A method and system for modeling the early failure evolution of a rolling bearing

Abstract

The application provides a kind of early fault evolution dynamics modeling method and system of rolling bearing, include the following steps: step one: set the geometric parameters of fault area and node name;Step two: establish the control equation of the fault evolution with randomness and irreversibility;Step three: establish the early fault evolution model between rolling body and fault area;Step four: build the early fault evolution dynamics model between rolling body and outer track fault;Step five: establish the early fault evolution dynamics model between rolling body and inner track fault;Step six: establish the lumped parameter model of rolling bearing as a whole;Step seven: based on energy contribution method, establish the early fault evolution dynamics model of rolling bearing;Step eight: write the code of dynamics model, solve the dynamics model using Newmark-β method.The application solves the shortcomings of high experimental cost, cannot detailedly show the early fault evolution process and evolution characteristics in rolling bearing, etc.

Description

Technical Field

[0001] This invention relates to the technical field of rolling bearing dynamics modeling, and particularly to a dynamics modeling method and system for the early failure evolution of rolling bearings. Background Technology

[0002] Rolling bearings, as power transmission components, are widely used in the electric propulsion systems of inland waterway vessels, unmanned vessels, and underwater vehicles. When a bearing fails, it directly affects the vessel's operational efficiency, increases vibration and noise, reduces survivability, and can even cause irreparable damage. Therefore, establishing a dynamic model that can accurately represent the early failure evolution of rolling bearings is of great significance for timely detection of potential faults. This model can solve problems such as high experimental costs, inability to accurately depict the evolution process of early failures, and inability to effectively simulate the characteristics of early failure evolution. Summary of the Invention

[0003] In view of this, the purpose of this invention is to provide a modeling method that can display the early failure evolution in rolling bearings in detail. It not only has the characteristics of accuracy, detail, practicality and pertinence, but also has the advantages of cost saving and convenient research. It can provide new ideas and methods for fault diagnosis of rolling bearings.

[0004] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0005] A dynamic modeling method for early failure evolution of rolling bearings includes the following steps:

[0006] Step 1: Set the location and geometric parameters of the fault area in the bearing, determine the critical point of the fault area, and clarify the actual constraint state of the rolling bearing during installation;

[0007] Step 2: Based on the evolution characteristics of early bearing failures, determine the evolution mode of early failures, quantify the degree of failure deterioration, and establish the control equations for the evolution of early failures.

[0008] Step 3: Taking the contact process between the rolling element and the fault area as the research object, establish an early fault evolution model between the rolling element and the fault area based on the control equation of early fault evolution and the non-smooth collision vibration system;

[0009] Step 4: Based on the established fault evolution model and the constraint method of the outer track, establish an early fault evolution model between the rolling element and the fault area when the outer track fails.

[0010] Step 5: Based on the established fault evolution model and the motion mode of the inner track, establish an early fault evolution model between the rolling element and the fault area when the inner track fails;

[0011] Step 6: Treat the rolling bearing as a stiffness-mass model, establish a Cartesian coordinate system, set the stress state of the bearing after loading, and derive the energy contributions of the inner ring, outer ring, rolling elements, shaft, and elastic deformation respectively.

[0012] Step 7: Derive the energy contribution expressions of the early failure evolution models of the inner and outer rings respectively. Using the energy contribution method, integrate the evolution models of early failures of the inner and outer rings into the overall dynamic model of the rolling bearing to establish a nonlinear dynamic model of early failure evolution of the rolling bearing.

[0013] Step 8: Solve the nonlinear dynamic model of early failure evolution of rolling bearings.

[0014] Furthermore, in step one, angular position is used to represent the location of the fault in the bearing, and the critical points of the fault are defined as the starting sidewall and the ending sidewall. The outer ring of the rolling bearing is fixed on the bearing housing, and the inner ring rotates together with the shaft.

[0015] Furthermore, in step two, a random function is used to simulate the step size of fault evolution, and the control equation for early fault evolution is as follows:

[0016] Δl=Δl+x (Δl≥0)

[0017] Where Δl is the distance between the starting sidewall and the ending sidewall, the initial value of Δl is 0, x=rand(a1,a2) is the step size of fault evolution, and a1 and a2 are the upper and lower limits of the random function, respectively.

[0018] Furthermore, in step three, the contact between the rolling element and the fault area is a typical rigid collision in a non-smooth collision vibration system. When the rolling element passes through the fault area, it will generate the following two motion systems in a reciprocating sequence:

[0019] (3) A three-dimensional motion system consisting of an inner ring, an outer ring, and rolling elements:

[0020]

[0021] Where M, C, and K are the mass matrix, damping matrix, and stiffness matrix, respectively, X is the displacement matrix, and F is the external load matrix, and their expressions are as follows:

[0022]

[0023] Where m i+r The sum of the masses of the shaft and the inner ring; m jLet be the mass of the rolling element; P1 and P2 be the loads on the inner ring and the rolling element, respectively; k1 and k2 be the stiffness between the inner ring and the rolling element, and between the outer ring and the rolling element, respectively; c1 and c2 be the damping between the inner ring and the rolling element, and between the outer ring and the rolling element, respectively; ω and τ be the angular velocity and the initial phase, respectively; x1 and x2 be the displacements of the inner ring and the rolling element, respectively.

[0024] (4) A two-dimensional rigid collision system consisting of rolling elements and inner or outer rings, where the rolling elements are in contact with the end sidewall. This motion system is represented by a rigid collision vibration system with the coefficient of restitution R.

[0025] The contact system between the rolling element and the fault area is a periodic system, and its periodic expression is: x1(0)=x1(2π / ω), x2(0)=x2(2π / ω),

[0026] Where ω is the angular velocity of the rolling element as it passes through the fault area, and x1 and x2 represent the displacements of the inner ring and the rolling element, respectively. and These represent the speeds of the inner ring and the rolling element, respectively. This represents the velocity of the rolling body after the collision, where π is the circumference ratio.

[0027] Furthermore, in step four, the outer track of the rolling bearing is fixed to the bearing housing, and the velocity and acceleration on the outer track are both 0. When the outer track fails, the dynamic model of the early failure evolution between the rolling element and the failure area is as follows:

[0028]

[0029] in and x1 represents the velocity of the rolling element before and after the collision, x2 represents the displacement of the rolling element in the fault region, and R represents the recovery coefficient.

[0030] Furthermore, in step five, the inner track of the rolling bearing engages with the shaft and rotates together with it. When the inner track fails, the dynamic model of the early failure evolution between the rolling element and the failure area is as follows:

[0031]

[0032] in, and These represent the speeds of the inner rings after the collision and before the collision, respectively. and These represent the velocities of the rolling element before and after the collision, respectively.

[0033] Furthermore, in step six, the rolling bearing is simplified into a stiffness-mass model, the outer ring is fixed, and a Cartesian coordinate system is established with the center of the bearing's large end face as the origin, using an included angle α. j ρ represents the position of the rolling element in the bearing after loading. j x represents the distance between the center of the scroll body and the center of the outer ring after loading. in and y in These represent the offset distances of the inner ring and the shaft after loading, respectively. The energy contribution expressions for the rolling element, inner ring, outer ring, and elastic deformation are derived respectively.

[0034] Furthermore, in step seven, using the Cartesian coordinate system as a reference, the energy contribution expressions for the established early fault evolution models of the inner and outer orbits are derived respectively:

[0035] (3) Energy contribution expression of the early fault evolution model of the outer orbit:

[0036]

[0037] Where m rotor The mass of the shaft is represented by m. in For the quality of the inner ring, and These represent the velocity components of the inner track on the x-axis and y-axis respectively when the outer track fails; and This represents the velocity components of the j-th rolling element on the x-axis and y-axis, respectively;

[0038] (4) Energy contribution expression of the early fault evolution model of the inner orbit:

[0039]

[0040] in and These represent the velocity components of the inner ring on the x-axis and y-axis respectively when the inner track fails; and This represents the velocity components of the j-th rolling element on the x-axis and y-axis, respectively;

[0041] By summing the energy contribution expressions for the rolling element, inner ring, outer ring, elastic deformation, and the early failure evolution models of the inner and outer rings, the dynamic models of early failure evolution of the inner and outer rings are effectively integrated. Substituting the summed expressions into the Lagrange equations, the ρ values ​​relative to the generalized coordinate system are calculated. j x in and y in The differential equations are then used to obtain the nonlinear dynamic model of early failure evolution in rolling bearings, as shown in the following expression:

[0042] Where F u Centrifugal force, g is the acceleration due to gravity, δ in and δ out These represent the contact deformation amounts when the rolling elements contact the inner and outer tracks, respectively, where Z is the number of rolling elements and λ is the number of rolling elements. out and λ in These are the control parameters for outer and inner track failures, respectively, χ. j Let j be the distance from the center of the j-th rolling element to the center of the inner track. Let W be the second derivative of the distance between the center of the rolling element and the center of the outer ring after loading, and let W be the external load. and These represent the acceleration components of the inner ring on the x-axis and y-axis respectively when the outer track fails; and This represents the acceleration components of the j-th rolling element along the x-axis and y-axis, respectively. and These represent the acceleration components of the inner ring on the x-axis and y-axis respectively when the inner track fails.

[0043] Furthermore, in step eight, the relevant parameters of the bearing and the Newmark-β method are set, MATLAB code is written based on the derived dynamic model, simulation calculations are performed, calculation results are collected, and the evolution process and deterioration degree of early faults are determined.

[0044] This invention also provides a dynamic modeling system for the early failure evolution of rolling bearings, comprising:

[0045] Module 1: It sets the location and geometric parameters of the fault area in the bearing, determines the critical point of the fault area, and clarifies the actual constraint state of the rolling bearing during installation.

[0046] Module 2: Based on the evolution characteristics of early bearing failures, determine the evolution mode of early failures, quantify the degree of failure deterioration, and establish the control equations for the evolution of early failures.

[0047] Module 3: Taking the contact process between the rolling element and the fault region as the research object, an early fault evolution model between the rolling element and the fault region is established based on the control equation of early fault evolution and the non-smooth collision vibration system.

[0048] Module 4: Based on the established fault evolution model and the constraint method of the outer track, establish an early fault evolution model between the rolling element and the fault area when the outer track fails.

[0049] Module 5: Based on the established fault evolution model and the motion mode of the inner track, establish an early fault evolution model between the rolling elements and the fault area when the inner track fails;

[0050] Module Six: Treat the rolling bearing as a stiffness-mass model, establish a Cartesian coordinate system, set the stress state of the bearing after loading, and derive the energy contributions of the inner ring, outer ring, rolling elements, shaft, and elastic deformation respectively.

[0051] Module 7: Derive the energy contribution expressions of the early failure evolution models of the inner and outer rings respectively. By using the energy contribution method, integrate the evolution models of early failures of the inner and outer rings into the overall dynamic model of the rolling bearing, and establish a nonlinear dynamic model of early failure evolution of the rolling bearing.

[0052] Step 8: Solve the nonlinear dynamic model of early failure evolution of rolling bearings.

[0053] Compared with the prior art, the beneficial effects of the present invention are:

[0054] 1. The dynamic model of this invention more realistically demonstrates the evolution characteristics of early failures.

[0055] 2. The dynamic model of this invention effectively integrates the lumped parameter model of rolling bearings and the early fault evolution model of the fault region by using the energy contribution method.

[0056] 3. The dynamic model of this invention can effectively and vividly express the evolution process of early failures, and can also predict the degree of deterioration of early failures.

[0057] 4. The dynamic model of this invention can be used to calculate the vibration signal of early fault evolution for different bearing models and different fault types, and has very good universality.

[0058] 5. The dynamic model of this invention solves the problems of high experimental cost and inability to show the evolution process of early faults in detail. Attached Figure Description

[0059] Figure 1 A simplified diagram of early-stage external track faults according to the present invention;

[0060] Figure 2 A simplified diagram of early track faults in this invention;

[0061] Figure 3 This is a simplified schematic diagram of the bearing of the present invention;

[0062] Figure 4 This is a schematic diagram of the calculation process of the present invention;

[0063] Figure 5 The spectrum and time-domain plots calculated for this invention;

[0064] Figure 6 The above are the measured spectrum and time domain diagrams of this invention.

[0065] Wherein, 1-inner ring, 2-outer ring, 3-rolling element, 4-outer ring center, 5-starting sidewall, 6-ending sidewall, 7-rigid collision point, 8-inner ring track after loading, 9-inner track center after loading, α j - Angular position of the j-th rolling element, β - Angular position of the outer ring fault center. Detailed Implementation

[0066] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, many other embodiments obtained by those skilled in the art without creative effort are all within the scope of protection of the present invention.

[0067] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0068] Example 1

[0069] like Figure 4 As shown, this invention provides a dynamic modeling method for the early failure evolution of rolling bearings. First, the geometric parameters of the fault region and the constraint state of the bearing are set, and the critical points of the fault region are reasonably divided. A dynamic model of the early failure evolution between the rolling element and the fault region is established when the inner and outer rings fail, including inner ring 1, outer ring 2, rolling element 3, initial sidewall 5, and final sidewall 6. Next, the energy contribution expressions for the early failure evolution dynamic models of the inner ring, outer ring, rolling element, inner ring, and outer ring are derived, as well as the energy contribution expression for elastic deformation. The energy contribution method is used to couple the early failure evolution model into the dynamic model of the rolling bearing. Finally, the dynamic model of the early failure evolution of the rolling bearing is derived using the Lagrange equation. The relevant parameters of the bearing and the Newmark-β method are set, and different loads are applied to simulate the bearing's working environment. Simulation calculations are performed using Matlab code to obtain the vibration signals during the early failure evolution process of the rolling bearing. The specific implementation steps of this invention are as follows:

[0070] Step 1: Set the bearing's geometric parameters: The masses of the inner ring, shaft, outer ring, and rolling elements are respectively expressed in m. in m rotor m out and m jThe stiffness between the inner ring and the rolling elements, and between the outer ring and the rolling elements, are represented by k1 and k2, respectively. The damping between the inner ring and the rolling elements, and between the outer ring and the rolling elements, is represented by c1 and c2, respectively. The outer ring remains fixed, while the inner ring is interference-fitted with the shaft and rotates with it. The critical points of the fault region are the starting sidewall and the ending sidewall, respectively. The starting edge of the fault region is named starting sidewall 5, and the ending edge of the fault region is named ending sidewall 6.

[0071] Step 2: Based on the randomness of fault evolution, a random function x = rand(a1,a2) is used to simulate the step size of fault evolution over time. The iterative formula for fault evolution is: Δl = Δl + x (Δl ≥ 0), where Δl is the quantized value of fault evolution, and its initial value is 0.

[0072] Step 3: Rolling bearings rotate at high speeds and have high rigidity. The collision between the rolling elements and the fault area is a typical rigid collision. During the entire contact process, two different motion systems will be generated sequentially:

[0073] (1) When the rolling element is between the starting sidewall and the ending sidewall (before contacting the ending sidewall), the three-dimensional motion system consisting of the inner ring, outer ring, and rolling element is expressed as follows:

[0074]

[0075] The expressions for M, C, K, X, and F are as follows:

[0076]

[0077] Where m in and m j ω represents the mass of the inner ring, outer ring, and rolling element, respectively; P1 and P2 represent the loads on the inner ring and rolling element, respectively; k1 and k2 represent the stiffness between the inner ring and the rolling element, and between the outer ring and the rolling element, respectively; c1 and c2 represent the damping between the inner ring and the rolling element, and between the outer ring and the rolling element, respectively; ω and τ represent the angular velocity and the initial phase, respectively; x1 and x2 represent the displacements of the inner ring and the rolling element, respectively.

[0078] (2) When the rolling element contacts the end sidewall, the rolling element will undergo a two-dimensional rigid collision with the end sidewall. This process can be represented by a rigid collision vibration system with a restoring coefficient R. The two-dimensional rigid collision system consists of the rolling element and the inner ring or the rolling element and the outer ring. The expression of the two-dimensional rigid collision system is different under different constraint conditions, and specific problems need to be analyzed specifically.

[0079] Each time the rolling element rotates, it will make contact with the fault area once, and this process repeats cyclically. Therefore, the contact between the rolling element and the fault area is a periodic system, and its periodic expression is: x1(0)=x1(2π / ω), x2(0)=x2(2π / ω),

[0080] Where ω is the angular velocity of the rolling element as it passes through the fault area, and x1 and x2 represent the displacements of the inner ring and the rolling element, respectively. and These represent the speeds of the inner ring and the rolling element, respectively. This indicates the velocity of the rolling element after the collision.

[0081] Step Four: As Figure 1 As shown, when the outer ring of the rolling bearing fails, since the outer ring is fixed to the bearing housing, the velocity and acceleration on the outer track are both zero. The dynamic model of the early failure evolution of the outer track is as follows:

[0082]

[0083] in and x1 represents the velocity of the rolling element before and after the collision, x2 represents the displacement of the rolling element in the fault region, and R represents the recovery coefficient.

[0084] Step 5: As Figure 2 As shown, when the inner ring of a rolling bearing fails, it will rotate along with the shaft, thus the inner raceway possesses a certain velocity or acceleration. The dynamic model for the early failure evolution of the inner raceway is as follows:

[0085]

[0086] in, and These represent the speeds of the inner rings after the collision and before the collision, respectively. and These represent the velocities of the rolling element before and after the collision, respectively.

[0087] Step Six: Derive the energy contribution expressions for the rolling elements, inner ring, outer ring, and elastic deformation in the bearing, simplifying the rolling bearing into a stiffness-mass model (e.g., ...). Figure 3 As shown), the outer ring is fixed, and a Cartesian coordinate system is established with the center of the bearing's large end face as the origin, using an included angle α. j This indicates the position of the rolling elements in the bearing after loading, and θ represents the angular difference between the two rolling elements. ρ is used in the derivation. j x represents the distance between the center of the scroll body and the center of the outer ring after loading. in and y inThese represent the offset distances of the inner ring and the shaft after loading, respectively. Furthermore, the kinetic and potential energy expressions for the rolling element, inner ring, and outer ring are derived, as is the potential energy expression for elastic deformation.

[0088] Step 7: Using the Cartesian coordinate system established in Step 6 as a reference, derive the energy contribution expressions for the early failure evolution models of the inner and outer orbits at the collision point:

[0089] (1) Energy contribution expression of the early fault evolution model of the outer orbit:

[0090]

[0091] in and These represent the velocity components of the inner track on the x-axis and y-axis respectively when the outer track fails; and This represents the velocity components of the j-th rolling element on the x-axis and y-axis, respectively.

[0092] (2) Energy contribution expression of the early fault evolution model of the inner track:

[0093]

[0094] in and These represent the velocity components of the inner ring on the x-axis and y-axis respectively when the inner track fails; and This represents the velocity components of the j-th rolling element on the x-axis and y-axis, respectively.

[0095] By summing the energy contribution expressions for the rolling element, inner ring, outer ring, elastic deformation, and early failure evolution models of the inner and outer rings, this method can effectively integrate the dynamic models of early failure evolution of the inner and outer rings. Substituting the summed expressions into the Lagrange equations, the energy contributions of ρ relative to the generalized coordinate system are calculated. j x in and y in The differential equations are then used to obtain the nonlinear dynamic model of early failure evolution in rolling bearings, as shown in the following expression:

[0096]

[0097] Where F u Centrifugal force, g is the acceleration due to gravity, δ in and δ out These represent the contact deformation amounts when the rolling elements contact the inner and outer tracks, respectively, where Z is the number of rolling elements and λ is the number of rolling elements. out and λ in These are the control parameters for outer and inner track failures, respectively, χ. jLet j be the distance from the center of the j-th rolling element to the center of the inner track. Let W be the second derivative of the distance between the center of the rolling element and the center of the outer ring after loading, and let W be the external load. and These represent the acceleration components of the inner ring on the x-axis and y-axis respectively when the outer track fails; and This represents the acceleration components of the j-th rolling element along the x-axis and y-axis, respectively. and These represent the acceleration components of the inner ring on the x-axis and y-axis respectively when the inner track fails.

[0098] Step 8: Write MATLAB code based on the derived dynamic model, and solve the dynamic model using the Newmark-β method. Figure 4 The calculation process is set up and solved, and the calculation results are collected to determine the evolution process and deterioration degree of early faults. Taking the LDK UER204 bearing as the research object, the bearing has an inner raceway diameter of 29.30 mm, an outer raceway diameter of 39.80 mm, a rolling element diameter of 7.92 mm, an inner ring mass of 0.7 kg, a rolling element mass of 0.09 kg, a coefficient of restitution of 0.8, a stiffness coefficient of 2.15*10^5, a damping coefficient of 322, a rotational speed of 2500 r / min, and an external load of 6.65 kN, i.e., P1 = 6.65 kN, P2 = 0 N. After simulation calculation, the vibration signal between the rolling element and the fault area and the spectrum after FFT processing can be obtained, as shown below. Figure 5 As shown, Figure 6 The spectrum of the measured vibration dataset under the same conditions is shown.

[0099] Figure 5 and Figure 6 The time-domain plots in the figures show the trend of vibration amplitude as the fault evolves during the early stages of an outer track fault. Both plots show a gradual upward trend in vibration amplitude, with essentially the same trend and very similar amplitude values. The size of the fault during the early evolution process can be obtained through simulation calculations. Figure 5 and Figure 6 The frequency spectrum of the rolling bearing showed the rotational frequency, outer ring fault frequency, and their higher harmonics. The simulation results and the measured characteristic frequencies were very close; the calculated rotational frequency of 37.99 Hz was close to the measured frequency of 36.85 Hz. The calculated outer ring fault frequency of 116 Hz was close to the measured outer ring fault frequency of 114.5 Hz.

[0100] By comparison Figure 5 and Figure 6It can be seen that both the calculated and measured time-domain plots exhibit significant periodic impact vibration, with similar vibration development trends and vibration response amplitudes. The rotational frequency, track fault frequency, and their multiple harmonics in the calculated and measured spectra are consistent. This demonstrates the correctness and effectiveness of the present invention.

[0101] Example 2

[0102] This invention also provides a dynamic modeling system for the early failure evolution of rolling bearings, comprising:

[0103] Module 1: It sets the location and geometric parameters of the fault area in the bearing, determines the critical point of the fault area, and clarifies the actual constraint state of the rolling bearing during installation.

[0104] Module 2: Based on the evolution characteristics of early bearing failures, determine the evolution mode of early failures, quantify the degree of failure deterioration, and establish the control equations for the evolution of early failures.

[0105] Module 3: Taking the contact process between the rolling element and the fault region as the research object, an early fault evolution model between the rolling element and the fault region is established based on the control equation of early fault evolution and the non-smooth collision vibration system.

[0106] Module 4: Based on the established fault evolution model and the constraint method of the outer track, establish an early fault evolution model between the rolling element and the fault area when the outer track fails.

[0107] Module 5: Based on the established fault evolution model and the motion mode of the inner track, establish an early fault evolution model between the rolling elements and the fault area when the inner track fails;

[0108] Module Six: Treat the rolling bearing as a stiffness-mass model, establish a Cartesian coordinate system, set the stress state of the bearing after loading, and derive the energy contributions of the inner ring, outer ring, rolling elements, shaft, and elastic deformation respectively.

[0109] Module 7: Derive the energy contribution expressions of the early failure evolution models of the inner and outer rings respectively. By using the energy contribution method, integrate the evolution models of early failures of the inner and outer rings into the overall dynamic model of the rolling bearing, and establish a nonlinear dynamic model of early failure evolution of the rolling bearing.

[0110] Step 8: Solve the nonlinear dynamic model of early failure evolution of rolling bearings.

[0111] The specific embodiments of the present invention have been described in detail above, but these are merely one example, and the present invention is not limited to the specific embodiments described above. For those skilled in the art, any equivalent modifications and substitutions to the present invention are also within the scope of the present invention. Therefore, all equivalent changes and modifications made without departing from the spirit and scope of the present invention should be covered within the scope of the present invention.

Claims

1. A dynamic modeling method for early failure evolution of rolling bearings, characterized in that, Includes the following steps: Step 1: Set the location and geometric parameters of the fault area in the bearing, determine the critical point of the fault area, and clarify the actual constraint state of the rolling bearing during installation; Step 2: Based on the evolution characteristics of early bearing failures, determine the evolution mode of early failures, quantify the degree of failure deterioration, and establish the control equations for the evolution of early failures. Step 3: Taking the contact process between the rolling element and the fault area as the research object, establish an early fault evolution model between the rolling element and the fault area based on the control equation of early fault evolution and the non-smooth collision vibration system; Step 4: Based on the established fault evolution model and the constraint method of the outer track, establish an early fault evolution model between the rolling element and the fault area when the outer track fails. Step 5: Based on the established fault evolution model and the motion mode of the inner track, establish an early fault evolution model between the rolling element and the fault area when the inner track fails; Step 6: Treat the rolling bearing as a stiffness-mass model, establish a Cartesian coordinate system, set the stress state of the bearing after loading, and derive the energy contributions of the inner ring, outer ring, rolling elements, shaft, and elastic deformation respectively. Step 7: Derive the energy contribution expressions of the early failure evolution models of the inner and outer rings respectively. Using the energy contribution method, integrate the evolution models of early failures of the inner and outer rings into the overall dynamic model of the rolling bearing to establish a nonlinear dynamic model of early failure evolution of the rolling bearing. Step 8: Solve the nonlinear dynamic model of early failure evolution of rolling bearings.

2. The dynamic modeling method for early failure evolution of rolling bearings as described in claim 1, characterized in that: In step one, angular position is used to represent the location of the fault in the bearing. The critical points of the fault are defined as the starting sidewall and the ending sidewall. The outer ring of the rolling bearing is fixed on the bearing housing, and the inner ring rotates with the shaft.

3. The dynamic modeling method for early failure evolution of rolling bearings as described in claim 1, characterized in that: In step two, a random function is used to simulate the step size of fault evolution. The control equation for early fault evolution is as follows: Δl=Δl+x (Δl≥0) Where Δl is the distance between the starting sidewall and the ending sidewall, the initial value of Δl is 0, x=rand(a1,a2) is the step size of fault evolution, and a1 and a2 are the upper and lower limits of the random function, respectively.

4. The dynamic modeling method for early failure evolution of rolling bearings as described in claim 3, characterized in that: In step three, the contact between the rolling element and the fault area is a typical rigid collision in a non-smooth collision vibration system. When the rolling element passes through the fault area, it will generate the following two motion systems in a reciprocating sequence: (1) A three-dimensional motion system consisting of an inner ring, an outer ring, and rolling elements: Where M, C, and K are the mass matrix, damping matrix, and stiffness matrix, respectively, X is the displacement matrix, and F is the external load matrix, and their expressions are as follows: Where m i+r The sum of the masses of the shaft and the inner ring; m j Let be the mass of the rolling element; P1 and P2 be the loads on the inner ring and the rolling element, respectively; k1 and k2 be the stiffness between the inner ring and the rolling element, and between the outer ring and the rolling element, respectively; c1 and c2 be the damping between the inner ring and the rolling element, and between the outer ring and the rolling element, respectively; ω and τ be the angular velocity and the initial phase, respectively; x1 and x2 be the displacements of the inner ring and the rolling element, respectively. (2) A two-dimensional rigid collision system consisting of rolling elements and inner or outer rings, where the rolling elements are in contact with the end sidewall. This motion system is represented by a rigid collision vibration system with the coefficient of restitution R. The contact system between the rolling element and the fault area is a periodic system, and its periodic expression is: x1(0)=x1(2π / ω), x2(0)=x2(2π / ω), Where ω is the angular velocity of the rolling element as it passes through the fault area, and x1 and x2 represent the displacements of the inner ring and the rolling element, respectively. and These represent the speeds of the inner ring and the rolling element, respectively. This represents the velocity of the rolling body after the collision, where π is the circumference ratio.

5. The dynamic modeling method for early failure evolution of rolling bearings as described in claim 4, characterized in that: In step four, the outer track of the rolling bearing is fixed to the bearing housing, and the velocity and acceleration on the outer track are both 0. When the outer track fails, the dynamic model of the early failure evolution between the rolling element and the failure area is as follows: in and x1 represents the velocity of the rolling element before and after the collision, x2 represents the displacement of the rolling element in the fault region, and R represents the recovery coefficient.

6. The dynamic modeling method for early failure evolution of rolling bearings as described in claim 4, characterized in that: In step five, the inner track of the rolling bearing engages with the shaft and rotates together with it. When the inner track fails, the dynamic model of the early failure evolution between the rolling element and the failure area is as follows: in, and These represent the speeds of the inner rings after the collision and before the collision, respectively. and These represent the velocities of the rolling element before and after the collision, respectively.

7. The dynamic modeling method for early failure evolution of rolling bearings as described in claim 1, characterized in that: In step six, the rolling bearing is simplified into a stiffness-mass model, the outer ring is fixed, and a Cartesian coordinate system is established with the center of the bearing's large end face as the origin, using an included angle α. j ρ represents the position of the rolling element in the bearing after loading. j x represents the distance between the center of the scroll body and the center of the outer ring after loading. in and y in These represent the offset distances of the inner ring and the shaft after loading, respectively. The energy contribution expressions for the rolling element, inner ring, outer ring, and elastic deformation are derived respectively.

8. The dynamic modeling method for early failure evolution of rolling bearings as described in claim 7, characterized in that: In step seven, using the Cartesian coordinate system as a reference, the energy contribution expressions of the established early fault evolution models for the inner and outer orbits are derived respectively: (1) Energy contribution expression of the early fault evolution model of the outer orbit: Where m rotor The mass of the shaft is represented by m. in For the quality of the inner ring, and These represent the velocity components of the inner track on the x-axis and y-axis respectively when the outer track fails; and This represents the velocity components of the j-th rolling element on the x-axis and y-axis, respectively; (2) Energy contribution expression of the early fault evolution model of the inner track: in and These represent the velocity components of the inner ring on the x-axis and y-axis respectively when the inner track fails; and This represents the velocity components of the j-th rolling element on the x-axis and y-axis, respectively; By summing the energy contribution expressions for the rolling element, inner ring, outer ring, elastic deformation, and the early failure evolution models of the inner and outer rings, the dynamic models of early failure evolution of the inner and outer rings are effectively integrated. Substituting the summed expressions into the Lagrange equations, the ρ values ​​relative to the generalized coordinate system are calculated. j x in and y in The differential equations are then used to obtain the nonlinear dynamic model of early failure evolution in rolling bearings, as shown in the following expression: Where F u Centrifugal force, g is the acceleration due to gravity, δ in and δ out These represent the contact deformation amounts when the rolling elements contact the inner and outer tracks, respectively, where Z is the number of rolling elements and λ is the number of rolling elements. out and λ in These are the control parameters for outer and inner track failures, respectively, χ. j Let j be the distance from the center of the j-th rolling element to the center of the inner track. Let W be the second derivative of the distance between the center of the rolling element and the center of the outer ring after loading, and let W be the external load. and These represent the acceleration components of the inner ring on the x-axis and y-axis respectively when the outer track fails; and This represents the acceleration components of the j-th rolling element along the x-axis and y-axis, respectively. and These represent the acceleration components of the inner ring on the x-axis and y-axis respectively when the inner track fails.

9. The dynamic modeling method for early failure evolution of rolling bearings as described in claim 1, characterized in that: In step eight, the relevant parameters of the bearing and the Newmark-β method are set, MATLAB code is written based on the derived dynamic model, simulation calculations are performed, calculation results are collected, and the evolution process and deterioration degree of early faults are determined.

10. A dynamic modeling system for early failure evolution of rolling bearings, characterized in that, include: Module 1: It sets the location and geometric parameters of the fault area in the bearing, determines the critical point of the fault area, and clarifies the actual constraint state of the rolling bearing during installation. Module 2: Based on the evolution characteristics of early bearing failures, determine the evolution mode of early failures, quantify the degree of failure deterioration, and establish the control equations for the evolution of early failures. Module 3: Taking the contact process between the rolling element and the fault region as the research object, an early fault evolution model between the rolling element and the fault region is established based on the control equation of early fault evolution and the non-smooth collision vibration system. Module 4: Based on the established fault evolution model and the constraint method of the outer track, establish an early fault evolution model between the rolling element and the fault area when the outer track fails. Module 5: Based on the established fault evolution model and the motion mode of the inner track, establish an early fault evolution model between the rolling elements and the fault area when the inner track fails; Module Six: Treat the rolling bearing as a stiffness-mass model, establish a Cartesian coordinate system, set the stress state of the bearing after loading, and derive the energy contributions of the inner ring, outer ring, rolling elements, shaft, and elastic deformation respectively. Module 7: Derive the energy contribution expressions of the early failure evolution models of the inner and outer rings respectively. By using the energy contribution method, integrate the evolution models of early failures of the inner and outer rings into the overall dynamic model of the rolling bearing, and establish a nonlinear dynamic model of early failure evolution of the rolling bearing. Step 8: Solve the nonlinear dynamic model of early failure evolution of rolling bearings.

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