Method for measuring and calculating the angle between two rotation axes

Abstract

The application provides a method for measuring and calculating the included angle between two rotating shafts, and belongs to the technical field of aero-engines. The method comprises the following steps: introducing a third smooth plane; obtaining the end face runout of the first smooth plane measured by a displacement sensor on the first rotating shaft when the first rotating shaft rotates, and obtaining a first measurement result; obtaining the end face runout of the first smooth plane measured by a displacement sensor on the second rotating shaft when the second rotating shaft rotates, and obtaining a second measurement result; obtaining the included angle between the two rotating shafts and the smooth plane; obtaining the angular displacement alpha and beta of the first rotating shaft corresponding to the minimum value in the first measurement result and the second measurement result, respectively; and finally, drawing the direction vectors of the first rotating shaft and the second rotating shaft in a three-dimensional Cartesian coordinate system, and solving the included angle between the two rotating shafts according to the definition of vector inner product, thereby solving the problem of measuring and calculating the included angle when the radial reference surfaces of the two rotating shafts are not completely exposed.

Description

Technical Field

[0001] This application relates to the field of aero engines, and in particular to a method for measuring and calculating the angle between two rotating shafts. Background Technology

[0002] During the assembly of an aero-engine, in order to ensure that the two connecting shafts rotate smoothly during operation, it is necessary to measure and control the included angle between the two shafts. When the included angle between the two connecting shafts is too large and exceeds the design requirements, abnormal wear will occur at the connection point of the two shafts during engine operation, which may prevent them from reaching their design life and lead to premature scrapping.

[0003] In traditional measurement methods, we often use mature equipment and methods such as moving coordinate measuring machines (CMMs) and laser trackers to collect data on the exposed reference surfaces of the two axes. The centerlines of the two axes are then fitted into computer software, and their included angle is calculated. However, aero-engines have complex structures, and measuring the included angle of the two axes in their entirety may not yield a suitable exposed reference surface. In such cases, traditional measurement methods such as CMMs and laser trackers are no longer suitable. Summary of the Invention

[0004] In view of this, this application provides a method for measuring and calculating the included angle between two rotating shafts, which solves the problem of measuring and calculating the included angle when the radial reference plane of the two rotating shafts is not completely exposed.

[0005] The method for measuring and calculating the included angle between two rotating shafts provided in this application adopts the following technical solution:

[0006] A method for measuring and calculating the angle between two rotating shafts includes the following steps:

[0007] A first smooth plane intersecting the axes of the two rotating shafts is selected and used as a reference plane. The first smooth plane remains stationary relative to the engine stator during the test.

[0008] A displacement sensor is fixedly installed on the first rotating shaft. The measurement direction of the displacement sensor is parallel to the axial direction of the first rotating shaft. The first rotating shaft is driven to rotate one revolution. The displacement sensor on the first rotating shaft measures the end face runout of the first smooth plane and obtains a first measurement result. The angular displacement of the first rotating shaft corresponding to the minimum value in the first measurement result is then measured. ;

[0009] The angle between the first rotating shaft and the first smooth plane is obtained based on the first measurement result. ;

[0010] One end of the second rotating shaft is assembled to one end of the first rotating shaft. A displacement sensor is fixedly installed on the second rotating shaft, with the measurement direction of the displacement sensor parallel to the axial direction of the second rotating shaft. The first rotating shaft is driven to rotate, causing the second rotating shaft to rotate one revolution. The displacement sensor on the second rotating shaft is used to measure the end face runout of the first smooth plane and obtain a second measurement result. The angular displacement of the first rotating shaft corresponding to the minimum value in the second measurement result is measured. ;

[0011] The angle between the second rotating shaft and the first smooth plane is obtained based on the second measurement result. ;

[0012] Plot the direction vector of the first axis of rotation in a three-dimensional Cartesian coordinate system. The direction vector of the second axis of rotation : , ;

[0013] Solve for the angle between the two axes of rotation using the definition of the vector dot product. It can be obtained using the following formula: .

[0014] Optionally, the angle between the first rotating shaft and the first smooth plane can be obtained based on the first measurement result. The steps include:

[0015] The minimum value in the first measurement result is obtained. and maximum value , ,in, This is the rotation radius of the displacement sensor on the first rotating shaft.

[0016] Optionally, the angle between the second rotating shaft and the first smooth plane can be obtained based on the second measurement result. The steps include:

[0017] The minimum value in the second measurement result is obtained. and maximum value , in, This is the rotation radius of the displacement sensor on the second rotating shaft.

[0018] Optionally, the direction vector of the first rotation axis can be plotted in a three-dimensional Cartesian coordinate system. The direction vector of the second axis of rotation : , The steps include:

[0019] Taking the first smooth plane as x - yEstablish a three-dimensional Cartesian coordinate system on the plane, determine the zero position of the angular displacement of the first axis of rotation, and... x - y Establish a polar coordinate system on a plane, aligning its origin with the origin of the three-dimensional Cartesian coordinate system. Align the zero displacement direction of the polar coordinate system with the zero displacement direction of the three-dimensional Cartesian coordinate system. x The positive direction coincides;

[0020] Based on the angular displacement of the first rotating shaft and the angle between the first pivot and the first smooth plane Plot the direction vector of the central axis of the first axis of rotation in a three-dimensional Cartesian coordinate system. Based on the angular displacement of the second shaft and the angle between the second pivot and the first smooth plane Plot the direction vector of the central axis of the second axis of rotation in a three-dimensional Cartesian coordinate system. ,set up A , B The two points are respectively at x - y Projection point of the plane A '、 B 'All are at the origin' O On the unit circle centered at the line segment OA Draw a point on the reverse extension line. C , making line segment OA With line segment OC If the vectors are of equal length, then... with vector The first axis of rotation is an opposite vector to the second axis of rotation. Vectors can be used with vector The included angle represents, , ;

[0021] get ;

[0022] .

[0023] Optionally, will and Substitution The included angle between the two shafts is obtained. for:

[0024] .

[0025] Optionally, the device may also include mounting a drive motor and an angular displacement sensor on a first rotating shaft, wherein the drive motor drives the first rotating shaft to rotate, and the angular displacement sensor measures the angular displacement of the first rotating shaft.

[0026] Optionally, the optical transceiver is mounted on the first rotating shaft, and the zero-position reflector is mounted on the stator component and kept in a fixed position during the test. The stator component is fixed relative to the drive motor. When the signal emitted by the optical transceiver is received and reflected by the zero-position reflector and the optical transceiver receives the signal emitted by the zero-position reflector, the angular displacement of the first rotating shaft is zero.

[0027] Optionally, when the optical transceiver rotates to the direction of the zero-position reflector to emit and receive signals, it transmits the zero-position signal to the computer. The computer marks the orientation of the first rotating shaft at this time as the zero position of the system's angular displacement. The computer calibrates the output signal of the angular displacement sensor and obtains the angular displacement of the first rotating shaft relative to the zero position in real time.

[0028] In summary, this application includes the following beneficial technical effects:

[0029] This application introduces a third smooth plane. When the first rotating shaft rotates, a displacement sensor on the first rotating shaft measures the end face runout of the first smooth plane and obtains a first measurement result. When the second rotating shaft rotates, a displacement sensor on the second rotating shaft measures the end face runout of the first smooth plane and obtains a second measurement result. The application also obtains the angles between the two rotating shafts and the smooth plane, and the angular displacement of the first rotating shaft corresponding to the minimum value between the first and second measurement results. and Finally, the direction vectors of the first and second rotation axes are plotted in a three-dimensional Cartesian coordinate system, and the angle between the two rotation axes is solved according to the definition of the dot product of vectors. This solves the problem of measuring and calculating the included angle when the radial reference planes of the two rotating shafts are not completely exposed. Attached Figure Description

[0030] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0031] Figure 1 This is a schematic diagram of the method for measuring and calculating the included angle between two rotating shafts in this application;

[0032] Figure 2 A schematic diagram showing the end face runout of the first smooth plane measured by the displacement sensor on the first rotating shaft of this application;

[0033] Figure 3 This is a schematic diagram showing the angular relationship between the first rotating shaft and the first smooth plane in this application;

[0034] Figure 4 A schematic diagram showing the end face runout of the first smooth plane measured by the displacement sensor on the second rotating shaft of this application;

[0035] Figure 5 This is a schematic diagram showing the angular relationship between the second rotating shaft and the first smooth plane in this application;

[0036] Figure 6 This is a three-dimensional spatial vector diagram of the central axis of the first rotating shaft in this application;

[0037] Figure 7 This is a schematic diagram of the three-dimensional spatial vector of the central axis of the second rotating shaft in this application;

[0038] Figure 8 This is a schematic diagram showing the included angle between the central axes of the first and second rotating shafts in this application.

[0039] Explanation of reference numerals in the attached drawings: 1. First rotating shaft; 2. Second rotating shaft; 3. First smooth plane; 4. Drive motor; 5. Angular displacement sensor; 6. Optical transceiver; 7. Zero-position reflector; 8. Displacement sensor; 9. Computer; 10. First clamp; 11. Second clamp. Detailed Implementation

[0040] The embodiments of this application will now be described in detail with reference to the accompanying drawings.

[0041] The following specific examples illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. This application can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0042] It should be noted that various aspects of embodiments within the scope of the appended claims are described below. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this application, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using structures and / or functionalities other than one or more of the aspects set forth herein.

[0043] It should also be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of this application. The drawings only show the components related to this application and are not drawn according to the actual number, shape and size of the components in the actual implementation. In the actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0044] Furthermore, specific details are provided in the following description to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that the described aspects can be practiced without these specific details.

[0045] This application provides a method for measuring and calculating the included angle between two rotating shafts.

[0046] A method for measuring and calculating the angle between two rotating shafts includes the following steps:

[0047] like Figure 1 As shown, a first smooth plane 3 intersecting the axes of the two rotating shafts is selected, and the first smooth plane 3 is used as a reference plane. The first smooth plane 3 remains stationary relative to the engine stator during the test.

[0048] A displacement sensor 8 is fixedly installed on the first rotating shaft 1. The measurement direction of the displacement sensor 8 is parallel to the axial direction of the first rotating shaft 1. The first rotating shaft 1 is driven to rotate one revolution, and the displacement sensor 8 on the first rotating shaft 1 is used to measure the end face runout of the first smooth plane 3 and obtain the first measurement result. Measure the angular displacement of the first rotating shaft 1 corresponding to the minimum value in the first measurement result. Specifically, the displacement sensor 8 on the first rotating shaft 1 is used to measure the end face runout of the first smooth plane 3 and obtain the first measurement result. The process can be understood as follows: during one revolution of the first rotating shaft 1, the displacement sensor 8 on the first rotating shaft 1 measures the distance from the displacement sensor 8 on the first rotating shaft 1 to the first smooth plane 3 when the first rotating shaft 1 rotates to different positions, and uses the measured distance values ​​as the first measurement result. That is, the distance measured by the displacement sensor 8 on the first rotating shaft 1, which varies with the angular displacement of the first rotating shaft 1, is taken as the first measurement result. .

[0049] The angle between the first rotating shaft 1 and the first smooth plane 3 is obtained based on the first measurement result. .

[0050] One end of the second rotating shaft 2 is assembled with one end of the first rotating shaft 1. A displacement sensor 8 is fixedly installed on the second rotating shaft 2. The measurement direction of the displacement sensor 8 is parallel to the axial direction of the second rotating shaft 2. The first shaft is driven to rotate, causing the second rotating shaft 2 to rotate one revolution. The displacement sensor 8 on the second rotating shaft 2 is used to measure the end face runout of the first smooth plane 3 and obtain the second measurement result. The angular displacement of the first rotating shaft 1 corresponding to the minimum value in the second measurement result is measured. Specifically, the displacement sensor 8 on the second rotating shaft 2 is used to measure the end face runout of the first smooth plane 3 and obtain the second measurement result. The process can be understood as follows: during one revolution of the second rotating shaft 2, the displacement sensor 8 on the second rotating shaft 2 measures the distance from the displacement sensor 8 on the second rotating shaft 2 to the first smooth plane 3 when the second rotating shaft 2 rotates to different positions, and uses the measured distance values ​​as the second measurement result. That is, the distance measured by the displacement sensor 8 on the second rotating shaft 2, which varies with the angular displacement of the second rotating shaft 2, is used as the second measurement result. .

[0051] The angle between the second rotating shaft 2 and the first smooth plane 3 is obtained based on the second measurement result. .

[0052] Plot the direction vector of the first rotation axis 1 in a three-dimensional Cartesian coordinate system. The direction vector of the second rotation axis 2 : , ;

[0053] Calculating vectors in three-dimensional space , and the included angle between the two pivots The angle between the two axes of rotation is calculated using the definition of the vector dot product. It can be obtained using the following formula:

[0054] .

[0055] Specifically, the method of this application involves installing the measuring equipment before starting the measurement. A drive motor 4 and an angular displacement sensor 5 are mounted on the first rotating shaft 1. The drive motor 4 drives the first rotating shaft 1 to rotate, and the angular displacement sensor 5 measures the angular displacement of the first rotating shaft 1. This angular displacement of the first rotating shaft 1 is used as the system's angular displacement. An optical transceiver 6 is mounted on the first rotating shaft 1, and a zero-position reflector 7 is mounted on a stator component. The stator component is fixed relative to the drive motor 4. When the signal emitted by the optical transceiver 6 is received and reflected by the zero-position reflector 7, and the optical transceiver 6 receives the signal emitted by the zero-position reflector 7, the angular displacement of the first rotating shaft 1 is zero. When the optical transceiver 6 rotates to the direction of the zero-position reflector 7 and emits and receives a signal, it transmits the zero-position signal to the computer 9. The computer 9 marks this position as the system zero position and calibrates the output signal of the angular displacement sensor 5 to obtain the real-time angular displacement of the first rotating shaft 1 relative to the zero position.

[0056] In one embodiment, the zero-position reflector 7 and the first smooth plane 3 are fixed references relative to the engine stator throughout the system. The first rotating shaft 1 is mounted on the engine mounting base via bearings. The drive motor 4 is rigidly connected to the first rotating shaft 1 to drive it to rotate at a constant speed. The angular displacement sensor 5 is rigidly connected to the drive motor 4 and can measure the angular displacement of the first rotating shaft 1 in real time, transmitting the measured signal to the computer 9. The zero-position reflector 7 is fixed in a specific direction on the stator component. When the first rotating shaft 1 rotates, the optical transceiver 6 rotates to the direction of the zero-position reflector 7 to emit and receive signals, transmitting the zero-position signal to the computer 9. The computer 9 marks the orientation of the first rotating shaft 1 at this time as the zero-position angular displacement of the system. At this time, the computer 9 calibrates the output signal of the angular displacement sensor 5, obtaining the angular displacement data relative to the system zero position in real time.

[0057] Displacement sensor 8 on the first rotating shaft 1 is fixed to the first rotating shaft 1 by a first clamp 10, forming a rigid connection between the displacement sensor 8, the first clamp 10, and the first rotating shaft 1. The measurement direction of displacement sensor 8 is parallel to the axis of the first rotating shaft 1. When the first rotating shaft 1 rotates, displacement sensor 8 can measure the end face runout of the first smooth plane 3 and transmit the displacement signal to computer 9. When displacement sensor 8 on the second rotating shaft 2 is fixed to the second rotating shaft 2 by a second clamp 11, displacement sensor 8, the second clamp 11, and the second rotating shaft 2 form a rigid connection. The measurement direction of displacement sensor 8 is parallel to the axis of the second rotating shaft 2. When the first rotating shaft 1 drives the second rotating shaft 2 to rotate together, displacement sensor 8 can measure the end face runout of the first smooth plane 3 and transmit the displacement signal to computer 9.

[0058] The first smooth plane 3 is a surface with very high flatness. It can be a high-precision reference surface on the engine's own structure, or a high-precision reference surface on a tooling fixture designed and manufactured for accurate measurement in this system. The final measurement and calculation results in this method are negligibly affected by the flatness of the first smooth plane 3 itself.

[0059] like Figure 2 and Figure 3 As shown, the angle between the first rotating shaft 1 and the first smooth plane 3 is obtained based on the first measurement result. The steps include:

[0060] The second rotating shaft 2 is not assembled onto the first rotating shaft 1. The second rotating shaft 2 is mounted on the engine mounting bracket via bearings. The drive motor 4 drives the first rotating shaft 1 to rotate. For each rotation of the first rotating shaft 1, the displacement sensor 8 on the first rotating shaft 1 measures the first measurement result of the end face runout of the first smooth plane 3. From the first measurement result Get the maximum value and minimum value The displacement sensor 8 on the first rotating shaft 1 measures the maximum value. and minimum value The two positions correspond to a system angular displacement difference of 180°, from which we obtain (Equation 2-1).

[0061] in, The rotation radius of the displacement sensor 8 on the first rotating shaft 1 is determined; and the minimum value in the first measurement result is obtained. Corresponding system angular displacement .

[0062] like Figure 4 and Figure 5As shown, the angle between the second rotating shaft 2 and the first smooth plane 3 is obtained based on the second measurement result. The steps include:

[0063] The second rotating shaft 2 is mounted coaxially with the first rotating shaft 1. Ideally, the first rotating shaft 1 and the second rotating shaft 2 are coaxial. However, due to installation errors, there is an angle between the axes of the first rotating shaft 1 and the second rotating shaft 2. The drive motor 4 drives the first rotating shaft 1 to rotate, and the first rotating shaft 1 drives the second rotating shaft 2 to rotate. After the second rotating shaft 2 rotates one revolution, the displacement sensor 8 on the second rotating shaft 2 measures the second measurement result of the runout of the end face of the first smooth plane 3. From the second measurement result Get the maximum value and minimum value The displacement sensor 8 on the second rotating shaft 2 measured the maximum value. and minimum value The two positions correspond to a system angular displacement difference of 180°, from which we obtain (Equation 2-2).

[0064] in, The rotation radius of the displacement sensor 8 on the second rotating shaft 2. Obtain the minimum value from the second measurement results. Corresponding system angular displacement

[0065] like Figure 6-8 As shown, with the first smooth plane 3 as... x - y Establish a three-dimensional Cartesian coordinate system on the plane, set the angular displacement of the zero-position reflector 7 as the zero angular displacement of the system, and... x - y Establish a polar coordinate system on a plane, aligning its origin with the origin of the three-dimensional Cartesian coordinate system. Align the zero displacement direction of the polar coordinate system with the zero displacement direction of the three-dimensional Cartesian coordinate system. x The positive directions coincide. Based on the angular displacement of the first rotating shaft 1. and the angle between the first rotating shaft 1 and the first smooth plane 3 Plot the direction vector of the central axis of the first rotation axis 1 in a three-dimensional Cartesian coordinate system. Based on the angular displacement of the second rotating shaft 2 and the angle between the second rotating shaft 2 and the first smooth plane 3 Plot the direction vector of the central axis of the second rotation axis 2 in a three-dimensional Cartesian coordinate system. ,.set up A , B The two points are respectively at x - y Projection point of the planeA '、 B 'All are at the origin' O On the unit circle centered at , the radius of the unit circle is 1. On line segment . OA Draw a point on the reverse extension line. C , making line segment OA With line segment OC If the vectors are of equal length, then... with vector They are opposite vectors. The angle between the first axis of rotation 1 and the second axis of rotation 2 can be represented by a vector. with vector The included angle express.

[0066] like Figure 6 As shown, we can obtain C The coordinates of the point are After trigonometric transformations, the following relationship can be obtained:

[0067] (Equation 2-3)

[0068] Substituting equation 2-1 into equation 2-3, we get:

[0069] (Equation 2-4)

[0070] so C Point coordinates can be represented as .

[0071] like Figure 7 As shown, we can obtain B The coordinates of the point are After trigonometric transformations, the following relationship can be obtained:

[0072] (Equation 2-5)

[0073] Substituting equation 2-2 into equation 2-5, we get:

[0074] (Equation 2-6)

[0075] so B Point coordinates can be represented as .

[0076] Then we can obtain the vector. , The expression in a three-dimensional Cartesian coordinate system:

[0077] (Equation 2-7)

[0078] (Equation 2-8)

[0079] Because vectors with vector Since they are opposite vectors, we have:

[0080] To calculate two three-dimensional space vectors , The included angle The solution can be found using the definition of the dot product of vectors. Given vectors... , ,vector , The included angle is So there are

[0081] (Equation 2-10)

[0082] So the included angle It can be represented as

[0083] (Equation 2-11)

[0084] According to the definitions of the inner product and modulus of three-dimensional vectors, we have

[0085] (Equation 2-12)

[0086] (Equation 2-13)

[0087] (Equation 2-14)

[0088] Substituting equations 2-12 to 2-14 into equation 2-11, we get:

[0089] (Equation 2-15)

[0090] set up

[0091] (Equation 2-16)

[0092] (Equation 2-17)

[0093] Substituting equations 2-16 and 2-17 into equation 2-15, we get:

[0094] (Equation 2-18)

[0095] Rearranging Equation 2-18, we obtain the included angle between the first rotating shaft 1 and the second rotating shaft 2. The expression is as follows:

[0096] (Equation 2-19)

[0097] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for measuring and calculating the included angle between two rotating shafts, characterized in that, Includes the following steps: A first smooth plane intersecting the axes of the two rotating shafts is selected and used as a reference plane. The first smooth plane remains stationary relative to the engine stator during the test. A displacement sensor is fixedly installed on the first rotating shaft. The measurement direction of the displacement sensor is parallel to the axial direction of the first rotating shaft. The first rotating shaft is driven to rotate one revolution. The displacement sensor on the first rotating shaft measures the end face runout of the first smooth plane and obtains a first measurement result. The angular displacement of the first rotating shaft corresponding to the minimum value in the first measurement result is then measured. ; The angle between the first rotating shaft and the first smooth plane is obtained based on the first measurement result. ; One end of the second rotating shaft is assembled to one end of the first rotating shaft. A displacement sensor is fixedly installed on the second rotating shaft, with the measurement direction of the displacement sensor parallel to the axial direction of the second rotating shaft. The first rotating shaft is driven to rotate, causing the second rotating shaft to rotate one revolution. The displacement sensor on the second rotating shaft is used to measure the end face runout of the first smooth plane and obtain a second measurement result. The angular displacement of the first rotating shaft corresponding to the minimum value in the second measurement result is measured. ; The angle between the second rotating shaft and the first smooth plane is obtained based on the second measurement result. ; Plot the direction vector of the first axis of rotation in a three-dimensional Cartesian coordinate system. The direction vector of the second axis of rotation : , ; Solve for the angle between the two axes of rotation using the definition of the vector dot product. It can be obtained using the following formula: .

2. The method for measuring and calculating the included angle between two rotating shafts according to claim 1, characterized in that, The angle between the first rotating shaft and the first smooth plane is obtained based on the first measurement result. The steps include: The minimum value in the first measurement result is obtained. and maximum value , ,in, This is the rotation radius of the displacement sensor on the first rotating shaft.

3. The method for measuring and calculating the included angle between two rotating shafts according to claim 2, characterized in that, The angle between the second rotating shaft and the first smooth plane is obtained based on the second measurement result. The steps include: The minimum value in the second measurement result is obtained. and maximum value , in, This is the rotation radius of the displacement sensor on the second rotating shaft.

4. The method for measuring and calculating the included angle between two rotating shafts according to claim 3, characterized in that, Plot the direction vector of the first axis of rotation in a three-dimensional Cartesian coordinate system. The direction vector of the second axis of rotation : , The steps include: Taking the first smooth plane as x - y Establish a three-dimensional Cartesian coordinate system on the plane, determine the zero position of the angular displacement of the first axis of rotation, and... x - y Establish a polar coordinate system on a plane, aligning its origin with the origin of the three-dimensional Cartesian coordinate system. Align the zero displacement direction of the polar coordinate system with the zero displacement direction of the three-dimensional Cartesian coordinate system. x The positive direction coincides; Based on the angular displacement of the first rotating shaft and the angle between the first pivot and the first smooth plane Plot the direction vector of the central axis of the first axis of rotation in a three-dimensional Cartesian coordinate system. Based on the angular displacement of the second shaft and the angle between the second pivot and the first smooth plane Plot the direction vector of the central axis of the second axis of rotation in a three-dimensional Cartesian coordinate system. ,set up A , B The two points are respectively at x - y Projection point of the plane A '、 B 'All are at the origin' O On the unit circle centered at the line segment OA Draw a point on the reverse extension line. C , making line segment OA With line segment OC If the vectors are of equal length, then... with vector The first axis of rotation is an opposite vector to the second axis of rotation. Vectors can be used with vector The included angle represents, , ; get ; 。 5. The method for measuring and calculating the included angle between two rotating shafts according to claim 4, characterized in that, Will and Substitution The included angle between the two shafts is obtained. for: 。 6. The method for measuring and calculating the included angle between two rotating shafts according to claim 1, characterized in that, It also includes mounting a drive motor and an angular displacement sensor on a first rotating shaft, wherein the drive motor drives the first rotating shaft to rotate, and the angular displacement sensor measures the angular displacement of the first rotating shaft.

7. The method for measuring and calculating the included angle between two rotating shafts according to claim 6, characterized in that, An optical transceiver is mounted on the first rotating shaft, and a zero-position reflector is mounted on a stator component and kept in a fixed position during the test. The stator component is fixed relative to the drive motor. When the signal emitted by the optical transceiver is received and reflected by the zero-position reflector and the optical transceiver receives the signal emitted by the zero-position reflector, the angular displacement of the first rotating shaft is zero.

8. The method for measuring and calculating the included angle between two rotating shafts according to claim 7, characterized in that, When the optical transceiver rotates to the direction of the zero-position reflector and emits and receives a signal, it transmits the zero-position signal to the computer. The computer marks the orientation of the first rotating shaft at this time as the zero position of the system's angular displacement. The computer calibrates the output signal of the angular displacement sensor and obtains the angular displacement of the first rotating shaft relative to the zero position in real time.

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