Inertia main shaft offset measurement method based on installation error compensation

Abstract

The invention relates to an inertial main shaft offset measurement method based on installation error compensation, and belongs to the technical field of inertial parameter measurement of high-speed rotating parts. Comprising the following steps: 1, establishing an inertia principal axis calculation model, and representing through an inertia product and rotational inertia; 2, mathematical expression of installation errors is carried out, and the installation errors are fused into an inertial principal axis calculation model; based on a traditional inertia main shaft calculation model, the influence of actual installation errors on the inclination angle of the inertia main shaft is considered; a measurement coordinate system and a workpiece coordinate system are established, mathematical expressions of installation errors are quantified in two aspects of positioning errors and orientation errors, and the mathematical expressions are fused into an inertial principal axis calculation model; for a rotation transformation matrix and a translation transformation vector, general mathematical expressions are given, in the actual measurement process, the expression forms of the rotation transformation matrix and the translation transformation vector can be adjusted in combination with a specific measurement mode, the reliability and precision are improved through quantitative expressions, the method is more suitable for actual working conditions, and the installation cost, the repair cost and the maintenance cost are reduced.

Description

TECHNICAL FIELD

[0001] The application relates to an inertia main shaft offset measurement method based on installation error compensation and belongs to the technical field of inertia parameter measurement of high-speed rotating parts. BACKGROUND

[0002] For high-speed rotating parts represented by an aero-engine rotor, geometric assembly accuracy between rotors (mainly considering the coaxiality after rotor stacking) is considered in the mechanical design stage, and inertia parameter such as a rotor inertia main shaft is also considered to face the high-speed rotating working condition of the rotor.

[0003] When measuring the inclination angle of the rotor inertia main shaft, installation errors exist between the lower end surface of the rotor and the measurement reference surface, including errors such as the misalignment of the center of the lower end surface of the rotor and the center of the reference surface and the non-parallelism between the lower end surface of the rotor and the reference surface. Therefore, how to consider and quantify the influence of the installation error on the measurement result of the inclination angle of the inertia main shaft is the key to improving the accuracy.

[0004] Therefore, it is urgent to propose an inertia main shaft offset measurement method based on installation error compensation to solve the above technical problems. SUMMARY

[0005] To solve the above problems, the inertia main shaft offset measurement method based on installation error compensation is provided, and a brief summary of the application is given below to provide a basic understanding of some aspects of the application. It should be understood that this summary is not an exhaustive summary of the application. It is not intended to determine the key or important parts of the application, nor is it intended to limit the scope of the application.

[0006] The technical scheme of the application is as follows: The inertia main shaft offset measurement method based on installation error compensation comprises the following steps: Step one, an inertia main shaft calculation model is established, and the inertia moment and the moment of inertia are used to represent the model. Step two, the mathematical expression of the installation error is obtained and integrated into the inertia main shaft calculation model.

[0007] Preferably, in step one, a space rectangular coordinate system is established, and the moments of inertia of the rotor around the axis, axis, axis , , and the inertia moments of the rotor around the axis, axis, axis , , are measured by the torsion pendulum method, and the inertia tensor matrix of the rotor is obtained. :

[0008] The eigenvectors of the inertia tensor matrix are found and unitized, i.e. the unit direction vectors of the principal axes of inertia, denoted as , where , , correspond to the direction cosines of the axis, axis, axis, respectively, and the direction angles are , , , respectively.

[0009] Preferred: in step one, a space rectangular coordinate system is established with the lower end surface of the rotor as the face, the center of the lower end surface of the rotor as the origin point, and the rotor axis as the axis.

[0010] Preferred: in step two, the measurement coordinate system is denoted as , and the workpiece coordinate system of the rotor itself is denoted as , and the positioning error and orientation error are quantified. Two points , are randomly taken on the space straight line where the principal axes of inertia are located, and their coordinate values in the measurement coordinate system are , and their coordinate values in the workpiece coordinate system of the rotor itself are , ; the attitude conversion relationship between different coordinates is obtained, and then the parametric equation of the space straight line where the principal axes of inertia are located in the workpiece coordinate system of the rotor itself is obtained.

[0011] Preferred: the measurement coordinate system is established with the reference center as the and the reference face as the .

[0012] Preferred: in step two, the positioning error and orientation error are quantified as follows: The positioning error is quantified as the offset of the center of the lower end surface of the rotor relative to the reference point on the axis, axis, axis , where , are the projection points of the origin in and the origin , respectively.eccentricity between the two axes, eccentricity direction and the clockwise angle between the two axes; quantify the orientation error as the angle between the normal vector of the plane and the normal vector of the plane ; the actual orientation of the lower end surface of the rotor is regarded as the reference surface, and the reference surface is rotated around the axis, axis, axis by 、 、 , and the rotation matrix corresponding to the rotation is obtained, and then 、 、 ;

[0013] Preferably: in step two, the coordinates , are obtained first in actual measurement, and then , are obtained by reverse calculation, and the difference between the two expressions is obtained ; since the linear transformation exists between the two coordinate systems, the length of the vector does not change, so the unit direction expression of the straight line where the principal axis of inertia is located is obtained by dividing both sides of the above formula by the modulus of the vector ; the parametric equation expression of the straight line where the principal axis of inertia is located in the rotor itself workpiece coordinate system is , and the inclination angles between the principal axis of inertia and the axis, axis, axis are , , .

[0014] The present application has the following beneficial effects: The present application is based on the traditional principal axis of inertia calculation model, considers the influence of actual installation error on the inclination angle of the principal axis of inertia, establishes a measurement coordinate system and a workpiece coordinate system, quantifies the mathematical expression of the installation error in terms of positioning error and orientation error, and integrates it into the principal axis of inertia calculation model; for the rotation transformation matrix and the translation transformation vector , the present application gives a general mathematical expression, and in the actual measurement process, the expression forms of the two can be adjusted in combination with the specific measurement method, the present application improves the reliability and accuracy through quantitative expression, is more suitable for actual working conditions, and reduces the cost of installation, maintenance and maintenance. BRIEF DESCRIPTION OF DRAWINGS

[0015] Figure 1The figure is a schematic diagram of an inertial principal axis based on an installation error compensation inertial principal axis offset measurement method.

[0016] Figure 2 The figure is a schematic diagram of a coordinate transformation based on an installation error compensation inertial principal axis offset measurement method. DETAILED DESCRIPTION

[0017] In order to make the objects, technical solutions and advantages of the present application clearer, the present application will be described below by specific embodiments shown in the drawings. However, it should be understood that these descriptions are only exemplary and are not intended to limit the scope of the present application. In addition, in the following description, the description of the known structures and technologies is omitted to avoid unnecessary confusion of the concept of the present application.

[0018] Embodiment 1: combined with Figures 1-2 In this embodiment, the installation error compensation based inertial principal axis offset measurement method includes the following steps: Step 1: Establish an inertial principal axis calculation model. When the rotating part is in a balanced state (i.e. the internal inertia forces of the part cancel each other out and do not exert any force on the outside), if there is a certain rotation axis that makes the inertia product of the part to the axis 0, then the rotation axis is called the inertial principal axis. The position of the inertial principal axis cannot be directly observed and needs to be indirectly determined by mechanical parameters. Its position can be mainly represented by two components of the inertia product and the moment of inertia. Step 2: Mathematical expression of installation error. The mathematical expression of installation error is quantified in terms of positioning error and directional error and is integrated into the inertial principal axis calculation model. The present application considers the influence of installation error on the measurement of the inclination angle of the inertial principal axis in combination with the traditional inertial principal axis calculation model, quantifies the expression form of the installation error, and improves the accuracy of the calculation results.

[0019] Embodiment 2: combined with Figures 1-2 In this embodiment, the installation error compensation based inertial principal axis offset measurement method includes the following steps: Step 1: Establish a space rectangular coordinate system. The moments of inertia of the rotor around the axis, axis, and the inertia products of the rotor around the axis, axis, are measured by the torsion pendulum method, respectively, and then the inertia tensor matrix of the rotor is obtained. :

[0020] ​​​​​Based on the definition of principal axes of inertia, the inertia tensor matrix is ​​obtained. The eigenvectors of the eigenvalue are normalized to form the unit direction vector of the principal axis of inertia, denoted as . ,in , , Corresponding to axis, axis, The direction cosine of the axis and the direction angles are respectively , , , 2 + 2 + 2 =1.

[0021] Specific implementation method three: Combining Figures 1-2 This embodiment describes an inertial spindle offset measurement method based on installation error compensation. In step one, the lower end face of the rotor (inertial spindle) is used as... The origin is the center of the lower end face of the rotor. Point, with the rotor axis as Establish a spatial rectangular coordinate system using axes, such as Figure 1 As shown.

[0022] Specific implementation method four: Combination Figures 1-2 This embodiment describes the inertial spindle offset measurement method based on installation error compensation. In step two, when calculating the moment of inertia, the rotor needs to be fixed on the clamping device of the attitude adjustment mechanism. This clamping process often introduces installation errors, specifically manifested as misalignment between the lower end face of the rotor and the reference center, and non-parallelism between the lower end face of the rotor and the reference plane. These can be characterized by positioning error and orientation error, respectively. Figure 2 As shown, the measurement coordinate system is denoted as... The rotor's own workpiece coordinate system is denoted as It can quantify the positioning error and orientation error. Choose any two points on the spatial straight line containing the principal axis of inertia. , They are in the measuring coordinate system The coordinates within are respectively , In the workpiece coordinate system The coordinates within are respectively , The attitude transformation relationship between different coordinates is obtained, and then the parametric equation of the straight line in the space where the inertial principal axis is located in the rotor's own workpiece coordinate system is obtained.

[0023] Specific Implementation Method Five: Combining Figures 1-2 This embodiment describes an inertial principal axis offset measurement method based on installation error compensation. The measurement coordinate system can be centered at a reference center. The reference plane is Establish a spatial rectangular coordinate system.

[0024] Specific Implementation Method Six: Combination Figures 1-2 This embodiment describes the inertial spindle offset measurement method based on installation error compensation. In step two, the quantifiable positioning error and orientation error are described as follows: Positioning error can be quantified as the distance between the center of the rotor's lower end face and the reference point. axis, axis, Offset on axis ,in , The origin exist The projection point and the origin within The eccentricity and the direction of the eccentricity are... The counterclockwise angle between the axes; Orientation error can be quantified as a plane With plane The angle between the normal vectors; the actual orientation of the rotor's lower end face can be considered as the reference planes revolving around each other. axis, axis, The axis rotated 、 、 This yields, and consequently, the rotation matrix. 、 、 ; Therefore:

[0025] in, For translation transformation vectors, Let be the rotation transformation matrix. To bypass The rotation matrix of the axis. To bypass Y The rotation matrix of the axis. To bypass The rotation matrix of the axis.

[0026] Specific implementation method seven: Combination Figures 1-2This embodiment describes an inertial spindle offset measurement method based on installation error compensation. In step two, during actual measurement, the coordinates are often obtained first. , Therefore, it is possible to find the answer in reverse. , The difference between the two equations is... Note that although vectors , The endpoint coordinates are expressed differently in different coordinate systems, but since the transformation between the two coordinate systems is linear (rotation and translation, no scaling transformation), the vector length does not change. Therefore, the above equation can be interpreted as follows: Dividing both sides by the magnitude of the vector yields the expression for the unit direction of the line containing the principal axis of inertia. The parametric equation of the straight line in the space containing the principal inertial shaft in the rotor's own workpiece coordinate system is expressed as follows: Principal axis of inertia and axis, axis, The inclination angles between the axes are respectively , , , The vector of the line containing the principal axis of inertia in the measurement coordinate system; This invention, based on the traditional inertial spindle calculation model, considers the influence of actual installation errors on the inertial spindle tilt angle; it establishes a measurement coordinate system and a workpiece coordinate system, quantifies the mathematical expression of installation errors in terms of positioning error and orientation error, and incorporates them into the inertial spindle calculation model; for the rotation transformation matrix... With translation transformation vector This invention provides a general mathematical expression. In actual measurement, the expression can be adjusted according to the specific measurement method. This invention can derive the allowable error and improve reliability and accuracy through quantitative expression, making it more suitable for actual working conditions and reducing installation, repair and maintenance costs.

[0027] Example 1: Combination Figures 1-2 The inertial spindle offset measurement method based on installation error compensation, shown below, takes a high-pressure compressor rotor of an aero-engine as an example. The rotor has a mass m = 25 kg, an axial length L = 300 mm, and a lower end diameter Φ = 120 mm. After the rotor is clamped, the eccentricity e = 0.1 mm, the eccentricity angle θ = 30°, and the axial offset dz = 0.05 mm are measured. The lower end face of the rotor forms an angle φ with the X1 axis. X =0.02rad, rotate φ about the Y1 axis Y =0.015rad, rotate φ about the Z1 axis Z=0.01rad (φ<<1, approximately cosφ=1, sinφ=φ).

[0028] Based on the above data, the translation transformation vector T is calculated. p =[0.1×cos30°, 0.1×sin30°, 0.05] T ≈[0.0866, 0.05, 0.05] T (mm); Rotation transformation matrix R X = [[1, 0, 0]; [0, 0.9998, -0.02]; [0,0.02, 0.9998]], R Y = [[0.99988, 0, 0.015]; [0, 1, 0]; [-0.015, 0, 0.99988]], R Z =[[0.99995, -0.01, 0]; [0.01, 0.99995, 0]; [0, 0, 1]], and thus T R = R X ×R Y ×R Z =[[0.99988, -0.01, 0.015]; [0.01003, 0.99978, -0.01999]; [-0.01497, 0.02001,0.99965]].

[0029] The inertial parameters of the rotor in the measurement coordinate system are measured using the torsional pendulum method: moment of inertia I. XX =1.25 I YY =1.26 I ZZ =0.82 Inertial product I XY =0.003 I YZ =0.002 I ZX =0.0015 The inertial tensor matrix I is obtained; two points A and B are selected on the line containing the principal axes of inertia, and their coordinates A1=[50, 40, 100] in the measurement coordinate system are measured using a laser displacement sensor. T (mm), B1=[30, 25, 200] T (mm).

[0030] Calculate the vector in the measurement coordinate system Its unit direction vector This leads to the unit direction vector of the principal axes of inertia in the workpiece coordinate system. .

[0031] In summary, the principal axis tilt angle is: α = arccos(s²(1)) ≈ 78.9 ° β=arccos(s2(2))≈81.8 ° γ=arccos(s2(3))≈163.7 ° .

[0032] It should be noted that in the above embodiments, as long as the technical solutions are not contradictory, they can be permuted and combined. Those skilled in the art can exhaust all possibilities based on the mathematical knowledge of permutation and combination. Therefore, the present invention will not describe the technical solutions after permutation and combination one by one, but it should be understood that the technical solutions after permutation and combination have been disclosed by the present invention.

[0033] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for measuring inertial spindle offset based on installation error compensation, characterized in that: Includes the following steps: Step 1: Establish a calculation model for the principal axis of inertia, expressed by the product of inertia and moment of inertia; Step 2: Mathematically express the installation error and incorporate it into the inertial spindle calculation model.

2. The inertial spindle offset measurement method based on installation error compensation according to claim 1, characterized in that: In step one, a spatial rectangular coordinate system is established, and the rotor winding is measured using the torsion pendulum method. axis, axis, Moment of inertia of the shaft , , And to axis, axis, Product of inertia of the axis , , The inertial tensor matrix of the rotor is obtained. : Find the inertia tensor matrix The eigenvectors of the eigenvalue are normalized to form the unit direction vector of the principal axis of inertia, denoted as . ,in , , Corresponding to axis, axis, The direction cosine of the axis and the direction angles are respectively , , .

3. The inertial spindle offset measurement method based on installation error compensation according to claim 2, characterized in that: In step one, the lower end face of the rotor is taken as... The origin is the center of the lower end face of the rotor. Point, with the rotor axis as Establish a spatial rectangular coordinate system using axes.

4. The inertial spindle offset measurement method based on installation error compensation according to claim 2 or 3, characterized in that: In step two, the measurement coordinate system is denoted as... The rotor's own workpiece coordinate system is denoted as Quantify the description of positioning error and orientation error; Choose any two points on the spatial straight line containing the principal axis of inertia. , They are in the measuring coordinate system The coordinates within are respectively , In the workpiece coordinate system The coordinates within are respectively , The attitude transformation relationship between different coordinates is obtained, and then the parametric equation of the straight line in the space where the inertial principal axis is located in the rotor's own workpiece coordinate system is obtained.

5. The inertial spindle offset measurement method based on installation error compensation according to claim 4, characterized in that: The measurement coordinate system is based on the reference center. The reference plane is Establish a spatial rectangular coordinate system.

6. The inertial spindle offset measurement method based on installation error compensation according to claim 4, characterized in that: In step two, the quantification of positioning error and orientation error are described as follows: Positioning error is quantified as the center of the rotor's lower end face relative to the reference point. axis, axis, Offset on axis ,in , The origin exist The projection point and the origin within The eccentricity and the direction of the eccentricity are... The counterclockwise angle between the axes; Orientation error quantized into a plane With plane The angle between the normal vectors; the actual orientation of the rotor's lower end face is considered as the reference plane around which the normal vectors are respectively... axis, axis, The axis rotated 、 、 This yields, and consequently, the rotation matrix. 、 、 ; 。 7. The inertial spindle offset measurement method based on installation error compensation according to claim 6, characterized in that: In step two, the coordinates were obtained first during the actual measurement. , Then, in reverse order, we can find the answer. , The difference between the two equations is... Since the transformation between the two coordinate systems is linear, the vector length remains unchanged. Therefore, dividing both sides of the above equation by the magnitude of the vector yields the expression for the unit direction of the line containing the principal axis of inertia. The parametric equation of the straight line in the space containing the principal inertial shaft in the rotor's own workpiece coordinate system is expressed as follows: Principal axis of inertia and axis, axis, The inclination angles between the axes are respectively , , .

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