting algorithm based on the least squares method unifies the coordinate axes of the irregularly shaped object with the central axis of the torsion stage; including: designing the stage as a cylinder;

[0040] In three-dimensional space, a cylinder is the set of points at a constant distance r from its central axis. A cylinder is uniquely determined by the following seven parameters: the point p0(x0, y0, z0) on the central axis, and the direction vector of the central axis. It is a unit vector, i.e., a 2 +b 2 +c 2=1, therefore the equation of the cylindrical surface can be expressed as:

[0041]

[0042] Define a data point set P = {p1, p2, ..., p...} N} represents the surface point cloud of the torsion stage acquired by a TOF depth camera, where N is the number of points and p j =(x j y j , z j ), p j ∈P, j∈[1,N];

[0043] In the least squares algorithm fitting process, the fitting error of a point is defined as the difference between the distance from the point to the central axis of the cylindrical stage and the radius of the torsion stage, expressed as:

[0044]

[0045]

[0046] The fitting algorithm based on geometric analysis linearizes the error equation of the formula, discards higher-order terms, and then iterates according to the Gauss-Newton method to obtain the final estimated value of the axis of the torsion stage in the camera coordinate system.

[0047] Preferably, calculating the angles between each axis of the irregularly shaped product and the torsion center axis of the stage in the camera coordinate system, and the distance from the centroid of the irregularly shaped product to the center axis of the torsion stage, includes: obtaining information A of the X, Y, and Z axes of the product coordinate system in the camera coordinate system. C Product centroid coordinates T(x) in camera coordinate system t y t , z t Information on the axis of the torsion stage in the camera coordinate system With p0;

[0048]

[0049]

[0050] p0(x0, y0, z0)

[0051] When t is a parameter in the parametric equation, the point-direction equation of the central axis is:

[0052]

[0053]

[0054] By applying the formula for the included angle of a vector and the formula for the distance from a point to a line, we can obtain the angles α, β, and γ of the product coordinate axes X, Y, and Z relative to the central axis of the torsion stage in the camera coordinate system, and the distance d from the product's center of mass to the central axis of the torsion stage.

[0055]

[0056]

[0057]

[0058]

[0059] The present invention also provides a device for measuring the moment of inertia of irregularly shaped products, comprising: a torsion pendulum table, a stage, a fixture, a photoelectric switch, a TOF depth camera, a base, and a host computer;

[0060] The stage is used to hold the product being tested.

[0061] The torsion pendulum table is used to generate torsional vibration motion;

[0062] The stage, in conjunction with the photoelectric switch, calculates the period T of the torsional vibration motion;

[0063] The fixture is used to stabilize the product under test and prevent it from moving during the measurement process;

[0064] The TOF depth camera acquires point cloud data of the product under test online and uploads the point cloud data to the host computer. The host computer then calculates the moment of inertia according to any of the methods described above.

[0065] Preferably, the operation process of the device includes:

[0066] The operation process of the rotational inertia measurement device for irregularly shaped products based on depth camera and torsional pendulum method is mainly divided into two parts.

[0067] Given the coordinates of the center of mass of the product under test in its own coordinate system and the stiffness coefficient k of the torsion pendulum measuring stage, the specific operating steps of this device are as follows:

[0068] 1) Based on the principle of the torsion pendulum method, before measuring products with irregular shapes, it is necessary to use the point cloud cylindrical axis fitting algorithm based on the least squares method to determine the axis information of the torsion pendulum stage in the camera coordinate system.

[0069] The torsional pendulum method requires at least six different orientations to solve the equations simultaneously, so the fixture's orientation will be different each time a measurement is taken. Before measuring the moment of inertia, the unloaded moment of inertia J of the current orientation needs to be calibrated. 0i , where i is the measurement attitude sequence number;

[0070] 2) Fix the product under test with a fixture, use a TOF depth camera to scan and obtain the point cloud of the product under test shape, match the point cloud with the digital model of the product under test, obtain the rigid body transformation matrix between the camera coordinate system and the world coordinate system of the CAD model, and then calculate the equation of the coordinate axis of the self-coordinate system defined by the CAD model of the product under test in the camera coordinate system, as well as the coordinate of the product's center of mass in the camera coordinate system.

[0071] 3) Calculate the angles α between the X, Y, and Z axes of the camera coordinate system and the center axis of the torsion stage using a unified coordinate axis algorithm based on depth camera point cloud information. i β i γ i The distance d from the product's center of mass to the central axis of the torsion stage i , where i represents the sequence number of the measured s attitude;

[0072] 4) Excite the torsional pendulum measuring stage to induce torsional vibration. Use a photoelectric switch to count the cycles and obtain the period Ti of the torsional vibration, thus obtaining the value of the moment of inertia measured in this experiment.

[0073]

[0074] 5) Change the posture of the product under test and repeat steps (2) to (4) until all 6 load postures have been measured.

[0075] Solve the following system of equations simultaneously:

[0076]

[0077] 6) The aforementioned system of equations is a linear system of equations, and the measured parameters can be obtained using methods such as Gaussian elimination: J x J y J z J xy J yz J xz This enables the measurement of rotational inertia and product of inertia.

[0078] (III) Beneficial Effects

[0079] This invention provides a method and apparatus for measuring the moment of inertia of irregularly shaped products. It includes the following features:

[0080] Beneficial effects:

[0081] To address the issue that the torsion pendulum method cannot be directly applied to the measurement of the rotational inertia of irregularly shaped products, this invention provides a method and apparatus for measuring the rotational inertia of irregularly shaped products. This invention uses a depth camera to acquire point cloud information of the stage of the torsion pendulum measurement system and the irregularly shaped product. Through point cloud data processing, a least-squares-based point cloud cylindrical axis fitting algorithm, and a point cloud-CAD model matching algorithm, the torsion pendulum center axis of the stage and the coordinate axes of the irregularly shaped product under test are calculated in the camera coordinate system. Based on these coordinates, the angles between each axis of the irregularly shaped product and the torsion pendulum center axis of the stage, as well as the distance from the product's center of mass to the torsion pendulum stage center axis, are calculated in the camera coordinate system. Finally, by performing at least six different pose measurements on the irregularly shaped product, the rotational inertia and product of inertia of the irregular object about its own coordinate axes are calculated using the parallel axis theorem and the rotation axis theorem.

[0082] 1) The TOF depth camera and point cloud-model matching algorithm are used to realize the online calculation of the product's rotational moment of inertia and product of inertia;

[0083] 2) Compared with the traditional torsion pendulum method, the present invention can measure the moment of inertia and product of inertia of any rotation axis of an irregularly shaped product, and no longer requires the axis of the product being measured to coincide with the central axis of the torsion pendulum stage.

[0084] 3) Compared to the traditional torsion pendulum method, which can only measure the moment of inertia of the product under test about the central axis of the torsion pendulum stage, this product can measure the moment of inertia and product of inertia of the product under test about the product coordinate axis. Attached Figure Description

[0085] Figure 1 A flowchart illustrating a method for measuring the moment of inertia of an irregularly shaped product, as provided in an embodiment of the present invention;

[0086] Figure 2 This invention provides a flowchart of the point cloud and CAD model matching process in a method for measuring the moment of inertia of an irregularly shaped product.

[0087] Figure 3 This invention provides a unified coordinate axis algorithm for measuring the moment of inertia of irregularly shaped products in an embodiment of the present invention.

[0088] Figure 4 This is a schematic diagram of a device for measuring the moment of inertia of an irregularly shaped product, provided in an embodiment of the present invention.

[0089] Figure 5 This is a schematic diagram of a device for measuring the moment of inertia of an irregularly shaped product under load, provided in an embodiment of the present invention. Detailed Implementation

[0090] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0091] When measuring the moment of inertia and product of inertia of an object using the torsional pendulum method, at least six different orientations are required. Conventional methods require adjusting the product's orientation so that its axis is completely aligned with the central axis of the torsional pendulum stage, and accurately recording the period of torsional vibration. This is impossible for irregularly shaped objects, or rather, achieving six orientations using mechanical tooling is extremely difficult.

[0092] A typical torsional pendulum method moment of inertia measuring stage's core component is an elastic element that drives the torsional pendulum motion. During measurement, the product to be measured is mounted on the stage, where it undergoes torsional vibration. The moment of inertia is calculated by measuring the torsional pendulum period. The calculation formula is as follows:

[0093]

[0094] In the formula, J is the measured moment of inertia, k is the stiffness coefficient of the elastic element, and T is the period of the torsional vibration.

[0095] When measuring the moment of inertia of a product along a certain axis, the product's position needs to be adjusted so that the product's axis is parallel to the central axis of the torsion stage.

[0096] The product of inertia is calculated using the ellipsoidal method by measuring the product's moment of inertia. It can then be obtained using the parallel axis theorem and the rotation axis theorem.

[0097] J-md 2 =J x cos 2 α+J y cos 2 β+Jzcos 2 γ-2J yz cosβcosγ-2J xz cosαcosγ-2J xy cosαcosβ

[0098] Where J is the moment of inertia of the tested product relative to the central axis of the torsion stage (the unloaded moment of inertia needs to be subtracted); m is the product mass; d is the distance from the product's center of mass to the central axis of the torsion stage. x J y J z Let be the moment of inertia of the product in three directions; α, β, and γ be the angles between the X, Y, and Z axes of the product coordinate system and the central axis of the torsion stage; J xy J yz J xz This is equivalent to the product's three inertial products.

[0099] By measuring at least six different orientations, a system of equations can be established to determine J. x J y J z and J xy J yz J xz The values ​​are calculated, thereby enabling the measurement of the moment of inertia and the product of inertia.

[0100] like Figure 1 As shown, the present invention provides a method for measuring the moment of inertia of an irregularly shaped product, comprising:

[0101] S1 acquires point cloud information of the stage of the torsion measurement system and the irregularly shaped product using a depth camera; and preprocesses the point cloud information.

[0102] S2 calculates the coordinate axes of the stage torsion center axis and the irregularly shaped product being measured in the camera coordinate system;

[0103] S3 calculates the angles between each axis of the irregularly shaped product being measured and the axis of the torsion center of the stage, as well as the distance from the center of mass of the irregularly shaped product to the axis of the torsion stage, in the camera coordinate system.

[0104] S4 performs at least 6 different pose measurements on the irregularly shaped product and calculates the moment of inertia and product of inertia of the irregularly shaped product about its own coordinate axis using the parallel axis theorem and the rotation axis theorem.

[0105] Preferably, the step of acquiring point cloud information of the stage of the torsion measurement system and the irregularly shaped product using a depth camera includes:

[0106] By using a TOF (Time of Flight) depth camera to acquire 3D point clouds of a stage and an irregularly shaped product, the TOF depth camera first actively emits light pulses onto the stage and the irregularly shaped product model, then receives the light pulses reflected back from the stage and the irregularly shaped product through a sensor, and finally calculates the distance of each point on the surface of the stage and the irregularly shaped product from the camera based on the round-trip time of the detected light pulses, thereby obtaining the 3D point cloud information of the stage and the irregularly shaped product.

[0107] like Figure 2 As shown, after obtaining the 3D point cloud information of the model, a mesh model extraction is performed on the 3D CAD model to improve the accuracy and speed of subsequent point cloud and CAD model matching. The transformation matrix of the product coordinate system is obtained by matching the point cloud with the CAD model. Finally, the product coordinate system is multiplied by the transformation matrix to obtain the representation of the product coordinate system in the measurement camera coordinates.

[0108] Preferably, the calculation of the torsion center axis of the stage in the camera coordinate system and the coordinate axis of the irregularly shaped product being measured includes: point cloud registration with the CAD model;

[0109] The point cloud and CAD model registration includes: CAD model acquisition, coarse point cloud matching, and precise point cloud matching;

[0110] After obtaining the 3D point cloud information of the stage and the irregularly shaped product, the 3D CAD model is extracted by triangular mesh model.

[0111] The transformation matrix of the product coordinate system is obtained by matching point cloud information with the CAD model;

[0112] Finally, multiplying the product coordinate system with the transformation matrix yields the representation of the product coordinate system in the measuring camera coordinates.

[0113] Preferably, the step of obtaining the transformation matrix of the product coordinate system by matching point cloud information with the CAD model includes:

[0114] PCA decomposition is performed on the covariance matrix of the object point cloud. The eigenvectors corresponding to its three eigenvalues ​​form the product coordinate system. This product coordinate system is basically consistent with the CAD product coordinate system and can be used as the initial pose of the object's CAD product coordinate system relative to the camera coordinate system.

[0115] PCA decomposition is used to map the original 3D point cloud into a new 3D orthogonal feature space, and the newly constructed feature vectors are used to construct the object coordinate system.

[0116] The idea behind PCA is to map N-dimensional data in the original space to a new linearly independent D-dimensional space. These D-dimensional features are reconstructed orthogonal features, representing the D directions with the largest divergence, i.e., the D-dimensional principal components of the original data. This paper uses PCA decomposition to map the original 3D point cloud to a new 3D orthogonal feature space, and uses the newly constructed feature vectors to build an object coordinate system.

[0117] Preferably, the step of mapping the original 3D point cloud to a new 3D orthogonal feature space using PCA decomposition, and constructing an object coordinate system using the newly constructed feature vectors, includes:

[0118] The three coordinate axes of the product coordinate system are represented by a set of unit vectors:

[0119]

[0120] The covariance matrix of a planar point cloud is calculated using the following formula:

[0121]

[0122]

[0123] In the formula r i represents a point in the point cloud; m is the number of points in the point cloud.

[0124] PCA decomposition of the covariance matrix yields the eigenvectors as shown in the formula:

[0125]

[0126] In the formula, Ni is the eigenvector corresponding to the eigenvalues ​​after PCA decomposition of the point cloud covariance matrix;

[0127] The rotation matrix of the product coordinate system relative to the camera coordinate system can be composed of eigenvectors:

[0128]

[0129] By calculating the centroid of the point cloud, the translation matrix of the product coordinate system relative to the camera coordinate system can be obtained:

[0130]

[0131] The transformation matrix of the product coordinate system relative to the camera coordinate system is:

[0132]

[0133] Finally, we obtain the representation of the three coordinate axes of the product coordinate system in the camera coordinate system:

[0134]

[0135] like Figure 3 As shown, three-dimensional digital detection technology is combined with the torsion pendulum method to measure the rotational inertia of an object. By matching point cloud with CAD model and fitting point cloud with cylinder and fitting point cloud cylinder axis based on least squares method, the coordinate axis of irregularly shaped object is unified with the central axis of the torsion pendulum stage.

[0136] To accurately measure the moment of inertia of a specific axis of an irregular product, the product's pose needs to be adjusted so that its axis is parallel to the central axis of the torsion stage, and the torsional vibration curve of the torsion stage needs to be accurately recorded. A depth camera, combined with a point cloud cylindrical axis fitting algorithm based on the least squares method and a CAD model matching algorithm, is used to calculate the angles between the torsion stage's central axis and each axis of the irregular product in the camera coordinate system, as well as the distance from the product's center of mass to the torsion stage's central axis. Photoelectric measurement methods are then used to record the torsional vibration motion.

[0137] Preferably, the calculation of the torsional axis of the stage and the coordinate axis of the irregularly shaped product under the camera coordinate system further includes: a point cloud cylindrical axis fitting algorithm based on the least squares method to unify the coordinate axis of the irregularly shaped object with the axis of the torsional stage.

[0138] Preferably, the point cloud cylindrical axis fitting algorithm based on the least squares method unifies the coordinate axes of the irregularly shaped object with the central axis of the torsion stage; including: designing the stage as a cylinder;

[0139] In three-dimensional space, a cylinder is the set of points at a constant distance r from its central axis. A cylinder is uniquely determined by the following seven parameters: the point p0(x0, y0, z0) on the central axis, and the direction vector of the central axis. It is a unit vector, i.e., a 2 +b 2 +c 2 =1, therefore the equation of the cylindrical surface can be expressed as:

[0140]

[0141] Define a data point set P = {p1, p2, ..., p...} N} represents the surface point cloud of the torsion stage acquired by a TOF depth camera, where N is the number of points and p j =(x j y j , z j ), p j ∈P, j∈[1,N];

[0142] In the least squares algorithm fitting process, the fitting error of a point is defined as the difference between the distance from the point to the central axis of the cylindrical stage and the radius of the torsion stage, expressed as:

[0143]

[0144]

[0145] The fitting algorithm based on geometric analysis linearizes the error equation of the formula, discards higher-order terms, and then iterates according to the Gauss-Newton method to obtain the final estimated value of the axis of the torsion stage in the camera coordinate system.

[0146] Preferably, calculating the angles between each axis of the irregularly shaped product and the torsion center axis of the stage in the camera coordinate system, and the distance from the centroid of the irregularly shaped product to the center axis of the torsion stage, includes: obtaining information A of the X, Y, and Z axes of the product coordinate system in the camera coordinate system. C Product centroid coordinates T(x) in camera coordinate system t y t , z t Information on the axis of the torsion stage in the camera coordinate system With p0;

[0147]

[0148]

[0149] p0(x0, y0, z0)

[0150] When t is a parameter in the parametric equation, the point-direction equation of the central axis is:

[0151]

[0152]

[0153] By applying the formula for the included angle of a vector and the formula for the distance from a point to a line, we can obtain the angles α, β, and γ of the product coordinate axes X, Y, and Z relative to the central axis of the torsion stage in the camera coordinate system, and the distance d from the product's center of mass to the central axis of the torsion stage.

[0154]

[0155]

[0156]

[0157]

[0158] like Figure 4 and Figure 5 As shown, this embodiment of the invention also provides a device for measuring the moment of inertia of irregularly shaped products, including: a torsion pendulum table 6, a stage 3, a clamp 2, a photoelectric switch 1, a TOF depth camera 4, a base 5, and a host computer;

[0159] The stage 3 is used to hold the product being tested.

[0160] The torsion table 6 is used to generate torsional vibration motion;

[0161] The stage 3 works in conjunction with the photoelectric switch 1 to calculate the period T of the torsional vibration motion;

[0162] The clamp 2 is used to stabilize the product under test and prevent the product under test from moving during the measurement process;

[0163] The TOF depth camera 4 acquires point cloud data of the product under test online and uploads the point cloud data to the host computer. The host computer then calculates the moment of inertia according to any of the methods described above.

[0164] Preferably, the operation process of the device includes:

[0165] The operation process of the rotational inertia measurement device for irregularly shaped products based on depth camera and torsional pendulum method is mainly divided into two parts.

[0166] Given the coordinates of the center of mass of the product under test in its own coordinate system and the stiffness coefficient k of the torsion pendulum measuring stage, the specific operating steps of this device are as follows:

[0167] 1) Based on the principle of the torsion pendulum method, before measuring products with irregular shapes, it is necessary to use the point cloud cylindrical axis fitting algorithm based on the least squares method to determine the axis information of the torsion pendulum stage in the camera coordinate system.

[0168] The torsional pendulum method requires at least six different orientations to solve the equations simultaneously, so the fixture's orientation will be different each time a measurement is taken. Before measuring the moment of inertia, the unloaded moment of inertia J of the current orientation needs to be calibrated. 0i , where i is the measurement attitude sequence number;

[0169] 2) Fix the product under test with a fixture, use a TOF depth camera to scan and obtain the point cloud of the product under test shape, match the point cloud with the digital model of the product under test, obtain the rigid body transformation matrix between the camera coordinate system and the world coordinate system of the CAD model, and then calculate the equation of the coordinate axis of the self-coordinate system defined by the CAD model of the product under test in the camera coordinate system, as well as the coordinate of the product's center of mass in the camera coordinate system.

[0170] 3) Calculate the angles α between the X, Y, and Z axes of the camera coordinate system and the center axis of the torsion stage using a unified coordinate axis algorithm based on depth camera point cloud information. i β i γ i The distance d from the product's center of mass to the central axis of the torsion stage i , where i represents the sequence number of the measured s attitude;

[0171] 4) Excite the torsional pendulum measuring stage to induce torsional vibration. Use a photoelectric switch to count the cycles and obtain the period Ti of the torsional vibration, thus obtaining the value of the moment of inertia measured in this experiment.

[0172]

[0173] 5) Change the posture of the product under test and repeat steps (2) to (4) until all 6 load postures have been measured.

[0174] Solve the following system of equations simultaneously:

[0175]

[0176] 6) The aforementioned system of equations is a linear system of equations, and the measured parameters can be obtained using methods such as Gaussian elimination: J x J y J z J xy J yz J xzThis enables the measurement of rotational inertia and product of inertia.

[0177] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for measuring the moment of inertia of an irregularly shaped product, characterized in that, include: Point cloud information of the stage of the torsion measurement system and the irregularly shaped product is collected using a depth camera. Preprocess the point cloud information; The acquisition of point cloud information of the stage and irregularly shaped product of the torsion measurement system by a depth camera includes: acquiring three-dimensional point cloud of the stage and irregularly shaped product by using a TOF depth camera. The TOF depth camera first actively emits light pulses to the stage and irregularly shaped product model, then receives the light pulses reflected back from the stage and irregularly shaped product through a sensor, and finally calculates the distance of each point on the surface of the stage and irregularly shaped product from the camera based on the round-trip time of the detected light pulses, thereby obtaining the three-dimensional point cloud information of the stage and irregularly shaped product. Calculate the axis of the stage torsion center in the camera coordinate system and the coordinate axis of the irregularly shaped product being measured; The calculation of the stage torsion center axis and the coordinate axis of the irregularly shaped product under test in the camera coordinate system includes: point cloud and CAD model registration. The point cloud and CAD model registration includes: CAD model acquisition, coarse point cloud matching, and precise point cloud matching; After obtaining the 3D point cloud information of the stage and the irregularly shaped product, the 3D CAD model is extracted by triangular mesh model. The transformation matrix of the product coordinate system is obtained by matching point cloud information with the CAD model; Finally, the product coordinate system is multiplied by the transformation matrix to obtain the representation of the product coordinate system in the measurement camera coordinates; Calculate the angles between each axis of the irregularly shaped product and the axis of the torsion center of the stage in the camera coordinate system, and the distance from the center of mass of the irregularly shaped product to the axis of the torsion stage. For products with irregular shapes, perform at least 6 different pose measurements and calculate the moment of inertia and product of inertia about their own coordinate axes using the parallel axis theorem and the rotation axis theorem.

2. The method for measuring the moment of inertia of an irregularly shaped product according to claim 1, characterized in that, The step of obtaining the product coordinate system transformation matrix by matching point cloud information with the CAD model includes: PCA decomposition is performed on the covariance matrix of the object point cloud. The eigenvectors corresponding to its three eigenvalues ​​form the product coordinate system. This product coordinate system is basically consistent with the CAD product coordinate system and can be used as the initial pose of the object's CAD product coordinate system relative to the camera coordinate system. PCA decomposition is used to map the original 3D point cloud into a new 3D orthogonal feature space, and the newly constructed feature vectors are used to construct the object coordinate system.

3. The method for measuring the moment of inertia of an irregularly shaped product according to claim 2, characterized in that, The step of mapping the original 3D point cloud to a new 3D orthogonal feature space using PCA decomposition, and constructing an object coordinate system using the newly constructed feature vectors, includes: The three coordinate axes of the product coordinate system are represented by a set of unit vectors: ； The covariance matrix of a planar point cloud is calculated using the following formula: In the formula r i represents a point in the point cloud; m is the number of points in the point cloud. PCA decomposition of the covariance matrix yields the eigenvectors as shown in the formula: In the formula, Ni is the eigenvector corresponding to the eigenvalues ​​after PCA decomposition of the point cloud covariance matrix; The rotation matrix of the product coordinate system relative to the camera coordinate system can be composed of eigenvectors: ； By calculating the centroid of the point cloud, the translation matrix of the product coordinate system relative to the camera coordinate system can be obtained: ； The transformation matrix of the product coordinate system relative to the camera coordinate system is: ； Finally, we obtain the representation of the three coordinate axes of the product coordinate system in the camera coordinate system: 。 4. The method for measuring the moment of inertia of an irregularly shaped product according to claim 3, characterized in that, The calculation of the torsion center axis of the stage and the coordinate axis of the irregularly shaped product under test in the camera coordinate system also includes: a point cloud cylindrical axis fitting algorithm based on the least squares method to unify the coordinate axis of the irregularly shaped object with the center axis of the torsion stage.

5. The method for measuring the moment of inertia of an irregularly shaped product according to claim 4, characterized in that, The point cloud cylindrical axis fitting algorithm based on the least squares method achieves the unification of the coordinate axes of irregularly shaped objects with the central axis of the torsion stage; including: designing the stage as a cylinder; In three-dimensional space, a cylinder is the set of points whose distance from its central axis is a constant *r*. A cylinder is uniquely determined by the following seven parameters: points on the central axis of the cylinder... p 0 ( x 0 ，y 0 ，z 0 ), Central axis direction vector It is a unit vector, i.e., a 2 +b 2 +c 2 =1, therefore the equation of the cylindrical surface can be expressed as: Define data point set This is the surface point cloud of the torsion stage acquired by a TOF depth camera, where N is the number of points. p j =( x j , y j , z j ), p j ∈ P , j ∈[1, N ]; In the least squares algorithm fitting process, the fitting error of a point is defined as the difference between the distance from the point to the central axis of the cylindrical stage and the radius of the torsion stage, expressed as: The fitting algorithm based on geometric analysis linearizes the error equation of the formula, discards higher-order terms, and then iterates according to the Gauss-Newton method to obtain the final estimated value of the axis of the torsion stage in the camera coordinate system.

6. The method for measuring the moment of inertia of an irregularly shaped product according to claim 5, characterized in that, The calculation of the angles between each axis of the irregularly shaped product and the torsion center axis of the stage in the camera coordinate system, and the distance from the centroid of the irregularly shaped product to the center axis of the torsion stage, includes: obtaining information on the X, Y, and Z axes of the product coordinate system in the camera coordinate system. A C Product centroid coordinates in camera coordinate system T ( x t , y t , z t Information on the axis of the torsion stage in the camera coordinate system and p 0 ; ； t When the equation is parametric, the point-direction equation of the central axis is: ； By applying the formulas for vector angles and point-to-line distances, we can obtain the angles between the X, Y, and Z axes of the product coordinate system in the camera coordinate system and the central axis of the torsion stage. α , β , γ The distance from the product's center of mass to the central axis of the torsion stage. d ; 。 7. A device for measuring the moment of inertia of an irregularly shaped product, characterized in that, include: Torsion stage, stage, fixture, photoelectric switch, TOF depth camera, base and host computer; The stage is used to hold the product being tested. The torsion pendulum table is used to generate torsional vibration motion; The stage, in conjunction with the photoelectric switch, calculates the period of torsional vibration. T； The fixture is used to stabilize the product under test and prevent it from moving during the measurement process; The TOF depth camera acquires point cloud data of the product under test online and uploads the point cloud data to the host computer. The host computer then calculates the moment of inertia according to any one of the methods described in claims 1-6.

8. The device for measuring the moment of inertia of an irregularly shaped product as described in claim 7, characterized in that, The operation process of the device includes: Given the coordinates of the center of mass of the product under test in its own coordinate system and the stiffness coefficient k of the torsion pendulum measuring stage, the specific operating steps of this device are as follows: 1) Based on the principle of the torsion pendulum method, before measuring irregularly shaped products, it is necessary to use a point cloud cylindrical axis fitting algorithm based on the least squares method to determine the axis information of the torsion pendulum stage in the camera coordinate system. The torsion pendulum method requires at least 6 different postures to solve the equations simultaneously, so the position of the fixture will be different each time it is measured. Before measuring the moment of inertia, it is necessary to first calibrate and obtain the unloaded moment of inertia of the current posture. J 0i , where i is the measurement attitude sequence number; 2) Fix the product under test with a fixture, use a TOF depth camera to scan and obtain the point cloud of the product under test shape, match the point cloud with the digital model of the product under test, obtain the rigid body transformation matrix between the camera coordinate system and the world coordinate system of the CAD model, and then calculate the equation of the coordinate axis of the self-coordinate system defined by the CAD model of the product under test in the camera coordinate system, as well as the coordinate of the product's center of mass in the camera coordinate system. 3) Calculate the angles of the X, Y, and Z axes relative to the central axis of the torsion stage using a unified coordinate axis algorithm based on depth camera point cloud information. α i , β i , γ i The distance from the product's center of mass to the central axis of the torsion stage d i ,in i Indicates the sequence number of the measured S-pose; 4) Excite the torsional pendulum measuring stage to induce torsional vibration, and use a photoelectric switch to count the cycles of the torsional vibration. Ti Thus, the value of the moment of inertia measured in this study is obtained: ； 5) Change the posture of the product under test and repeat steps (2) to (4) until all 6 load postures have been measured; Solve the following system of equations simultaneously: ； 6) The aforementioned system of equations is a linear system of equations, and the measured parameters can be obtained using the Gaussian elimination method: J x , J y , J z , J xy , J yz , J xz This enables the measurement of rotational inertia and product of inertia.

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