Method for analyzing vibration characteristics of non-centering bearing-rotor system under basic motion

Abstract

The invention belongs to the technical field of bearing-rotor system vibration characteristic analysis, and discloses a method for analyzing the vibration characteristic of a non-centering bearing-rotor system under basic motion. Dispersing the rotating shaft into a plurality of beam units; obtaining a kinetic energy expression and a potential energy expression of a beam unit under the foundation motion; substituting the kinetic energy and potential energy expressions into a Lagrange equation to obtain a stiffness matrix, a mass matrix and an additional effect matrix of the unit; and obtaining a matrix corresponding to the rotating shaft. A disc is considered as a concentrated mass point, and a mass matrix and an additional effect matrix of the concentrated mass point are obtained by adopting a modeling method the same as that of a beam unit. The influence of misalignment of the angular contact bearing on bearing contact is considered; solving a ball contact angle in a non-centering state and a clearance between the ball and a raceway based on a function method; the contact deformation between the balls and the raceway is calculated on the basis of further considering the displacement of the inner ring and the outer ring of the bearing, and finally the supporting force of the misalignment angular contact bearing is obtained.

Description

Technical Field

[0001] The invention relates to the technical field of vibration characteristic analysis of a bearing-rotor system, and in particular to a vibration characteristic analysis method of a misaligned bearing-rotor system under basic motion. Background Art

[0002] In rotating machinery, bearings are the main supporting components, and their performance is crucial to the overall stability and life of the system. However, rotating machinery is not only affected by internal unbalanced excitations, but is often also disturbed by base motion excitations. Base motion may come from external environmental factors such as waves of ships, maneuvering flights of aircraft, and rough terrain of vehicles. This movement exerts additional forces on the bearings, especially axial loads, which in turn changes the contact characteristics of the bearings and may shorten their service life. Existing studies have mostly focused on the vibration characteristics under fixed bases, while ignoring the impact of base motion on the bearing and rotor system. Therefore, it is of great significance to study the impact of base motion on the nonlinear vibration of the rotor-bearing system, which can not only optimize the system design, but also provide guidance for the reliable operation of the equipment.

[0003] At the same time, the bearing misalignment problem caused by bearing assembly errors is also an important factor affecting the performance of rotating machinery. Existing studies have shown that the load characteristics and vibration responses of different types of bearings such as deep groove ball bearings and cylindrical roller bearings change significantly when they are misaligned, especially angular contact ball bearings under the action of axial force. However, most current studies only consider the impact of a single factor on the system, and there are few dynamic models that simultaneously study the base motion and bearing misalignment. Therefore, developing a dynamic model that can take into account the base motion and bearing misalignment, and analyzing their impact on vibration characteristics and contact characteristics, will provide a valuable theoretical basis for the optimal design of the bearing-rotor system. Summary of the invention

[0004] In view of the lack of a modeling method that takes into account the misalignment of angular contact bearings in the dynamic analysis technology of a misaligned bearing-rotor system under basic motion, the present invention proposes a vibration characteristic analysis method for a misaligned bearing-rotor system under basic motion. As a method for establishing a dynamic simulation model of a bearing-rotor system under basic motion, the method takes into account the additional effect matrix of the rotating shaft and the disk caused by the basic motion, and establishes a contact force model of the misaligned bearing based on the deformation coordination relationship of the bearing. Combined with the unbalanced force, the additional load caused by the basic motion and the bearing force, a dynamic simulation model of the misaligned bearing-rotor system under basic motion is established.

[0005] The technical solution of the present invention is as follows: A method for analyzing vibration characteristics of a misaligned bearing-rotor system under basic motion comprises the following steps:

[0006] S1. According to the concentrated mass method, a concentrated mass unit is used to establish a disk; the kinetic energy expression and potential energy expression of the concentrated mass unit under the basic motion are obtained, and after substituting the kinetic energy expression and potential energy expression into the Lagrange equation, the stiffness matrix, mass matrix and additional effect matrix of the concentrated mass unit are obtained;

[0007] S2. According to the Timoshenko beam unit theory, the Timoshenko beam unit is used to establish the rotation axis; the kinetic energy expression and potential energy expression of the beam unit under the basic motion are obtained; after substituting the kinetic energy expression and potential energy expression into the Lagrange equation, the stiffness matrix, mass matrix and additional effect matrix of the beam unit are obtained;

[0008] The concentrated mass unit and the beam unit are group units; the stiffness matrix, mass matrix and additional effect matrix corresponding to the rotating shaft are obtained according to the stiffness matrix, mass matrix and additional effect matrix of the group unit;

[0009] S3. Considering the influence of misalignment of angular contact bearings on bearing contact, the ball contact angle and the clearance between the ball and the raceway under misalignment are solved based on the function method. The contact deformation between the ball and the raceway is further calculated based on the displacement of the inner and outer rings of the bearing, and finally the supporting force of the misaligned angular contact bearing is obtained.

[0010] S4. Based on the obtained stiffness matrix, mass matrix and additional effect matrix of the rotating shaft / disk, the supporting force of the misaligned bearing is introduced, and finally the dynamic model of the misaligned bearing-rotor system under basic motion is established.

[0011] In step S1, the mass matrix and the additional effect matrix of the concentrated mass unit are obtained as follows:

[0012] S1.1 The translational kinetic energy and rotational kinetic energy of the concentrated mass unit in the basic motion state are:

[0013]

[0014] Among them, T t is the translational kinetic energy of the concentrated mass unit, m d is the mass of the disk, v ord is the translational velocity vector of the concentrated mass unit, is the translational velocity of the base motion coordinate system in the global coordinate system, is the translational velocity of the concentrated mass unit in the base motion coordinate system, is the rotational velocity of the foundation, r is the displacement vector of the concentrated mass unit in the foundation motion coordinate system;

[0015]

[0016] in, is the velocity matrix; T r is the rotational kinetic energy of the concentrated mass unit, I d ,I p is the moment of inertia and polar moment of inertia of the disk, α, β, γ represent the Euler angles of coordinate transformation and the superscript dot represents the angular velocity corresponding to the Euler angle, a represents the Euler angle;

[0017] S1.2 Based on the translational kinetic energy expression and rotational kinetic energy expression obtained in step S1.1, the total kinetic energy expression is:

[0018] T=T t +T r , (3)

[0019] Where T is the total kinetic energy;

[0020] S1.3 According to the total kinetic energy obtained in step S1.2, the mass matrix and additional effect matrix of the concentrated mass unit are obtained based on the Lagrange equation:

[0021]

[0022] Among them, q i , represents generalized displacement and generalized velocity; Q i represents generalized force; U represents potential energy;

[0023] Since a=θ x , β=θ y ,γ=θ z +Ωt, the differential equation of motion of the concentrated mass unit is

[0024]

[0025] Among them, Ω represents the rotation speed of the disk, M d , G d represents the mass matrix and gyro matrix of the disk, θ Bx , represents the angular displacement, angular velocity, and angular acceleration of the disk around the x-axis, θ By , represents the angular displacement, angular velocity, and angular acceleration of the disk around the y-axis, θ Bz , represents the angular displacement, angular velocity, and angular acceleration of the disk around the z-axis; q d , Represents the displacement vector, velocity vector, and acceleration vector of the disk axis; C Bzd , C Byd , C Bxd Represents the additional damping matrix caused by the rotation of the base motion around the x, y, and z axes; C dz , Cdy , C dx , H dz , H dy , H dx , K rd , K Bzd , K Bxd , K Byd , K Bxyd , K Byzd , K Bxzd represents the additional stiffness matrix caused by the foundation motion; F Bd Represents the additional load vector due to base motion.

[0026] In step S2, the stiffness matrix, mass matrix and additional effect matrix of the beam unit are obtained as follows:

[0027] S2.1 The kinetic energy expression and potential energy expression of the Timoshenko beam element in the basic motion state are:

[0028]

[0029] in, is the potential energy of the beam element, is the kinetic energy of the beam element, is the diametric moment of inertia and polar moment of inertia of the unit per unit length, A represents the cross-sectional area, ρ is the density of the unit, E and G represent the elastic modulus and Poisson's ratio, J represents the torsional section moment of inertia, I x ,I y They represent the section moment around the x-axis and the section moment around the y-axis, respectively, and κ x , κ y represents the shear correction coefficient around the x-axis and the shear correction coefficient around the y-axis; u, v, w are the displacements of any section on the x, y, and z axes relative to the origin, θ, φ, represents the angular displacement of any cross section, l k represents the length of the beam unit; u′, v′, w′ are the position velocities of any section on the x, y, and z axes relative to the origin; θ′, φ′, represents the angular velocity of any cross section;

[0030] S2.2 According to the kinetic energy expression and potential energy expression obtained in step S2.1, the motion differential equation of the beam element is obtained by substituting them into the Lagrange equation:

[0031]

[0032] in, Represents the acceleration vector, velocity vector, and displacement vector of the beam element; represents the mass matrix, gyro matrix, and stiffness matrix of the beam element; CBzdsh , C Bydsh , C Bxdsh represents the additional damping matrix caused by the foundation motion; C dzsh , C dysh , C dxsh , H dzsh , H dysh , H dxsh , K rdsh , K Bzdsh , K Bxdsh , K Bydsh , K Bxydsh , K Byzdsh , K Bxzdsh Represents the additional stiffness matrix caused by foundation motion; C1, K1, K2, K3 are intermediate variables.

[0033] In step S3, the supporting force of the misaligned angular contact bearing is obtained as follows:

[0034] S3.1 The coordinate expression of the raceway curvature center of the angular contact bearing in a healthy state is:

[0035]

[0036] Among them, f i 、f o Indicates the curvature coefficient of the inner raceway and the curvature coefficient of the outer raceway, r b Indicates the ball radius, r p represents the bearing pitch radius, α0 represents the initial contact angle between the ball and the raceway, and x i 、z i Indicates the coordinate of the center of curvature of the inner raceway; x o 、z o Indicates the coordinates of the center of curvature of the outer raceway;

[0037] S3.2 Based on the coordinates of the center of raceway curvature obtained in step S3.1, taking into account the rotor vibration and axial, radial and angular assembly errors, the equivalent misalignment is expressed as:

[0038]

[0039] Among them, α ieq , α oeq Indicates the equivalent misalignment angle of the inner ring and the outer ring, α ix , α iy Indicates the inclination angle of the inner circle around the x and y axes; α ox , α oy The tilt angle of the outer ring around the x and y axes, θ ix ,θ iy Indicates the angular displacement of the inner ring around the x and y axes due to vibration; θ ox,θ oy It represents the angular displacement of the outer ring around the x and y axes due to vibration, e iaeq 、e oaeq Indicates the equivalent axial misalignment distance of the inner ring and the equivalent axial misalignment distance of the outer ring, e ia 、e oa Indicates the static axial misalignment distance of the inner ring and the static axial misalignment distance of the outer ring, z ia 、z oa represents the axial misalignment caused by vibration, e ireq 、e oreq Indicates the equivalent radial misalignment distance of the inner ring and the equivalent radial misalignment distance of the outer ring, e irx 、e iry Indicates the static radial misalignment distance of the inner ring; e orx 、e ory Indicates the static radial misalignment distance of the outer ring, x ir ,y ir 、x or ,y or Indicates radial misalignment caused by vibration;

[0040] S3.3 According to the misalignment obtained in step S3.2, the coordinates of the center of curvature of the raceway under misalignment are calculated as follows:

[0041]

[0042] Among them, x im 、z im Indicates the coordinate of the center of curvature of the inner raceway; x om 、z om Indicates the coordinates of the center of curvature of the outer raceway;

[0043] S3.4 Based on the coordinates of the center of curvature of the raceway under the misaligned state obtained in step S3.3, the bearing clearance and ball contact angle are calculated as:

[0044]

[0045] Among them, c m Indicates the clearance of misaligned bearings, α m Indicates the bearing contact angle;

[0046] S3.5 Based on the clearance of the misaligned bearing obtained in step S3.4, the contact deformation between the ball and the raceway is calculated by the following formula:

[0047]

[0048] Among them, δ j represents the contact deformation of the jth ball;

[0049] S3.6 Based on the contact deformation between the ball and the raceway obtained in step S3.5 and the ball contact angle obtained in step S3.4, the contact force and contact torque of the misaligned bearing are:

[0050]

[0051] Among them, F x 、F x 、F z is the contact force, M x 、M y is the contact torque, k b represents the contact stiffness, and r1 represents the distance from the contact point to the axis.

[0052] In step S4, the dynamic model of the misaligned bearing-rotor system under the basic motion is established as follows:

[0053] The stiffness matrix, mass matrix, gyro matrix, and additional effect matrix of the S4.1 group unit, and the motion differential equation of the misaligned bearing-rotor system under basic motion are:

[0054]

[0055] Among them, M, C, G, and K represent the total mass matrix, damping matrix, gyro matrix, and stiffness matrix of the misaligned bearing-rotor system under basic motion; q represents the acceleration, velocity, and displacement vector of the misaligned bearing-rotor system under basic motion; F un 、F b Represents the unbalanced force model and the bearing force model.

[0056] The beneficial effect of the present invention is that the present invention takes into account the influence of base motion and bearing misalignment at the same time, proposes a nonlinear restoring force calculation method for angular contact ball bearings with 5 degrees of freedom, and introduces a dynamic model of misaligned bearing-rotor system under basic motion in combination with base motion. By incorporating the angular, radial and axial deviations of bearing misalignment into the contact force calculation formula, the contact characteristics and axial force response of the bearing under different working conditions are accurately obtained. Based on this model, the vibration characteristics of the rotor under the combined action of base motion and bearing misalignment are further analyzed, and the influence of the increase in base angular velocity on the amplitude of the bearing variable stiffness frequency is revealed. This model is closer to the actual working conditions, especially in complex systems where bearing misalignment and base motion coexist, and provides a more accurate simulation basis for the optimization design and fault diagnosis of the bearing-rotor system. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 is a schematic diagram of the bearing-rotor system;

[0058] Figure 2 is a schematic diagram of a beam element;

[0059] Figure 3 The following are the geometric relationship diagrams of bearings; (a) is the bearing with the large end facing right; (b) is the bearing with the large end facing left.

[0060] Figure 4 It is a three-dimensional spectrum diagram; (a) is the displacement spectrum diagram at bearing 1; (b) is the displacement spectrum diagram at bearing 4; (c) is the bearing contact force spectrum diagram at bearing 1; (d) is the bearing contact force spectrum diagram at bearing 4.

[0061] Figure 5 is the influence of basic motion speed on the bearing; (a) is the bearing contact angle change diagram; (b) is the ball contact force change diagram; (c) is the bearing contact stiffness change diagram; (d) is the bearing z-direction contact force; (e) is the bearing y-direction contact force; (f) is the bearing x-direction contact force.

[0062] Figure 6 is the contact load area of ​​the bearing. (a) is the radar diagram of the contact force at bearing 1 when the foundation is stationary; (b) is the radar diagram of the contact force at bearing 4 when the foundation is stationary; (c) is the radar diagram of the contact force at bearing 1 when the foundation is moving; (d) is the radar diagram of the contact force at bearing 4 when the foundation is moving. DETAILED DESCRIPTION

[0063] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. 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.

[0064] Example 1

[0065] Step 1 Calculate the differential equation of the disk motion in the basic motion state

[0066] S1.1 Bearing-rotor system Figure 1 As shown. First, the translational kinetic energy and rotational kinetic energy of the concentrated mass unit in the basic motion state are;

[0067]

[0068] Among them, T t is the translational kinetic energy of the concentrated mass unit, m d is the mass of the disk, v ord is the translational velocity vector of the concentrated mass unit, is the translational velocity of the base motion coordinate system in the global coordinate system, is the translational velocity of the concentrated mass unit in the base motion coordinate system, is the rotational velocity of the foundation, and r is the displacement vector of the concentrated mass unit in the foundation motion coordinate system.

[0069]

[0070] Among them, T r is the rotational kinetic energy of the concentrated mass unit, I d ,I p is the moment of inertia and polar moment of inertia of the disk, α, β, γ represent the Euler angles of coordinate transformation, and the superscript dot represents the angular velocity corresponding to the Euler angles. S1.2 Based on the expressions of translational kinetic energy and rotational kinetic energy obtained in step S1.1, the total kinetic energy expression is:

[0071] T=T t +T r , (3)

[0072] Where T is the total kinetic energy.

[0073] S1.3 According to the total kinetic energy obtained in step 1.2, the mass matrix and nearby effect matrix of the concentrated mass unit are obtained based on the Lagrange equation:

[0074]

[0075] Among them, q i , represents generalized displacement and generalized velocity; Q i represents generalized force; U represents potential energy.

[0076] Since a=θ x , β=θ y ,γ=θ z +Ωt, the differential equation of motion of the concentrated mass unit is

[0077]

[0078] Among them, Ω represents the rotation speed of the disk, M d , G d represents the mass matrix and gyro matrix of the disk, θ Bx , It represents the angular displacement, angular velocity and angular acceleration of the disk around the x, y and z axes. d , Represents the displacement vector, velocity vector, and acceleration vector of the disk axis. Bzd , C Byd , C Bxd represents the additional damping matrix caused by the foundation motion. C dz , C dy , C dx , H dz , Hdy , H dx , K rd , K Bzd , K Bxd , K Byd , K Bxyd , K Byzd , K Bxzd represents the additional stiffness matrix caused by the foundation motion. Bd Represents the additional load vector due to base motion.

[0079] Step 2 Calculate the differential equation of motion of the beam element in the basic motion state

[0080] S2.1 Timoshenko beam element Figure 2 As shown. The kinetic energy and potential energy expressions of the Timoshenko beam element in the basic motion state are:

[0081]

[0082] in, is the potential energy of the unit, is the kinetic energy of the unit, is the diametric moment of inertia and polar moment of inertia of the unit per unit length, A represents the cross-sectional area, ρ is the density of the unit, E and G represent the elastic modulus and Poisson's ratio, J represents the torsional section moment of inertia, I x ,I y represents the section moment around the x and y axes, κ x , κ y The shear correction coefficients u, v, and w around x and y are the displacements of any section on the x, y, and z axes relative to the origin, θ, φ, represents the angular displacement of any cross section, l k Indicates the length of the unit.

[0083] S2.2 According to the kinetic energy and potential energy expressions obtained in step S2.1, the differential equation of motion of the unit is obtained by substituting them into the Lagrange equation:

[0084]

[0085] in, Represents the displacement, velocity, and acceleration vectors of the beam element. K s e h Represents the mass matrix, gyro matrix, and stiffness matrix of the unit. Bzdsh , C Bydsh , C Bxdsh represents the additional damping matrix caused by the foundation motion. C dzsh , C dysh , Cdxsh , H dzsh , H dysh , H dxsh , K rdsh , K Bzdsh , K Bxdsh , K Bydsh , K Bxydsh , K Byzdsh , K Bxzdsh Represents the additional stiffness matrix caused by the foundation motion. C1, K1, K2, K3 are intermediate variables used to simplify the expression.

[0086] Step 3 Calculation of contact force of angular contact bearing under misalignment

[0087] S3.1 Bearing geometry is as follows Figure 3 As shown. The coordinate expression of the raceway curvature center of the angular contact bearing in a healthy state is:

[0088]

[0089] Among them, f i 、f o Indicates the curvature coefficient of the inner and outer raceways, r b Indicates the ball radius, r p represents the bearing pitch radius, α0 represents the initial contact angle between the ball and the raceway, and x i 、z i 、x o 、z o Indicates the coordinates of the center of curvature of the inner and outer raceways.

[0090] S3.2 Based on the coordinates of the raceway curvature center obtained in step S3.1, taking into account the rotor vibration and axial, radial and angular assembly errors, the equivalent misalignment is expressed as

[0091]

[0092] Among them, α ieq , α oeq Indicates the equivalent misalignment angle of the inner ring and the outer ring, α ix , α iy , α ox , α oy Indicates the equivalent misalignment angle of the inner ring and the tilt angle of the outer ring around the x and y axes, θ ix ,θ iy ,θ ox ,θ oy It represents the angular displacement of the inner ring around the x and y axes due to vibration, and the angular displacement of the outer ring around the x and y axes due to vibration, e iaeq 、e oaeqIndicates the equivalent axial misalignment distance of the inner ring and the equivalent axial misalignment distance of the outer ring, e ia 、e oa Indicates the static axial misalignment distance of the inner ring and the static axial misalignment distance of the outer ring, z ia 、z oa represents the axial misalignment caused by vibration, e ireq 、e oreq Indicates the equivalent radial misalignment distance of the inner ring and the equivalent radial misalignment distance of the outer ring, e irx 、e iry 、e orx 、e ory Indicates the static radial misalignment distance of the inner ring and the static radial misalignment distance of the outer ring, x ir ,y ir 、x or ,y or Indicates radial misalignment caused by vibration.

[0093] S3.3 Based on the misalignment obtained in step S3.2, calculate the coordinates of the center of curvature of the raceway under misalignment:

[0094]

[0095] Among them, x im 、z im 、x om 、z om Indicates the coordinates of the center of curvature of the inner raceway and the center of curvature of the outer raceway.

[0096] S3.4 Based on the coordinates of the raceway curvature center under the misaligned state obtained in step S3.3, calculate the bearing clearance and ball contact angle as follows:

[0097]

[0098] Among them, c m Indicates the clearance of misaligned bearings, α m Indicates the bearing contact angle.

[0099] S3.5 Based on the clearance of the misaligned bearing obtained in step S3.4, the contact deformation between the ball and the raceway can be calculated by the following formula

[0100]

[0101] Among them, δ j represents the contact deformation of the jth ball.

[0102] S3.6 Based on the contact deformation between the ball and the raceway obtained in step S3.5 and the ball contact angle obtained in step S3.4, the contact force and contact torque of the misaligned bearing are:

[0103]

[0104] Among them, F x 、F x 、F z is the contact force, M x 、M y is the contact torque, k b represents the contact stiffness, and r1 represents the distance from the contact point to the axis.

[0105] Step 4 Dynamic modeling of misaligned bearing-rotor system under basic motion

[0106] The stiffness matrix, mass matrix, gyro matrix, and additional effect matrix of the S4.1 group unit, and the motion differential equation of the misaligned bearing-rotor system under basic motion are:

[0107]

[0108] Among them, M, C, G, and K represent the total mass matrix, damping matrix, gyro matrix, and stiffness matrix of the misaligned bearing-rotor system under basic motion. q represents the acceleration, velocity, and displacement vector of the system. un 、F b Represents the unbalanced force and bearing force model.

[0109] According to the dynamic analysis model in step 4, the dynamic response of the system is solved according to the Newmark-β time domain integration method, and the dynamic response of the rotor system is analyzed. It is found that there is a combined frequency of the bearing characteristic frequency and the rotation frequency in the spectrum diagram.

[0110] At different base movement speeds, the spectrum of the bearing node displacement in the x direction is as follows: Figure 4 As shown. As the base movement speed increases, the rotation frequency f r The amplitude of the overall decreases, while the frequency f vc1 The amplitude of the bearing 5 is increased. In addition, the VC frequency f vc5 The amplitude first increases, then decreases, and finally increases again, such as Figure 4 (b) This is because the base motion first offsets the misalignment effect of the bearing. Some combined frequencies also appear in the spectrum cascade, including f vc1 -f r and f vc1 +f r .also, Figure 4 We can also see the frequency fvc2 As the speed increases, the amplitude of the frequency fr increases first, then remains constant, and finally Figure 4 (c) and 4(d). In addition, the frequency f vc The amplitude of the frequency increases significantly, and its amplitude is greater than the frequency f r The amplitude of .

[0111] Figure 5 The effect of base motion on bearing contact characteristics is intuitively demonstrated. As the base motion speed increases, the following phenomena are observed: (1) The maximum contact angle and maximum contact stiffness of bearing 1 decrease monotonically, while those of bearing 4 increase monotonically. The contact angle variation ranges of bearings 1 and 4 are approximately 10° and 6°, respectively. This indicates that the base motion has a significant effect on α m1 The impact of α m4 The influence of F is more significant. (2) The maximum rolling contact force also gradually increases. The rolling contact force of bearing 1 is greater than that of bearing 4. b1 The change of F is greater, and the base movement has a greater b1 The impact of F b4 The influence of is more obvious. (3) In addition, the contact force of the bearing in the z direction and y direction also gradually increases, such as Figure 5 (d) and 5(e). The contact force F of bearing 4 in the y direction is y1 Greater than F of bearing 1 y4 (4) Compared with the contact force of the bearing in the x-direction and the y-direction, the F y4 (F y1 ) is greater than F x4 (F x1 ). This is a non-uniform load phenomenon caused by the base movement. Another phenomenon caused by the base movement is that the axial force of the bearing increases significantly, which worsens the load environment of the bearing. (5) The reasons for the increase in axial load at different base movement speeds are summarized as follows: The axial excitation force caused by the base movement gradually increases, which intensifies the axial vibration of the rotor and ultimately leads to an increase in the axial force of the bearing.

[0112] Figure 6 Shown in and Radar diagram of the bearing contact load distribution of bearings 1 and 4, considering the misalignment of bearing 1. Figure 6 In (a), the contact range is distributed between -57° to 57° and 130° to 230°, and the bearing contact force in the right area is greater than that in the left area. This is because the left area (i.e. Figure 1 The clearance between the rolling element and the raceway (in the y direction) decreases. Figure 6 In (b), the bearing contact force is always greater than 0N. When the base moves, the additional force Figure 6 There is only one contact interval in (c), ranging from -62° to 62°. Figure 6 In (d), the bearing contact force is always greater than 0N. This is also because the bearing is compressed in the axial direction, causing the rolling elements and raceways to always maintain contact.

[0113] The embodiments of the present invention are given for the purpose of illustration and description, and are not intended to be exhaustive or to limit the invention to the disclosed forms. Many modifications and variations will be apparent to those of ordinary skill in the art. The embodiments are selected and described in order to better illustrate the principles and practical applications of the present invention and to enable those of ordinary skill in the art to understand the present invention and thereby design various embodiments with various modifications suitable for specific uses.

Claims

1. A method for analyzing vibration characteristics of misaligned bearing-rotor system under basic motion, characterized in that: The steps include: S1. According to the concentrated mass method, a concentrated mass unit is used to establish a disk; the kinetic energy expression and potential energy expression of the concentrated mass unit under the basic motion are obtained, and after substituting the kinetic energy expression and potential energy expression into the Lagrange equation, the stiffness matrix, mass matrix and additional effect matrix of the concentrated mass unit are obtained; S2. According to the Timoshenko beam unit theory, the Timoshenko beam unit is used to establish the rotation axis; the kinetic energy expression and potential energy expression of the beam unit under the basic motion are obtained; after substituting the kinetic energy expression and potential energy expression into the Lagrange equation, the stiffness matrix, mass matrix and additional effect matrix of the beam unit are obtained; The concentrated mass unit and the beam unit are group units; the stiffness matrix, mass matrix and additional effect matrix corresponding to the rotating shaft are obtained according to the stiffness matrix, mass matrix and additional effect matrix of the group unit; S3. Considering the influence of misalignment of angular contact bearings on bearing contact, the ball contact angle and the clearance between the ball and the raceway under misalignment are solved based on the function method. The contact deformation between the ball and the raceway is further calculated based on the displacement of the inner and outer rings of the bearing, and finally the supporting force of the misaligned angular contact bearing is obtained. S4. Based on the obtained stiffness matrix, mass matrix and additional effect matrix of the rotating shaft / disk, the supporting force of the misaligned bearing is introduced, and finally the dynamic model of the misaligned bearing-rotor system under basic motion is established.

2. The vibration characteristic analysis method of a misaligned bearing-rotor system under basic motion according to claim 1 is characterized in that: In step S1, the mass matrix and the additional effect matrix of the concentrated mass unit are obtained as follows: S1.1 The translational kinetic energy and rotational kinetic energy of the concentrated mass unit in the basic motion state are: Among them, T t is the translational kinetic energy of the concentrated mass unit, m d is the mass of the disk, v ord is the translational velocity vector of the concentrated mass unit, is the translational velocity of the base motion coordinate system in the global coordinate system, is the translational velocity of the concentrated mass unit in the base motion coordinate system, is the rotational velocity of the foundation, r is the displacement vector of the concentrated mass unit in the foundation motion coordinate system; in, is the velocity matrix; T r is the rotational kinetic energy of the concentrated mass unit, I d ,I p is the moment of inertia and polar moment of inertia of the disk, α, β, γ represent the Euler angles of coordinate transformation and the superscript dot represents the angular velocity corresponding to the Euler angle, a represents the Euler angle; S1.2 Based on the translational kinetic energy expression and rotational kinetic energy expression obtained in step S1.1, the total kinetic energy expression is: T=T t +T r , (3) Where T is the total kinetic energy; S1.3 According to the total kinetic energy obtained in step S1.2, the mass matrix and additional effect matrix of the concentrated mass unit are obtained based on the Lagrange equation: Among them, q i , represents generalized displacement and generalized velocity; Q i represents generalized force; U represents potential energy; since a=θ x , β=θ y ,γ=θ z +Ωt, the differential equation of motion of the concentrated mass unit is Among them, Ω represents the rotation speed of the disk, M d , G d represents the mass matrix and gyro matrix of the disk, θ Bx , represents the angular displacement, angular velocity, and angular acceleration of the disk around the x-axis, θ By , represents the angular displacement, angular velocity, and angular acceleration of the disk around the y-axis, θ Bz , represents the angular displacement, angular velocity, and angular acceleration of the disk around the z-axis; q d , Represents the displacement vector, velocity vector, and acceleration vector of the disk axis; C Bzd , C Byd , C Bxd Represents the additional damping matrix caused by the rotation of the base motion around the x, y, and z axes; C dz , C dy , C dx , H dz , H dy , H dx , K rd , K Bzd , K Bxd , K Byd , K Bxyd , K Byzd , K Bxzd represents the additional stiffness matrix caused by the foundation motion; F Bd Represents the additional load vector due to base motion.

3. The vibration characteristic analysis method of misaligned bearing-rotor system under basic motion according to claim 1 is characterized in that: In step S2, the stiffness matrix, mass matrix and additional effect matrix of the beam unit are obtained as follows: S2.1 The kinetic energy expression and potential energy expression of the Timoshenko beam element in the basic motion state are: in, is the potential energy of the beam element, is the kinetic energy of the beam element, is the diametric moment of inertia and polar moment of inertia of the unit per unit length, A represents the cross-sectional area, ρ is the density of the unit, E and G represent the elastic modulus and Poisson's ratio, J represents the torsional section moment of inertia, I x ,I y They represent the section moment around the x-axis and the section moment around the y-axis, respectively, and κ x , κ y represents the shear correction coefficient around the x-axis and the shear correction coefficient around the y-axis; u, v, w are the displacements of any section on the x, y, and z axes relative to the origin, θ, φ, represents the angular displacement of any cross section, l k represents the length of the beam element; u′, v′ , w′ is the velocity of any section on the x, y, z axis relative to the origin; θ′, φ′, represents the angular velocity of any cross section; S2.2 According to the kinetic energy expression and potential energy expression obtained in step S2.1, the motion differential equation of the beam element is obtained by substituting them into the Lagrange equation: in, Represents the acceleration vector, velocity vector, and displacement vector of the beam element; represents the mass matrix, gyro matrix, and stiffness matrix of the beam element; C Bzdsh , C Bydsh , C Bxdsh represents the additional damping matrix caused by the foundation motion; C dzsh , C dysh , C dxsh , H dzsh , H dysh , H dxsh , K rdsh , K Bzdsh , K Bxdsh , K Bydsh , K Bxydsh , K Byzdsh , K Bxzdsh Represents the additional stiffness matrix caused by foundation motion; C1, K1, K2, K3 are intermediate variables.

4. The vibration characteristic analysis method of misaligned bearing-rotor system under basic motion according to claim 1 is characterized in that: In step S3, the supporting force of the misaligned angular contact bearing is obtained as follows: S3.1 The coordinate expression of the raceway curvature center of the angular contact bearing in a healthy state is: Among them, f i 、f o Indicates the curvature coefficient of the inner raceway and the outer raceway, r b Indicates the ball radius, r p represents the bearing pitch radius, α0 represents the initial contact angle between the ball and the raceway, and x i 、z i Indicates the coordinate of the center of curvature of the inner raceway; x o 、z o Indicates the coordinates of the center of curvature of the outer raceway; S3.2 Based on the coordinates of the center of raceway curvature obtained in step S3.1, taking into account the rotor vibration and axial, radial and angular assembly errors, the equivalent misalignment is expressed as: Among them, α ieq , α oeq Indicates the equivalent misalignment angle of the inner ring and the outer ring, α ix , α iy Indicates the inclination angle of the inner circle around the x and y axes; α ox , α oy The tilt angle of the outer ring around the x and y axes, θ ix ,θ iy Indicates the angular displacement of the inner ring around the x and y axes due to vibration; θ ox ,θ oy It represents the angular displacement of the outer ring around the x and y axes due to vibration, e iaeq 、e oaeq Indicates the equivalent axial misalignment distance of the inner ring and the equivalent axial misalignment distance of the outer ring, e ia 、e oa Indicates the static axial misalignment distance of the inner ring and the static axial misalignment distance of the outer ring, z ia 、z oa represents the axial misalignment caused by vibration, e ireq 、e oreq Indicates the equivalent radial misalignment distance of the inner ring and the equivalent radial misalignment distance of the outer ring, e irx 、e iry Indicates the static radial misalignment distance of the inner ring; e orx 、e ory Indicates the static radial misalignment distance of the outer ring, x ir ,y ir 、x or ,y or Indicates radial misalignment caused by vibration; S3.3 According to the misalignment obtained in step S3.2, the coordinates of the center of curvature of the raceway under misalignment are calculated as follows: Among them, x im 、z im Indicates the coordinates of the center of curvature of the inner raceway; xom, z om Indicates the coordinates of the center of curvature of the outer raceway; S3.4 Based on the coordinates of the center of curvature of the raceway under the misaligned state obtained in step S3.3, the bearing clearance and ball contact angle are calculated as: Among them, c m Indicates the clearance of misaligned bearings, α m Indicates the bearing contact angle; S3.5 Based on the clearance of the misaligned bearing obtained in step S3.4, the contact deformation between the ball and the raceway is calculated by the following formula: Among them, δ j represents the contact deformation of the jth ball; S3.6 Based on the contact deformation between the ball and the raceway obtained in step S3.5 and the ball contact angle obtained in step S3.4, the contact force and contact torque of the misaligned bearing are: Among them, F x 、F x 、F z is the contact force, M x 、M y is the contact torque, k b represents the contact stiffness, and r1 represents the distance from the contact point to the axis.

5. The vibration characteristic analysis method of misaligned bearing-rotor system under basic motion according to claim 1 is characterized in that: In step S4, the dynamic model of the misaligned bearing-rotor system under the basic motion is established as follows: The stiffness matrix, mass matrix, gyro matrix, and additional effect matrix of the S4.1 group unit, and the motion differential equation of the misaligned bearing-rotor system under basic motion are: Among them, M, C, G, and K represent the total mass matrix, damping matrix, gyro matrix, and stiffness matrix of the misaligned bearing-rotor system under basic motion; q represents the acceleration, velocity, and displacement vector of the misaligned bearing-rotor system under basic motion; F un 、F b Represents the unbalanced force model and the bearing force model.

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