Vortex trajectory algorithm for rotor system vibration and method for determining the position of the major and minor semi-axes

Abstract

The invention discloses a vortex trajectory algorithm for rotor system vibration, a method for determining the position of the major and minor semi-axes, and a vortex trajectory generation algorithm for rotor system vibration, including: obtaining the vibration frequency of the rotor system according to the vibration differential equation of the rotor system, obtaining the complex amplitude of the current cross-section geometric center along the X-axis direction and the complex amplitude along the Y-axis direction; using complex form to establish the motion trajectory equation of the cross-section center of the rotor system. The present invention utilizes the rotor vibration response data to determine the vortex trajectory of the rotor system under unbalanced excitation under general circumstances. By determining the size of the vortex trajectory, the energy distribution of the rotor vibration can be understood, the minimum vibration time and energy distribution can be analyzed, the harmful vibration of the system can be reduced, and the rotor system with less harmful vibration can be designed conveniently.

Description

Technical Field

[0001] The present invention belongs to the technical field of rotor system vibration, and in particular relates to a vortex trajectory algorithm for rotor system vibration and a method for determining the positions of major and minor semi-axes. Background Art

[0002] A rotor refers to a mechanical part that rotates around an axis. A system consisting of multiple rotating parts that rotate around an axis is called a rotor system. Rotor dynamics is a discipline that studies the vibration of a rotor system. It mainly studies the stability, inherent characteristics, and response characteristics of rotor motion. On this basis, the design of the rotor system is carried out so that the system can meet the requirements of different applications.

[0003] When studying the radial vibration of a rotor system (also called lateral vibration, which refers to the vibration perpendicular to the axis of the rotor), modeling and analysis are usually performed separately in two orthogonal directions. In each direction, the vibration of the rotor system is manifested as the reciprocating motion of the geometric center of each section of the rotor about its equilibrium position. The synthesis of the vibrations in the two orthogonal directions is the true vibration image of the rotor system in space. Theoretical studies have shown that the motion trajectory of the geometric centers of the rotor in space is an ellipse, or a circle or a straight line in special cases.

[0004] Since the vibration of the rotor system is small, and the vibration amplitude of the rotor system in engineering is usually measured in microns, the true vibration image of the rotor cannot be observed visually. However, only by having a detailed understanding of the vibration of each part of the rotor can a system that meets the working performance requirements be designed. Therefore, how to achieve "visualization" of the true form of the vibration of the rotor system has become an unavoidable problem. So far, there is no comprehensive public information that provides a method for generating vortex trajectories of rotating system vibrations. Summary of the invention

[0005] In order to solve at least one of the above-mentioned technical problems, the first purpose of the present invention is to use rotor vibration response data to draw a vortex trajectory algorithm for the vibration of the rotor system under unbalanced excitation under general circumstances (referring to the situation where the major axis and minor axis of the ellipse do not necessarily coincide with the orthogonal coordinate axes).

[0006] A second objective of the present disclosure is to provide a method for determining the positions of the major and minor semi-axes of a rotor system vibrating under unbalanced excitation.

[0007] A third object of the present disclosure is to provide a readable storage medium.

[0008] A fourth objective of the present disclosure is to provide an electronic device.

[0009] In order to achieve the first objective of the present disclosure, the technical solution adopted by the present disclosure is as follows:

[0010] An algorithm for generating vortex trajectories of rotor system vibrations, comprising:

[0011] Obtain the vibration frequency of the rotor system according to the vibration differential equation of the rotor system, and obtain the complex amplitude of the geometric center of the current cross section along the X-axis direction and the complex amplitude along the Y-axis direction;

[0012] The motion trajectory equation of the center of the rotor system cross section is established in complex form.

[0013] Alternatively, the oscillating differential equation is:

[0014] Where M is the mass matrix of the rotor system, C is the damping matrix of the rotor system, ω is the unbalanced vibration frequency, G is the gyroscopic matrix of the rotor system, K is the stiffness matrix of the rotor system, and Fe is j ωt is the vector of the excitation force of the rotor system, and X is the vector of the vibration displacement of the rotor system, including the complex amplitude of the current node along the X-axis and the complex amplitude of the current node along the Y-axis.

[0015] Optionally, the motion trajectory equation of the center of the rotor system cross section is obtained by the following method:

[0016] The vibration displacement equations of the centers of each section of the rotor system are established in complex form;

[0017] The motion trajectory equation of the center of the rotor system cross section is obtained based on the vibration displacement equation.

[0018] Alternatively, the vibration displacement equation expressing the center of each cross section of the rotor system in complex form is:

[0019]

[0020]

[0021] x(t) is the X-direction displacement of the geometric center at time t, y(t) is the Y-direction displacement of the geometric center at time t, A x is the complex amplitude of the current node along the X-axis, A y is the complex amplitude of the current node along the Y axis, A x The phase angle, A y The phase angle of .

[0022] Optionally, the equation of motion from the center of the rotor system section to the equilibrium position is:

[0023]

[0024] In the formula, x is the X-axis coordinate of the center of the cross section, and y is the Y-axis coordinate of the center of the cross section.

[0025] Alternatively, the distance from the center of the rotor system section to the equilibrium position is expressed as:

[0026]

[0027] s is the distance from the center of the rotor system section to the equilibrium position.

[0028] In order to achieve the second objective of the present disclosure, the technical methods adopted by the present disclosure are as follows:

[0029] A method for determining the major and minor semi-axes positions of a rotor system vibration.

[0030] According to the above motion trajectory equation, the distance expression from the center of the rotor system section to the equilibrium position is obtained;

[0031] According to the distance expression, calculate the first and second derivatives of the distance from the center of the section to the equilibrium position with respect to the position angle;

[0032] Set the first-order derivative to zero, obtain the first expression, and solve the solution of the position angle in the first expression;

[0033] When the second-order derivative is less than zero, the solved position angle corresponds to the major semi-axis. When the second-order derivative is greater than zero, the solved position angle corresponds to the minor semi-axis.

[0034] Optionally, after determining the major semi-axis or minor semi-axis corresponding to the solved position angle θ, the positions of the other three semi-axes with position angles of θ+π / 2, θ+π, and θ+3π / 2 are determined according to the phase relationship between the major semi-axis and the minor semi-axis of the ellipse.

[0035] In order to achieve the third objective of the present disclosure, the technical solutions adopted by the present disclosure are as follows:

[0036] A readable storage medium has executable instructions thereon, and when the executable instructions are executed, a computer is caused to execute the steps of the vortex trajectory generation algorithm for rotor system vibration as described above.

[0037] In order to achieve the fourth objective of the present disclosure, the technical solutions adopted by the present disclosure are as follows:

[0038] An electronic device comprises a processor and a memory, wherein the memory stores computer program instructions suitable for execution by the processor, and when the computer program instructions are executed by the processor, the steps of the above-mentioned vortex trajectory generation algorithm for rotor system vibration are executed.

[0039] The present disclosure utilizes rotor vibration response data to determine the vortex trajectory of the rotor system under unbalanced excitation under general circumstances (referring to the situation where the major axis and minor axis of the ellipse do not necessarily coincide with the orthogonal coordinate axes). By determining the size of the vortex trajectory, the energy distribution of the rotor vibration intensity can be understood, the minimum vibration time and energy distribution can be analyzed, the harmful vibration of the system can be reduced, and the design of a rotor system with less harmful vibration can be facilitated. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] The accompanying drawings illustrate exemplary embodiments of the present disclosure and together with the description serve to explain the principles of the present disclosure. These drawings are included to provide a further understanding of the present disclosure and are incorporated in and constitute a part of this specification.

[0041] Figure 1 is a simplified structural diagram of the rotor system in the present disclosure;

[0042] Figure 2 is a vortex trajectory diagram of the rotor system vibration in the present disclosure;

[0043] Figure 3 is a method principle diagram of the vortex trajectory generation algorithm of the rotor system vibration in the present disclosure;

[0044] Figure 4 It is a schematic diagram of the instantaneous position of the center of the cross section of the rotor system in the method for determining the positions of the major and minor semi-axes of the rotor system vibration disclosed in the present invention;

[0045] Figure 5 It is a schematic diagram of the method for determining the major and minor semi-axes positions of the rotor system vibration in the present disclosure. DETAILED DESCRIPTION

[0046] The present disclosure is further described in detail below in conjunction with the accompanying drawings and implementations. It is understood that the specific implementations described herein are only used to explain the relevant content, rather than to limit the present disclosure. It should also be noted that, for ease of description, only the parts related to the present disclosure are shown in the accompanying drawings.

[0047] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in the present disclosure may be combined with each other. The present disclosure will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0048] Embodiment 1

[0049] See also Figure 1 , Figure 2 , the rotor system under unbalanced excitation can be divided into multiple sections, and each geometric center g of the section i Each corresponds to a vortex trajectory. In this embodiment, the geometric center g is determined by way of example. iThe corresponding elliptical vortex trajectory and major and minor semi-axis positions; the method for determining the elliptical vortex trajectory and major and minor semi-axis positions of other geometric centers g is the same as the method in this embodiment.

[0050] See also Figure 3 As shown, an algorithm for generating a vortex trajectory of a rotor system vibration includes:

[0051] According to the g of the rotor system i The vibration differential equation of the node obtains the vibration frequency of the rotor system, the complex amplitude of the current cross-section geometric center along the X-axis direction, and the complex amplitude of the current cross-section geometric center along the Y-axis direction; the vibration differential equation can be:

[0052]

[0053] Where M is the mass matrix of the rotor system, C is the damping matrix of the rotor system, ω is the unbalanced vibration frequency, G is the gyro matrix of the rotor system, K is the stiffness matrix of the rotor system, and Fe is jωt is the vector of the excitation force of the rotor system, X is the vector of the vibration displacement of the rotor system, including the complex amplitude A of the current node along the X-axis direction x and the complex amplitude A of the current node along the Y axis y ;

[0054] The unbalanced vibration frequency ω can be obtained through the above formula; at the same time, the complex amplitude A along the X-axis direction can also be obtained x and the complex amplitude A of the current node along the Y axis y .

[0055] The rotor system cross-sectional center g is established in complex form i Expression for the distance to the equilibrium position; the distance from the center of the section to the equilibrium position can be determined by:

[0056] The vibration displacement equation of the center of each section of the rotor system is expressed in complex form; solving equation (1), the geometric center g of the i-th section of the rotor system under the unbalanced force with a vibration frequency of ω is obtained. i The vibration displacements along the two radial orthogonal directions Ox and Oy are:

[0057] x(t)=A x e jωt (2)

[0058] y(t)=A y e jωt (3)

[0059] Where ω is the frequency of unbalanced excitation, A xis the complex amplitude of the current node along the X-axis, A y is the complex amplitude of the current node along the Y axis, that is, A x and A y is a vector, containing magnitude and phase information, which can be expressed as:

[0060]

[0061]

[0062] A x The phase angle, A y The phase angle of , equations (2) and (3) can be re-expressed as:

[0063]

[0064]

[0065] x(t) is the X-displacement of the geometric center at time t, and y(t) is the Y-displacement of the geometric center at time t.

[0066] It can be seen that the cross-section center g i The vibration in the Ox direction is the rotation vector A x The projection in the Ox direction. Similarly, the center of the cross section g i The vibration in the Oy direction is the rotation vector A y Projection in the Oy direction. Rotation vector A y Relative to A x The phase difference is:

[0067]

[0068] See also Figure 4 As shown, it is the rotation vector A at time t = 0 y Relative to A x The geometric position of

[0069] According to mathematical theory, g i The trajectory of is an ellipse, and the parametric equation describing its trajectory is:

[0070]

[0071] Where x is the X-axis coordinate of the center of the cross section, and y is the Y-axis coordinate of the center of the cross section.

[0072] make, Then there is Re-state equation (9) to obtain the equation of motion for the center of the rotor system cross section;

[0073]

[0074] According to the motion trajectory equation of the center of the rotor system section, the distance from the center of the rotor system section to the equilibrium position can be determined:

[0075]

[0076] s is the distance from the center of the rotor system section to the equilibrium position, and also the distance from any point on the ellipse to the equilibrium position. So far, the vortex trajectory of the rotor system under unbalanced excitation has been completed.

[0077] Embodiment 2

[0078] Next, determine the major and minor semi-axis positions of the rotor system vibration under unbalanced excitation.

[0079] Combination Figure 2 , Figure 5 As shown in the figure, a method for determining the position of the major and minor semi-axes of a rotor system vibration is used. In the rotor vibration, due to the phase difference between the two rotating vectors Usually not zero, so in general, g i The major and minor axes of the ellipse corresponding to the trajectory have lengths equal to the magnitude of the rotation vector |A x | and |A y |There is no corresponding and equal relationship. In addition, the major and minor axes of the ellipse are generally not located on the coordinate axes of the local coordinate system. The solution proposed in this application uses the method of finding extreme values ​​to determine the positions of the major and minor axes. The specific implementation method is as follows:

[0080] According to the distance expression, calculate the first and second derivatives of the square of the distance from the center of the section to the equilibrium position with respect to the position angle; calculate s 2 The first and second order derivatives of θ are as follows:

[0081]

[0082]

[0083] Then order s 2 The first derivative of θ is zero, which gives the first expression:

[0084]

[0085] Newton's method is used to solve the first expression (13). The obtained θ is the position angle of a major semi-axis or a minor semi-axis. Then the θ value is substituted into the formula (12). By judging d 2 s 2 / dθ 2 The sign of determines whether θ corresponds to the major or minor semiaxis.

[0086] When the second-order derivative is less than zero, the position angle to be solved corresponds to the major semi-axis. When the second-order derivative is greater than zero, the position angle to be solved corresponds to the minor semi-axis. The position angle can be used to obtain the position of the major semi-axis or minor semi-axis of the rotor system under unbalanced excitation; and the position angle at the position of θ+π / 2 can be obtained by rotating to determine the position of the other corresponding minor semi-axis or major semi-axis. The length corresponding to the position angle to be solved can be obtained by substituting θ into (11), and the value of s obtained is the length of the semi-axis corresponding to the position angle.

[0087] This method uses rotor vibration response data to determine the major and minor axis positions of the elliptical vortex trajectory of any cross-section center point when the rotor system vibrates under unbalanced excitation under general circumstances (referring to the situation where the major and minor axes of the ellipse do not necessarily coincide with the orthogonal coordinate axes). After understanding the major and minor axis positions, guidance can be provided for the coating of wear-resistant coatings on aircraft engine casings. The specific principle is: the major and minor axis positions of the rotor vortex trajectory ellipse correspond to the position where the rotor amplitude is the largest when the rotor makes a circumferential rotational motion, and this position corresponds to the maximum risk position of friction between the rotor and the aircraft engine casing. A thicker wear-resistant coating can be applied at the corresponding position of the casing to reduce the damage of the rotor friction to the blades and the aircraft engine casing; correspondingly, the minor and minor axis positions of the rotor vortex trajectory ellipse correspond to the position where the rotor amplitude is the smallest when the rotor makes a circumferential rotational motion, and this position corresponds to the minimum risk position of friction between the rotor and the aircraft engine casing. The wear-resistant coating can be applied thinner to improve the coating efficiency and reduce the difficulty of the processing technology.

[0088] After determining the position of a major semi-axis / minor semi-axis by solving the position angle θ and the corresponding amplitude, the positions and corresponding semi-axis lengths of the other three semi-axes with position angles of θ+π / 2, θ+π, and θ+3π / 2 can be determined according to the phase relationship between the major semi-axis and the minor semi-axis of the ellipse, thereby obtaining the positions of the four semi-axes of the elliptical trajectory.

[0089] Embodiment 3

[0090] An electronic device disclosed in the present invention includes a processor and a memory, wherein the memory stores computer program instructions suitable for execution by the processor, and the computer program instructions are executed by the processor to execute the steps of the vortex trajectory generation algorithm of the rotor system vibration. The processor can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application-specific integrated circuit (ASIC), or other programmable logic devices, discrete gates or transistor logic devices, and discrete hardware components; the memory may include a random access memory (RAM), and may also include a non-volatile memory, such as at least one disk memory. The memory can also be an internal memory of the random access memory (RAM) type, and the processor and the memory can be integrated into one or more independent circuits or hardware, such as an application-specific integrated circuit (ASIC). It should be noted that the computer program in the above-mentioned memory can be implemented in the form of a software functional unit and can be stored in a computer-readable storage medium when it is sold or used as an independent product. Based on this understanding, the technical solution of the present invention is essentially or the part that contributes to the prior art or the part of the technical solution can be embodied in the form of a software product, and the computer software product is stored in a storage medium, including a number of instructions for a computer device (which can be a personal computer, an electronic device, or a network device, etc.) to perform all or part of the steps of the methods of various embodiments of the present invention.

[0091] Embodiment 4

[0092] A readable storage medium disclosed in the present invention has executable instructions thereon, and when the executable instructions are executed, the computer is caused to execute the steps of the vortex trajectory generation algorithm for the vibration of the rotor system as described above. The readable storage medium can be: an electronic medium, a magnetic medium, an optical medium, an electromagnetic medium, an infrared medium or a semiconductor system or a propagation medium. The readable storage medium can also include a semiconductor or solid-state memory, a magnetic tape, a removable computer disk, a random access memory (RAM), a read-only memory (ROM), a hard disk and an optical disk. The optical disk can include a compact disk-read only memory (CD-ROM), a compact disk-read / write (CD-RW) and a DVD.

[0093] The present invention utilizes rotor vibration response data to determine a method for determining an elliptical vortex trajectory of any midpoint of a rotor system vibration under unbalanced excitation under general circumstances (referring to a situation where the major axis and the minor axis of the ellipse do not necessarily coincide with the orthogonal coordinate axes). By solving the elliptical vortex trajectories of all midpoints in the rotor system, the vortex range of the rotor system can be obtained.

[0094] In the description of this specification, the description with reference to the terms "one embodiment / method", "some embodiments / methods", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment / method or example are included in at least one embodiment / method or example of the present application. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment / method or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments / methods or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments / methods or examples described in this specification and the features of the different embodiments / methods or examples, unless they are contradictory.

[0095] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of the features. In the description of this application, the meaning of "plurality" is at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0096] Those skilled in the art should understand that the above embodiments are only for the purpose of clearly illustrating the present disclosure, and are not intended to limit the scope of the present disclosure. For those skilled in the art, other changes or modifications may be made based on the above disclosure, and these changes or modifications are still within the scope of the present disclosure.

Claims

1. A method for generating a vortex trajectory of a rotor system vibration, characterized in that: include: Obtain the vibration frequency of the rotor system according to the vibration differential equation of the rotor system, and obtain the complex amplitude of the geometric center of the current cross section along the X-axis direction and the complex amplitude along the Y-axis direction; The motion trajectory equation of the center of the rotor system cross section is established in complex form; The oscillating differential equation is: Where M is the mass matrix of the rotor system, C is the damping matrix of the rotor system, ω is the unbalanced vibration frequency, G is the gyro matrix of the rotor system, K is the stiffness matrix of the rotor system, and Fe is jωt is the vector composed of the excitation force of the rotor system, X is the vector composed of the vibration displacement of the rotor system, including the complex amplitude of the current node along the X-axis direction and the complex amplitude of the current node along the Y-axis direction; The vibration displacement equation expressing the center of each section of the rotor system in complex form is: x(t) is the X-direction displacement of the geometric center at time t, y(t) is the Y-direction displacement of the geometric center at time t, A x is the complex amplitude of the current node along the X-axis, A y is the complex amplitude of the current node along the Y axis, A x The phase angle, A y The phase angle of The equation of motion from the center of the rotor system section to the equilibrium position is: In the formula, x is the X-axis coordinate of the center of the cross section, and y is the Y-axis coordinate of the center of the cross section.

2. The method for generating a vortex trajectory of a rotor system vibration according to claim 1, characterized in that: The motion trajectory equation of the center of the rotor system section is obtained by the following method: The vibration displacement equations of the centers of each section of the rotor system are established in complex form; The motion trajectory equation of the center of the rotor system cross section is obtained based on the vibration displacement equation.

3. The method for generating a vortex trajectory of a rotor system vibration according to claim 2, characterized in that: The distance from the center of the rotor system section to the equilibrium position is expressed as: s is the distance from the center of the rotor system section to the equilibrium position.

4. A method for determining the major and minor semi-axes positions of a rotor system vibration, characterized in that: According to the motion trajectory equation of claim 1, an expression for the distance from the center of the rotor system cross section to the equilibrium position is obtained; According to the distance expression, calculate the first and second derivatives of the distance from the center of the section to the equilibrium position with respect to the position angle; Set the first-order derivative to zero, obtain the first expression, and solve the solution of the position angle in the first expression; When the second-order derivative is less than zero, the solved position angle corresponds to the major semi-axis. When the second-order derivative is greater than zero, the solved position angle corresponds to the minor semi-axis.

5. The method for determining the major and minor semi-axis positions of the rotor system vibration according to claim 4, characterized in that: After determining the major or minor semi-axis corresponding to the solved position angle θ, the positions of the other three semi-axes with position angles of θ+π / 2, θ+π, and θ+3π / 2 are determined according to the phase relationship between the major and minor semi-axes of the ellipse.

6. A readable storage medium, characterized in that: There are executable instructions thereon, and when the executable instructions are executed, the computer executes the steps of the method for determining the major and minor semi-axes positions of the rotor system vibration as claimed in claim 4 or 5.

7. An electronic device, characterized in that: The device comprises a processor and a memory, wherein the memory stores computer program instructions suitable for execution by the processor, and when the computer program instructions are executed by the processor, the steps of the method for determining the major and minor semi-axes positions of the rotor system vibration as claimed in claim 4 or 5 are executed.

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