Main shaft deflection coupling transmission and regulation method based on minimum envelope multi-stage rotor inertia
By calculating the inertia tensor matrix and using the Gram-Schmidt orthogonalization method, an inertia principal axis skew control model was established, which solved the problem of difficult control of the inertia principal axis skew in multi-stage rotors, minimized the coaxiality of the inertia principal axis, and improved the dynamic balance and stability of the rotor system.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-28
- Publication Date
- 2026-03-13
AI Technical Summary
The inertial spindle skew of multi-stage rotors is coupled with assembly form and position errors, making it difficult to control the inertial spindle skew. This results in an increase in unbalanced excitation force and inertial torque of the rotor under high-speed rotation, affecting the reliability and service life of the equipment.
By employing a minimum envelope multi-stage rotor inertial shaft skew coupling transmission and control method, the inertial tensor matrix is calculated, and QR decomposition is performed using the Gram-Schmidt orthogonalization method. An inertial shaft skew control model is established to control the assembly phase of each stage of the rotor, thereby achieving optimal coaxiality assembly of the inertial shaft.
Precise quantitative analysis of the inertial spindle skew error controls the spatial deviation of the inertial spindle relative to the rotation axis, significantly improving the dynamic balance performance and operational stability of the high-speed rotor system.
Smart Images
Figure CN121663922A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a method for transmitting and controlling the skew coupling of multi-stage rotor inertia spindles based on minimum envelope, and belongs to the field of rotor assembly technology. Background Technology
[0002] The rotor is the core component of modern rotating machinery, and the assembly quality of multi-stage rotors determines the reliability and safety of the entire machine. With the development of modern industrial equipment, there is a need for more comprehensive control over various rotor characteristics. Among these, the inertial axis skew of multi-stage rotors is coupled with assembly form and position errors. This means that even with very small form and position errors, it is difficult to minimize the inertial axis skew, resulting in increased unbalanced excitation forces and inertial torques during high-speed rotation. This leads to increased amplitude of the multi-stage rotors, causing the equipment to fail to meet actual needs and shortening its service life. Currently, the control of multi-stage rotor stacking assembly still focuses primarily on controlling geometric errors, lacking consideration and analysis of the inertial axis of the multi-stage rotors, which is no longer sufficient to meet engineering requirements. Summary of the Invention
[0003] To address the problem that the lack of consideration and analysis of the inertial spindle of multi-stage rotors in multi-stage rotor stacking assembly fails to meet engineering requirements, this invention proposes a method for the skew coupling transmission and control of the inertial spindle of multi-stage rotors based on minimum envelope.
[0004] The technical solution adopted by the present invention to solve the above problems is as follows: The present invention includes the following steps: Step 1: Based on the transformation relationship between the rotor's centroid coordinate system, centroid coordinate system, and assembly coordinate system, calculate the inertia tensor matrix in the assembly coordinate system of a single-stage rotor. Step 2: Calculate based on the multi-stage rotor assembly mechanism. n The inertia tensor matrix of the stage rotor in the rotating coordinate system after assembly; Step 3: Perform Gram-Schmidt orthogonalization on the inertia tensor matrix. QR Decompose the equations to obtain the spatial equations of the principal axes of inertia. Step 4: Project the principal axes of inertia at different assembly angles onto the rotary coordinate system. x r o r y r In the plane, by solving for the minimum envelope circle diameter of the projection point of the principal axis of inertia and the origin of the rotation coordinate system, an inertial axis skew adjustment model is established. Step 5: Based on the established inertial spindle skew control model, the coaxiality of the inertial spindle can be controlled by adjusting the assembly phase of each stage of the rotor, thus achieving optimal assembly.
[0005] Furthermore, step 1 specifically includes: Let the firsti The inertia tensor matrix of the stage rotor in the center-of-mass coordinate system is: Its centroid position matrix in the centroid coordinate system is Based on the parallel axis generalization theorem, determine the rotor's inertial tensor translation transformation matrix from the centroidal coordinate system to the assembly coordinate system. And calculate and obtain the rotation transformation matrix. ; Combined with translation transformation matrix and the i The inertial tensor matrix of the stage rotor in the center-of-mass coordinate system Obtain the first centroid coordinate system i stage rotor inertia tensor matrix ; Combined with the centroid coordinate system, the first i stage rotor inertia tensor matrix and rotation transformation matrix Get the i The inertial tensor matrix of the stage rotor after rotating from the centroidal coordinate system to the assembly coordinate system ; right n After the stage rotor is assembled, its inertia tensor matrix in the assembly coordinate system is obtained. ; The first in the centroid coordinate system i stage rotor inertia tensor matrix The expression is: (1); In formula (1), For the first i The mass of the stage rotor, For the first i The inertia tensor matrix of the stage rotor in the center-of-mass coordinate system. For the first i The inertial tensor translation transformation matrix from the centroid coordinate system to the centroid coordinate system of the stage rotor; Inertia tensor matrix The calculation formula is: (2); In formula (2), For the first i The spatial pose rotation matrix of the stage rotor from the centroid coordinate system to the assembly coordinate system. T For transpose; n The inertial tensor matrix after the stage rotor assembly The calculation formula is: (3); In formula (3), Let be the inertial tensor translation transformation matrix of the i-th stage rotor from the centroid coordinate system to the assembly coordinate system.
[0006] Rotor inertial tensor translation transformation matrix from centroidal coordinate system to assembly coordinate system for: (4); In formula (4), and Let A and B be antisymmetric matrices related to the translation vector, and let A and B be commutators of the matrix. , , Let be the displacement difference between particle B and A in the x, y, and z directions in the centroidal coordinate system. , and These are the displacement components between the centroid coordinate system and the assembly coordinate system.
[0007] In the assembly coordinate system The direction vector is In the rotating coordinate system, The direction vector is ,in, To assemble the origin of the coordinate system, Let the origin of the rotating coordinate system be the origin. It is the geometric center of the upper end face in the centroidal coordinate system of the last stage rotor; According to the rotary coordinate system, the assembly coordinate system can bypass its origin. o r spatial axis l Obtained by rotation, based on the direction vector and direction vector Calculate spatial axes l Direction vector Based on direction vector Get direction vector and direction vector The included angle ; Combining the included angle Determine the rotation matrix of the rotor from the assembly coordinate system to the rotary coordinate system. Combined with rotation matrix and inertial tensor matrix Obtain the inertia tensor matrix of each rotor stage in the slewing coordinate system. ; Direction vector of rotation axis The expression is: (5); In formula (5), The direction between the origin of the assembly coordinate system and the geometric center of the upper end face of the last stage rotor is... ; Let be the direction vector between the origin of the rotary coordinate system and the geometric center of the upper end face of the last stage rotor. ; Direction vector and direction vector The included angle The calculation formula is: (6); Rotation matrix of the rotor from the assembly coordinate system to the rotation coordinate system The expression is: (7); In formula (7), Direction vector unit vector, Angle cosine, Angle The sine of; The inertial tensor matrix of each rotor stage in the rotating coordinate system The expression is: (8); In formula (8), , , Let be the moment of inertia about the three coordinate axes. , , It is the product of inertia perpendicular to the direction of rotation.
[0008] Furthermore, step 3 specifically includes: Gram-Schmidt orthogonalization is used to transform the inertia tensor matrix into a set of orthogonal vectors. The orthogonal vector set obtained by orthogonalization is then decomposed into a QR decomposition to obtain an orthogonal matrix Q and an upper triangular matrix R. The column vectors in the orthogonal matrix Q are normalized to obtain a standard orthogonal vector matrix. Q ; According to the orthogonal vector matrix Q The column vectors in the equation are used to obtain the direction of the principal axis of inertia, and then selected. The direction vector of the principal axis of inertia in the rotating coordinate system The spatial equation of the principal axis of inertia is obtained by combining the coordinates of the rotor's center of mass. The expression for an orthogonal vector group is: (9); (10); In formulas (9) and (10), , , These are the column vectors of the inertia tensor matrix. , , Let x, y, and z be the moments of inertia along the x, y, and z axes in the rotating coordinate system. , , This is the product of inertia perpendicular to the direction of rotation in the rotating coordinate system; The direction vector of the principal axis of inertia in the rotating coordinate system is: (11); In formula (11), The vectors in the orthogonal matrix obtained after QR decomposition of the inertia tensor matrix through Gram-Schmidt orthogonalization are... T For transpose, for The amount; The spatial equation of the principal axis of inertia is: (12); In formula (12), , , The coordinates of the rotor's center of mass in the rotary coordinate system.
[0009] Furthermore, step 4 specifically includes: The intersection points of the inertial spindle and the upper and lower end faces of the rotor at different assembly angles T r , B r and rotor centroid C r Project to x r o r y r Plane, calculation points T r , C r , B r The minimum envelope circle diameter is formed, and an inertial principal axis skew control model is established, wherein, in the plane x r o r y r The coordinates in are , , ; The expression for the inertial principal axis skew control model is: (13); In formula (13), The minimum envelope circle diameter of the projection point of the principal axis of inertia. The angle of rotation of the rotor around the Z-axis.
[0010] The beneficial effects of this invention are: This invention calculates the spatial equation of the principal inertial axis, constructs a principal inertial axis skew transmission model, and controls the minimum envelope circle diameter between the principal inertial axis and the rotation axis to ensure minimal coaxiality of the assembled multi-stage rotor principal inertial axes, thus minimizing the skew of the multi-stage rotor principal inertial axis. This invention precisely quantifies and analyzes the error of principal inertial axis skew during assembly. Based on the optimization objective of the minimum envelope circle diameter, it effectively controls the spatial deviation distribution of the principal inertial axis relative to the rotation axis, thereby achieving active compensation and precision allocation of principal inertial axis skew in the overall assembly. Compared with traditional methods relying on coaxiality, this invention directly starts from the spatial consistency of the principal inertial axis, more fundamentally controlling the rotor vibration characteristics and significantly improving the dynamic balance performance and operational stability of the high-speed rotor system. Attached Figure Description
[0011] Figure 1 This is a flowchart illustrating the method for transmission and control of multi-stage rotor inertial spindle skew coupling based on minimum envelope. Figure 2 This is a schematic diagram showing the positional relationship between the centroids of the first and last stage rotors. Figure 3 A schematic diagram for solving the coaxiality of the principal axes of inertia; Figure 4 A schematic diagram of the assembly and adjustment of multi-stage rotor stacking; Figure 5 A schematic diagram showing the coaxiality of the principal shafts of the three-stage rotor inertia. Figure 6 The image shows the simulation results of the three-stage rotor assembly. Detailed Implementation
[0012] like Figure 1 As shown, the steps of the method for transmission and control of skew coupling based on minimum envelope multi-stage rotor inertial spindle skew described in this embodiment include: S1: Perform a translation transformation of the rotor's inertia tensor from the centroid coordinate system to the assembly coordinate system; Define the first centroid coordinate system i The stage rotor inertia tensor matrix is expressed as: (1); In formula (1), For the first i The first stage rotorj The mass of a point mass i The number of stages of the rotor. j Indicates the number of the mass point. , , The first i The first stage rotor j A point mass in the centroid coordinate system x , y , z Coordinate components.
[0013] Based on the parallel axis generalization theorem, this invention performs a translation transformation of the inertia tensor from the centroidal coordinate system to the assembly coordinate system, and defines the matrix operation rules as follows: (2); Then, the inertial tensor translation transformation matrix of the i-th stage rotor from the centroid coordinate system to the assembly coordinate system in equation (2) is: (3); In formulas (2) and (3), and Let A and B be antisymmetric matrices related to the translation vector, and let A and B be commutators of the matrix. , , Let be the displacement difference between particle B and A in the x, y, and z directions in the centroidal coordinate system. , and These are the displacement components between the centroid coordinate system and the assembly coordinate system.
[0014] No. i The inertia tensor matrix of the stage rotor after translation from the centroidal coordinate system to the assembly coordinate system is expressed as: (4); Let the first i The inertia tensor matrix of the stage rotor in the center-of-mass coordinate system is: The position matrix of the centroid in the centroid coordinate system is Then the first i The inertia tensor matrix of the stage rotor in the centroidal coordinate system is expressed as: (5); In formula (5), For the first i The mass of the stage rotor, For the first i The inertia tensor matrix of the stage rotor in the center-of-mass coordinate system. For the first i The inertial tensor translation transformation matrix from the centroid coordinate system to the centroid coordinate system of the stage rotor; Then the firsti The inertia tensor matrix of the stage rotor after rotating from the centroidal coordinate system to the assembly coordinate system is expressed as: (6); In formula (6), For the first i The spatial pose rotation matrix of the stage rotor from the centroid coordinate system to the assembly coordinate system. T For transpose; Therefore n After the stage rotor is assembled, the inertia tensor matrix in the assembly coordinate system is expressed as: (7); In formula (7), Let be the inertial tensor translation transformation matrix of the i-th stage rotor from the centroid coordinate system to the assembly coordinate system.
[0015] S2: Calculate the inertia tensor matrix of the n-stage rotor in the rotating coordinate system after assembly; like Figure 2 As shown, in the assembly coordinate system, The direction vector is In a rotating coordinate system, The direction vector is .in, To assemble the origin of the coordinate system, Let the origin of the rotating coordinate system be the origin. The geometric center of the upper end face in the centroid coordinate system of the final stage rotor; vector From vector Around the axis l Obtained by rotation, the axis of rotation l The direction vector is represented as: (8); In formula (8), The direction between the origin of the assembly coordinate system and the geometric center of the upper end face of the last stage rotor is... ; Let be the direction vector between the origin of the rotary coordinate system and the geometric center of the upper end face of the last stage rotor. ; The unit vector representation of this vector is: (9); In formula (9), The direction vector of the rotation axis , unit vector; vector and The included angle is: (10); Therefore, the rotation matrix from the assembly coordinate system to the rotary coordinate system as follows: (11); In formula (11), Direction vector unit vector, Angle cosine, Angle The sine of; n The inertia tensor matrix of the stage rotor in the rotating coordinate system after assembly is expressed as: (12); In formula (12), , , Let be the moment of inertia about the three coordinate axes. , , It is the product of inertia perpendicular to the direction of rotation.
[0016] S3: The inertial tensor matrix is decomposed into QR values using the Gram-Schmidt orthogonalization method. In this embodiment, the Gram-Schmidt orthogonalization method is used to perform... QR The decomposition yields the corresponding eigenvalues and their eigenvectors, representing the moments of inertia about the principal axes of x, y, and z, as follows: The inertia tensor matrix is transformed into an orthogonal vector group. The orthogonal vector group is then decomposed into QR decomposition to obtain an orthogonal matrix Q and an upper triangular matrix R. The orthogonal matrix Q is shown below: (13); The elements are shown below: (14); In formulas (13) and (14), , , These are the column vectors of the inertia tensor matrix. , , Let x, y, and z be the moments of inertia along the x, y, and z axes in the rotating coordinate system. , , This is the product of inertia perpendicular to the direction of rotation in the rotating coordinate system; Normalize the orthogonalized column vectors to obtain the decomposed m×n orthogonal matrix: (15); After decomposition n × n The upper triangular matrix is: (16); The direction vector of the principal axis of inertia in the rotating coordinate system is: (17); Given that the principal axis of inertia passes through the center of mass, its spatial equation can be expressed as: (18); In formulas (17) and (18), The vectors in the orthogonal matrix obtained after QR decomposition of the inertia tensor matrix through Gram-Schmidt orthogonalization are... T For transpose, for The amount, , , For spatial coordinate variables in a rotating coordinate system, , , The coordinates of the rotor's center of mass in the rotary coordinate system.
[0017] S4: Project the principal axes of inertia at different assembly angles onto the rotary coordinate system. x r o r y r In the plane, by solving for the minimum envelope circle diameter of the projection point of the principal axis of inertia and the origin of the rotation coordinate system, an inertial axis skew adjustment model is established. like Figure 3 As shown, this invention projects the principal axis of inertia at different assembly angles onto a rotary coordinate system. x r o r y r In a plane, by solving for the minimum envelope circle diameter between the projection point of the principal inertia axis and the origin of the rotation coordinate system, the coaxiality values of the principal inertia axis under different assembly angles can be obtained. The projection of the principal inertia axis in a multi-stage rotor assembly is shown in the figure below; the principal inertia axis passes through the center of mass. C r It intersects with the upper and lower end faces of the rotor at points respectively after assembly. T r , B r .point T r , C r , B rexist x r o r y r The projection point on the plane is , , Assuming n The height of the stage rotor after assembly is z n Then point T r , C r , B r In plane x r o r y r The coordinates in are , , .
[0018] Solving for the coaxiality of the principal axes of inertia, i.e., solving for the point... T r , C r , B r The minimum envelope circle diameter and the coaxiality of the principal axes of inertia are expressed as follows: (19); In formula (19), The minimum envelope circle diameter is the projection point of the principal axis of inertia.
[0019] The model for adjusting the coaxiality and skewness of the principal axes of inertia is expressed as follows: (20); In formula (20), The minimum envelope circle diameter of the projection point of the principal axis of inertia. The angle of rotation of the rotor around the Z-axis. For the first i stage rotor rotation The minimum envelope circle diameter of the projection point of the principal axis of inertia after the angle.
[0020] S5: Adjusting the assembly phase of each rotor stage can regulate the coaxiality of the inertial spindle and achieve optimal assembly; In summary, this invention calculates the spatial equation of the principal inertial axis, constructs a principal inertial axis skew transmission model, and minimizes the minimum envelope circle diameter between the principal inertial axis and the rotation axis to ensure minimal coaxiality of the assembled multi-stage rotor principal inertial axes, thus achieving minimization of principal inertial axis skew. This invention precisely quantifies and analyzes the error of principal inertial axis skew during assembly. Based on the optimization objective of the minimum envelope circle diameter, it effectively controls the spatial deviation distribution of the principal inertial axis relative to the rotation axis, thereby achieving active compensation and precision allocation of principal inertial axis skew in the overall assembly. Compared with traditional methods relying on coaxiality, this invention directly starts from the spatial consistency of the principal inertial axis, more fundamentally controlling the rotor vibration characteristics and significantly improving the dynamic balance performance and operational stability of the high-speed rotor system.
[0021] After completing the rotor assembly described above, this embodiment underwent the following simulation verification; based on the assembly method in this embodiment, a three-stage rotor was assembled, and the assembly scheduling model is as follows. Figure 4 As shown, the coaxiality of the three-stage rotor inertial principal shafts is as follows: Figure 5 As shown, the simulation results are as follows: Figure 6 As shown in the figure, when the rotor form and position error is constant, i.e., the eccentricity error of all three rotor stages is 0.1 mm and the tilt error is 10′, the coaxiality of the inertial main shaft changes with the assembly angle of each rotor stage during assembly. It can be seen from the figure that when the assembly angle of the second and third rotor stages is [199°, 293°], the coaxiality of the inertial main shaft is the smallest, at 0.164 mm, at which point the centroid of the multi-stage rotor is very close to the rotation axis. When the assembly angle of the second and third rotor stages becomes [113°, 145°], the coaxiality of the inertial main shaft is the largest, at 0.923 mm. Therefore, by adjusting the assembly angle, the skewness of the inertial main shaft can be controlled, and the coaxiality of the inertial main shaft can be reduced by a maximum of 0.759 mm, a reduction of 82.2%.
[0022] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. 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 some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent substitutions, and improvements made to the above embodiments without departing from the scope of the present invention, based on the technical essence of the present invention and within the spirit and principles of the present invention, shall still fall within the protection scope of the present invention.
Claims
1. A method for transmission and control of skew coupling of multi-stage rotor inertial spindle based on minimum envelope, characterized in that, include: Step 1: Based on the transformation relationship between the rotor's centroid coordinate system, centroid coordinate system, and assembly coordinate system, calculate the inertia tensor matrix in the assembly coordinate system of a single-stage rotor. Step 2: Calculate based on the multi-stage rotor assembly mechanism. n The inertia tensor matrix of the stage rotor in the rotating coordinate system after assembly; Step 3: Perform Gram-Schmidt orthogonalization on the inertia tensor matrix. QR Decompose the equations to obtain the spatial equations of the principal axes of inertia. Step 4: Project the principal axes of inertia at different assembly angles onto the rotary coordinate system. x r o r y r In the plane, solve for the minimum envelope circle diameter of the projection point of the principal axis of inertia and the origin of the rotation coordinate system, and establish a principal axis of inertia skew adjustment model; Step 5: Based on the established inertial spindle skew control model, the coaxiality of the inertial spindle can be controlled by adjusting the assembly phase of each stage of the rotor, thus achieving optimal assembly.
2. The method for transmission and control of multi-stage rotor inertial spindle skew coupling based on minimum envelope as described in claim 1, characterized in that, Step 1 specifically includes: Let the first i The inertia tensor matrix of the stage rotor in the center-of-mass coordinate system is: Its centroid position matrix in the centroid coordinate system is Based on the parallel axis generalization theorem, determine the rotor's inertial tensor translation transformation matrix from the centroidal coordinate system to the assembly coordinate system. And calculate and obtain the rotation transformation matrix. ; Combined with translation transformation matrix and the i The inertial tensor matrix of the stage rotor in the center-of-mass coordinate system Obtain the first centroid coordinate system i stage rotor inertia tensor matrix ; Combined with the centroid coordinate system, the first i stage rotor inertia tensor matrix and rotation transformation matrix Get the i The inertial tensor matrix of the stage rotor after rotating from the centroidal coordinate system to the assembly coordinate system ; right n After the stage rotor is assembled, its inertia tensor matrix in the assembly coordinate system is obtained. ; The first in the centroid coordinate system i stage rotor inertia tensor matrix The expression is: （1）； In formula (1), For the first i The mass of the stage rotor, For the first i The inertia tensor matrix of the stage rotor in the center-of-mass coordinate system. For the first i The inertial tensor translation transformation matrix from the centroid coordinate system to the centroid coordinate system of the stage rotor; Inertia tensor matrix The calculation formula is: （2）； In formula (2), For the first i The spatial pose rotation matrix of the stage rotor from the centroidal coordinate system to the assembly coordinate system. T For transpose; n The inertial tensor matrix after the stage rotor assembly The calculation formula is: （3）； In formula (3), For the first i The inertial tensor translation transformation matrix of the stage rotor from the centroid coordinate system to the assembly coordinate system; Rotor inertial tensor translation transformation matrix from centroidal coordinate system to assembly coordinate system for: （4）。 3. The method for transmission and control of skew coupling of multi-stage rotor inertial spindle based on minimum envelope as described in claim 1, characterized in that, Step 2 specifically includes: In the assembly coordinate system The direction vector is In the rotating coordinate system, The direction vector is ,in, To assemble the origin of the coordinate system, Let the origin of the rotating coordinate system be the origin. It is the geometric center of the upper end face in the centroidal coordinate system of the last stage rotor; According to the rotary coordinate system, the assembly coordinate system can bypass its origin. o r spatial axis l Obtained by rotation, based on the direction vector and direction vector Calculate spatial axes l Direction vector Based on direction vector Get direction vector and direction vector The included angle ; Combining the included angle Determine the rotation matrix of the rotor from the assembly coordinate system to the rotary coordinate system. Combined with rotation matrix and inertial tensor matrix Obtain the inertia tensor matrix of each rotor stage in the slewing coordinate system. ; Direction vector of rotation axis The expression is: （5）； In formula (5), The direction between the origin of the assembly coordinate system and the geometric center of the upper end face of the last stage rotor is... ; Let be the direction vector between the origin of the rotary coordinate system and the geometric center of the upper end face of the last stage rotor. ; Direction vector and direction vector The included angle The calculation formula is: （6）； Rotation matrix of the rotor from the assembly coordinate system to the rotation coordinate system The expression is: （7）； In formula (7), Direction vector unit vector, Angle cosine, Angle The sine of; The inertial tensor matrix of each rotor stage in the rotating coordinate system The expression is: （8）； In formula (8), , , Let be the moment of inertia about the three coordinate axes. , , It is the product of inertia perpendicular to the direction of rotation.
4. The method for transmission and control of multi-stage rotor inertial spindle skew coupling based on minimum envelope as described in claim 1, characterized in that, Step 3 specifically includes: Gram-Schmidt orthogonalization is used to transform the inertia tensor matrix into a set of orthogonal vectors. The orthogonal vector set obtained by orthogonalization is then decomposed into a QR decomposition to obtain an orthogonal matrix Q and an upper triangular matrix R. The column vectors in the orthogonal matrix Q are normalized to obtain a standard orthogonal vector matrix. Q ; According to the orthogonal vector matrix Q The column vectors in the equation are used to obtain the direction of the principal axis of inertia, and then selected. The direction vector of the principal axis of inertia in the rotating coordinate system The spatial equation of the principal axis of inertia is obtained by combining the coordinates of the rotor's center of mass. The expression for an orthogonal vector group is: （9）； （10）； In formulas (9) and (10), , , These are the column vectors of the inertia tensor matrix. , , Let x, y, and z be the moments of inertia along the x, y, and z axes in the rotating coordinate system. , , This is the product of inertia perpendicular to the direction of rotation in the rotating coordinate system; The direction vector of the principal axis of inertia in the rotating coordinate system is: （11）； In formula (11), The vectors in the orthogonal matrix obtained after QR decomposition of the inertia tensor matrix through Gram-Schmidt orthogonalization are... T For transpose, for The amount; The spatial equation of the principal axis of inertia is: （12）； In formula (12), , , The coordinates of the rotor's center of mass in the rotary coordinate system; Orthogonal vector matrix Q The expression is: (13).
5. The method for transmission and control of multi-stage rotor inertial spindle skew coupling based on minimum envelope as described in claim 1, characterized in that, Step 4 specifically includes: The intersection points of the inertial spindle and the upper and lower end faces of the rotor at different assembly angles T r , B r and rotor centroid C r Project to x r o r y r Plane, calculation points T r , C r , B r The minimum envelope circle diameter is formed, and an inertial principal axis skew control model is established, wherein, in the plane x r o r y r The coordinates in are , , ; The expression for the inertial principal axis skew control model is: （14）； In formula (14), The minimum envelope circle diameter of the projection point of the principal axis of inertia. The angle of rotation of the rotor around the Z-axis. For the first i stage rotor rotation The minimum envelope circle diameter of the projection point of the principal axis of inertia after the angle.