Mechanical calculation method for bearing outer ring running fault

Abstract

The invention belongs to the technical field of bearing running outer ring fault research, and discloses a bearing running outer ring fault mechanical calculation method which comprises the following steps: S1, acquiring initial parameters of a bearing inner ring, a rolling body, a bearing outer ring, a raceway and a bearing seat required by calculation; s2, establishing a dynamical model of a bearing seat-bearing system; s3, calculating the contact force between the outer ring and the bearing seat; S4, calculating the maximum static friction force and the maximum static friction torque applied to the outer ring by the bearing seat and the driving force and the driving torque applied to the outer ring by the rolling body; s5, the friction force and the friction torque borne by the outer ring from the bearing seat are determined; according to the method, the exciting force parameters are accurately calculated, the mechanical model more conforming to the actual working condition is established, the vibration generation mechanism under the bearing outer ring running fault is revealed, theoretical basis and technical support are provided for fault diagnosis, service life prediction and optimization design, and the vacancy of a bearing outer ring running fault modeling method at the present stage is made up.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of bearing outer ring fault research, in particular to a bearing outer ring fault mechanical calculation method. BACKGROUND

[0002] As core components of major equipment such as wind turbines, aero-engines and special vehicles, rolling bearings directly affect the overall performance and safety of the equipment. Bearing outer ring fault refers to the relative sliding between the bearing outer ring and the bearing seat during equipment operation, which breaks the normal fixed fit state of the bearing. Under normal circumstances, the bearing outer ring and the bearing seat are tightly connected through interference fit or transition fit, ensuring that the inner ring rotates with the shaft while the outer ring remains stable, and the rolling elements roll normally between the inner and outer rings. However, in actual application, loose fit or long-term vibration can cause the outer ring and the bearing seat to fail to cooperate, resulting in relative sliding, i.e. outer ring fault. The occurrence of this fault can cause abnormal vibration of the system, seriously affecting the reliability and service life of the equipment. When the bearing has an outer ring fault, the stress state of the rolling elements and the raceway changes, causing the equipment to vibrate more severely. Long-term operation in such a high-vibration environment greatly increases the contact force between the rolling elements and the raceway, greatly increasing the risk of raceway fatigue damage, and thus leading to premature failure of the bearing, and even possibly causing systemic failure of major equipment, resulting in serious economic losses and safety hazards.

[0003] Although the bearing outer ring fault is harmful, there are still many deficiencies in current research. Most existing research ignores the assembly gap between the bearing and the bearing seat and the influence of loose fit, and the vibration behavior of rotating machinery under bearing ring fault is relatively scarce, resulting in unclear typical vibration characteristics. In addition, existing research on bearing loose fit only considers radial excitation and does not consider the outer ring slip phenomenon caused by inner ring guide bearing loose fit, which is quite different from the actual working condition and cannot truly reflect the running state of the bearing in a complex working environment. In actual application, bearing ring fault changes the characteristic frequency value of the rolling bearing, seriously interfering with the prediction of the bearing vibration characteristic frequency. Therefore, an effective method for mechanical calculation of bearing outer ring fault is urgently needed. SUMMARY

[0004] The application aims to provide a bearing outer ring fault mechanical calculation method. Finally, the contact force, friction and friction torque acting on the outer ring are introduced into the bearing seat-bearing system dynamics model to obtain a bearing-bearing seat system dynamics modeling method containing bearing outer ring fault. The application fills the gap in the modeling method of bearing outer ring fault at the present stage. The problems in the background art are solved.

[0005] To achieve the above-mentioned purpose, the application provides the following technical solutions:

[0006] A bearing outer ring failure mechanics calculation method, comprising the following steps:

[0007] S1, determine the initial conditions:

[0008] Obtain the initial parameters of the bearing inner ring, rolling body, bearing outer ring, raceway and bearing seat required for calculation;

[0009] S2, establish the dynamics model of the bearing seat-bearing system:

[0010] The dynamics model of the bearing seat-bearing system is established based on the lumped parameter method, wherein the bearing inner ring and the bearing seat both contain radial freedom degrees in x and y directions; the outer ring and each rolling body both contain two radial freedom degrees and a rotation freedom degree around its own axis;

[0011] S3, calculate the contact force between the outer ring and the bearing seat:

[0012] According to the dynamics model of the bearing seat-bearing system, the contact deformation between the outer ring and the bearing seat inner hole is calculated, and the Hertz contact stiffness coefficient between the bearing outer ring and the bearing seat inner hole is calculated based on the Hertz contact theory. When the contact deformation is <0, the contact force between the bearing outer ring and the bearing seat is 0; when the contact deformation is >0, the contact force between the bearing outer ring and the bearing seat is calculated using the Hertz contact stiffness coefficient and the contact deformation;

[0013] S4, calculate the maximum static friction force and torque of the bearing seat to the outer ring, and the driving force and torque of the rolling body to the outer ring:

[0014] Based on the contact force between the bearing outer ring and the bearing seat obtained in step S4, the maximum static friction force and torque of the bearing seat to the outer ring are calculated; based on the driving force model and the driving torque model, the driving force and torque of the rolling body to the outer ring are calculated respectively;

[0015] S5, determine the friction force and torque of the outer ring from the bearing seat:

[0016] Calculate the relative sliding speed between the outer ring and the bearing seat;

[0017] When the contact deformation is ≤0, the friction force and torque of the bearing seat to the outer ring are both 0;

[0018] When the contact deformation is >0 and the relative sliding speed is 0, the static friction force of the bearing seat to the outer ring is determined based on the maximum static friction force, the maximum static friction torque, and the driving force and torque obtained in step S4;

[0019] When the contact deformation is >0, the dynamic friction force of the bearing seat to the outer ring is calculated based on the relative sliding speed and the contact force;

[0020] The contact force, friction force and friction torque of the outer ring are introduced into a bearing seat-bearing system dynamics model to obtain a bearing-bearing seat system dynamics model containing a bearing outer ring fault.

[0021] Further, the initial parameters include: the number N of rolling elements contained in the rolling bearing b ; the rolling bearing includes a bearing inner ring, rolling elements and a bearing outer ring, and the masses of the bearing inner ring, rolling elements and bearing outer ring are m i , m r and m o , respectively; the rotational inertias of the rolling elements and the outer ring are J r and J o , respectively; the diameter of the rolling elements is d; the diameters of the inner and outer raceways are D i and D o , respectively; the outer diameter of the bearing is D out ; the length of the outer ring is l b ; the maximum static friction coefficient and dynamic friction coefficient between the outer ring and the bearing seat are μ s and μ d , respectively; the looseness gap between the outer ring and the bearing seat is c b ; and the radial clearance of the bearing is γ.

[0022] Further, the expression of the contact deformation δ op is as follows:

[0023]

[0024] In the expressions, x p and y p are the radial vibration displacements of the bearing seat, and x o and y o are the radial vibration displacements of the bearing outer ring.

[0025] The calculation expression of the Hertz contact stiffness coefficient k op is as follows:

[0026]

[0027] The expression of the contact force F p between the bearing outer ring and the bearing seat is as follows:

[0028]

[0029] Further, the expressions of the maximum static friction force F fmax and the maximum static friction torque T fmax are as follows:

[0030] F fmax = μ s F p , T fmax = 0.5Dout μ s F p ;

[0031] F p is the contact force between the outer ring and the bearing housing;

[0032] The expression of the driving force F o and the driving torque T o is:

[0033]

[0034] wherein, Fj is the friction force between the jth rolling element and the outer ring, and the expression is:

[0035]

[0036] wherein, μ o j is the friction coefficient between the jth rolling element and the outer raceway, Δv o j is the relative sliding speed between the jth rolling element and the outer raceway, Fj is the normal contact force between the jth rolling element and the outer raceway, and the expression is:

[0037]

[0038] wherein, x r j , y r j , θ r j are the radial vibration displacement and the rotation angle of the jth rolling element, respectively; k o j is the contact stiffness between the jth rolling element and the outer ring; p is the load-deformation coefficient, which is 10 / 9 for a cylindrical roller bearing and 3 / 2 for a ball bearing; δ o j is the contact deformation between the jth rolling element and the outer ring; ω c is the angular velocity of the rolling element, is the angular position of the jth rolling element, and the expression is:

[0039]

[0040] wherein, is the initial position azimuth angle of the first rolling element; ω i and ω o are the rotation speeds of the inner and outer rings of the bearing, respectively.

[0041] Furthermore, the relative sliding speed Δv between the outer ring and the bearing housing op The expression is:

[0042]

[0043] Where β is the position angle when the outer ring contacts the bearing housing, and its expression is:

[0044]

[0045] When δ op >0 and Δv op When F = 0, the frictional force F t and frictional torque T t They are respectively:

[0046]

[0047] When contact deformation Δv op When the dynamic friction force F applied by the bearing housing to the outer ring is greater than 0, t and frictional torque T t The expressions are as follows:

[0048]

[0049] In the formula, F p This refers to the contact force between the outer ring of the bearing and the bearing housing.

[0050] The dynamic model expression for the bearing housing-bearing system with outer race slippage fault is as follows:

[0051]

[0052] In the formula, M, C, and K are the system mass matrix, damping matrix, and stiffness matrix, respectively; U, These represent the system's displacement vector, velocity vector, and acceleration vector, respectively; F represents the system's net external force vector; the expressions for each matrix are:

[0053]

[0054] In the formula, M S M I M R M O M P These represent the mass matrices of the shaft, bearing inner ring, rolling elements, outer ring, and bearing housing, respectively; C I C O C P The damping matrices for the inner ring-rolling element, outer ring-rolling element, and bearing housing, respectively, are represented by K; S and K Prespectively, are the stiffness matrix of the rotating shaft and the support stiffness matrix of the bearing chock; K B and C B respectively, are the support stiffness and damping matrix of the bearing; F I , F O respectively, are the contact force and friction force vectors of the inner ring-rolling element and the outer ring-rolling element; F P is the contact force and friction force vector between the bearing outer ring and the bearing chock; F U and F R are respectively the unbalance force vector and the radial load vector of the rotating shaft; G S , G I , G R , G O , G P respectively, are the gravity vectors of the rotating shaft, the bearing inner ring, the rolling element, the outer ring and the bearing chock; C S is the damping matrix of the rotating shaft, and the expression is as follows:

[0055] C S = alpha1M S + beta1K S

[0056] In the formula, alpha1 and beta1 are Rayleigh damping coefficients.

[0057] The beneficial effects of the technical scheme are as follows:

[0058] The bearing outer ring fault mechanical calculation method provided by the application calculates the elastic deformation between the bearing outer ring and the bearing chock inner hole and the Hertz contact stiffness coefficient between the two, simulates the contact force between the bearing outer ring and the bearing chock based on the nonlinear Hertz contact theory, calculates the maximum static friction force, the maximum static friction torque, the dynamic friction force and the dynamic friction torque of the outer ring according to the maximum static friction coefficient and the dynamic friction coefficient between the outer ring and the bearing chock and the contact force between the two, and judges the direction of the friction force according to the relative sliding speed between the bearing outer ring and the bearing chock inner hole. The driving force and the driving torque of the outer ring are obtained by calculating the friction torque of the rolling element on the outer ring. The friction force and the friction torque of the bearing outer ring are judged according to the elastic deformation between the outer ring and the bearing chock inner hole and the relative sliding speed between the two. Finally, the contact force, the friction force and the friction torque of the outer ring are introduced into the bearing chock-bearing system dynamics model to obtain the bearing-bearing chock system dynamics modeling method containing the bearing outer ring fault. By accurately calculating these excitation force parameters, a more actual working condition mechanical model can be established, the vibration generation mechanism under the bearing outer ring fault is revealed, theoretical basis and technical support are provided for fault diagnosis, life prediction and optimization design, and the vacancy of the bearing outer ring fault modeling method at the present stage is made up. BRIEF DESCRIPTION OF DRAWINGS

[0059] Figure 1 Fig. 2 is a schematic diagram of the interaction between the inner hole of the bearing seat and the outer ring of the bearing in Example 2 of the present application;

[0060] Figure 2 Fig. 3 is a schematic diagram of the shaft-bearing-bearing seat system in Example 2 of the present application; in the figure, (a) is a schematic diagram of the three-dimensional structure of the system; (b) is a front view of the system; (c) is a top view of the system;

[0061] Figure 3 Fig. 4 is a schematic diagram of the structure of the shaft and a dynamic model in Example 2 of the present application; in the figure, (a) is a schematic diagram of the structure of the shaft, and (b) is a lumped parameter model of the shaft;

[0062] Figure 4 Fig. 5 is the shaft center trajectory, time domain waveform and frequency spectrum of the shaft under different running circle fault degrees (loose clearance) in Example 2 of the present application; in the figure, (a1) is the shaft center trajectory when c b = 0 μm, (a2) is the time domain waveform when c b = 0 μm, (a3) is the frequency spectrum when c b = 0 μm; (b1) is the shaft center trajectory when c b = 20 μm, (b2) is the time domain waveform when c b = 20 μm, (b3) is the frequency spectrum when c b = 20 μm; (c1) is the shaft center trajectory when c b = 50 μm, (c2) is the time domain waveform when c b = 50 μm, (c3) is the frequency spectrum when c b = 50 μm;

[0063] Figure 5 Fig. 6 is the rotation angle and angular velocity of the outer ring of the bearing under different running circle fault degrees in Example 2 of the present application; in the figure, (a) is a curve graph of the angular displacement, and (b) is a curve graph of the average angular velocity;

[0064] Figure 6 Fig. 7 is the contact force between the outer ring of the bearing and the bearing seat under different running circle fault degrees (loose clearance) in Example 2 of the present application; (a) is a curve graph of the contact force when the loose clearance is 0 μm, (b) is a curve graph of the contact force when the loose clearance is 20 μm, (c) is a curve graph of the contact force when the loose clearance is 50 μm, (d) is a curve graph of the contact force when the loose clearance is 80 μm, and (e) is a curve graph of the contact force when the loose clearance is 150 μm;

[0065] Figure 7 Fig. 8 is the inner ring-rolling element contact force F ni , the outer ring-rolling element contact force F no , and the outer ring-bearing seat contact force Fp the change curve.

[0066] The names of the corresponding marks in the drawings are:

[0067] 1, outer ring; 2, inner ring; 3, rolling element; 4, bearing seat one, 5, bearing seat two, 6, bearing seat three, 7, bearing one, 8, bearing two, 9, bearing three, 10, bearing four, 11, rotating shaft. DETAILED DESCRIPTION

[0068] The application will be further described in detail below in combination with the drawings and embodiments:

[0069] Example 1

[0070] A bearing outer ring running fault mechanical calculation method, comprising the following steps:

[0071] S1, determining initial conditions:

[0072] Obtaining initial parameters of the bearing inner ring, rolling element, bearing outer ring, raceway and bearing seat required for calculation; the initial parameters include: the number of rolling elements contained in the rolling bearing N b ; the rolling bearing includes a bearing inner ring, rolling elements and a bearing outer ring, and the masses of the bearing inner ring, rolling elements and bearing outer ring are m i , m r and m o ; the moments of inertia of the rolling elements and the outer ring are J r and J o ; the diameter of the rolling elements is d; the diameters of the inner and outer raceways are D i and D o ; the outer diameter of the bearing is D out ; the length of the outer ring is l b ; the maximum static friction coefficient and dynamic friction coefficient between the outer ring and the bearing seat are μ s and μ d ; the looseness gap between the outer ring and the bearing seat is c b ; the radial clearance of the bearing is γ.

[0073] S2, establishing a dynamics model of the bearing seat-bearing system:

[0074] The dynamics model of the bearing seat-bearing system is established based on the lumped parameter method, wherein the bearing inner ring and the bearing seat each contain two degrees of freedom, i.e., the radial degrees of freedom in the x and y directions; the outer ring and each rolling element each contain three degrees of freedom, i.e., two radial degrees of freedom and a rotational degree of freedom around its own axis;

[0075] S3, calculating the contact force between the outer ring and the bearing seat:

[0076] The contact deformation between the outer ring and the inner hole of the bearing housing is calculated based on the dynamic model of the bearing housing-bearing system. The Hertz contact stiffness coefficient between the outer ring and the inner hole of the bearing housing is calculated based on the Hertz contact theory. When the contact deformation is <0, the contact force between the outer ring and the bearing housing is 0. When the contact deformation is >0, the contact force between the outer ring and the bearing housing is calculated using the Hertz contact stiffness coefficient and the contact deformation.

[0077] The specific calculation steps are as follows:

[0078] S301. Based on the dynamic model of the bearing housing-bearing system, the radial vibration displacement x of the bearing housing can be obtained. p y p Radial vibration displacement x of the bearing outer ring o y o The contact deformation δ between the outer ring and the inner hole of the bearing housing is then... op for:

[0079]

[0080] S302. Based on Hertz contact theory, calculate the Hertzian contact stiffness coefficient k between the bearing outer ring and the bearing housing inner bore. op :

[0081]

[0082] S302, when contact deformation δ op When the value is greater than 0, the outer ring contacts the bearing housing, and the contact force F between the outer ring and the bearing housing is... p The expression is:

[0083]

[0084] S4. Calculate the maximum static friction force and maximum static friction torque exerted by the bearing housing on the outer ring, as well as the driving force and driving torque exerted by the rolling elements on the outer ring:

[0085] Based on the contact force between the bearing outer ring and the bearing housing obtained in step S4, calculate the maximum static friction force and maximum static friction torque exerted by the bearing housing on the outer ring; calculate the driving force and driving torque exerted by the rolling elements on the outer ring based on the driving force model and the driving torque model, respectively.

[0086] The maximum static friction force F exerted by the bearing housing on the outer ring fmax Maximum static friction torque T fmax It can be calculated using the following formula:

[0087] F fmax =μ s F p ,T fmax =0.5D out μs F p ;

[0088] F p is the contact force between the outer ring and the bearing housing;

[0089] The driving force F o and the driving torque T o are provided by the friction torque of the rolling elements on the outer ring, and the expression is:

[0090]

[0091] wherein, is the friction force between the jth rolling element and the outer ring, and the expression is:

[0092]

[0093] wherein, μ o j is the friction coefficient between the jth rolling element and the outer raceway, Δv o j is the relative sliding speed between the jth rolling element and the outer raceway, is the normal contact force between the jth rolling element and the outer raceway, and the expression is:

[0094]

[0095] wherein, x r j , y r j , θ r j are the radial vibration displacement and the rotation angle of the jth rolling element, respectively; k o j is the contact stiffness between the jth rolling element and the outer ring; p is the load-deformation coefficient, which is 10 / 9 for a cylindrical roller bearing and 3 / 2 for a ball bearing; δ o j is the contact deformation between the jth rolling element and the outer ring; ω c is the angular velocity of the rolling element, is the angular position of the jth rolling element, and the expressions are:

[0096]

[0097] wherein, is the initial position azimuth angle of the first rolling element; ω i and ω oThe rotational speeds of the inner and outer rings of the bearing are respectively ωin and ωout, and the rotational speed of the inner ring is assumed to be the same as that of the shaft. The rotational speed of the outer ring can also be written as follows:

[0098]

[0099] S5, determine the friction force and friction torque on the outer ring from the bearing seat:

[0100] Calculate the relative sliding speed between the outer ring and the bearing seat;

[0101] The relative sliding speed between the outer ring and the bearing seat Δv op is expressed as:

[0102]

[0103] where β is the position angle at which contact occurs between the outer ring and the bearing seat, and the expression is:

[0104]

[0105] When the contact deformation δ op ≤ 0, the outer ring of the bearing is not in contact with the bearing seat, and at this time the friction force F t and the friction torque T t applied by the bearing seat to the outer ring are both 0;

[0106] When the contact deformation δ op > 0 and the relative sliding speed Δv op = 0, the outer ring of the bearing does not slide relative to the bearing seat, and at this time the friction force applied by the bearing seat to the outer ring is the static friction force, and the friction force and the friction torque can be written as:

[0107]

[0108] When the contact deformation Δv op > 0, the outer ring of the bearing begins to slide relative to the bearing seat, and at this time the friction force applied by the bearing seat to the outer ring is the dynamic friction force, and the friction force and the friction torque can be further expressed as:

[0109]

[0110] In the formula, F p is the contact force between the outer ring of the bearing and the bearing seat;

[0111] Introduce the contact force, friction force, and friction torque on the outer ring into the bearing seat-bearing system dynamics model to obtain a bearing-bearing seat system dynamics model containing a bearing outer ring running fault.

[0112] The bearing-bearing seat system dynamics model containing a bearing outer ring running fault is:

[0113]

[0114] In the formula, M, C, and K are the system mass matrix, damping matrix, and stiffness matrix, respectively; U, These represent the system's displacement vector, velocity vector, and acceleration vector, respectively; F represents the system's net external force vector; the expressions for each matrix are:

[0115]

[0116] In the formula, M S M I M R M O M P These represent the mass matrices of the shaft, bearing inner ring, rolling elements, outer ring, and bearing housing, respectively; C I C O C P The damping matrices for the inner ring-rolling element, outer ring-rolling element, and bearing housing, respectively, are represented by K; S and K P These are the stiffness matrices of the shaft and the support stiffness matrix of the bearing housing, respectively; K B and C B These represent the bearing's support stiffness and damping matrix, respectively; F I F O These are the contact force and friction force vectors between the inner ring and the rolling element, and between the outer ring and the rolling element, respectively. F P F represents the vector of contact and friction forces between the bearing outer ring and the bearing housing. U and F R The vectors are, in order, the unbalanced force vector and the radial load vector of the rotating shaft; G S G I G R G O G P Let C represent the gravity vectors of the shaft, inner bearing ring, rolling element, outer ring, and bearing housing, respectively; S The damping matrix of the rotating shaft is expressed as:

[0117] C S =α1M S +β1K S

[0118] In the formula, α1 and β1 are Rayleigh damping coefficients.

[0119] Example 2

[0120] Taking a rolling bearing-shaft-bearing housing system as an example, the bearing includes an outer ring 1, an inner ring 2, and rolling elements 3. A schematic diagram of the interaction between the inner bore of the bearing housing and the outer ring 1 of the bearing is shown below. Figure 1As shown; the structure of the bearing-shaft-bearing housing system is as follows: Figure 2 As shown, it consists of a rotating shaft 11, four bearings (bearing 1 7, bearing 2 8, bearing 3 9, bearing 4 10), and three bearing housings (bearing housing 1 4, bearing housing 2 5, bearing housing 3 6). A lumped parameter method is used to establish the dynamic model of the system, as described in Example 1. The structure of the rotating shaft 11 is as follows... Figure 3 As shown, the total length of shaft 11 is 204 mm. The system is supported by 6011 deep groove ball bearings, and the bearing parameters are shown in Table 1. The system's mass parameters are shown in Table 2, and the system's stiffness parameters are shown in Table 3. The Newmark-β method was used to numerically calculate the dynamic model of the bearing-bearing housing system with outer race failure obtained in Example 1. 300 cycles were calculated, and the steady-state solutions of the last 200 cycles were extracted for analysis. Each calculation cycle contained 1024 integration steps.

[0121] Table 1 Bearing Parameters

[0122] Bearing parameter Value Bearing parameter Value Inner raceway diameter D i (mm) 62.18 Number of rolling elements N b ]] 12 outer race diameter D o (mm) 82.82 Rolling element diameter d (mm) 10.32 Outer ring diameter D out (mm) 90 Bearing gap γ (μm) 4 bearing width l b (mm) 16

[0123] Table 2 System Quality Parameters

[0124]

[0125] Table 3 System stiffness parameters

[0126] Shaft stiffness Value (N / m) Support stiffness Value (N / m) ​ 4.3643 x 10 8 ]]> k b2,3 ]]> 1 x 10 7 ]]> <k2> 3.496 x 10 10 ]] k p ]]> 1 x 10 7 ]]

[0127] By changing the loose clearance c between the outer ring 1 and the bearing housing b Simulate the degree of failure of the outer race of the bearing, i.e., c b The higher the value, the more severe the lap time malfunction. Different values ​​for c... b The system vibration response results under the value are as follows Figure 4 As shown, when c b At 0 μm, the trajectory of the rotating shaft 11 is a single elliptical ring, and the time-domain waveform exhibits a relatively standard sine curve. Due to gravity, it can be seen from both the shaft center trajectory and the time-domain waveform that the equilibrium position of the rotating shaft 11 in the vertical direction is located in the negative y-axis direction. In the frequency spectrum, only the rotational frequency f exists. r The above analysis shows that when there is no looseness between the outer ring 1 of the bearing and the bearing housing, the main source of vibration in the system is the imbalance of the shaft 11. When c b At 20μm and 50μm respectively, with Figure 4(a1-a3) It can be seen that the bearing outer ring 1 collides with the bearing seat inner hole due to the existence of the looseness gap between the bearing outer ring 1 and the bearing seat, which further affects the vibration response of the rotating shaft 11. The movement trajectory of the rotating shaft 11 is no longer an ellipse. In one rotation period of the rotating shaft 11, multiple wave peaks appear in the vibration waveform. In the frequency spectrum, the multiple frequency components of the rotating frequency begin to appear (see Figure 4 (b3)). When the looseness gap is further expanded to 50 μm, the odd multiple frequency of the rotating frequency becomes particularly obvious.

[0128] The rotating angle and average angular velocity of the bearing outer ring 1 under different looseness gaps are shown in Figure 5 . Under normal circumstances, the bearing inner ring 2 rotates with the rotating shaft 11, and the bearing outer ring 1 does not rotate. However, as the value of c b increases, the rotating angle and average angular velocity of the outer ring 1 increase. This indicates that the bearing outer ring 1 rotates under the driving force of the rolling element 3 under a larger looseness gap. This also indicates that the constraint of the bearing seat on the bearing outer ring 1 is weakened, and the outer ring 1 has a relatively slow speed and a runout phenomenon.

[0129] To analyze the influence of the bearing runout fault on the contact characteristics between the bearing sleeve and the bearing seat. The contact force variation between the bearing outer ring 1 and the bearing seat under the conditions of c b values of 0 μm, 20 μm, 50 μm, 80 μm, and 150 μm is extracted, and the results are shown in Figure 6 . It can be seen from the figure that when there is no looseness gap, the bearing outer ring 1 is in contact with the bearing seat inner hole in the whole circumferential direction. As the value of c b increases, the contact time between the bearing outer ring 1 and the bearing seat is shortened, the non-contact time is prolonged, and the impact force when the bearing outer ring 1 contacts the bearing seat is increased. This indicates that the collision and friction between the bearing outer ring 1 and the bearing seat inner hole occur. These rules indicate that once the bearing has a loose fit, it is not conducive to the stable operation of the entire system, and the larger impact force will also shorten the service life of the bearing and cause the bearing to appear contact fatigue damage prematurely.

[0130] The peak-to-peak values of the contact force between the rolling element 3 and the inner ring 2, the contact force between the rolling element 3 and the outer ring 1, and the contact force between the outer ring 1 and the bearing seat under different looseness gaps are further extracted, and the results are shown in Figure 7 . Due to the centrifugal force of the rolling element 3, the contact force between the rolling element 3 and the outer ring 1 is slightly greater than the contact force between the rolling element 3 and the inner ring 2. As the degree of runout fault increases, the peak-to-peak values of the three contact forces increase. Among them, the contact force between the outer ring 1 and the bearing seat increases most obviously.

[0131] The application provides a bearing outer ring fault mechanics calculation method, and the application calculates the elastic deformation between the bearing outer ring and the bearing seat inner hole and the Hertz contact stiffness coefficient between the bearing outer ring and the bearing seat inner hole, simulates the contact force between the bearing outer ring and the bearing seat based on the nonlinear Hertz contact theory, calculates the maximum static friction force, the maximum static friction torque, the dynamic friction force and the dynamic friction torque of the outer ring according to the maximum static friction coefficient and the dynamic friction coefficient between the outer ring and the bearing seat and the contact force between the outer ring and the bearing seat, and judges the direction of the friction force according to the relative sliding speed between the bearing outer ring and the bearing seat inner hole. The driving force and the driving torque of the outer ring are obtained by calculating the friction torque of the rolling body on the outer ring. The friction force and the friction torque of the bearing outer ring are judged according to the elastic deformation between the outer ring and the bearing seat inner hole and the relative sliding speed between the outer ring and the bearing seat inner hole. Finally, the contact force, the friction force and the friction torque of the outer ring are introduced into the bearing seat-bearing system dynamics model, the bearing-bearing seat system dynamics modeling method containing the bearing outer ring fault is obtained, the mechanics model more in line with the actual working condition can be established by accurately calculating the excitation force parameters, the vibration generation mechanism under the bearing outer ring fault is revealed, theoretical basis and technical support are provided for fault diagnosis, life prediction and optimal design, and the vacancy of the bearing outer ring fault modeling method at the present stage is made up.

[0132] The above is only the embodiment of the application, and the specific technical solutions or common knowledge of the scheme are not described in detail. It should be noted that for those skilled in the art, without departing from the technical solutions of the application, some modifications and improvements can be made, which should also be considered as the protection scope of the application, and these will not affect the effect and practicality of the application. The protection scope of the present application should be subject to the content of its claims, and the specific embodiments in the specification can be used to explain the content of the claims.

Claims

1. A mechanical calculation method for bearing outer race run-off faults, characterized in that, Includes the following steps: S1. Determine the initial conditions: Obtain the initial parameters required for the calculation, including the bearing inner ring, rolling elements, outer ring, raceway, and bearing housing. S2. Establish the dynamic model of the bearing housing-bearing system: A dynamic model of the bearing housing-bearing system is established based on the lumped parameter method. The inner ring of the bearing and the bearing housing both have radial degrees of freedom in the x and y directions; the outer ring and each rolling element each have two radial degrees of freedom and rotational degrees of freedom about their own axis. S3. Calculate the contact force between the outer ring and the bearing housing: The contact deformation between the outer ring and the inner hole of the bearing housing is calculated based on the dynamic model of the bearing housing-bearing system. The Hertz contact stiffness coefficient between the outer ring and the inner hole of the bearing housing is calculated based on the Hertz contact theory. When the contact deformation is <0, the contact force between the outer ring and the bearing housing is 0. When the contact deformation is >0, the contact force between the outer ring and the bearing housing is calculated using the Hertz contact stiffness coefficient and the contact deformation. S4. Calculate the maximum static friction force and maximum static friction torque exerted by the bearing housing on the outer ring, as well as the driving force and driving torque exerted by the rolling elements on the outer ring: Based on the contact force between the bearing outer ring and the bearing housing obtained in step S4, calculate the maximum static friction force and maximum static friction torque exerted by the bearing housing on the outer ring; calculate the driving force and driving torque exerted by the rolling elements on the outer ring based on the driving force model and the driving torque model, respectively. S5. Determine the frictional force and frictional torque acting on the outer ring from the bearing housing: Calculate the relative sliding speed between the outer ring and the bearing housing; When the contact deformation is ≤0, the frictional force and frictional torque applied by the bearing housing to the outer ring are both 0; When the contact deformation is greater than 0 and the relative sliding speed is 0, the static friction force applied by the bearing housing to the outer ring is determined based on the maximum static friction force, maximum static friction torque, driving force and driving torque obtained in step S4. When the contact deformation is greater than 0, the dynamic friction force applied by the bearing housing to the outer ring is calculated based on the relative sliding speed and contact force. By incorporating the contact force, friction force, and friction torque experienced by the outer ring into the dynamic model of the bearing housing-bearing system, a dynamic model of the bearing-bearing housing system containing the bearing outer ring slippage fault is obtained.

2. The mechanical calculation method for bearing outer race runout fault according to claim 1, characterized in that, The initial parameters include: the number N of rolling elements in the rolling bearing. b A rolling bearing consists of an inner ring, rolling elements, and an outer ring, with masses m and m, respectively. i m r and m o The moments of inertia of the rolling elements and the outer ring are respectively J r and J o The diameter of the rolling element is d; the diameters of the inner and outer raceways are D respectively. i and D o The bearing outer diameter is D. out The outer ring length is l b The maximum static friction coefficient and dynamic friction coefficient between the outer ring and the bearing housing are μ s and μ d The loose clearance between the outer ring and the bearing housing is c. b The radial clearance of the bearing is γ.

3. The mechanical calculation method for bearing outer race runout fault according to claim 2, characterized in that, Contact deformation δ op The expression is: In the formula, x p y p x represents the radial vibration displacement of the bearing housing. o y o This represents the radial vibration displacement of the outer ring of the bearing. Hertzian contact stiffness coefficient k op The calculation expression is: Contact force F between the bearing outer ring and the bearing housing p The expression is:

4. The mechanical calculation method for bearing outer race runout fault according to claim 2, characterized in that, Maximum static friction force F fmax Maximum static friction torque T fmax The expressions are as follows: F fmax =μ s F p ,T fmax =0.5D out μ s F p ; In the formula, F p This refers to the contact force between the outer ring of the bearing and the bearing housing. The driving force F of the outer ring o and driving torque T o The expression is: in, The frictional force between the j-th rolling element and the outer ring is expressed as: In the formula, Let be the coefficient of friction between the j-th rolling element and the outer raceway. Let be the relative sliding speed between the j-th rolling element and the outer raceway. The normal contact force between the j-th rolling element and the outer raceway is expressed as follows: In the formula, These are the radial vibration displacement and rotation angle of the j-th rolling element, respectively; denoted as , where is the contact stiffness between the j-th rolling element and the outer ring; p is the load-deformation coefficient, which is 10 / 9 for cylindrical roller bearings and 3 / 2 for ball bearings. ω represents the contact deformation between the j-th rolling element and the outer ring. c Let be the angular velocity of the rolling element's revolution. Let j be the angular position of the j-th rolling element, and its expressions are as follows: In the formula, ω is the initial position azimuth angle of the first rolling element; i and ω o These are the rotational speeds of the inner and outer rings of the bearing, respectively.

5. The mechanical calculation method for bearing outer race runout fault according to claim 2, characterized in that, The relative sliding speed Δv between the outer ring and the bearing housing op The expression is: Where β is the position angle when the outer ring contacts the bearing housing, and its expression is: When δ op >0 and Δv op When F = 0, the frictional force F t and frictional torque T t They are respectively: When contact deformation Δv op When the dynamic friction force F applied by the bearing housing to the outer ring is greater than 0, t and frictional torque T t The expressions are as follows: In the formula, F p This refers to the contact force between the outer ring of the bearing and the bearing housing. The dynamic model expression for the bearing housing-bearing system with outer race slippage fault is as follows: In the formula, M, C, and K are the system mass matrix, damping matrix, and stiffness matrix, respectively; U, These represent the system's displacement vector, velocity vector, and acceleration vector, respectively; F represents the system's net external force vector; the expressions for each matrix are: In the formula, M S M I M R M O M P These represent the mass matrices of the shaft, bearing inner ring, rolling elements, outer ring, and bearing housing, respectively; C I C O C P The damping matrices for the inner ring-rolling element, outer ring-rolling element, and bearing housing, respectively, are represented by K; S and K P These are the stiffness matrices of the shaft and the support stiffness matrix of the bearing housing, respectively; K B and C B These represent the bearing's support stiffness and damping matrix, respectively; F I F O These are the contact force and friction force vectors between the inner ring and the rolling element, and between the outer ring and the rolling element, respectively; F P F represents the vector of contact and friction forces between the bearing outer ring and the bearing housing. U and F R The vectors are, in order, the unbalanced force vector and the radial load vector of the rotating shaft; G S G I G R G O G P Let C represent the gravity vectors of the shaft, inner bearing ring, rolling element, outer ring, and bearing housing, respectively; S The damping matrix of the rotating shaft is expressed as: C S =α1M S +β1K S In the formula, α1 and β1 are Rayleigh damping coefficients.

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