Method for constructing dynamic simulation model of double-rotor system under inter-rotor rub-impact fault

Abstract

The application provides a kind of rotor inter-rubbing fault under the double-rotor system dynamics simulation model construction method, including obtaining the normal force of rub; considering the speed difference of inner rotor and outer rotor and the vortex speed of rotor, the friction force of rotor-rotor rub is calculated;According to Newton's third law, the rub force acting on the inner and outer rotors is calculated;The double-rotor system dynamics simulation model is established by considering rotor-rotor rub.This method can accurately simulate the rub between the rotor and the rotor.Based on the planar motion of rigid body, the vortex speed of the rotor, the tangential velocity of the rubbing point, the absolute velocity of the rubbing point and the relative velocity of the rubbing point are accurately calculated.Taking into account the uncertainty of the relative velocity direction of the rubbing point caused by the vortex speed of the rotor, the uncertainty of the friction direction of the rubbing point, the relative velocity between the rubbing points of the rotor is solved by the velocity vector, and the direction of the friction between the rotors is accurately characterized.The application fills the gap of the current tracked vehicle rotor rub dynamics accurate analysis method.

Description

Technical Field

[0001] This invention relates to the field of mechanical dynamics, specifically to the characterization and dynamic analysis of inter-rotor rubbing faults in a dual-rotor system, and particularly to a method for constructing a dynamic simulation model of a dual-rotor system under inter-rotor rubbing faults. Background Technology

[0002] In rotating machinery such as aircraft engines, marine gas turbines, and tracked vehicles, the design clearance between rotors is becoming increasingly smaller in order to improve various aspects of the mechanical system's performance (such as sealing). This can easily lead to rotor-to-rotor rubbing failures during operation. Consequently, designers find it difficult to simultaneously achieve both zero rubbing and minimal clearance, impacting the safe and reliable operation of the system. Rotor-to-rotor rubbing can cause system damage and other malfunctions, even leading to catastrophic accidents. This will directly or indirectly cause economic and property losses or threaten the lives of personnel involved. Especially for tracked vehicles, frequent rotor-to-rotor rubbing failures significantly affect the safe operation of these vehicles.

[0003] Regarding methods for characterizing rotor-to-rotor rubbing, some researchers simplify it to two concentric Jeffcott rotors, neglecting the influence of potential intermediate bearings between the shafts on rubbing faults, and also ignoring the impact of the speed difference between the inner and outer rotors. Other researchers have established rotor-to-rotor rubbing characterization models that consider the speed difference, taking into account the effects of whirl velocity and relative velocity on rubbing friction. However, this model only represents the speed difference by adding or subtracting the magnitudes of the velocities, ignoring the influence of the velocity direction. Therefore, it can be concluded that scalar models cannot accurately characterize rotor-to-rotor rubbing faults. Furthermore, current research on rubbing faults primarily focuses on rotor-to-stator rubbing faults, neglecting research on rotor-to-rotor rubbing faults. Summary of the Invention

[0004] To address the aforementioned problems, this invention discloses a method for constructing a dynamic simulation model of a dual-rotor system under rotor-to-rotor rubbing faults. Specifically, it addresses the lack of rotor-to-rotor rubbing models that consider rotor whirl velocity and the dry friction instability caused by rubbing faults in existing rotor-to-rotor rubbing fault characterization models and dynamic analysis techniques. This method considers the influence of rotor whirl velocity on rubbing friction, accurately calculates the relative velocity between rotors, solves for the magnitude of rubbing friction based on Coulomb friction theory, further obtains the rubbing friction vector, simulates the shaft of the dual-rotor system using Timoshenko beam theory, and establishes a dynamic simulation model of the dual-rotor system under rubbing faults by combining unbalanced forces and rubbing forces.

[0005] The technical means employed in this invention are as follows:

[0006] A method for constructing a dynamic simulation model of a dual-rotor system under inter-rotor rubbing fault includes the following steps:

[0007] S1. Establish a finite element model of the dual rotor system based on the unit and node information of the dual rotor system, and calculate the dynamic response of the system at each moment based on the finite element model to obtain the rubbing normal force.

[0008] S2. Considering the speed difference between the inner and outer rotors and the whirl velocity of the rotors, calculate the frictional force of rotor-rotor contact.

[0009] S3. Calculate the frictional forces acting on the inner and outer rotors according to Newton's third law.

[0010] S4. Considering rotor-rotor rubbing, establish a dynamic simulation model of the dual-rotor system.

[0011] Furthermore, a finite element model of the dual-rotor system is established based on the element and node information of the dual-rotor system. The dynamic response of the system at each moment is calculated based on the finite element model to obtain the rubbing normal force, including:

[0012] S1.1. Based on the rotor's eddy displacement using the finite element model, determine the direction vector of the rubbing normal force, including calculating the reverse direction vector of the rubbing normal force of the inner rotor at a certain moment using the following formula:

[0013] n = [x0 - x1, y0 - y1]

[0014] Where n represents the opposite direction vector of the rubbing normal force, (x0, y0) represents the coordinates of the inner rotor center point, and (x1, y1) represents the coordinates of the outer rotor center point;

[0015] S1.2. Based on the opposite direction vector of the rubbing normal force, the unit vector is obtained by normalizing the vector:

[0016]

[0017] Where, n e Let represent the first unit vector, and n represent the vector in the opposite direction of the rubbing normal force;

[0018] S1.3. Based on the rotor's whirl displacement, calculate the distance between the inner and outer rotors using the two-point distance formula, including calculating the normal relative intrusion amount using the following formula:

[0019]

[0020] Where δ represents the normal relative intrusion amount, (x0, y0) represents the coordinates of the inner rotor center point, (x1, y1) represents the coordinates of the outer rotor center point, and σ represents the gap value between the inner and outer rotors.

[0021] S1.4. Based on the unit direction vector and the relative normal intrusion amount, and according to the linear rubbing model, the rubbing normal force vector is obtained as follows:

[0022]

[0023] Among them, F N k represents the normal force vector of the friction. r The contact stiffness between the inner and outer rotors is represented by δ, which represents the normal relative intrusion amount, and n e This represents the first unit vector.

[0024] Furthermore, a finite element model of the dual-rotor system is established based on the element and node information of the dual-rotor system. The dynamic response of the system at each moment is calculated based on the finite element model to obtain the rubbing normal force. This also includes:

[0025] S1.5. Obtain the projections of the rubbing normal force vector onto the x-axis and y-axis as the rubbing normal force:

[0026]

[0027] Among them, F Nx F represents the projection of the normal force vector of friction onto the x-axis. Ny F represents the projection of the normal force vector of friction onto the y-axis. N (1,1) represents vector F N The first component; F N (1,2) represents vector F N The second component.

[0028] Furthermore, considering the speed difference between the inner and outer rotors and the rotor whirl velocity, the rotor-to-rotor friction force is calculated, including:

[0029] S2.1 Calculate the velocity vector of the inner rotor relative to the outer rotor based on the inner rotor velocity, outer rotor velocity, and whirl velocity of the dual rotor system;

[0030] S2.2 Projecting the velocity vector of the inner rotor relative to the outer rotor into the direction perpendicular to the normal force of the friction, we can obtain the projected unit vector as follows:

[0031]

[0032] Among them, v e 'Represents relative velocity v' i-o The projection vector in the direction of friction, ve Let v represent the second unit vector. i-o n represents the velocity vector of the inner rotor relative to the outer rotor. e Represents the first unit vector;

[0033] S2.3 According to Coulomb's theory of friction, the frictional force can be obtained as follows:

[0034] F f =-v e ·μ·F N

[0035] Among them, F f V represents the vector of frictional force. e F represents the second unit vector, μ represents the friction coefficient between the rotors, and F N This represents the magnitude of the normal force vector caused by friction.

[0036] Furthermore, considering the speed difference between the inner and outer rotors and the rotor whirl velocity, the rotor-to-rotor friction force is calculated, including:

[0037] S2.4 Obtain the projections of the frictional force vector onto the x-axis and y-axis as the frictional force:

[0038]

[0039] Among them, F fx F represents the x-component of the frictional force vector. fy Let F be the component of the frictional force vector on the y-axis. f (1,1) represents vector F f The first component, F f (1,2) represents vector F f The second component.

[0040] Furthermore, the velocity vector of the inner rotor relative to the outer rotor is calculated based on the inner rotor speed, outer rotor speed, and whirl velocity of the dual-rotor system, including:

[0041] S2.1.1 Based on the rotational speeds of the inner and outer rotors, the linear velocity vector at the contact point can be obtained as follows:

[0042]

[0043] Among them, v ir Let ω1 represent the linear velocity vector of the inner rotor's contact point, and r represent the angular velocity of the inner rotor. i t represents the radius of the inner rotor. ir v represents the direction vector of the rotational linear velocity at the contact point of the inner rotor. or Let ω2 represent the linear velocity vector of the outer rotor's contact point, and r represent the angular velocity of the outer rotor.o t represents the outer rotor radius. or The direction vector representing the rotational linear velocity of the contact point of the outer rotor;

[0044] S2.1.2 Based on the whirl velocity of the inner and outer rotors, the whirl velocity vectors of the inner and outer rotors at a certain moment can be obtained as follows:

[0045]

[0046] Among them, v iw v represents the whirl velocity vector at the contact point of the inner rotor. x0 The vortex velocity in the x-direction at the contact point of the inner rotor, v y0 The y-axis vortex velocity at the contact point of the inner rotor, v ow v represents the whirl velocity vector at the contact point of the outer rotor. x1 The vortex velocity in the x-direction at the contact point of the outer rotor, v y1 This indicates the y-axis vortex velocity at the contact point of the outer rotor;

[0047] Based on the planar motion principle of rigid bodies, and according to the eddy current velocity and the linear velocity at the contact point, the resultant velocity vector of the rotor at the contact point can be obtained as follows:

[0048]

[0049] Among them, v i v represents the absolute velocity vector at the point of contact between the inner rotors. iw The eddy velocity vector, v, represents the eddy velocity vector at the contact point of the inner rotor. ir v represents the linear velocity vector of the inner rotor's contact point. o v represents the absolute velocity vector at the point of contact between the outer rotors. ow The eddy velocity vector at the contact point of the outer rotor, v or This represents the linear velocity vector of the outer rotor's contact point.

[0050] S2.1.4 Based on the combined velocity vector of the rotor at the friction point, and using the vector triangle rule, the velocity vector of the inner rotor relative to the outer rotor can be obtained as follows:

[0051] v i-o =v i -v o

[0052] Among them, v i-o The velocity vector v represents the velocity of the inner rotor relative to the outer rotor. i v represents the absolute velocity vector at the point of contact between the inner rotors. o This represents the absolute velocity vector at the point of contact between the outer rotor and the outer rotor.

[0053] Furthermore, according to Newton's third law, the frictional forces acting on the inner and outer rotors are calculated, including the resultant forces of the inner and outer rotors in the x and y directions calculated using the following formula:

[0054]

[0055] Among them, F xi F represents the force on the inner rotor in the x-direction. Nx F represents the projection of the normal force of friction in the x-direction. fx F represents the projection of frictional force in the x-direction. yi F represents the force on the inner rotor in the y-direction. Ny F represents the projection of the normal force of friction in the y-direction. fy F represents the projection of frictional force in the y-direction. xo F represents the force on the outer rotor in the x-direction. xi F represents the force on the inner rotor in the x-direction. yo F represents the force on the outer rotor in the y-direction. yi This indicates the force acting on the inner rotor in the y-direction.

[0056] Furthermore, the dynamic simulation model of the dual-rotor system is as follows:

[0057]

[0058] Among them, M sys C sys K sys These represent the system's mass, damping, and stiffness matrices, respectively, and q, F represents the displacement, velocity, and acceleration vectors of the system, respectively. e The vector of external forces acting on the rotor system is expressed as follows:

[0059] F e =[...,F uix ,F uiy ,0,0,0,0,...,F xi ,F yi ,0,0,0,0,...F uox ,F uoy ,0,0,0,0,...,F xo ,F yo ,0,0,0,0,...] T

[0060] Among them, F uix F uiy F uox F uoyThis represents the projection of the unbalanced forces of the inner and outer rotors in the x and y directions. The unbalanced force node of the inner rotor is numbered 15, and the unbalanced force node of the outer rotor is numbered 24. The friction force node of the inner rotor is numbered 12, and the friction force node of the outer rotor is numbered 36. Each node has 6 degrees of freedom, and the force at the other node positions is 0.

[0061] Compared with the prior art, the present invention has the following advantages:

[0062] This invention considers the influence of rotor whirling velocity on the direction of friction force, calculates the relative velocity between rotors at the rubbing position, substitutes the relative velocity into the rubbing force calculation model to obtain the accurate direction of rubbing friction force, further calculates the radial projection of the rubbing force of rotor-rotor rubbing, and then uses Timoshenko beam theory to simulate the shaft of the dual-rotor system to establish a dynamic simulation model of the dual-rotor system under rubbing failure. The vibration response under the combined action of mass imbalance force and rubbing force is obtained. The rubbing model considering whirling velocity is closer to the actual situation in the simulation calculation of dry friction instability, providing a more accurate model for the simulation of rubbing failure of dual-rotor systems of tracked vehicles, especially the dry friction instability system caused by rubbing. Attached Figure Description

[0063] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0064] Figure 1 This is a flowchart of a method for constructing a dynamic simulation model of a dual-rotor system under inter-rotor rubbing fault according to the present invention.

[0065] Figure 2 This is a schematic diagram of a rubbing fault in an embodiment of the present invention, where (a) represents a healthy state and (b) represents a fault state.

[0066] Figure 3 This is a vector diagram of velocity and force under the rubbing state in an embodiment of the present invention, where (a) is the velocity direction, (b) is the relative velocity direction, and (c) is the friction force.

[0067] Figure 4 This is a schematic diagram of the finite element model of the dual-rotor system in an embodiment of the present invention.

[0068] Figure 5The diagram shows the dynamic response of the dual-rotor system rotating in the same direction at different speeds in an embodiment of the present invention, where (a) is a speed of 2100 rev / min, (b) is a speed of 2200 rev / min, and (c) is a speed of 3600 rev / min.

[0069] Figure 6 The diagram shows the dynamic response of the reversing dual-rotor system at different speeds in an embodiment of the present invention, where (a) is a speed of 2100 rev / min, (b) is a speed of 2200 rev / min, and (c) is a speed of 3600 rev / min. Detailed Implementation

[0070] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0071] like Figure 1 As shown, this invention provides a method for constructing a dynamic simulation model of a dual-rotor system under inter-rotor rubbing faults, specifically including the following steps:

[0072] S1. Establish a finite element model of the dual rotor system based on the unit and node information of the dual rotor system, and calculate the dynamic response of the system at each moment based on the finite element model to obtain the rubbing normal force.

[0073] Specifically, it includes:

[0074] S1.1 Figure 2 A schematic diagram of the rubbing is provided. A finite element model of the dual-rotor system is established using element and node information to calculate the dynamic response at each moment. The direction vector of the rubbing normal force is determined based on the rotor's eddy displacement. Figure 3 This shows the forces acting on the system and the rotor velocity at a certain moment. For the inner rotor, the reverse vector of the frictional normal force at a certain moment is:

[0075] n=[x0-x1,y0-y1] (1)

[0076] Where n represents the opposite direction vector of the rubbing normal force, (x0, y0) represents the coordinates of the inner rotor center point, and (x1, y1) represents the coordinates of the outer rotor center point.

[0077] S1.2 Based on the reverse direction vector of the rubbing normal force obtained in step S1.1, the unit vector is obtained by normalization:

[0078]

[0079] Where, n e Let n denote the first unit vector, and let n denote the vector in the opposite direction of the rubbing normal force.

[0080] S1.3 Based on the rotor's eddy displacement, the distance between the inner and outer rotors is calculated using the two-point distance formula. The normal relative intrusion is:

[0081]

[0082] Where δ represents the normal relative intrusion amount, (x0, y0) represents the coordinates of the inner rotor center point, (x1, y1) represents the coordinates of the outer rotor center point, and σ represents the gap value between the inner and outer rotors.

[0083] S1.4 Based on the unit direction vector obtained in step S1.2 and the relative intrusion amount obtained in step S1.3, and according to the linear rubbing model, the rubbing normal force vector is derived as follows:

[0084]

[0085] Among them, F N k represents the normal force vector of the friction. r The contact stiffness between the inner and outer rotors is represented by δ, which represents the normal relative intrusion amount, and n e This represents the first unit vector.

[0086] S1.5 Since the components of the force vector are projections onto the x-axis and y-axis, based on the rubbing normal force vector obtained in step S1.4, the projections of the rubbing normal force vector onto the x-axis and y-axis are:

[0087]

[0088] Among them, F Nx F represents the projection of the normal force vector of friction onto the x-axis. Ny F represents the projection of the normal force vector of friction onto the y-axis. N (1,1) represents vector F N The first component; F N (1,2) represents vector F N The second component.

[0089] S2. Considering the speed difference between the inner and outer rotors and the rotor whirling speed, calculate the frictional force of rotor-to-rotor contact. Specifically, this includes:

[0090] S2.1 Calculate the velocity vector of the inner rotor relative to the outer rotor based on the inner rotor speed, outer rotor speed, and whirl velocity of the dual rotor system.

[0091] First, based on the rotational speeds of the inner and outer rotors, the linear velocity vector at the contact point can be obtained as follows:

[0092]

[0093] Among them, v ir Let ω1 represent the linear velocity vector of the inner rotor's contact point, and r represent the angular velocity of the inner rotor. i t represents the radius of the inner rotor. ir v represents the direction vector of the rotational linear velocity at the contact point of the inner rotor. or Let ω2 represent the linear velocity vector of the outer rotor's contact point, and r represent the angular velocity of the outer rotor. o t represents the outer rotor radius. or This represents the direction vector of the rotational linear velocity at the contact point of the outer rotor.

[0094] Secondly, based on the whirl velocity of the inner and outer rotors, the whirl velocity vectors of the inner and outer rotors at a certain moment can be obtained as follows:

[0095]

[0096] Among them, v iw v represents the whirl velocity vector at the contact point of the inner rotor. x0 The vortex velocity in the x-direction at the contact point of the inner rotor, v y0 The y-axis vortex velocity at the contact point of the inner rotor, v ow v represents the whirl velocity vector at the contact point of the outer rotor. x1 The vortex velocity in the x-direction at the contact point of the outer rotor, v y1 This indicates the y-axis vortex velocity at the contact point of the outer rotor.

[0097] Furthermore, based on the principle of planar motion of rigid bodies, and according to the eddy current velocity and the linear velocity at the contact point, the resultant velocity vector of the rotor at the contact point can be obtained as follows:

[0098]

[0099] Among them, v i v represents the absolute velocity vector at the point of contact between the inner rotors. iw The eddy velocity vector, v, represents the eddy velocity vector at the contact point of the inner rotor. ir v represents the linear velocity vector of the inner rotor's contact point. o v represents the absolute velocity vector at the point of contact between the outer rotors. ow The eddy velocity vector at the contact point of the outer rotor, v or This represents the linear velocity vector of the outer rotor's contact point.

[0100] Subsequently, based on the resultant velocity vector of the rotor, and according to the vector triangle rule, the velocity vector of the inner rotor relative to the outer rotor can be obtained as follows:

[0101] v i-o =v i -v o (9)

[0102] Among them, v i-o The velocity vector v represents the velocity of the inner rotor relative to the outer rotor. i v represents the absolute velocity vector at the point of contact between the inner rotors. o This represents the absolute velocity vector at the point of contact between the outer rotor and the outer rotor.

[0103] S2.2 After considering the rotor's whirl velocity, the relative velocity direction may not be perpendicular to the direction of the rubbing normal force. Therefore, the relative velocity vector needs to be projected into a direction perpendicular to the rubbing normal force, resulting in the projected unit vector:

[0104]

[0105] Among them, v e 'Represents relative velocity v' i-o The projection vector in the direction of friction, v e Let v represent the second unit vector. i-o n represents the velocity vector of the inner rotor relative to the outer rotor. e This represents the first unit vector.

[0106] S2.3 Since the frictional force at the point of contact is perpendicular to the normal force of contact and opposite in direction to the projected unit vector obtained in S2.2, according to Coulomb's friction theory, the frictional force can be obtained as follows:

[0107] F f =-v e ·μ·F N (11)

[0108] Among them, F f V represents the vector of frictional force. e F represents the second unit vector, μ represents the friction coefficient between the rotors, and F N This represents the magnitude of the normal force vector caused by friction.

[0109] S2.4 Based on the frictional force vector obtained in step S2.3, since each component of the force vector represents the projected force on the x-axis and y-axis, the projections of the frictional force vector on the x-axis and y-axis are:

[0110]

[0111] Among them, F fx F represents the x-component of the frictional force vector.fy Let F be the component of the frictional force vector on the y-axis. f (1,1) represents vector F f The first component, F f (1,2) represents vector F f The second component.

[0112] S3. According to Newton's third law, calculate the frictional forces acting on the inner and outer rotors. Specifically, based on the principle of force composition and Newton's third law, the resultant forces of the inner and outer rotors in the x and y directions are:

[0113]

[0114] Among them, F xi F represents the force on the inner rotor in the x-direction. Nx F represents the projection of the normal force of friction in the x-direction. fx F represents the projection of frictional force in the x-direction. yi F represents the force on the inner rotor in the y-direction. Ny F represents the projection of the normal force of friction in the y-direction. fy F represents the projection of frictional force in the y-direction. xo F represents the force on the outer rotor in the x-direction. xi F represents the force on the inner rotor in the x-direction. yo F represents the force on the outer rotor in the y-direction. yi This indicates the force acting on the inner rotor in the y-direction.

[0115] S4. Considering rotor-rotor rubbing, establish a dynamic simulation model of the dual-rotor system. Specifically, Figure 4 The schematic diagram of the finite element simulation model of the dual-rotor system is shown below. The dynamic model of the dual-rotor system under rubbing failure is established as follows:

[0116]

[0117] Among them, M sys C sys K sys These are the mass, damping, and stiffness matrices of the system, respectively. q, Let F represent the displacement, velocity, and acceleration vectors of the system, respectively. e The vector of external forces acting on the rotor system is expressed as follows:

[0118] F e =[...,F uix ,F uiy ,0,0,0,0,...,F xi ,F yi ,0,0,0,0,...F uox,F uoy ,0,0,0,0,...,F xo ,F yo ,0,0,0,0,...] T (15)

[0119] Among them, F uix F uiy F uox F uoy This represents the projection of the unbalanced forces of the inner and outer rotors in the x and y directions. The node number for the unbalanced force of the inner rotor is 15, and the node number for the unbalanced force of the outer rotor is 24. The node number for the rubbing force of the inner rotor is 12, and the node number for the rubbing force of the outer rotor is 36. Each node has 6 degrees of freedom, and the force at the remaining node positions is 0. Specifically, in the above expression for the external force vector acting on the rotor system, the first ellipsis indicates that 11 × 6 zeros have been omitted, the second ellipsis indicates that 2 × 6 zeros have been omitted, the third ellipsis indicates that 8 × 6 zeros have been omitted, the fourth ellipsis indicates that 11 × 6 zeros have been omitted, and the fifth ellipsis indicates that 2 × 6 zeros have been omitted.

[0120] Based on the collision fault analysis model in S4, the dynamic response of the system is solved by the Newmark-β time-domain integration method. The dynamic response of the dual-rotor system when rotating in the same direction and in reverse direction is analyzed. It is found that there is a combination frequency of the dual rotor rotation frequency and the natural frequency of the system in the spectrum.

[0121] Figure 5 The dynamic response of the dual-rotor system rotating in the same direction is shown at three typical speeds: 2100 r / min represents no friction, 2200 r / min represents local friction, and 3600 r / min represents dry friction instability. Some obvious phenomena can be observed: (1) With the increase of speed, the dynamic behavior of the system can be divided into three stages: no friction, local friction, and dry friction instability. The friction force under dry friction instability is much greater than that under local friction, which shows that the impact of dry friction instability caused by friction on the system is catastrophic. (2) There is no obvious change in the time domain waveform between local friction and no friction, which is due to the small friction force and the weak friction fault. However, there is an obvious change in the spectrum diagram, with the appearance of combined frequencies between rotational frequencies, such as 2fr2-fr1. Especially under the dry friction instability state, a new frequency fn8 (8th natural frequency) appears in the system, and its amplitude greatly exceeds the amplitude of the rotational frequencies fr1 and fr2.

[0122] Figure 6The dynamic response of the reversing dual-rotor system at three typical speeds is shown. 2100 r / min represents no friction, 2200 r / min represents local friction, and 3600 r / min represents dry friction instability. Some obvious phenomena can be observed: (1) The dynamic behavior of the system can be divided into three stages as the speed increases: no friction, local friction, and dry friction instability. Under the action of dry friction instability, the friction force amplitude of the reversing dual-rotor system is much greater than that of the co-rotating dual-rotor system. This indicates that the dry friction instability of the reversing dual-rotor system is far more harmful to the system than that of the co-rotating dual-rotor system. (2) At ω1 = 3600 r / min, a new frequency fn8 appears. This frequency component is the same as the instability characteristic frequency component of the co-rotating dual-rotor system, both representing the 8th natural frequency of the system.

[0123] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for constructing a dynamic simulation model of a dual-rotor system under inter-rotor rubbing fault, characterized in that, Includes the following steps: S1. Establish a finite element model of the dual rotor system based on the unit and node information of the dual rotor system, and calculate the dynamic response of the system at each moment based on the finite element model to obtain the rubbing normal force. S2. Considering the speed difference between the inner and outer rotors and the whirl velocity of the rotors, calculate the frictional force of rotor-rotor contact. S3. Calculate the frictional forces acting on the inner and outer rotors according to Newton's third law. S4. Considering rotor-rotor rubbing, establish a dynamic simulation model of the dual-rotor system; A finite element model of the dual-rotor system is established based on the element and node information. The dynamic response of the system at each moment is calculated based on the finite element model to obtain the rubbing normal force, including: S1.

1. Based on the rotor's eddy displacement using the finite element model, determine the direction vector of the rubbing normal force, including calculating the reverse direction vector of the rubbing normal force of the inner rotor at a certain moment using the following formula: in, This represents the vector in the opposite direction of the normal force during contact. Indicates the coordinates of the center point of the inner rotor. Indicates the coordinates of the center point of the outer rotor; S1.

2. Based on the opposite direction vector of the rubbing normal force, the unit vector is obtained by normalizing the vector: in, Denotes the first unit vector. This represents the vector in the opposite direction of the normal force of friction. S1.

3. Based on the rotor's whirl displacement, calculate the distance between the inner and outer rotors using the two-point distance formula, including calculating the normal relative intrusion amount using the following formula: in, Indicates the relative intrusion amount in the normal direction. Indicates the coordinates of the center point of the inner rotor. Indicates the coordinates of the center point of the outer rotor. This indicates the clearance value between the inner and outer rotors; S1.

4. Based on the unit direction vector and the relative normal intrusion amount, and according to the linear rubbing model, the rubbing normal force vector is obtained as follows: in, This represents the normal force vector of the contact. Indicates the contact stiffness between the inner and outer rotors. Indicates the relative intrusion amount in the normal direction. Represents the first unit vector; A finite element model of the dual-rotor system is established based on the element and node information of the dual-rotor system. The dynamic response of the system at each moment is calculated based on the finite element model to obtain the rubbing normal force. The method also includes: S1.

5. Obtain the projections of the rubbing normal force vector onto the x-axis and y-axis as the rubbing normal force: in, This represents the projection of the normal force vector of friction onto the x-axis. This represents the projection of the normal force vector of friction onto the y-axis. Representing vectors F N The first component; Representing vectors F N The second component; Considering the speed difference between the inner and outer rotors and the rotor whirl velocity, calculate the rotor-to-rotor friction force, including: S2.1 Calculate the velocity vector of the inner rotor relative to the outer rotor based on the inner rotor velocity, outer rotor velocity, and whirl velocity of the dual rotor system; S2.2 Projecting the velocity vector of the inner rotor relative to the outer rotor into the direction perpendicular to the normal force of the friction, we can obtain the projected unit vector as follows: in, Relative velocity v i-o The projection vector in the direction of friction. Describes the second unit vector. This represents the velocity vector of the inner rotor relative to the outer rotor. Represents the first unit vector; S2.3 According to Coulomb's theory of friction, the frictional force can be obtained as follows: in, This represents the vector of frictional force. Describes the second unit vector. Indicates the coefficient of friction between rotors. This represents the magnitude of the normal force vector caused by friction. Considering the speed difference between the inner and outer rotors and the rotor whirl velocity, calculate the rotor-to-rotor friction force, including: S2.4 Obtain the projections of the frictional force vector onto the x-axis and y-axis as the frictional force: in, Let x be the component of the frictional force vector along the x-axis. Let be the y-component of the frictional force vector. Representing vectors F f The first component, Representing vectors F f The second component; The dynamic simulation model of the dual-rotor system is as follows: in, , , These are the system's mass, damping, and stiffness matrices, respectively. , , These represent the displacement, velocity, and acceleration vectors of the system, respectively. The vector of external forces acting on the rotor system is expressed as follows: in, , , , This represents the projection of the unbalanced forces of the inner and outer rotors in the x and y directions. The unbalanced force node of the inner rotor is numbered 15, and the unbalanced force node of the outer rotor is numbered 24. The friction force node of the inner rotor is numbered 12, and the friction force node of the outer rotor is numbered 36. Each node has 6 degrees of freedom, and the force at the other node positions is 0.

2. The method for constructing a dynamic simulation model of a dual-rotor system under inter-rotor rubbing fault according to claim 1, characterized in that, The velocity vector of the inner rotor relative to the outer rotor is calculated based on the inner rotor speed, outer rotor speed, and whirl velocity of the dual-rotor system, including: S2.1.1 Based on the rotational speeds of the inner and outer rotors, the linear velocity vector at the contact point can be obtained as follows: in, This represents the linear velocity vector of the inner rotor's contact point. This indicates the rotational angular velocity of the inner rotor. Indicates the radius of the inner rotor. This represents the direction vector of the rotational linear velocity at the contact point of the inner rotor. This represents the linear velocity vector of the outer rotor's contact point. Indicates the rotational angular velocity of the outer rotor. Indicates the outer rotor radius. The direction vector representing the rotational linear velocity of the contact point of the outer rotor; S2.1.2 Based on the whirl velocity of the inner and outer rotors, the whirl velocity vectors of the inner and outer rotors at a certain moment can be obtained as follows: in, This represents the whirl velocity vector at the contact point of the inner rotor. This indicates the vortex velocity in the x-direction at the contact point of the inner rotor. This indicates the y-axis vortex velocity at the contact point of the inner rotor. This represents the whirl velocity vector at the contact point of the outer rotor. This indicates the vortex velocity in the x-direction at the contact point of the outer rotor. This indicates the y-axis vortex velocity at the contact point of the outer rotor; S2.1.3 Based on the principle of planar motion of rigid bodies, and according to the eddy current velocity and the linear velocity at the contact point, the resultant velocity vector of the rotor at the contact point can be obtained as follows: in, This represents the absolute velocity vector at the contact point of the inner rotor. This represents the whirl velocity vector at the contact point of the inner rotor. This represents the linear velocity vector of the inner rotor's contact point. This represents the absolute velocity vector at the point of contact between the outer rotors. This represents the whirl velocity vector at the contact point of the outer rotor. This represents the linear velocity vector of the outer rotor's contact point. S2.1.4 Based on the combined velocity vector of the rotor at the friction point, and using the vector triangle rule, the velocity vector of the inner rotor relative to the outer rotor can be obtained as follows: in, This represents the velocity vector of the inner rotor relative to the outer rotor. This represents the absolute velocity vector at the contact point of the inner rotor. This represents the absolute velocity vector at the point of contact between the outer rotor and the outer rotor.

3. The method for constructing a dynamic simulation model of a dual-rotor system under inter-rotor rubbing fault according to claim 1, characterized in that, According to Newton's third law, calculate the frictional forces acting on the inner and outer rotors, including calculating the resultant forces of the inner and outer rotors in the x and y directions using the following formula: in, This indicates the force acting on the inner rotor in the x-direction. This represents the projection of the normal force of friction in the x-direction. This represents the projection of the frictional force in the x-direction. This indicates the force on the inner rotor in the y-direction. This represents the projection of the normal force of friction in the y-direction. This represents the projection of the frictional force in the y-direction. This indicates the force on the outer rotor in the x-direction. This indicates the force acting on the inner rotor in the x-direction. This indicates the force on the outer rotor in the y-direction. This indicates the force acting on the inner rotor in the y-direction.

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