Fault location method and system for gas turbine power turbine end bearing-rotor system

Abstract

The present invention discloses a fault locating method and system for a bearing-rotor system at a power turbine end of a gas engine, and relates to the technical field of fault locating. A system dynamics model of the bearing-rotor system at the power turbine end of a gas engine under a bearing fault condition is first established, and then the system dynamics model is solved to obtain an acceleration response vector of the bearing-rotor system. Fault locating is performed according to the acceleration response vector, so that the rolling bearing fault can be quickly and accurately located without disassembling the power turbine end of the gas engine.

Description

Technical Field

[0001] The present invention relates to the technical field of fault location, and in particular to a method and system for locating a fault of a gas turbine power turbine end bearing-rotor system. Background Art

[0002] In the gas turbine power turbine system, rolling bearings and power turbine rotors are important components. The friction and vibration between rolling bearings and power turbine rotors will generate strong interference noise, which will affect the efficiency and stability of the gas turbine power turbine system. At present, when a rolling bearing fails, if the gas turbine power turbine system is not disassembled, it is impossible to determine the fault location of the rolling bearing, which is very inconvenient.

[0003] Based on this, there is an urgent need for a technology for locating rolling bearing faults without disassembling the gas turbine power turbine system. Summary of the invention

[0004] The purpose of the present invention is to provide a method and system for locating faults in a bearing-rotor system at a power turbine end of a gas turbine, which can quickly and accurately locate faults in rolling bearings without disassembling the power turbine end of the gas turbine.

[0005] To achieve the above object, the present invention provides the following solutions:

[0006] A method for locating a fault of a gas turbine power turbine end bearing-rotor system, the method comprising:

[0007] Establish a system dynamics model of the bearing-rotor system at the power turbine end of a gas turbine considering bearing failure conditions;

[0008] The system dynamics model is solved to obtain an acceleration response vector of the bearing-rotor system, and fault location is performed according to the acceleration response vector.

[0009] A fault locating system for a gas turbine power turbine end bearing-rotor system, the fault locating system comprising:

[0010] Model building module, used to establish the system dynamics model of the bearing-rotor system at the power turbine end of the gas turbine under bearing failure conditions;

[0011] The fault location module is used to solve the system dynamics model to obtain the acceleration response vector of the bearing-rotor system and perform fault location according to the acceleration response vector.

[0012] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0013] The present invention is used to provide a fault locating method and system for a bearing-rotor system at a power turbine end of a gas turbine. First, a system dynamics model of the bearing-rotor system at the power turbine end of a gas turbine under bearing fault conditions is established, and then the system dynamics model is solved to obtain an acceleration response vector of the bearing-rotor system. Fault locating is performed based on the acceleration response vector, thereby enabling rapid and accurate rolling bearing fault locating without disassembling the power turbine end of the gas turbine. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0015] Figure 1 A method flow chart of a fault location method provided in Example 1 of the present invention;

[0016] Figure 2 A schematic diagram of the contact between the rolling element and the inner and outer rings provided in Example 1 of the present invention;

[0017] Figure 3 A schematic diagram of the relative deformation of the rolling element and the inner and outer rings provided in Example 1 of the present invention;

[0018] Figure 4 Another schematic diagram of the relative deformation of the rolling element and the inner and outer rings provided in Example 1 of the present invention;

[0019] Figure 5 A schematic diagram of a point contact model between a rolling element and a raceway provided in Example 1 of the present invention;

[0020] Figure 6 A schematic diagram of a rolling bearing outer ring failure provided in Example 1 of the present invention;

[0021] Figure 7 A schematic diagram of a rolling bearing inner ring failure provided in Example 1 of the present invention;

[0022] Figure 8 A schematic diagram of a rolling element failure of a rolling bearing provided in Example 1 of the present invention;

[0023] Fig. 9 A schematic diagram of a Timoshenko beam unit provided in Example 1 of the present invention;

[0024] Fig.10 A schematic diagram of the geometric structure of a rolling bearing provided in Example 1 of the present invention;

[0025] Fig.11 The outer ring fault bearing simulation signal provided by Example 1 of the present invention;

[0026] Fig.12 The outer ring fault bearing test signal provided in Example 1 of the present invention;

[0027] Fig.13 A three-dimensional spectrum diagram of vibration response of an outer ring fault test under different defect widths provided in Example 1 of the present invention;

[0028] Fig.14 The test response of the rotor system with outer ring fault under the defect width of 0.4 mm provided in Example 1 of the present invention;

[0029] Fig.15 The test response of the rotor system with outer ring fault under the defect width of 1 mm provided in Example 1 of the present invention;

[0030] Fig.16 The inner ring fault bearing simulation signal provided by Embodiment 1 of the present invention;

[0031] Fig.17 The inner ring fault bearing test signal provided in Example 1 of the present invention;

[0032] Fig.18 A three-dimensional spectrum diagram of vibration response of an inner race fault test under different defect widths provided in Example 1 of the present invention;

[0033] Fig.19 The test response of the rotor system with inner ring fault under the defect width of 0.4 mm provided in Example 1 of the present invention;

[0034] Fig. 20 The test response of the rotor system with inner ring fault under the defect width of 1 mm provided in Example 1 of the present invention;

[0035] Fig.21 The rolling element fault bearing simulation signal provided in Example 1 of the present invention;

[0036] Fig. 22 The rolling element fault bearing test signal provided in Example 1 of the present invention;

[0037] Fig.23 A three-dimensional spectrum diagram of vibration response of a rolling element fault test under different defect widths provided in Example 1 of the present invention;

[0038] Fig.24 The test response of the rotor system with rolling element failure under the defect width of 0.4 mm provided in Example 1 of the present invention;

[0039] Fig.25The test response of the rotor system with rolling element failure under the defect width of 1 mm provided in Example 1 of the present invention;

[0040] Fig.26 The vibration response of the bearing under the outer ring fault provided in Example 1 of the present invention;

[0041] Fig. 27 The vibration response of the bearing under the inner ring fault provided by Example 1 of the present invention;

[0042] Fig.28 The vibration response of the bearing under the rolling element failure provided in Example 1 of the present invention;

[0043] Fig.29 This is a system block diagram of the fault location system provided in Example 2 of the present invention. DETAILED DESCRIPTION

[0044] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0045] The purpose of the present invention is to provide a method and system for locating faults in a bearing-rotor system at a power turbine end of a gas turbine, which can quickly and accurately locate faults in rolling bearings without disassembling the power turbine end of the gas turbine.

[0046] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0047] Embodiment 1:

[0048] This embodiment is used to provide a method for locating a fault of a gas turbine power turbine end bearing-rotor system. Figure 1 As shown, the fault location method includes:

[0049] S1: Establish a system dynamics model of the bearing-rotor system at the power turbine end of a gas turbine considering bearing failure conditions;

[0050] S2: Solving the system dynamics model to obtain the acceleration response vector of the bearing-rotor system, and locating the fault according to the acceleration response vector.

[0051] In this embodiment, establishing a system dynamics model of the bearing-rotor system at the power turbine end of the gas turbine under the condition of bearing failure may include:

[0052] (1) Establish a dynamic analysis model for rolling bearings.

[0053] 1) Contact deformation of rolling bearings:

[0054] Before the rolling bearing is subjected to external load, the contact between the rolling element and the inner and outer rings is as follows: Figure 2 As shown, Figure 2 In the figure, the x direction is the axial direction, the r direction is the radial direction, and i is the center of curvature of the inner groove, O o is the center of curvature of the groove of the outer ring, and the initial contact angle between the rolling element and the inner and outer rings is α0, O i and O o The initial distance between the inner and outer rings is A0. When the rolling bearing is subjected to external load, the elastic deformation of the rolling element and the inner and outer rings is as follows: Figure 3 and Figure 4 As shown, assuming the outer ring is faulty, the center of curvature of the outer ring groove is O o The position remains unchanged, and the center of curvature of the inner groove is O i Position changes to O' i , therefore, the contact angle after the load is α j , the distance between the inner and outer ring groove curvature centers after loading is A j , the contact deformation of the jth rolling element in the contact normal direction is δ j , combined with Figure 2-4 It can be seen that the contact deformation δ j for:

[0055]

[0056] In formula (1), δ j A is the contact deformation of the jth rolling element in the contact normal direction; j is the distance between the centers of curvature of the inner and outer grooves after loading; A0 is the initial distance between the centers of curvature of the inner and outer grooves before loading.

[0057] The distance A0 before the bearing is loaded can be expressed as:

[0058] A0=(f o +f i -1)d b ; (2)

[0059] In formula (2), f o f is the curvature radius coefficient of the outer raceway; i is the curvature radius coefficient of the inner race; d b is the diameter of the rolling element.

[0060] Distance A after the bearing is loaded j It can be expressed as:

[0061]

[0062] In formula (3), α0 is the initial contact angle; δ xj is the axial elastic deformation of the bearing; rj is the radial elastic deformation of the bearing.

[0063]

[0064] In formula (4), δ x is the acceleration response of the rolling element in the x direction; R j is the radius of the inner raceway groove curvature center trajectory; φ y is the torsional displacement of the rolling element around the y direction; ψ j is the azimuth angle of the jth rolling element; φ z is the torsional displacement of the rolling element around the z direction; δ y is the acceleration response of the rolling element in the y direction; z is the acceleration response of the rolling element in the z direction.

[0065]

[0066] In formula (5), d m is the pitch diameter of the bearing; D is the diameter of the rolling element.

[0067] Assume the number of rolling elements is m and the speed of the inner ring is ω i , the outer ring is fixed, the outer ring speed ω o =0, outer raceway radius Inner raceway radius The cage rotation speed can be obtained as:

[0068]

[0069] In formula (6), ω c is the cage rotation speed.

[0070] Therefore, the azimuth angle ψ of the jth rolling element at time t is j for:

[0071]

[0072] 2) Elliptical contact equivalent model of rolling bearing:

[0073] Before performing a complete dynamic modeling of a rolling bearing, it is necessary to convert the rolling bearing into an equivalent model. In order to analyze the interaction between the rolling element and the inner and outer raceways, this embodiment applies the Hertz contact theory to obtain the contact deformation distribution inside the bearing, and then solves the nonlinear contact force and torque of the rolling bearing. The point contact model between the rolling element and the raceway is as follows: Figure 5shown.

[0074] Assuming that the convex surface of the rolling element and the ring point contact friction pair is positive and the concave surface is negative, the main curvature of the ball-inner ring contact ellipse can be expressed as:

[0075]

[0076] In formula (8), ρ bxj is the principal curvature of the jth rolling element in the x direction; r bx is the curvature radius of the jth rolling element in the x direction; ρ byj is the principal curvature of the jth rolling element in the y direction; r by is the curvature radius of the jth rolling element in the y direction; ρ ixj is the principal curvature of the inner raceway in the x direction; r ix D is the curvature radius of the inner raceway in the x direction; m is the bearing pitch diameter; α ij is the contact angle between the rolling element and the inner ring; ρ iyj is the principal curvature of the inner raceway in the y direction; r iy is the curvature radius of the inner raceway in the y direction.

[0077] Similarly, the principal curvature of the ball-outer ring contact ellipse can be expressed as:

[0078]

[0079] In formula (9), ρ oxj is the principal curvature of the outer raceway in the x direction; r ox is the curvature radius of the outer raceway in the x direction; α oj is the contact angle between the rolling element and the outer ring; ρ oyj is the principal curvature of the outer raceway in the y direction; r oy is the curvature radius of the outer raceway in the y direction.

[0080] The sum of the principal curvatures of the ball-inner ring at the contact ellipse is:

[0081] Σρ ij =ρ bxj +ρ byj +ρ ixj +ρ iyj ; (10)

[0082] Similarly, the sum of the principal curvatures of the ball-outer ring at the contact ellipse is:

[0083] Σρ oj =ρ bxj +ρ byj +ρ oxj +ρ oyj ; (11)

[0084] According to the Hertz contact theory, the load-deformation coefficient k of the rolling element and the inner and outer rings can be obtained nij , k noj , whose expression is:

[0085]

[0086] In formula (12), E′ ij , E′ oj is the comprehensive elastic modulus of the rolling element and the inner and outer rings; Σρ ij and Σρ oj It is the sum of the principal curvatures of the rolling element and the inner and outer rings at the contact ellipse; and is the inner ring load deformation coefficient factor and the outer ring load deformation coefficient factor, which are calculated by the following formula:

[0087]

[0088] In formula (13), K eij is the first kind elliptic integral of the rolling element and the inner ring; e ij E is the equivalent ellipticity of the rolling element and the inner ring; eij is the second kind elliptic integral of the rolling element and the inner ring; K eoj is the first kind elliptic integral of the rolling element and the outer ring; e oj E is the equivalent ellipticity of the rolling element and the outer ring; eoj is the second kind of elliptic integral of the rolling element and the outer ring; they are all obtained by Hamrock and Dowson through the approximate formula of curve fitting, as follows:

[0089]

[0090] In formula (14), R y is the equivalent radius of curvature in the y direction; R x is the equivalent radius of curvature in the x direction.

[0091] From this, the total load-deformation coefficient k between the ball and the inner and outer rings can be obtained n , whose expression is:

[0092]

[0093] In formula (15), n is the contact index, and for ball bearings, n=1.5 can be set.

[0094] In order to obtain the total load-deformation coefficient k n and the normal deformation δ of the jth rolling element j Then, the contact force Q of the jth rolling element on the inner ring of the bearing along the normal direction can be obtained according to the Hertz contact theory. j,Right now:

[0095]

[0096] Therefore, the bearing forces acting on the shaft in the X, Y and Z directions are as follows:

[0097]

[0098] In formula (17), F X is the bearing force component of the rolling bearing along the X axis; m is the number of rolling elements; Q j is the contact force of the jth rolling element on the inner ring of the bearing along the normal direction; α j is the contact angle after loading; F Y is the bearing force component of the rolling bearing along the Y axis; ψ j is the azimuth angle of the jth rolling element; F Z is the bearing force component of the rolling bearing along the Z axis.

[0099] The bearing torque is as follows:

[0100]

[0101] In formula (18), M Y is the torque component of the rolling bearing around the Y axis; R j M is the radius of the inner raceway groove curvature center trajectory; Z is the torque component of the rolling bearing around the Z axis.

[0102] Formula (17) and Formula (18) constitute the dynamic analysis model of this embodiment. Based on the above dynamic analysis model, taking the rolling bearing at the power turbine end of the gas turbine as the object, the bearing force component and torque component of the bearing can be obtained, and the movement and force of the bearing can be analyzed.

[0103] (2) A fault model of a rolling bearing under bearing failure conditions is established, wherein the fault model includes an outer ring fault model, an inner ring fault model and a rolling element fault model.

[0104] 1) Modeling of outer ring fault excitation force:

[0105] like Figure 6 As shown in the figure, when the outer ring of the bearing is worn, the rolling element will generate impact vibration on the entire rotor when passing through the fault point. Assuming that the wear fault point is a pit, the geometric relationship of the local defect shows that the geometric size of the fault area determines whether the rolling element will form an impact at the damaged location if and only if When the outer ring is damaged, the impact will be generated. Otherwise, harmonic excitation will be generated. For early wear failures, the fault area is small, which usually meets the above requirements and forms impact vibration. Where L is the diameter of the fault area, d bis the diameter of the rolling element, and a is the wear fault depth.

[0106] When the rolling element passes through the outer ring fault point, the outer ring fault model assumes that the clearance between the bearing elements increases suddenly, and the contact force of the bearing approaches 0. Figure 6 It can be seen that the increase in bearing clearance caused by the fault is D for:

[0107]

[0108] In formula (19), λ D The increase in bearing clearance; d b is the diameter of the rolling element; L is the diameter of the fault area. Formula (19) is the outer ring fault model of this embodiment.

[0109] 2) Inner race fault excitation force modeling:

[0110] like Figure 7 As shown in the figure, the inner ring wear fault is simulated by pits. During the movement of the bearing-rotor system, the relative position of the inner ring and the rotor remains unchanged. As the rotor rotates, the speed of the cage and the inner ring is different. Every time the rolling element passes through the inner ring fault point, the contact stiffness coefficient between the rolling element and the inner ring changes, resulting in a change in the contact stress. Similar to the outer ring fault, when the rolling element passes through the inner ring fault point, a pulse vibration will be generated in the entire bearing-rotor system. Figure 7 As shown, L is the diameter of the fault area, a is the wear fault depth, so there is When the rolling element passes through the inner ring fault point, the inner ring fault model assumes that the clearance between the bearing elements increases suddenly, and the contact force of the bearing approaches 0. Figure 7 It can be seen that the bearing clearance increase λ when the rolling element passes the inner ring failure point D for:

[0111]

[0112] In formula (20), λ D The increase in bearing clearance; d b is the diameter of the rolling element; L is the diameter of the fault area. Formula (20) is the inner ring fault model of this embodiment.

[0113] 3) Rolling element fault excitation force modeling:

[0114] like Figure 8As shown, for rolling element failure, this embodiment uses local depressions to simulate the wear points on the rolling element surface. During the movement, the rolling bearing rotates on its own and contacts with the inner and outer rings every time it rotates, which causes the stiffness and damping of the bearing itself to change, causing the bearing-rotor system to produce a periodic impact response result with a frequency equal to the rolling element failure frequency.

[0115] Assume that the diameter of the rolling element wear failure point is L, and the rolling element failure angle is β3, and the expression is:

[0116]

[0117] Therefore, when the rolling element's rotation angle θ K When the following formula (22) is satisfied, it can be considered that the fault point on the rolling element is in contact with the inner and outer rings of the bearing:

[0118]

[0119] Formula (22) is the rolling element failure model of this embodiment. According to Hertz contact theory, the contact stiffness deformation coefficient n of the rolling bearing will increase to 3, and the bearing clearance will surge, generating bearing impact force, achieving the purpose of simulating rolling element failure in the bearing-rotor system.

[0120] (3) The dynamic analysis model and the fault model are integrated to obtain the fault excitation force model of the rolling bearing. The fault excitation force model includes the outer ring fault excitation force model, the inner ring fault excitation force model and the rolling element fault excitation force model.

[0121] In the process of numerically solving the bearing dynamics, it is only necessary to satisfy When δ in formula (16) j Replace with δ j and λ in formula (19) D At the same time, based on the Hertz contact theory, when there is no fault on the bearing contact surface, the contact index n is 1.5, and when the rolling element passes the fault point, the contact index n is 3. The first formula in formula (22) is used for judgment, that is, when the first formula in formula (22) is satisfied, let n in formula (16) be 3, otherwise let n in formula (16) be 1.5, so as to obtain the outer ring fault excitation force model.

[0122] In the process of numerically solving the bearing dynamics, it is only necessary to satisfy When δ in formula (16) j Replace with δ j and λ in formula (20) DAt the same time, based on the Hertz contact theory, when there is no fault on the bearing contact surface, the contact index n is 1.5, and when the rolling element passes the fault point, the contact index n is 3. The second formula in formula (22) is used for judgment, that is, when the second formula in formula (22) is satisfied, let n in formula (16) be 3, otherwise let n in formula (16) be 1.5, so as to obtain the inner ring fault excitation force model.

[0123] In the process of numerically solving the bearing dynamics, it is only necessary to replace δ in equation (16) when equation (22) is satisfied. j Replace with δ j and the sum of L. At the same time, based on the Hertz contact theory, when there is no fault on the bearing contact surface, the contact index n is 1.5, and when the rolling element passes the fault point, the contact index n is 3. It is judged by formula (22), that is, when formula (22) is satisfied, let n in formula (16) be 3, otherwise let n in formula (16) be 1.5, so as to obtain the rolling element fault excitation force model.

[0124] (4) The finite element method is used to perform dynamic modeling of the rotor and obtain the rotor's motion equation.

[0125] Before performing rotor dynamics modeling, the rotor needs to be divided into several beam elements, each of which can be regarded as linear elastic. In this embodiment, Timoshenko beam elements are used for modeling, such as Fig. 9 As shown, each node has five degrees of freedom of displacement in the axial, lateral and bending directions. The motion equation of the rotor in this embodiment includes the motion equations of multiple beam units. The beam unit is obtained by dividing the rotor. The internal damping of the beam unit is not considered. The motion equation of the beam unit can be expressed as:

[0126]

[0127] In formula (23), M b is the beam element mass matrix; is the acceleration response vector of the beam element; K is the stiffness matrix of the bearing-rotor system; G b is the antisymmetric beam unit gyro matrix; is the velocity response vector of the beam element; K b is the beam element stiffness matrix; Ω is the speed of the bearing-rotor system; is the additional mass matrix of the beam element when the centrifugal force is considered; u is the displacement response vector of the beam element, u={δ x ,δ y ,δ z ,φ y ,φ z}, δ x ,δ y,δ z is the contact deformation of the beam element along the x, y, and z directions, φ y ,φ z is the torsional displacement of the beam element around the y and z directions; F b is the external force vector of the beam element.

[0128] The motion equation of the rotor can be obtained by assembling the motion equation of each beam element of the rotor using the finite element method.

[0129] (5) The fault excitation force model and the motion equation are integrated to obtain the system dynamics model of the bearing-rotor system at the power turbine end of the gas turbine. The system dynamics model includes the outer ring fault system dynamics model, the inner ring fault system dynamics model and the rolling element fault system dynamics model.

[0130] By integrating the outer ring fault excitation force model and the motion equation, the outer ring fault system dynamics model can be obtained. By integrating the inner ring fault excitation force model and the motion equation, the inner ring fault system dynamics model can be obtained. By integrating the rolling element fault excitation force model and the motion equation, the rolling element fault system dynamics model can be obtained.

[0131] System dynamics models include:

[0132]

[0133] In formula (24), M s is the mass matrix of the bearing-rotor system; is the acceleration response vector of the bearing-rotor system; C s is the bearing-rotor system damping matrix. This embodiment uses the Ruili damping, i.e., C s =c0M s +c1K s , where c0, c1 are constants related to the first-order natural frequency and the second-order natural frequency; Ω is the speed of the bearing-rotor system; G s is the gyro matrix of the bearing-rotor system; is the speed response vector of the bearing-rotor system; K s is the bearing-rotor system stiffness matrix; u s is the displacement response vector of the bearing-rotor system, which includes the displacement of the rolling bearing; Q s is the external force vector of the bearing-rotor system, including the rotor unbalance force and the bearing nonlinear contact force. The bearing nonlinear contact force is the bearing force component obtained through the dynamic analysis model of the rolling bearing.

[0134] In S2, the system dynamics model is solved to obtain the acceleration response vector of the bearing-rotor system. Fault location is performed according to the acceleration response vector, which may include:

[0135] (1) The outer ring fault system dynamics model is solved to obtain the first acceleration response vector of the bearing-rotor system, and whether the outer ring of the rolling bearing of the bearing-rotor system is faulty is determined based on the first acceleration response vector.

[0136] (2) Solving the inner ring fault system dynamics model to obtain a second acceleration response vector of the bearing-rotor system, and judging whether the inner ring of the rolling bearing of the bearing-rotor system is faulty according to the second acceleration response vector.

[0137] (3) Solving the rolling element fault system dynamics model to obtain the third acceleration response vector of the bearing-rotor system, and judging whether the rolling element of the rolling bearing of the bearing-rotor system is faulty according to the third acceleration response vector.

[0138] In this embodiment, the Newmark-β method can be used to solve the outer ring fault system dynamics model, the inner ring fault system dynamics model and the rolling element fault system dynamics model.

[0139] Among them, judging whether the outer ring of the rolling bearing of the bearing-rotor system is faulty according to the first acceleration response vector may include: performing time-frequency transformation on the first time domain diagram of the first acceleration response vector changing with time to obtain a first frequency domain diagram; performing envelope processing on the first frequency domain diagram to obtain a first envelope spectrum diagram; judging whether the first envelope spectrum diagram has a resonance peak at the multiple frequency of the first fault frequency, if so, determining that the outer ring of the rolling bearing of the bearing-rotor system is faulty, if not, determining that the outer ring of the rolling bearing of the bearing-rotor system is not faulty, so as to judge whether the outer ring of the rolling bearing of the bearing-rotor system is faulty. Multiple frequency refers to the first multiple frequency, double multiple frequency, ..., N multiple frequency, etc. of the first fault frequency. If the resonance peak appears only at one multiple frequency, it can be considered as a fault, and the resonance peak refers to the peak value.

[0140] Among them, judging whether the inner ring of the rolling bearing of the bearing-rotor system is faulty according to the second acceleration response vector can include: performing time-frequency transformation on a second time domain graph of the second acceleration response vector changing with time to obtain a second frequency domain graph; performing envelope processing on the second frequency domain graph to obtain a second envelope spectrum graph; judging whether a resonance peak appears in the second envelope spectrum graph at a multiple of the second fault frequency, and if so, determining that the inner ring of the rolling bearing of the bearing-rotor system is faulty, and if not, determining that the inner ring of the rolling bearing of the bearing-rotor system is not faulty, so as to judge whether the inner ring of the rolling bearing of the bearing-rotor system is faulty.

[0141] Among them, judging whether the rolling element of the rolling bearing of the bearing-rotor system is faulty according to the third acceleration response vector may include: performing time-frequency transformation on a third time domain graph of the third acceleration response vector changing with time to obtain a third frequency domain graph; performing envelope processing on the third frequency domain graph to obtain a third envelope spectrum graph; judging whether a resonance peak appears in the third envelope spectrum graph at a multiple of the third fault frequency, and if so, determining that the rolling element of the rolling bearing of the bearing-rotor system is faulty, and if not, determining that the rolling element of the rolling bearing of the bearing-rotor system is not faulty, so as to judge whether the rolling element of the rolling bearing of the bearing-rotor system is faulty.

[0142] When the working surface of a rolling bearing is locally worn, a series of broadband shock vibrations will be generated. These shocks will excite the bearing system and cause a series of shock attenuation responses, such as Fig.10 shown.

[0143] (1) Characteristic frequency analysis of rolling bearing considering outer ring failure:

[0144] Calculate the outer race fault frequency f out Essentially, it is to calculate how many rolling elements pass the outer ring's fault point during one rotation of the inner ring. Relative to the stationary outer ring, the rolling element rotates around the outer ring axis, and the rotation angle is:

[0145]

[0146] Therefore, a single rolling element is equivalent to a revolution of 1 / 2 (1-d b / D p cosα) circle, which is equivalent to contacting the outer circle fault point by 1 / 2 (1-d b / D p cosα) times. When the number of rolling elements is N b When the inner ring rotates once, each rolling element is in contact with the outer ring for N times. b / 2(1-d b / D p cosα) times, then the outer ring fault frequency f out It is obtained from the following formula that the expression of the first fault frequency is:

[0147]

[0148] In formula (26), f out is the first fault frequency; N b is the number of rolling elements; f c is the rolling element revolution frequency; d b D is the diameter of the rolling element; p is the bearing pitch diameter; α is the contact angle; f s is the inner ring rotation frequency.

[0149] (2) Characteristic frequency analysis of rolling bearing considering inner ring failure:

[0150] Calculate the inner race fault frequency f in Essentially, it is to calculate how many rolling elements pass the inner ring failure point during one rotation of the inner ring. Here, we use and calculate f out The same idea applies. Therefore, during one rotation of the inner ring, the rolling element rotates at an angle θ relative to the inner ring. ib for:

[0151] θ ib =π(1+d b / D p ); (27)

[0152] Therefore, the expression of the second fault frequency is:

[0153]

[0154] In formula (28), f in is the second fault frequency.

[0155] (3) Characteristic frequency analysis of rolling bearings considering rolling element failure:

[0156] Since the outer ring of the bearing is fixed, Fig.10 The velocity of point B is 0, and the velocity relationship between points A and C is V A =2V C =πf s (D p -d b cosα)=2πf c d p , from which we can get:

[0157]

[0158] In formula (29), f c is the frequency of the rolling element's revolution around its axis.

[0159] Assume that the rotation frequency of the rolling element when rolling in the raceway is f b , f b The solution process is as follows: The rolling element rotates once, and the rolling element failure point contacts the inner ring and the outer ring once respectively. The circumference of the rolling element is πd b The period of one rotation of the rolling element is d b / f c (D p +d b cosα), substitute into the above f c , the rolling element rotation frequency can be obtained, that is, the expression of the third fault frequency is:

[0160]

[0161] In formula (30), f ball is the third fault frequency.

[0162] The fault frequency is calculated as follows:

[0163] Table 1 Rolling bearing fault characteristic frequency

[0164]

[0165] This embodiment takes into account the influence of factors such as nonlinear Hertzian contact force and variable compliance vibration (VC vibration) caused by changes in rolling bearing stiffness, and establishes three fault excitation force models for rolling bearings. By analyzing the mechanisms of three typical fault types, a corresponding system dynamics model of the rolling bearing-rotor system is established, and the Newmark-β method is used to solve it. By analyzing the coupled vibration characteristics of the faulty rolling bearing-rotor, the interaction between the rolling bearing and the rotor in the mechanical system can be better understood and predicted, and the change process of the vibration characteristics of the bearing-rotor system under the condition of the faulty bearing is brought about, which can realize the rapid positioning of the bearing-rotor fault position under the premise that the turbine end rotor of the gas turbine is difficult to disassemble.

[0166] This embodiment further studies the influence of rolling bearings on the vibration characteristics of the power turbine bearing-rotor system under different fault degrees, and verifies the accuracy of the typical fault excitation force model of rolling bearings by comparing with the test results of the vibration characteristics test bench of the faulty rolling bearing-rotor system.

[0167] The test bench used to verify the model adopts a faulty bearing-rotor test bench. The motor is driven by a three-phase AC servo motor, and the test speed is set to 1000r / min. The left side of the rotor is supported by an N1004 roller bearing, and the right side uses a 7204B angular contact ball bearing as a support, and the angular contact ball bearing is set as the faulty bearing. The mass of the three discs on the rotor is 4kg, 5kg, and 2.5kg from left to right, and the system can apply a vertical upward radial load on the faulty bearing. The AC controller can display the actual speed of the motor and the size of the radial load, and control the size of the speed and the start of the test bench. A three-phase accelerometer is used to collect the vibration acceleration signal at the faulty bearing seat during the test. The accelerometer is connected to the computer through a 3-channel data line, and the vibration acceleration signal is collected using LMS. During this test, the sampling frequency was set to 6.4kHz, and the sampling time for each set of data was 16s.

[0168] The test process is as follows:

[0169] (1) Arrange and install the acceleration sensor, and debug the installation position of the sensor.

[0170] (2) Use an Ethernet cable to connect the computer and the data acquisition instrument.

[0171] (3) Power on the system, turn on the data collector and computer, change the IP address, and connect to the front end.

[0172] (4) Open the software, set the sensitivity of each sensor, and set the acceleration sensor unit, power supply mode, range, analysis frequency, number of lines, time domain sampling frequency and other parameters. Start the vibration response test.

[0173] (5) While conducting on-site testing, quickly analyze the time domain signal and spectrum of the vibration response, focusing on whether the results contain the rolling bearing failure frequency.

[0174] (6) Record any abnormal or special phenomena encountered during the test.

[0175] The dimensional parameters of the faulty rolling bearing 7204B are listed in Table 2 below:

[0176] Table 2 Geometric parameters of faulty bearing 7204B

[0177]

[0178] According to the above parameters, the characteristic frequency of rolling bearing fault can be calculated as shown in Table 3:

[0179] Table 3 Rolling bearing fault characteristic frequency

[0180]

[0181] The bearing faults used in the test were machined using electrospark machining. Cracks with widths of 0.4mm, 0.8mm and 1mm were machined on the inner and outer raceways of the rolling bearing to simulate the impact caused by damage to the outer and inner raceways. Pit holes with diameters of 0.4mm, 0.8mm and 1mm and a depth of about 1mm were cut out on the rolling element to simulate the impact caused by damage to the ball.

[0182] (1) Vibration response and test verification of the bearing-rotor system with outer ring failure:

[0183] This example analyzes the vibration characteristics of a rolling bearing-rotor system with an outer ring fault. The fault width is 0.8 mm, and the initial position of the outer ring defect is 6 o'clock. At the same time, the system initial displacement x0 is set to 0, and the initial speed The rotor speed is 1000r / min and the load is 3.6KN. Fig.11 It can be seen that due to the local defect of the outer ring, the bearing-rotor system will produce periodic impact vibration with the inverse of the fault frequency as the pulse interval. Fig.11(b) It can be seen that under the influence of the outer ring fault, the bearing-rotor system excites a resonance frequency of 482Hz, and a sideband equivalent to the outer ring fault frequency appears near the main resonance frequency. In the outer ring fault envelope spectrum, frequency domain features dominated by the outer ring fault frequency and its multiples appear, and its main characteristic frequency is 75Hz.

[0184] The vibration signal at the bearing seat under the bearing outer ring fault required in this embodiment is obtained through the fault bearing-rotor test bench. During the test, the speed is set to 1000r / min and the sampling frequency is 6400Hz. The test uses an angular contact ball bearing with a fault width of 0.8mm. Fig.12 As shown in (a), the time domain vibration curve of the test signal shows periodic pulsation; Fig.12 As shown in (b), the resonance peak of the test signal appears at 496.29 Hz, which is 2.8% different from the resonance peak position of the simulation signal. Fig.12 In the envelope spectrum of (c), frequency domain peaks close to the outer race fault frequency and its multiples appear, which are 79.57 Hz, 153.13 Hz, and 303.26 Hz, respectively, which are close to the simulation results.

[0185] Depend on Fig.11 and Fig.12 It can be seen that by comparing the fault characteristic frequencies of the simulation and test signals, the maximum error is 2.2%. The reason for the error may be that the established bearing dynamics model only considers the pure rolling between the rolling elements and the raceways, and ignores the influence of background noise in the actual test site.

[0186] The influence of different fault degrees on the vibration response of the system under the action of the outer ring fault of the rolling bearing was analyzed. The outer ring fault width was set to vary in the range of 0.4mm to 1mm. The three-dimensional spectrum of the test results is shown in the figure. Fig.13 As shown, the results show that the corresponding f out The acceleration amplitude at the frequency is the largest, and combined with Table 4, it can be seen that as the fault width changes, the system vibration response will intensify as the width increases, that is, the vibration acceleration amplitude increases.

[0187] Table 4 Amplitudes at typical frequencies of bearings with outer ring faults at different fault levels

[0188]

[0189] Fig.14 The time domain diagram, frequency domain diagram and envelope spectrum diagram of the test signal when the defect width is 0.4mm are listed. Fig.15 The time domain diagram, frequency domain diagram and envelope spectrum diagram of the test signal with a defect width of 1 mm are listed. Fig.14 , Fig.15As can be seen from Table 4, the defect width only affects the intensity of the vibration signal, but does not affect the characteristic frequency distribution. At the same time, the defect width will change the resonance peak position and shift to the high-frequency area as the width value increases. The fundamental reason is that as the defect width area increases, the contact stiffness changes faster during rotation, thereby increasing the high-frequency natural frequency.

[0190] (2) Vibration response and test verification of the bearing-rotor system with inner ring failure:

[0191] like Fig.16 As shown in the figure, through the frequency domain analysis and envelope spectrum analysis of the simulation signal of the rolling bearing with local defects in the inner ring, it can be found that the impact characteristic phenomenon is obvious and the amplitude modulation phenomenon is prominent, and the frequency in the envelope spectrum is very close to the characteristic frequency of the inner ring fault and its multiples. In addition, it can be observed from the envelope spectrum that there are local rotation frequencies and their combined frequencies. The reason is that the angular position of the internal defects of the bearing will change with the rotation time of the shaft, causing the contact load between the rolling element and the inner ring fault point to change periodically with the spatial position.

[0192] In this embodiment, the fault parameters are set as follows: defect width 0.8 mm, defect depth 1.5 mm, and the signal characteristics of the inner ring fault of the 7204B angular contact ball bearing are obtained through experiments. Fig.17 is the test signal at the bearing seat under inner ring failure, Fig.17 It can be seen that the frequency peaks in the envelope spectrum of the inner ring fault are mainly 16.79Hz, 105.76Hz, and 121.62Hz, which are close to the characteristic frequency of the simulated inner ring fault, and the maximum error does not exceed 2.7%. In addition, the combined frequency of the rotation frequency and the characteristic frequency of the inner ring fault also appears in the test results. At the same time, the resonance peak position of the test results is consistent with the simulation results, which proves the accuracy of the model.

[0193] In order to explore the influence of different inner ring fault degrees on the vibration characteristics of the rotor system, the three-dimensional envelope spectra of the inner ring fault widths of 0.4 mm, 0.8 mm, and 1 mm are analyzed, such as Fig.18 As shown in the figure, the amplitudes of the characteristic frequency of the inner race fault and its higher harmonics increase with the increase of the defect width. At the same time, the amplitude of the rotation frequency combination frequency also changes in different amplitudes, but it will not cause the rotation frequency amplitude change affected only by the balanced fault.

[0194] Table 5 Amplitude at typical frequencies of rolling bearings with local defects on the inner ring at different defect widths

[0195]

[0196] Fig.19 is the experimental vibration response result of the bearing-rotor system when the inner ring fault width is 0.4 mm,

[0197] Fig. 20is the experimental vibration response result of the bearing-rotor system under the condition of inner ring fault width of 1 mm. Fig.19 , Fig. 20 As can be seen from Table 5, as the defect width increases, the amplitude of the system vibration response increases. This is because the change in the inner ring defect width will affect the contact stiffness inside the rolling bearing, so the increase in defect width will cause the resonance peak to shift to the high-frequency region.

[0198] (3) Vibration response and test verification of bearing-rotor system with rolling element failure:

[0199] In order to study the vibration response of the bearing-rotor system under rolling element failure, the simulation response at the bearing seat of the 7204B angular contact ball bearing is as follows: Fig.21 As shown in (a), the amplitude of the impact response is affected by the change in the rolling element fault clearance. In other words, the vibration signal is highly modulated. Fig.21 In (c), frequencies such as 68.75 Hz, 137.5 Hz, and 206.7 Hz can be found, which are close to the first three multiples of the characteristic frequency of the rolling element fault.

[0200] Fig. 22 The test signal at the bearing seat under the condition of inner ring failure of 7204B angular contact ball bearing is set with defect width of 0.8mm and defect depth of 1mm. It can be observed that the time domain signal peaks of the test and simulation results are basically consistent, but the background interference under the actual test conditions is not considered in the simulation process, so the impact vibration of the test signal is not obvious; in the envelope spectrum, it can be found that there is an obvious spectrum line at the characteristic frequency of rolling element failure (66.87Hz), which is very close to the characteristic frequency of rolling element failure 68.53Hz. The difference between this test result and the simulation result is 2.8%, and there is no frequency doubling of the characteristic frequency of rolling element failure in the envelope spectrum of the test result. This is because the simulation model does not consider the sliding factor, and the rolling element cannot guarantee that it will contact the inner and outer raceways once every rotation during the test.

[0201] like Fig.23 As shown in Figure 6, different defect width variation conditions have different degrees of influence on the vibration response of the rotor system with local defects in the inner ring. In order to more clearly analyze the influence of defect width on the response amplitude, Table 6 lists the amplitudes of the characteristic frequency of rolling element fault and its multiples. Fig.23 As shown in Table 6, the characteristic frequency of rolling element fault and its multiples show a monotonically increasing trend as the defect width increases.

[0202] Table 6 Amplitudes at typical frequencies of rolling element fault rolling bearings with different defect widths

[0203]

[0204]

[0205] Fig.24 is the vibration response result of the rolling bearing-rotor system when the rolling element width is 0.4 mm, Fig.25 The vibration response of the rolling bearing-rotor system when the rolling element width is 1 mm is shown in Figure 2. Fig.24 , Fig.25 It can be seen from Table 6 that as the defect width increases, the amplitude of the system vibration response increases; affected by the defect width variable working condition, the resonance peak position shifts significantly, and the shift trend shifts significantly to the high-frequency area. The fundamental reason is that the change in defect stiffness causes the contact stiffness to change accordingly, so it shifts to the high-frequency area.

[0206] (1) Analysis of fault dynamic characteristics of power turbine bearing-rotor system under outer ring fault:

[0207] Assume that the fault diameter of the outer ring of the rolling bearing is L = 1 mm, the fault depth is a = 2.794 mm, the damage position is the vertical bottom of the outer ring, and the rotor speed is ω R =3270r / min, speed f R =54.5Hz, Fig.26 (a) Fig.26 (b) is the signal waveform of the vibration velocity and vibration acceleration of the power turbine bearing-rotor system at the bearing. It can be seen from the figure that the outer ring fault causes the periodic change of the impact signal. The impact period of the damage is T = 0.00328s, which is consistent with the outer ring fault frequency f out =303.96Hz, the time interval corresponding to is basically the same. In addition, the acceleration vibration response impact effect at the bearing is stronger. From the figure, it can be seen that the pulse sequence generated by the rolling element when passing through the outer ring fault point, and as the rolling element leaves the fault area, the pulse signal shows a decay trend.

[0208] like Fig.26 As shown in (c), the spectrum analysis of the acceleration time domain response shows that under the action of pulse vibration, resonance peaks are generated near 1200Hz and 1600Hz, and the interval between each resonance peak is 303.16Hz; using HHT to analyze the vibration signal at the bearing, it can be seen that the outer ring fault frequency of 303Hz and its peak gradually attenuated multiples can be clearly seen in the envelope spectrum, which is consistent with the interval between the resonance peaks, further verifying the accuracy of the fault extraction method and the dynamic model.

[0209] (2) Analysis of the fault dynamic characteristics of the power turbine bearing-rotor system under inner ring fault:

[0210] Assume that the fault diameter of the inner ring of the rolling bearing is L = 1 mm, and the fault depth is a = 2.794 mm. The position of the inner ring damage changes with the rotation of the inner ring. The rotor speed ω R =3270r / min, that is, the rotation frequency f R =54.5Hz. Fig. 27 (a) Fig. 27 (b) is the time domain waveform curve of the vibration velocity and acceleration of the power turbine bearing-rotor system at the bearing when the inner ring fails. From the acceleration time domain results, it can be seen that the magnitude of the impact vibration caused by the inner ring failure and the pulse interval are highly irregular. The time intervals between the velocity impact responses are 0.00196s and 0.0175s, respectively, which correspond to the characteristic frequency of the inner ring failure and the inverse of the rotor rotation frequency. The main reason for this phenomenon is that the position of the inner ring failure will rotate with the rotor, and the inner ring failure will cause deformation and imbalance of the local structure of the bearing, making the motion trajectory of the inner ring of the bearing irregular, and then generating a modulation signal with a frequency equal to the rotor speed.

[0211] Spectral analysis of the acceleration vibration signal shows that the power turbine bearing-rotor system excites two resonance peaks at 1100Hz and 1500Hz, and sidebands with frequencies close to the rotation frequency appear near the resonance peaks, which is consistent with the impact interval of 0.0175s in the time domain signal, further proving that the inner ring fault is modulated by the rotor rotation; moreover, the frequency interval between the resonance peaks is 514.34Hz, which is close to the theoretical result of the fault frequency. Combined with the envelope spectrum analysis of the acceleration vibration signal, the envelope spectrum also reflects the inner ring fault frequency and the modulation frequency with the rotation frequency as the sideband, further verifying the accuracy of the diagnostic method and the inner ring fault excitation force model of this embodiment.

[0212] (3) Analysis of the dynamic characteristics of the power turbine bearing-rotor system failure under rolling element failure:

[0213] Assume that the fault diameter of the rolling element fault point in the rolling bearing is L = 1 mm, and the depth of the fault point on the rolling element is a = 2 mm. The position of the rolling element fault will change with the rotation of the cage and its own rotation. The rotor frequency is set to f R =54.5Hz. Fig.28 (a) is the time domain curve of the vibration velocity of the rolling bearing-rotor system at the bearing of the power turbine end. The figure shows that the impact vibration time interval is 0.004977s, which is consistent with the rolling element failure frequency of 200.506Hz after the inverse conversion to frequency. Fig.28 (b) is the envelope spectrum of the vibration acceleration signal at the rolling bearing. From the figure, we can see the rolling element fault characteristic frequency value 200.969Hz and the theoretical fault frequency f ball=200.506Hz, it can be seen that under the influence of the bearing rolling element failure, multiple peaks represented by the rolling element failure frequency and its multiple frequencies appear in the envelope spectrum, which corresponds to the fact that the rolling element failure will lead to the enhancement of vibration signals of multiple frequencies.

[0214] This embodiment conducts a dynamic analysis method for faulty bearings and rotor systems. For the actual power turbine rolling bearing-rotor system, a five-degree-of-freedom rolling bearing fault dynamic analysis model is proposed. It is combined with the rotor dynamics model to establish a bearing-rotor dynamic analysis model under the action of a faulty bearing, and is verified by a rolling bearing fault test bench. Through experimental verification, it is found that the fault width has a great influence on the vibration response. When the fault degree increases, the vibration degree increases significantly, and the resonance peak also moves to the high frequency. For the actual model of a gas turbine power turbine rotor, the dynamic performance of the bearing-rotor system under different types of faulty bearings is studied. The results show that when the outer ring or rolling element fails, the main frequencies in the envelope spectrum are the outer ring characteristic frequency and the rolling element characteristic frequency, while the inner ring fault will excite the rotor rotation frequency and the inner ring fault characteristic frequency. In summary, the calculation results of the bearing-rotor system under the action of rolling element faults fully reveal the influence of rolling element faults on the characteristics of the power turbine rotor, and also verify the accuracy of the modeling of the rolling element fault excitation force in this embodiment, providing a theoretical basis for the dynamic modeling of the bearing-rotor-casing. At the same time, for the actual model of a gas turbine power turbine rotor, the dynamic performance under different fault conditions is studied. When the outer ring or rolling element fails, the main frequencies in the envelope spectrum are the characteristic frequency of the outer ring and the characteristic frequency of the rolling element, while the inner ring failure will excite the rotor rotation frequency and the inner ring failure characteristic frequency. When there is an actual failure at the turbine end of the gas turbine, the fault signal can be identified and judged based on the above conclusions.

[0215] Embodiment 2:

[0216] In order to execute the method corresponding to the above-mentioned embodiment 1 to achieve the corresponding functions and technical effects, a fault location system of a gas turbine power turbine end bearing-rotor system is provided below, such as Fig.29 As shown, the fault location system includes:

[0217] Model building module M1, used to establish a system dynamics model of the bearing-rotor system at the power turbine end of the gas turbine under bearing failure conditions;

[0218] The fault location module M2 is used to solve the system dynamics model to obtain the acceleration response vector of the bearing-rotor system and perform fault location according to the acceleration response vector.

[0219] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0220] The principles and implementation methods of the present invention are described in this article using specific examples. The description of the above embodiments is only used to help understand the method and core idea of ​​the present invention. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A method for locating a fault in a gas turbine power turbine end bearing-rotor system, characterized in that: The fault location method comprises: Establish a system dynamics model of the bearing-rotor system at the power turbine end of a gas turbine considering bearing failure conditions; Solving the system dynamics model to obtain an acceleration response vector of the bearing-rotor system, and locating the fault according to the acceleration response vector; The establishment of a system dynamics model of a bearing-rotor system at a power turbine end of a gas turbine considering a bearing failure condition specifically includes: Establish the dynamic analysis model of rolling bearing; Establishing a fault model of a rolling bearing under bearing fault conditions; the fault model includes an outer ring fault model, an inner ring fault model and a rolling element fault model; The dynamic analysis model and the fault model are integrated to obtain a fault excitation force model of the rolling bearing; the fault excitation force model includes an outer ring fault excitation force model, an inner ring fault excitation force model and a rolling element fault excitation force model; The finite element method is used to model the rotor's dynamics and obtain the rotor's motion equation; The fault excitation force model and the motion equation are integrated to obtain a system dynamics model of the bearing-rotor system at the power turbine end of the gas turbine; the system dynamics model includes an outer ring fault system dynamics model, an inner ring fault system dynamics model and a rolling element fault system dynamics model.

2. A method for locating a fault of a gas turbine power turbine end bearing-rotor system according to claim 1, characterized in that: The dynamic analysis model includes: Among them, F X is the bearing force component of the rolling bearing along the X axis; m is the number of rolling elements; Q j is the contact force of the jth rolling element on the inner ring of the bearing along the normal direction; α j is the contact angle after loading; F Y is the bearing force component of the rolling bearing along the Y axis; ψ j is the azimuth angle of the jth rolling element; F Z is the bearing force component of the rolling bearing along the Z axis; Among them, M Y is the torque component of the rolling bearing around the Y axis; R j M is the radius of the inner raceway groove curvature center trajectory; Z is the torque component of the rolling bearing around the Z axis.

3. A method for locating a fault of a gas turbine power turbine end bearing-rotor system according to claim 1, characterized in that: The outer ring fault model includes: Among them, λ D The increase in bearing clearance; d b is the diameter of the rolling element; L is the diameter of the fault area; The inner race fault model includes: Among them, λ D The increase in bearing clearance; d b is the diameter of the rolling element; L is the diameter of the fault area; The rolling element fault model includes: Among them, θ K is the rotation angle of the rolling body; β3 is the failure angle of the rolling body.

4. A method for locating a fault of a gas turbine power turbine end bearing-rotor system according to claim 1, characterized in that: The motion equation includes motion equations of multiple beam units, where the beam units are obtained by dividing the rotor; the motion equations of the beam units include: Among them, M b is the beam element mass matrix; is the acceleration response vector of the beam element; K is the stiffness matrix of the bearing-rotor system; G b is the beam unit gyro matrix; is the velocity response vector of the beam element; K b is the beam element stiffness matrix; Ω is the speed of the bearing-rotor system; is the additional mass matrix of the beam element; u is the displacement response vector of the beam element; F b is the external force vector of the beam element.

5. A method for locating a fault of a gas turbine power turbine end bearing-rotor system according to claim 1, characterized in that: The system dynamics model includes: Among them, M s is the mass matrix of the bearing-rotor system; is the acceleration response vector of the bearing-rotor system; C s is the damping matrix of the bearing-rotor system; Ω is the speed of the bearing-rotor system; G s is the gyro matrix of the bearing-rotor system; is the speed response vector of the bearing-rotor system; K s is the bearing-rotor system stiffness matrix; u s is the displacement response vector of the bearing-rotor system; Q s is the external force vector of the bearing-rotor system.

6. A method for locating a fault in a gas turbine power turbine end bearing-rotor system according to claim 1, characterized in that: Solving the system dynamics model to obtain the acceleration response vector of the bearing-rotor system, and locating the fault according to the acceleration response vector, specifically includes: Solving the outer ring fault system dynamics model to obtain a first acceleration response vector of the bearing-rotor system, and judging whether the outer ring of the rolling bearing of the bearing-rotor system is faulty according to the first acceleration response vector; Solving the inner ring fault system dynamics model to obtain a second acceleration response vector of the bearing-rotor system, and judging whether the inner ring of the rolling bearing of the bearing-rotor system is faulty according to the second acceleration response vector; The rolling element fault system dynamics model is solved to obtain a third acceleration response vector of the bearing-rotor system, and whether the rolling element of the rolling bearing of the bearing-rotor system is faulty is determined according to the third acceleration response vector.

7. A method for locating a fault of a gas turbine power turbine end bearing-rotor system according to claim 6, characterized in that: Judging whether the outer ring of the rolling bearing of the bearing-rotor system is faulty according to the first acceleration response vector, specifically comprising: performing time-frequency transformation on a first time domain graph of the first acceleration response vector changing with time to obtain a first frequency domain graph; performing envelope processing on the first frequency domain graph to obtain a first envelope spectrum graph; judging whether a resonance peak appears in the first envelope spectrum graph at a multiple of the first fault frequency, and if so, determining that the outer ring of the rolling bearing of the bearing-rotor system is faulty, and if not, determining that the outer ring of the rolling bearing of the bearing-rotor system is not faulty, so as to judge whether the outer ring of the rolling bearing of the bearing-rotor system is faulty; Judging whether the inner ring of the rolling bearing of the bearing-rotor system is faulty according to the second acceleration response vector specifically includes: performing time-frequency transformation on a second time domain graph of the second acceleration response vector changing with time to obtain a second frequency domain graph; performing envelope processing on the second frequency domain graph to obtain a second envelope spectrum graph; judging whether a resonance peak appears in the second envelope spectrum graph at a multiple of the second fault frequency, and if so, determining that the inner ring of the rolling bearing of the bearing-rotor system is faulty, and if not, determining that the inner ring of the rolling bearing of the bearing-rotor system is not faulty, so as to judge whether the inner ring of the rolling bearing of the bearing-rotor system is faulty; Judging whether the rolling element of the rolling bearing of the bearing-rotor system is faulty according to the third acceleration response vector specifically includes: performing time-frequency transformation on a third time domain graph of the third acceleration response vector changing with time to obtain a third frequency domain graph; performing envelope processing on the third frequency domain graph to obtain a third envelope spectrum graph; judging whether a resonance peak appears in the third envelope spectrum graph at a multiple of the third fault frequency, and if so, determining that the rolling element of the rolling bearing of the bearing-rotor system is faulty, and if not, determining that the rolling element of the rolling bearing of the bearing-rotor system is not faulty, so as to judge whether the rolling element of the rolling bearing of the bearing-rotor system is faulty.

8. A method for locating a fault of a gas turbine power turbine end bearing-rotor system according to claim 7, characterized in that: The expression of the first fault frequency is: Among them, f out is the first fault frequency; N b is the number of rolling elements; d b is the diameter of the rolling element; D p is the bearing pitch diameter; α is the contact angle; f s is the inner ring rotation frequency; The expression of the second fault frequency is: Among them, f in is the second fault frequency; The expression of the third fault frequency is: Among them, f ball is the third fault frequency.

9. A fault location system for a gas turbine power turbine end bearing-rotor system, characterized in that: The fault location system comprises: Model building module, used to establish the system dynamics model of the bearing-rotor system at the power turbine end of the gas turbine under bearing failure conditions; A fault location module, used to solve the system dynamics model to obtain the acceleration response vector of the bearing-rotor system, and perform fault location according to the acceleration response vector; The establishment of a system dynamics model of a bearing-rotor system at a power turbine end of a gas turbine considering a bearing failure condition specifically includes: Establish the dynamic analysis model of rolling bearing; Establishing a fault model of a rolling bearing under bearing fault conditions; the fault model includes an outer ring fault model, an inner ring fault model and a rolling element fault model; The dynamic analysis model and the fault model are integrated to obtain a fault excitation force model of the rolling bearing; the fault excitation force model includes an outer ring fault excitation force model, an inner ring fault excitation force model and a rolling element fault excitation force model; The finite element method is used to model the rotor's dynamics and obtain the rotor's motion equation; The fault excitation force model and the motion equation are integrated to obtain a system dynamics model of the bearing-rotor system at the power turbine end of the gas turbine; the system dynamics model includes an outer ring fault system dynamics model, an inner ring fault system dynamics model and a rolling element fault system dynamics model.

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