Vibration analysis method and system for intermediate bearing in double-rotor system

Abstract

The invention provides a vibration analysis method and system for an intermediate bearing in a double-rotor system. The method comprises the following steps: determining a rolling body entering a defect area at the current moment and a rolling body with the maximum contact deformation based on bearing parameters, an operation state, defect information, contact rigidity and damping parameters; respectively calculating the time-varying displacement and impact force of the rolling body entering the defect area and the rolling body with the maximum contact deformation, and the angle difference between the time-varying displacement and the impact force; the impact force is corrected through the angle difference between the rolling body entering the defect area and the rolling body with the largest contact deformation and serves as external force input of a nonlinear kinetic equation of an intermediate bearing system of the double-rotor system; and calculating a nonlinear bearing force in the nonlinear kinetic equation based on the time-varying displacement of the rolling body entering the defect area and the rolling body with the maximum contact deformation. And solving the nonlinear kinetic equation. According to the method, the vibration analysis precision under the condition of the defect of the intermediate bearing in the double-rotor system is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of intermediate bearings, and in particular relates to a vibration analysis method and system for an intermediate bearing of a dual-rotor system. Background Art

[0002] Intermediate bearings are widely used in aircraft engines and marine gas turbines. Unlike other supporting bearings, intermediate bearings are located between the high-pressure and low-pressure rotors that rotate at high speed. The inner ring is fixed on the low-pressure rotor, and the outer ring is fixed on the high-pressure rotor. Both the inner and outer rings rotate with the high and low-pressure rotors. Due to long-term operation in harsh environments such as high temperature, high speed and frequent load changes, intermediate bearings are prone to failures such as dents, peeling and cracks. When an intermediate bearing fails, the fault vibration signal will reach the measuring point through a complex transmission path, which is easily interfered by noise and other signals, making it difficult to find the fault characteristics. The failure of the intermediate bearing of the dual-rotor system is one of the most difficult problems to detect and deal with in aeroengines in a timely manner. Therefore, accurate modeling and vibration analysis of the intermediate bearing of the dual-rotor system to reveal its failure mechanism and characteristics are of great significance for timely monitoring and troubleshooting of such faults.

[0003] Although the vibration analysis of bearing-rotor systems with local defects has achieved fruitful results, there are still some limitations:

[0004] 1. In fault defect modeling, the impact force is often simplified, and the time-varying characteristics of the contact process are not fully studied. Some existing technologies take into account the defect size and bearing speed, and derive the time-varying impact force excitation function of the local bearing defect, but ignore the effect of alternating loads on the impact force. The alternating changes in the unbalanced excitation of the high- and low-pressure rotors result in different loads when the roller collides with the defect edge, and the effect of different loads on the impact force amplitude cannot be ignored.

[0005] 2. The bearing load area is closely related to the combined force of the rotor unbalance force and gravity. The change in the position of the defect and the load area makes the contact between the roller and the local defect more complicated. The fault characteristics of local defects under the influence of actual alternating loads are significantly different from those under constant load conditions. Some existing technologies have studied the vibration characteristics of unbalanced rotor systems, but have not conducted in-depth analysis of the vibration characteristics of faulty bearing-dual rotor systems under alternating loads.

[0006] 3. The intermediate bearing is the bearing that supports the inner and outer rotors. It is subject to the interaction of the loads of the two rotors. Its vibration needs to be transmitted through the rotor to reach the nearest bearing seat measurement point. Therefore, the failure characteristics of each bearing in the dual-rotor-bearing-casing system are more complex than the support bearings of a single rotor. Previous models often only focus on bearings at specific locations and simplify bearings at other locations into linear spring dampers. In order to clarify the failure performance of each bearing, it is necessary to analyze its unique failure characteristics based on the load and structural characteristics of each bearing. Summary of the invention

[0007] The purpose of the present invention is to address the deficiencies in the above-mentioned background technology and to provide a vibration analysis method and system for the intermediate bearing of a dual-rotor system, which takes into account the relative motion difference between the actual equipment load area and the defect position, and improves the vibration analysis accuracy in the case of defects in the intermediate bearing of the dual-rotor system.

[0008] The technical solution adopted by the present invention is: a vibration analysis method for the intermediate bearing of a dual-rotor system, comprising the following steps:

[0009] Determine the rolling element that has entered the defect area and the rolling element with the largest contact deformation at the current moment based on bearing parameters, operating status, defect information, contact stiffness and damping parameters;

[0010] The time-varying displacement and impact force of the rolling element entering the defect area and the rolling element with the largest contact deformation, as well as the angle difference between the two are calculated respectively;

[0011] The impact force is corrected by the angle difference between the rolling body entering the defect area and the rolling body with the largest contact deformation and used as the external force input of the nonlinear dynamic equation of the intermediate bearing system of the dual-rotor system; the nonlinear bearing force in the nonlinear dynamic equation is calculated based on the time-varying displacement of the rolling body entering the defect area and the rolling body with the largest contact deformation;

[0012] The nonlinear dynamic equations are solved to obtain the vibration signal of the intermediate bearing of the dual-rotor system at the current moment.

[0013] In the above technical solution, the process of determining the rolling body entering the defect area at the current moment includes: calculating the position of each rolling body based on bearing parameters, operating status, defect information, contact stiffness and damping parameters; and taking the corresponding rolling body whose relative relationship between the rolling body position and the defect area position meets the set conditions as the rolling body entering the defect area.

[0014] In the above technical solution, the following formula is used to calculate the time-varying displacement and contact deformation of the i-th rolling element:

[0015]

[0016] θ i=arcsin(B / 2R ii );

[0017] θ f =w i t+θ f0 ;

[0018]

[0019] Among them, H i represents the time-varying displacement or contact deformation of the ith rolling element; ψ i represents the angle between the center of the i-th rolling element and the center of the inner raceway defect area; θ i represents the defect angle formed by the inner ring defect edge and the defect center; d represents the rolling element diameter; R ii Indicates the inner raceway radius of the intermediate bearing; θ f Indicates the angle of the defect area center relative to the x-axis at the current moment; θ bk Indicates the angle of the kth rolling element relative to the x-axis at the current moment; θ f0 represents the angle of the defect area center relative to the x-axis at the initial moment; t represents the current moment, ω i Indicates the angular velocity of the inner ring of the bearing; ω c Indicates the angular velocity of the bearing cage; θ b0 Indicates the angle of the first rolling body relative to the x-axis at the initial moment; Z indicates the number of rolling bodies.

[0020] In the above technical solution, the corrected impact force f of the ith rolling element is calculated using the following formula: im-ii :

[0021]

[0022] Where ζ represents the correction coefficient, m b Indicates the quality of the rolling element; B indicates the width of the defect.

[0023] In the above technical solution, the correction coefficient of the impact force is calculated using the following formula:

[0024]

[0025] Among them, C d Indicates the maximum offset of bearing clearance, δ r It represents the maximum displacement in the bearing load zone; n is the load-deformation index; ε represents the load distribution factor; Ψ(t) represents the angle between the direction of the corresponding rolling element in the load zone and its angular position direction.

[0026] In the above technical solution, the expression of the nonlinear dynamic equation is as follows:

[0027]

[0028] Where M is the mass matrix, g is the gravitational acceleration, X and Y are the displacement matrices in the x and y directions; F bx and F by are the bearing force vector matrices in the x-direction and y-direction, F ex and F ey are the external force matrices in the x-direction and y-direction caused by the unbalanced amount, F im-iix 、F im-iiy are the impact force matrices in the x and y directions respectively, C x , K x and C y , K y are the damping and stiffness matrices in the x-direction and y-direction respectively.

[0029] In the above technical solution, the nonlinear dynamic equation is dimensionless and then solved; the expression of the dimensionless nonlinear dynamic equation is as follows:

[0030]

[0031] For the low pressure rotor:

[0032] For high pressure rotors there are:

[0033] Where j is the rolling element number, τ is the dimensionless time, and F j represents the force of the jth rolling element on the contact point, F j,x represents the force in the x direction of the jth rolling element at the contact point, F j,y represents the force in the y direction of the jth rolling element at the contact point, k b Indicates the contact stiffness of the bearing rolling element; x j Represents the contact deformation of the jth rolling element;

[0034]

[0035] ω represents the angular velocity of the bearing rotor, e represents the eccentricity of the bearing rotor; α represents the speed ratio of the high-pressure and low-pressure rotors.

[0036] The present invention also provides a vibration analysis system for an intermediate bearing of a dual-rotor system, and the system is used to implement the vibration analysis method for an intermediate bearing of a dual-rotor system described in the above technical solution of the claims.

[0037] The present invention also provides a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, the vibration analysis method of the intermediate bearing of the dual-rotor system described in the above technical solution is implemented.

[0038] The present invention also provides an electronic device, comprising: a memory and a processor, wherein the memory and the processor are communicatively connected to each other, the memory stores computer instructions, and the processor executes the vibration analysis method of the intermediate bearing of the dual-rotor system as described in the above technical solution by executing the computer instructions.

[0039] The beneficial effects of the present invention are as follows: the present invention proposes a dynamic analysis method based on the interaction between the rolling body and the defective area, combined with time-varying displacement and time-varying impact force, including the dynamic state of the rolling body, contact deformation, angle difference correction of impact force, and solution of nonlinear dynamic equations. The present invention comprehensively considers the time-varying displacement of the rolling body entering the defective area and the time-varying impact force caused by the collision, reflects the global dynamic influence of these forces on the system through the dynamic equation, and more comprehensively describes the complex influence of defects on the vibration characteristics of the system. The nonlinear dynamic equation proposed by the present invention combines inertia, damping, stiffness and corrected external force input, which can accurately reflect the dynamic behavior of the intermediate bearing of the dual-rotor system, and solves the problem that complex dynamic behavior cannot be described by relying on a single mechanical model. The present invention corrects the impact force through the angle difference of the rolling body, increases the accuracy of the model, improves the model's ability to describe the interaction between rolling bodies, and is closer to actual working conditions.

[0040] Furthermore, the present invention determines the process of the rolling body entering the defect area, clarifies the method based on the rolling body and defect position, contact parameters and dynamic judgment of the rolling body position, and accurately judges whether the rolling body enters the defect area based on the relative geometric relationship between the rolling body position and the defect area. It solves the problem of precise positioning of the interaction between the rolling body and the defect under dynamic conditions, is suitable for dynamic analysis of rolling bodies under conditions of defects of different sizes and rotation speeds, and provides a basis for defect fault diagnosis under complex working conditions.

[0041] Furthermore, the present invention proposes a refined time-varying displacement progressive excitation function for describing the dynamic interaction between the rolling body and the defect edge. By considering the curvature of the defect edge, a refined time-varying displacement function is established, which can more accurately reflect the geometric dynamic relationship between the rolling body and the defect, improve the model's description accuracy of the dynamic effect of the defect edge, and is suitable for the dynamic response of the rolling body when no collision occurs, especially for the working condition when the rolling body does not collide with the trailing edge of the defect, which solves the description error caused by the traditional model ignoring the curvature of the defect edge.

[0042] Furthermore, the present invention proposes a method for calculating the time-varying impact force of a rolling body, taking into account the load characteristics and the influence of the rotation speed when the rolling body collides with the trailing edge of the defect. The time-varying impact force function combines the dynamic behavior of the collision between the rolling body and the trailing edge of the defect, taking into account the influence of the load and the rotation speed, and can accurately describe the impact of the defect collision on the system vibration. The established impact force model can reflect the dynamic modulation of the impact force by the alternating load, and is suitable for defect vibration analysis under high load or high-speed conditions.

[0043] Furthermore, the present invention proposes a correction coefficient for calculating the impact force, and adjusts the impact force based on the relative dynamic position of the rolling element and the defect. The correction coefficient takes into account the relative dynamic angle relationship between the rolling element and the defect, avoids the force distribution error, and more accurately describes the change of the impact force in the dynamic process; the introduction of the correction coefficient enables the model to adapt to complex dynamic environments and improves the accuracy of the model under different working conditions.

[0044] Furthermore, the present invention proposes an expression for a nonlinear dynamic equation for solving the vibration of the system; the dynamic equation integrates the inertia, damping, stiffness and external force of the system, can globally describe the dynamic response of the system, and provides a global perspective for the analysis of the vibration characteristics of the system; time-varying external force input including corrected impact force can reflect the dynamic modulation of defect faults on the system vibration, and realizes the coupled analysis of defects and system responses.

[0045] Furthermore, the present invention proposes a dimensionless processing method for nonlinear dynamic equations to reduce computational complexity; the dimensionless processing makes the solution of the dynamic model more efficient and suitable for numerical calculations, improves the computability and practicality of the model, and the dimensionless model can adapt to systems of different sizes and speeds, facilitating rapid simulation and analysis under a variety of working conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 It is a schematic diagram of the method flow of the present invention;

[0047] Figure 2 A relative position diagram of a rolling element passing through a defective area in a specific embodiment;

[0048] Figure 3 It is a geometric relationship diagram of the rolling element and the defect at a certain moment of a specific embodiment;

[0049] Figure 4 This is a relative position diagram of the rolling element and the defect angle when the inner ring fails and rotates in the same direction in a specific embodiment;

[0050] Figure 5 This is a schematic diagram of a rolling element hitting a fault edge in a specific embodiment;

[0051] Figure 6The bearing load distribution under a constant radial load in a specific embodiment;

[0052] Figure 7a It is a simulation signal diagram of the acceleration of the intermediate bearing with inner ring fault in a specific embodiment;

[0053] Figure 7b It is a simulation signal diagram of the envelope spectrum of the intermediate bearing with inner ring fault in a specific embodiment;

[0054] Figure 7c This is a signal diagram of the acceleration experiment of the intermediate bearing with inner ring fault in a specific embodiment;

[0055] Figure 7d It is an experimental signal diagram of the envelope spectrum of the intermediate bearing with inner ring fault in a specific embodiment;

[0056] Figure 7e It is a normal intermediate bearing acceleration experimental signal diagram of a specific embodiment;

[0057] Figure 7f It is a normal intermediate bearing envelope spectrum experimental signal diagram of a specific embodiment;

[0058] Figure 8 It is a schematic diagram of calculation results of a specific embodiment. DETAILED DESCRIPTION

[0059] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments to facilitate a clear understanding of the present invention, but they do not constitute a limitation on the present invention.

[0060] Example 1

[0061] like Figure 1 As shown, the present invention provides a vibration analysis method for an intermediate bearing of a dual-rotor system, comprising the following steps:

[0062] S1, based on bearing parameters, operating status, defect information, contact stiffness and damping parameters, determine the rolling element that enters the defect area at the current moment and the rolling element with the largest contact deformation;

[0063] S2, respectively calculates the time-varying displacement and impact force of the rolling element entering the defect area and the rolling element with the largest contact deformation, as well as the angle difference between the two;

[0064] S3, correcting the impact force by the angle difference between the rolling body entering the defect area and the rolling body with the largest contact deformation and using it as the external force input to the nonlinear dynamic equation of the intermediate bearing system of the dual-rotor system; calculating the nonlinear bearing force in the nonlinear dynamic equation based on the time-varying displacement of the rolling body entering the defect area and the rolling body with the largest contact deformation;

[0065] S4, solving the nonlinear dynamic equation to obtain the vibration signal of the intermediate bearing of the dual-rotor system at the current moment.

[0066] The principle of the invention is further explained below with reference to specific embodiments.

[0067] This embodiment is used for a certain type of marine gas turbine which is a modified aircraft engine, wherein the medium bearing is a cylindrical roller bearing commonly used in aircraft engines, and its supporting force model is established according to the Hertz contact theory.

[0068] When the rolling bearing is working, the contact deformation of the jth rolling element unit is j for:

[0069] χ j =(x i -x o )cosθ j +(y i -y o )sinθ j -Gr (1)

[0070] Among them, x o and o are the displacements of the center of the bearing outer ring in the x and y directions, respectively. i and i are the displacements of the center of the bearing inner ring in the x and y directions, Gr is the initial clearance between the rolling element and the contact raceway, θ j is the angle between the center of the jth rolling element and the x-axis, as shown in formula (2).

[0071]

[0072] Where N b is the number of bearing rolling elements, ω c ,ω i and ω o are the angular velocities of the bearing cage, inner ring and outer ring respectively. For the supporting bearing, ω o = 0, d and D m are the rolling element and pitch circle diameters respectively, and θ0 is the initial angle of the first rolling element relative to the x-axis.

[0073] When the contact deformation χ j When ≤0, there is no pressure between the rolling element and the raceway, so the Heaviside function is introduced, that is,

[0074]

[0075] The nonlinear bearing force of rolling bearings is derived based on Hertz contact theory, and the force formula (3) is obtained:

[0076]

[0077] χ j =(x i -x o )cosθ j +(y i -y o )sinθ j -Gr where k b is the nonlinear Hertz contact stiffness. When the bearing is a ball bearing, n = 3 / 2; when the bearing is a cylindrical roller bearing, n = 10 / 9.

[0078] This paper studies the dynamic vibration characteristics of the intermediate bearing fault of the dual rotor system under time-varying excitation. The article considers the nonlinear factors of all bearings and establishes a dynamic model of the dual rotor-support-casing system with intermediate bearing fault. Based on the previous work, a multi-process time-varying excitation model of local defects in the intermediate bearing is proposed. The vibration response characteristics of the inner ring fault of the intermediate bearing of the dual rotor system under alternating loads are deeply analyzed.

[0079] Specifically, in step S1, the contact deformation of each rolling element at the current moment is calculated based on bearing parameters, operating status, defect information, contact stiffness and damping parameters, and the rolling element with the largest positive contact deformation is selected and marked as K1.

[0080] When the rolling body enters the fault area and does not collide with the rear edge of the fault, the present invention considers the curvature of the rolling body and the inner ring edge, establishes a refined time-varying displacement progressive excitation function, and calculates the contact deformation of each rolling body based on the time-varying displacement progressive excitation function.

[0081] Under the action of alternating loads, the relative position of the rolling element will change when it passes through the defect area. Establishing an accurate time-varying displacement excitation function is of great significance for understanding the vibration characteristics of the intermediate bearing defect. The present invention establishes a model of local fault of the inner ring of the intermediate bearing, considering that the inner ring rectangular defect penetrates, the defect width is smaller than the rolling element diameter, and the rolling element passes through the defect area and undergoes displacement changes but does not touch the bottom of the defect.

[0082] like Figure 2 As shown, H c is the maximum value of the actual displacement change of the rolling element, but H c Without considering the influence of the inner ring edge curvature, H m To consider the maximum value of the rolling element displacement change of the inner ring curvature, it can be expressed as

[0083]

[0084] Where B is the width of the defect, Hd is the height of the defect, Rii is the inner raceway radius of the intermediate bearing, θ i is the defect angle formed by the inner circle defect edge and the defect center, which can be expressed as

[0085] θ i =arcsin(B / 2R ii ) (6)

[0086] like Figure 3 As shown, at a certain moment, the angle between the center of the rolling element and the center of the inner raceway defect area is When the rolling element and the inner raceway defect contact point to the rolling element center and the inner raceway center line distance h i It can be expressed as

[0087]

[0088] At this moment, the contact deformation or time-varying displacement H of the i-th rolling element considering the curvature of the inner raceway i for

[0089]

[0090] It can be expressed as

[0091]

[0092] In the formula, θ f is the angle of the defect center relative to the x-axis at a certain moment, θ bk is the angle of the kth rolling body relative to the x-axis at a certain moment. Figure 4 Medium R i , R o , R oo , R m They are the inner ring radius, outer ring radius, outer raceway radius and pitch circle radius respectively. If the counterclockwise direction is specified as the positive direction, the inner ring speed, cage speed and outer ring speed are all counterclockwise. Combined with the actual engine operation, w o >w i , so the rolling element rotates in the direction w b Also in the counterclockwise direction, the relative position sequence of the rolling element in contact with the defect area is Figure 2 1->2->3. θ b0 is the angle of the first rolling body relative to the x-axis at the initial moment, θ f0 is the angle of the defect center relative to the x-axis at the initial moment.

[0093] θ f and θ bk It can be expressed as:

[0094] θ f =w i t+θ f0 (10)

[0095]

[0096] Specifically, in step S1, the position of each rolling body is calculated based on bearing parameters, operating status, defect information, contact stiffness and damping parameters; the corresponding rolling body whose relative relationship between the rolling body position and the defect area position meets the set conditions is taken as the rolling body K2 entering the defect area.

[0097] Specifically, in step S2, formula (8-11) is used to calculate the time-varying displacement of rolling elements K1 and K2 and the angle relative to the x-axis, thereby calculating the angle difference between the two.

[0098] like Figure 5 As shown in the figure, when the rolling element moves to the position shown in the figure, it collides with the trailing edge of the defect, generating an impact force instantly. In the dual-rotor system, the combined force of the high- and low-pressure rotor unbalance force and gravity constitutes an alternating load, resulting in different load intensities when the rolling element collides with the defect, so the amplitude of the impact force also changes accordingly. Therefore, this paper comprehensively considers the rotation speed and defect size, and derives the impact force excitation function under the action of the alternating load.

[0099] When the rolling element contacts the trailing edge of the defect, the velocity of the rolling element can be decomposed into the tangential velocity v t and radial velocity v r Indicates that v r It can be expressed by taking the derivative of the actual displacement change of the rolling element. At this time, the actual displacement change of the roller H c express.

[0100] Displacement change at a certain moment H c It can be expressed as follows

[0101]

[0102] V r The displacement change H c The first-order derivative of

[0103]

[0104] According to the impulse theorem, the following equation can be obtained in the radial direction:

[0105] f im-i cosη△t=m b v r (14)

[0106] In the formula, f im-i is the magnitude of the impact force, η is the angle between the impact force direction and the radial direction, m b is the mass of the rolling element, and t is the duration of the collision, which is assumed here to be the time from the collision to leaving the defect area.

[0107] Since both the rolling element and the inner ring rotate counterclockwise, cosη and △t are expressed as follows:

[0108]

[0109] The inner ring and the cage have the same direction, and the cage has a higher speed than the inner ring. im-i for

[0110]

[0111] When the contact point is reached, The above simplification

[0112]

[0113] like Figure 6 As shown in the figure, when a loading device is used to apply a vertical downward load to the bearing through the rotating shaft, its range of action is limited to the lower half of the bearing, and there is almost no radial force on the rolling elements in the upper half. The radial force at any angle in the load zone is calculated by the following formula:

[0114]

[0115] Where ψ(t) is the angle between a certain direction in the load zone and the radial direction at time t, ψ(t)<π / 2, Q m is the maximum load component in the load area. ε is the load distribution factor, which can be expressed as 0.5(1-C d / 2δ r ), C d and δ r They represent the bearing clearance and the maximum displacement in the load zone respectively. n is the load-deformation index. For cylindrical roller bearings, n=10 / 9.

[0116] The load borne by the bearing-rotor system is not a simple radial load, but changes with the rotor imbalance force and gravity. The alternating unbalanced forces of the inner and outer rotors of the dual-rotor system make the load on the intermediate bearing more complicated, and the magnitude of the impact force is closely related to the load intensity. When the system runs to a certain moment, the deformation of the bearing at the maximum load also reaches a maximum. The present invention reversely infers the direction of the maximum load component of the bearing based on the displacement deformation of the inner and outer rotors of the actual bearing, and makes an assumption: at a certain transient moment, there is always one rolling body among the Nb rolling bodies whose contact deformation with the raceway is the maximum value. The angular position of the rolling body is defined as the generalized load position of the bearing, corresponding to Max{(χ j ,j=1,2,...,N b )}. The loads in other directions are then calculated based on the angles between the directions of other rolling elements and the generalized load position.

[0117] The present invention proposes an impact force correction coefficient in combination with the above load distribution formula, and the specific expression is as follows:

[0118]

[0119] Where ψ(t) is the angle between the direction of a rolling element in the load zone and the direction of the generalized load position, ψ(t)<π / 2.

[0120] Therefore, the impact force of the alternating load is:

[0121]

[0122] The expressions of impact force along the x and y directions are:

[0123]

[0124] In the formula, sin(η) and cos(η) are the components of the impact force in the x and y directions, and Determine the direction of the impact force on the x-axis at time t. Similarly, the direction of the component of the impact force on the y-axis is also determined based on the corresponding conditions.

[0125] Specifically, in step S2, the impact force of rolling elements K1 and K2 is calculated using formula (19-21).

[0126] Specifically, in step S3, the nonlinear dynamic differential equations of the system are obtained according to the Lagrange equation of motion and the rotor dynamics theory:

[0127]

[0128] Where M is the mass matrix, X and Y are the displacement matrices, and F bx 、F by is the bearing force vector matrix, F ex 、F ey is the external force matrix caused by the unbalanced quantity, F im-iix 、F im-iix is the impact force matrix, C x , K x and C y , K y are the damping and stiffness matrices in the x and y directions respectively, C y , K y Just need to C x , K x The subscripts of the stiffness and damping coefficients between the middle casing and the foundation can be modified to the y direction.

[0129] Dimensionlessness can extract important characteristic quantities in physical problems, reduce the number of variables in differential equations, and improve solution efficiency. In step S4, the present invention introduces a dimensionless length parameter ξ and performs dimensionless processing on the system of equations according to the following formula:

[0130]

[0131] Where τ is the dimensionless time, for ball bearings, h = 1 / 2; for cylindrical roller bearings, h = 1 / 9. Where ω1 is the speed of the low-pressure rotor, ω2 is the speed of the high-pressure rotor, and the speed ratio α = ω2 / ω1. Formula (22) is dimensionlessly processed to obtain:

[0132]

[0133] in is the dimensionless time-varying impact force, which can be calculated according to formulas xx and xx. F by is the dimensionless nonlinear bearing force of the rolling bearing, and its dimensionless formula (25) is obtained:

[0134]

[0135] For rolling bearings 1 and 4, n=3 / 2; for cylindrical roller bearings 2 and 3, n=10 / 9. F ey is the dimensionless rotor unbalance force. For the low-pressure rotor, the dimensionless formula (26) is obtained:

[0136]

[0137] For the high pressure rotor, the dimensionless formula (27) is obtained:

[0138]

[0139] After determining the rolling element that enters the defect area and the rolling element with the largest contact deformation in step S2, its time-varying displacement, impact force and the angle difference between the two are used as input variables and substituted into the dimensionless nonlinear dynamic equation. This equation comprehensively considers the characteristics of the system such as displacement, velocity, contact stiffness, damping parameters and external force, and solves to obtain the vibration signal of the bearing system.

[0140] The vibration signal is the manifestation of the system dynamic response caused by the dynamic contact between the rolling element and the defective area during the operation of the bearing system. The vibration signal obtained by solving the dimensionless nonlinear dynamic equation contains the time domain and frequency domain characteristic information of the system. For example, the impact amplitude and interval of the time domain signal reflect the contact deformation and impact force of the rolling element, and the characteristic frequency of the frequency domain signal is closely related to the type of bearing defect. Further analysis of the vibration signal can extract the impact characteristics, thereby calculating the impact force on the system, diagnosing the fault location or evaluating the system performance.

[0141] The following specific data are collected to verify the effectiveness of the present invention.

[0142] Since the system has strong nonlinearity, this embodiment uses a fixed-step fourth-order Runge-Kutta method to perform numerical integration to solve the differential equations to obtain the high and low pressure rotor and casing responses, and further analyzes and verifies the system. The parameters used for the model and bearings are shown in Tables 1 and 2. Unless otherwise specified, the model operates according to the data in the table.

[0143] Table 1 Rotor parameters

[0144]

[0145]

[0146] The stiffness of each shaft section of the double-disc structure supported at both ends can be derived from the structural relationship of the plane beam. The distance between bearing 1 and bearing 3 is l1, the distance between bearing 3 and disk 3 is l2, the distance between disk 3 and bearing 4 is l3, the distance between bearing 2 and disk 1 is l4, the distance between disk 1 and disk 2 is l5, and the distance between disk 2 and bearing 3 is l6. The stiffness of the bearing support sections on both sides of the high and low pressure rotors can be obtained. Intermediate shaft section stiffness Assuming that the two shafts have the same material and shaft diameter, the elastic modulus E of each section and the cross-sectional diameter I of the shaft section are i Similarly, the length of each shaft segment satisfies l2=l3=l4=l6=l5 / 2=l1 / 5, then the stiffness of each shaft segment satisfies the relationship k1=k / 125, k2=4k, k5=k / 2, k3=k4=k6=k, where k is the stiffness of the shaft.

[0147] Table 2 Bearing parameters

[0148]

[0149]

[0150] In order to study the working characteristics of the intermediate bearing failure, a dual-rotor intermediate bearing failure test bench was built in the laboratory according to the typical dual-rotor structure of the gas turbine. The test bench consists of a high-pressure rotor, a low-pressure rotor, a rolling bearing, a drive motor, etc., which can simulate the failure state of the intermediate bearing under different working conditions. The sensors are located in the horizontal and vertical directions of different bearing seats. The 8 sensors used in the test are all BK acceleration sensors, which have the same model and good performance.

[0151] The test bench uses a high-speed motor to adjust the speed of the high-pressure and low-pressure rotors. The left-side drive motor uses an elastic coupling to directly drive the low-pressure inner rotor, and the right-side drive motor uses a belt to drive the high-pressure outer rotor. The squeeze film damper is used as a stabilizer at bearing 2 to prevent the vibration of the motor from interfering with the system. The intermediate bearing 3 is between the high-pressure rotor and the low-pressure rotor to support the high-pressure and low-pressure rotors. Figure 6 As shown, the intermediate bearing used in the test is a HRB series FAG NU1005M1 rolling bearing. In addition to the normal state, the intermediate bearing is set with a rectangular fault through a cutting process, and a local defect fault with a width of 2 mm and a depth of 1 mm is set.

[0152] In the test, the sampling frequency was set to 25.6kHz, and the sensors were used to collect signals under different working conditions. Each sampling time was 10 seconds, and the sampling continued after an interval of 5 seconds. Five multivariate time series were collected for each fault type and normal state under each working condition. During the test, the motor can be used to adjust the speed of the high and low pressure rotors, and the vibration data of some important speed conditions of the gas turbine can be collected, which can provide a reference for the stable operation of the unit.

[0153] In the inner ring failure analysis, the inner ring speed is set to 1920 rpm and the outer ring speed is set to 4020 rpm. The fault frequency can be obtained according to the inner ring fault characteristic frequency formula.

[0154]

[0155] Among them, f i Indicates the characteristic frequency of the inner race fault, n o represents the speed of the outer ring, ni represents the speed of the inner ring, D m represents the pitch diameter of the bearing, and α represents the contact angle.

[0156] It can be obtained that the inner ring rotation frequency is 32Hz, the outer ring rotation frequency is 67Hz, and the characteristic frequency of the inner ring fault is 302.60Hz. In order to more clearly compare the signal characteristics of the simulation and the test, the simulation and test signals are normalized.

[0157] Figures 7a-7fThey are the time domain and envelope spectra of simulation and test respectively. The impact phenomenon can be found in the time domain diagram. Since the simulation signal has no interference from the noise signal, the impact phenomenon is more obvious. The fault-free bearings in the test also have certain impact phenomena. This is because the equipment is unbalanced, and the alternating influence of the centrifugal force and gravity of the inner and outer rotors causes the fault-free bearings under normal circumstances to have impact phenomena. Therefore, it is not feasible to perform fault analysis on the bearing only through time domain signals.

[0158] The envelope spectrum of the simulation signal can reveal the rotational frequency of the high- and low-pressure rotors and their multiples, modulation frequency, inner ring damage frequency, and sidebands centered on the high-pressure rotational speed and fault frequency. The frequency of the simulated fault signal is 302.34Hz, which differs from the theoretical calculation formula by 0.26Hz, with a relative error of 0.08%. At the same time, the double and triple fault frequencies and their sidebands can be observed, and their amplitudes decrease as the multiples increase. The amplitude of the high-pressure rotor rotational frequency also tends to decrease as the multiples increase, but at 4 times the high-pressure rotational frequency, its amplitude increases sharply. This is because the frequency is close to the 4 times rotational frequency, and the coupling of the two increases its frequency.

[0159] exist Figure 7c to Figure 7f In addition to the rotational frequencies of the high and low pressure rotors and their multiples, modulation frequencies, and inner ring damage frequencies, side frequencies around the high pressure rotational speed and the center of the fault frequency can also be observed. However, these frequencies appear more complex due to the influence of other interference components and noise factors. The fault frequency and the rotational frequency are superimposed on each other, resulting in a less obvious trend of the side frequencies centered on the fault frequency. Through analysis, the fault frequency is 303Hz, and the difference with the simulation frequency is 0.66Hz, with a relative error of 0.2%. In order to further verify that 303Hz is the fault frequency rather than the modulation frequency, it is compared with the envelope spectrum of the normal bearing. The results show that near the inner ring damage frequency of 302.60Hz, two components with frequencies of 301Hz and 304Hz appear. Further analysis shows that 301Hz is the side frequency of four times the high pressure rotation frequency (4fh+fl), while 304Hz is the side frequency of five times the high pressure rotation frequency (5fh-fl).

[0160] It can be seen that the relative error between the simulation signal and the theoretical calculation formula and the test is small, which verifies the accuracy of the simulation calculation. Since the simulation signal receives less interference, it is more advantageous to use the nonlinear dynamic equation proposed in the embodiment to analyze the vibration characteristics of the signal.

[0161] The present invention can further analyze the bearing characteristics based on the calculation results of the nonlinear dynamic model. Figure 8As shown in the figure, the bearing force, total bearing force and acceleration in the y direction of the first five rollers of the intermediate bearing change. The green rectangle in the figure represents the entry defect, and the purple rectangle represents the exit defect. When passing through the fault area, the contact pressure on the ball will suddenly decrease to 0 because the ball enters the peeling area, and there is a contact separation phenomenon when the ball passes through the fault area. The Hertz force on the ball in the load area oscillates at the beginning and end of the fault event, and this oscillation will be transmitted to the adjacent loaded balls, causing the oscillation of the Hertz contact force in the load area of ​​two adjacent balls, but this oscillation will decay, which is not as strong as the oscillation caused in the load area of ​​the ball. When the ball passes through the inner ring fault area, it will cause a ball in the load area to suddenly be unloaded. In this process, as the number of balls carried in the load area decreases, the load is redistributed among the remaining balls, and the Hertz contact force of the loaded balls outside the fault area increases. After passing through the fault area, the load on the ball is redistributed again, and the load on the unit ball decreases. This sudden change in the unit ball load will cause the instability of the system, and the amplitude of the vibration signal response will increase accordingly. The above-mentioned impact oscillation is caused by this reason. As the number of loaded balls decreases, the overall stiffness of the bearing also decreases.

[0162] It can be found that the Hertz contact total force and the acceleration time domain waveform also show a strong correlation. The Hertz total force at the time of the fault always decreases suddenly and then increases; the corresponding time domain waveform vibration amplitude shows a trend of first increasing and then decreasing. The Hertz total force and time domain waveform have obvious impact oscillation characteristics, and the impact oscillation caused by the ball passing through the fault area will be directly reflected in its time domain waveform. At the same time, it was observed that the impact on the corresponding ball at certain fault moments was also very small, which proves that the intensity of the impact oscillation on the time domain waveform is positively correlated with the degree of Hertz force impact oscillation on the ball at the corresponding moment, and the intensity of the impact oscillation is affected by the load size. The larger the load, the stronger the impact oscillation.

[0163] At the same time, it can be found that when a collision occurs, it will also affect the acceleration, but the collision time is short, which has little effect on the signal fluctuation and only works for a moment. When the roller entering the defect is in the middle of the load zone, the double impact phenomenon caused by the accelerated entry and exit can be found, while there is only a single impact phenomenon of entry and exit on the edge. The double impact time can estimate the size of the fault. In this embodiment, the simulated double impact time is 0.001038s, which is 0.28% different from the theoretical double impact time of 0.001035s, which further verifies the accuracy of the model.

[0164] Example 2

[0165] The present invention provides a vibration analysis system for an intermediate bearing of a dual-rotor system, and the system is used to implement the vibration analysis method for the intermediate bearing of a dual-rotor system described in Example 1.

[0166] Example 3

[0167] The present invention provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the vibration analysis method for the intermediate bearing of the dual-rotor system described in Example 1 is implemented.

[0168] Example 4

[0169] The present invention provides an electronic device, comprising: a memory and a processor, wherein the memory and the processor are communicatively connected to each other, the memory stores computer instructions, and the processor executes the vibration analysis method of the intermediate bearing of a dual-rotor system as described in Example 1 by executing the computer instructions.

[0170] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0171] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0172] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0173] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0174] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation modes, which are merely illustrative rather than restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the present invention and the claims, all of which are within the protection of the present invention.

[0175] The contents not described in detail in this specification belong to the prior art known to professional and technical personnel in this field.

Claims

1. A vibration analysis method for an intermediate bearing of a dual-rotor system, characterized in that: The following steps are involved: Determine the rolling element that has entered the defect area and the rolling element with the largest contact deformation at the current moment based on bearing parameters, operating status, defect information, contact stiffness and damping parameters; The time-varying displacement and impact force of the rolling element entering the defect area and the rolling element with the largest contact deformation, as well as the angle difference between the two are calculated respectively; The impact force is corrected by the angle difference between the rolling element entering the defect area and the rolling element with the largest contact deformation and used as the external force input of the nonlinear dynamic equation of the intermediate bearing system of the dual rotor system; The nonlinear bearing force in the nonlinear dynamic equation is calculated based on the time-varying displacement of the rolling element entering the defect area and the rolling element with the largest contact deformation; The nonlinear dynamic equations are solved to obtain the vibration signal of the intermediate bearing of the dual-rotor system at the current moment.

2. A method according to claim 1, characterized in that: The process of determining the rolling body that has entered the defect area at the current moment includes: calculating the position of each rolling body based on bearing parameters, operating status, defect information, contact stiffness and damping parameters; and taking the corresponding rolling body whose relative relationship between the rolling body position and the defect area position meets the set conditions as the rolling body that has entered the defect area.

3. A method according to claim 1, characterized in that: The time-varying displacement and contact deformation of the i-th rolling element are calculated using the following formula: θ i =arcsin(B / 2R ii ); i f =w i t+θ f0 ; Among them, H i represents the time-varying displacement or contact deformation of the ith rolling element; ψ i represents the angle between the center of the i-th rolling element and the center of the inner raceway defect area; θ i represents the defect angle formed by the inner ring defect edge and the defect center; d represents the rolling element diameter; R ii Indicates the inner raceway radius of the intermediate bearing; θ f Indicates the angle of the defect area center relative to the x-axis at the current moment; θ bk Indicates the angle of the kth rolling element relative to the x-axis at the current moment; θ f0 represents the angle of the defect area center relative to the x-axis at the initial moment; t represents the current moment, ω i Indicates the angular velocity of the inner ring of the bearing; ω c Indicates the angular velocity of the bearing cage; θ b0 Indicates the angle of the first rolling body relative to the x-axis at the initial moment; Z indicates the number of rolling bodies.

4. A method according to claim 3, characterized in that: The corrected impact force f of the ith rolling element is calculated using the following formula: im-ii : Where ζ represents the correction coefficient, m b Indicates the quality of the rolling element; B indicates the width of the defect.

5. A method according to claim 4, characterized in that: The correction factor for impact force is calculated using the following formula: Among them, C d Indicates the maximum offset of bearing clearance, δ r It represents the maximum displacement in the bearing load zone; n is the load-deformation index; ε represents the load distribution factor; Ψ(t) represents the angle between the direction of the corresponding rolling element in the load zone and its angular position direction.

6. A method according to claim 5, characterized in that: The expression of the nonlinear dynamic equation is as follows: Where M is the mass matrix, g is the gravitational acceleration, X and Y are the displacement matrices in the x- and y-directions; F bx and F by are the bearing force vector matrices in the x-direction and y-direction, respectively, ex and F ey are the external force matrices in the x-direction and y-direction caused by the unbalanced amount, F im-iix 、F im-iiy are the impact force matrices in the x and y directions respectively, C x , K x and C y , K y are the damping and stiffness matrices in the x-direction and y-direction respectively.

7. A method according to claim 6, characterized in that: The nonlinear dynamics equation is dimensionless and then solved; the expression of the dimensionless nonlinear dynamics equation is as follows: For the low pressure rotor: For high pressure rotors there are: Where j is the rolling element number, τ is the dimensionless time, and F j represents the force of the jth rolling element on the contact point, F j,x represents the force in the x direction of the jth rolling element at the contact point, F j,y represents the force in the y direction of the jth rolling element at the contact point, k b Indicates the contact stiffness of the bearing rolling element; x j Represents the contact deformation of the jth rolling element; ω represents the angular velocity of the bearing rotor, e represents the eccentricity of the bearing rotor; α represents the speed ratio of the high-pressure and low-pressure rotors.

8. A vibration analysis system for the intermediate bearing of a dual rotor system, characterized in that: The system is used to implement the vibration analysis method of the intermediate bearing of the dual-rotor system described in any one of claims 1-7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the vibration analysis method for the intermediate bearing of a dual-rotor system according to any one of claims 1 to 7 is implemented.

10. An electronic device, characterized in that: include: A memory and a processor, wherein the memory and the processor are communicatively connected to each other, the memory stores computer instructions, and the processor executes the vibration analysis method for the intermediate bearing of a dual-rotor system as described in any one of claims 1-7 by executing the computer instructions.

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