A method for modeling the vibration of rolling bearings considering non-ideal Hertzian contact

Abstract

This invention relates to a method for modeling the vibration of rolling bearings considering non-ideal Hertzian contact, belonging to the field of bearing vibration modeling technology, and includes the following steps: S1: Obtaining the basic geometric and material parameters of the rolling bearing; S2: Calculating the angular range of the load zone of the rolling bearing; S3: Calculating the geometric parameters of the contact between the rolling elements and the healthy raceway; S4: Calculating the mechanical parameters of the contact between the rolling elements and the healthy raceway; S5: Calculating the cage angular velocity parameters; S6: Calculating the angular position and angular velocity parameters of the rolling element's circumferential motion; S7: Calculating the deformation and contact force generated by all rolling elements in contact with the healthy raceway of the bearing; S8: Calculating the time-varying mechanical parameters implied by the contact between the rolling elements and the defect; S9: Dynamic modeling of the vibration excitation mechanism of the rolling bearing defect.

Description

Technical Field

[0001] This invention belongs to the field of bearing vibration modeling technology, and relates to a method for modeling the vibration of rolling bearings that considers non-ideal Hertzian contact. Background Technology

[0002] The service health condition of rolling bearings has a significant impact on the operational stability, accuracy, reliability, vibration, and noise of such equipment. In severe cases, rolling bearing failure can lead to equipment downtime, causing economic losses and even casualties. Therefore, exploring its failure mechanism, elucidating its inherent failure excitation mechanism, and revealing the mapping relationship between its failure mechanism and vibration response are of great significance for establishing rolling bearing failure theory and effective condition monitoring methods.

[0003] Dynamic modeling of rolling bearings based on kinematics, physics, and dynamics can partially replace time-consuming and costly experimental research, reducing reliance on data from conditions where testing is difficult. It enhances our understanding of the mapping mechanism between bearing vibration response and fault excitation mechanisms, solidifies the theoretical foundation for bearing fault diagnosis, and can also fill gaps and establish a theoretical research system for rolling bearing fault excitation mechanisms based on kinematics, collision mechanics, and contact mechanics. This has significant theoretical research value and practical engineering application value.

[0004] Existing rolling bearing dynamics modeling methods all use rectangular notch faults to model actual irregular-shaped defects. That is, the model considers raceway defects as regular shapes such as rectangular notches, which contradicts reality and makes it difficult to objectively and effectively reflect the inherent collision process between the rolling element and the defect, and to reveal the underlying mechanical evolution mechanism. To date, there is a lack of systematic research on more reasonable and effective modeling methods for irregular-shaped defects under actual working conditions. Furthermore, existing rolling bearing dynamics modeling still bases the collision between the rolling element and the defect on perfectly elastic Hertzian contact theory. That is, existing dynamic models, in studying the time-varying mechanical parameters induced by rolling element-defect collisions, are mostly based on Hertzian perfectly elastic contact theory, but in the actual collision process between the rolling element and irregular-shaped defects, there are accompanying hysteresis damping characteristics, resulting in non-ideal Hertzian contact. Currently, there is a lack of research on the evolution mechanism of mechanical parameters inherent in non-ideal Hertzian collisions between rolling elements and irregular-shaped defects. Summary of the Invention

[0005] In view of this, the purpose of this invention is to establish a rolling bearing defect model by parameterizing fault atoms, and to replace the rolling element defect collision with the rolling element-fault atom collision. By applying hysteresis damping theory and collision mechanics, a mechanical parameter evolution mechanism model of the non-ideal Hertzian collision between the rolling element and the irregularly shaped defect is established. Based on the ring assumption theory and the excitation mechanism of the rolling element-irregularly shaped defect collision, a rolling bearing vibration mechanism modeling method considering non-ideal Hertzian collision is proposed. This method aims to improve the accuracy of rolling bearing fault modeling and provide theoretical support for the theoretical research system of rolling bearing fault excitation mechanism based on kinematics, collision mechanics, and contact mechanics.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A method for modeling the vibration of rolling bearings considering non-ideal Hertzian contact includes the following steps:

[0008] S1: Obtain the dimensional parameters of each component of the rolling bearing, as well as the bearing material parameters;

[0009] S2: Based on the external radial load on the rolling bearing, establish the contact force balance equation, and calculate the load zone angle range of the rolling bearing through an iterative method;

[0010] S3: Calculate the contact geometry parameters formed by the contact between the rolling element and the healthy raceway;

[0011] S4: Calculate the contact mechanical parameters between the rolling element and the inner and outer raceways;

[0012] S5: Calculate the angular velocity of the cage rotation;

[0013] S6: Calculate the rotational angular velocity and spin angular velocity of the rolling elements around the center of the outer ring, and calculate the circumferential angular position of all rolling elements;

[0014] S7: Calculate the contact deformation and contact force between the rolling element and the inner and outer raceways using Hertzian contact theory;

[0015] S8: Calculate the time-varying contact force generated by the non-ideal Hertzian contact between the rolling element and the defect;

[0016] S9: Using a concentrated spring-mass model, considering the non-ideal Hertzian contact between the rolling elements and defects, a mechanical equilibrium analysis of the rolling bearing is performed, and a 2-DOF rolling bearing dynamic model is established.

[0017] Furthermore, the dimensional parameters of each component of the rolling bearing mentioned in step S1 include: rolling element radius. Outer radius Inner radius Pitch circle radius Number of rolling elements N band radial clearance C r The bearing material parameters include the elastic modulus E of the inner and outer rings of the bearing. i / o And Poisson's ratio ρ i / o And the elastic modulus E of the rolling element b And Poisson's ratio ρ b .

[0018] Furthermore, step S2 specifically includes the following steps:

[0019] The contact area between the rolling element and the inner and outer rings is divided into two planes: a plane V perpendicular to the bearing and a plane P parallel to the bearing. The principal curvatures of the contact pairs formed by the rolling element and the inner ring, and the rolling element and the outer ring, are calculated in planes V and P, respectively. The contact pair curvature and Σ are also calculated. r and curvature difference S r ; Calculate the equivalent elastic modulus E of the contact between the rolling element and the raceway. q ; Calculate the dimensionless semi-major axis parameter a* and semi-minor axis parameter b* of the contact ellipse formed by the contact between the rolling element and the raceway, the length of the semi-major axis a and the length of the semi-minor axis b of the actual contact ellipse and their corresponding ellipticity parameter κ; Calculate the first-type elliptic integral ξ1 and the second-type elliptic integral ξ2 formed by the contact between the rolling element and the raceway and the outer raceway, respectively.

[0020] Furthermore, step S3 specifically includes the following steps:

[0021] Based on Hertzian contact theory, the contact deformation δ between the rolling element and the inner and outer raceways is calculated using the first and second kind elliptic integrals, ellipticity parameters, curvature parameters, equivalent elastic modulus parameters, and pi of the contact pair formed by the contact between the rolling element and the inner and outer raceways. bi and δ bo Finally, the total equivalent contact stiffness K between the rolling element and the inner and outer raceways is calculated. T :

[0022]

[0023] In the formula, K bi and K bo These represent the contact stiffness between the rolling element and the inner and outer rings, respectively, and n represents the load deformation index;

[0024] According to Hertzian contact theory, the geometric characterization model of the total contact deformation generated by the contact between the rolling element and the healthy inner and outer raceways within the load zone is as follows:

[0025]

[0026] In the formula, X and Y represent the inner circle together with the axis of rotation in the coordinate system. The displacements in the x and y directions, where θ iFor the i-th load region th The circumferential angle of each rolling element when it contacts the inner and outer raceways.

[0027] Furthermore, step S4 specifically includes: applying a given external radial load Q E Establish its relationship with N b K T C r And the mathematical balance formula between n, through trial and error, yields the effective load range angle range [-Φ] of the rolling bearing under external load. z ,Φ z ].

[0028] Furthermore, step S5 specifically includes:

[0029] By bearing speed N s Calculate the angular velocity parameter ω of the cage's circular motion. cage :

[0030]

[0031] In the formula ω s The bearing's rotational angular velocity is expressed as:

[0032] ω s =πN s ×30 -1

[0033] Where α is the rolling bearing load angle.

[0034] Furthermore, step S6 specifically includes:

[0035] Calculate the time-varying angular position parameters of each rolling element by using the circumferential angular velocity of the cage; calculate the angular velocity parameters of the rolling element rotating around the center of the outer ring; calculate the angular velocity parameters of the rolling element rotating around itself.

[0036]

[0037] Where i is the i-th i th Rolling body, For the first rolling body in the coordinate system The initial angle position is given by t, where t is time.

[0038] Furthermore, step S7 specifically includes:

[0039] Calculate the sum of contact forces generated by the contact between the rolling element and the inner and outer raceways using the total equivalent contact stiffness and contact displacement of the rolling element and the inner and outer raceways:

[0040]

[0041] In the formula L i The parameter representing the deformation of the i-th rolling element in contact with the inner and outer raceways within the load zone is mathematically described as follows:

[0042]

[0043] Furthermore, step S8 specifically includes:

[0044] By applying the kinetic energy theorem before and after the collision between the rolling element and the faulty atom, an equilibrium equation is established, yielding an expression for the energy lost during the collision:

[0045]

[0046] In the formula, ΔE represents the energy lost during the rolling element-defect contact process. (a) ΔE represents the total energy after the collision between the rolling element and the faulty atom. (b) This represents the total energy of the rolling element and the faulty atom before they come into contact. and These represent the velocities of the rolling element and the defect atom after the collision, respectively. and These represent the velocities of the rolling element and the defect atom before the collision, respectively.

[0047] The momentum theorem states the following before and after the rolling element collides with the faulty atom:

[0048]

[0049] The energy lost due to the contact between the rolling element and the defect is expressed as:

[0050]

[0051] In the formula V rv The relative velocity between the rolling element and the faulty atom in the collision direction is defined as V. rv =dδ×dt -1 Solving the simultaneous equations, we get λ. d :

[0052]

[0053] In the formula V ra The relative approach velocity of the atoms before the collision of the rolling element fault atoms is expressed as:

[0054]

[0055] V R The collision restitution coefficient between two contacting bodies is defined as:

[0056]

[0057] Considering the maximum deformation when the rolling element and the faulty atom come into contact, Newton's second law is applied to the rolling element and the faulty atom to establish the equivalent mass, contact acceleration, and contact force. The integral of the equivalent relationship over time is obtained and combined with the initial conditions before the collision to solve the mathematical equations between the equivalent mass, relative velocity, relative contact deformation, and force-deformation exponent.

[0058] Using the relative velocity corresponding to the moment of maximum deformation upon contact as input, the functional model of the maximum deformation upon contact between the rolling element and the faulty unit is obtained.

[0059] At the moment of maximum deformation upon contact, the maximum contact force is obtained based on the force-deformation relationship;

[0060] Based on the theory of energy conservation and hysteresis damping, the entire non-perfectly elastic contact process is an energy loss process. The energy lost during the process from contact to maximum deformation is obtained by integrating the hysteresis damping force with respect to the contact deformation.

[0061] Based on the parameters obtained above, a time-varying contact force model for non-ideal Hertzian collision involving irregularly shaped defects of rolling elements is established:

[0062]

[0063] γ i The contact parameters between the rolling element and the faulty atom are expressed as:

[0064]

[0065] Then, during the entire operation of the rolling bearing, the i-th... th The total contact force between each rolling element and the inner and outer raceways is expressed as:

[0066]

[0067] The combined contact force model generated by the contact between all rolling elements and the inner and outer raceways of the rolling bearing within the load zone is expressed as follows:

[0068]

[0069] Furthermore, step S9 specifically includes:

[0070] Taking deep groove ball bearings as the research object, a Cartesian coordinate system is established with the horizontal direction as the x-axis and the vertical direction as the y-axis in the simulation. A concentrated spring-mass model is adopted, and the non-ideal Hertzian contact between the rolling elements and defects is considered. Mechanical equilibrium analysis of the deep groove ball bearing is performed, and parameters of the rolling elements and defects, as well as parameters of the rolling elements within the load zone, are introduced. Based on Newton's second law and the rigid ring assumption theory, a 2-DOF rolling bearing dynamic model is established:

[0071]

[0072] In the formula m eq D represents the equivalent mass of the inner ring and the shaft of the rolling bearing. f W represents the damping coefficient of a rolling bearing system. x and W y These represent the external loads on the rolling bearing in the coordinate system. The load components along the x and y directions.

[0073] The beneficial effects of this invention are as follows: It addresses the problems existing in current methods for modeling rolling bearing fault vibration and provides a robust and accurate method and model for modeling rolling bearing outer raceway fault vibration. Considering that raceway defects are irregular in shape in actual processes, traditional modeling methods assume these defects to be regular in shape, making it difficult to accurately and effectively characterize the bearing vibration characteristics caused by defects in actual processes. This invention proposes a method for establishing a realistic defect model using fault atom parameterization. In existing rolling bearing dynamics modeling methods, the collision between the rolling element and the defect is still based on perfect elasticity under Hertzian contact theory. However, under actual working conditions, during the collision between the rolling element and the irregularly shaped defect, hysteresis damping characteristics accompany the collision. In addition to the Hertzian contact force, there is also a hysteresis damping force during the collision between the rolling element and the defect. This invention establishes the kinematic and mechanical equilibrium equations for the collision between the rolling element and the defect atoms based on collision theory, momentum conservation, and the kinetic energy theorem. By solving for the velocities of the rolling element and the faulty atom before and after the collision, a time-varying contact force model is obtained for the entire process of the rolling element-defect collision, providing a theoretical basis for accurately establishing a rolling bearing fault vibration dynamics model.

[0074] ① This invention uses a series of fault atoms with different radii, radial angle positions, and a certain number to equivalently replace the natural spalling defects of the rolling bearing raceway, and establishes a parameterized mathematical model of the rolling bearing raceway defects. This is beneficial for: (a) multi-parameter synergistic equivalent characterization of rolling bearing defects, facilitating the study of the influence of defect size parameters on bearing vibration response; (b) establishing a mathematical model of the evolution mechanism of time-varying mechanical parameters inherent in the collision process between the rolling element and the defect, and exploring the mapping relationship between the evolution law of time-varying mechanical parameters and the impact vibration response caused by the fault; (c) establishing a more realistic parameterized mathematical model of rolling bearing defects, ultimately improving the accuracy and reliability of the rolling bearing fault vibration mechanism modeling method.

[0075] ② This invention, through the investigation of the physical event of rolling element-defect collision, and based on the concept of hysteresis damping, studies the time-varying mechanical parameter evolution mechanism induced by rolling element-defect collision using collision theory, momentum conservation, kinetic energy theorem, and other theories and methods. It is beneficial in: (a) revealing the evolution law of mechanical parameters inherent in rolling element-defect collision from a mechanistic perspective, and clarifying the mapping relationship between the interaction mechanism of rolling element-defect and the impact vibration response; (b) establishing a mathematical model of the time-varying displacement of the bearing inner ring and shaft caused by rolling element-defect collision; and (c) establishing the intrinsic connection and excitation mechanism between the time-varying mechanical parameter evolution law caused by rolling element-defect collision and the stiffness change of the bearing system.

[0076] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0077] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0078] Figure 1 Flowchart for modeling rolling bearing vibration considering non-ideal Hertzian contact;

[0079] Figure 2 This is a schematic diagram illustrating the principle of radial displacement variation of the rolling element.

[0080] Figure 3 This is a schematic diagram illustrating the contact between a rolling element and a defect.

[0081] Figure 4 In the image, (a) shows the simulated vibration acceleration signal, and (b) shows the vibration acceleration signal obtained from the actual test.

[0082] Figure 5 In the image, (a) is the envelope spectrum of the simulated vibration acceleration signal, and (b) is the envelope spectrum of the vibration acceleration signal obtained from the actual test.

[0083] Figure 6 In the table, (a) represents a single simulated vibration shock response, (b) represents the time-frequency distribution characteristics of a single simulated vibration shock response, (c) represents the measured vibration shock signal, and (d) represents the time-frequency distribution characteristics of a single measured vibration shock signal. Detailed Implementation

[0084] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0085] It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Therefore, the drawings only show the components related to the present invention and are not drawn according to the actual number, shape and size of the components in the actual implementation. In the actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0086] In the following description, numerous details are explored to provide a more thorough explanation of embodiments of the invention. However, it will be apparent to those skilled in the art that embodiments of the invention may be practiced without these specific details. In other embodiments, well-known structures and devices are shown in block diagram form rather than in detail to avoid obscuring embodiments of the invention.

[0087] Example 1: As Figure 1-6 As shown, a method for quantitatively estimating raceway defects in the outer ring of a rolling bearing includes:

[0088] Basic geometric and material parameters of rolling bearings: The dimensional parameters of each component of the rolling bearing and the bearing material parameters are obtained, as shown in Table 1.

[0089] Table 1

[0090]

[0091] Calculation of the load zone angle range of rolling bearings: Based on the external radial load on the rolling bearing, establish the contact force balance equation, and calculate the load zone angle range of the rolling bearing through an iterative method.

[0092] Calculation of contact geometry parameters between rolling elements and healthy raceways: Calculate the contact geometry parameters formed by the contact between the rolling elements and healthy raceways, such as contact radius and contact curvature.

[0093] Calculation of contact mechanical parameters between rolling elements and healthy raceways: Calculate the contact mechanical parameters between rolling elements and inner and outer raceways, such as contact stiffness and contact deformation.

[0094] Cage angular velocity parameter calculation: Calculate the angular velocity of cage rotation.

[0095] Calculation of rolling element circumferential motion angular position and angular velocity parameters: Calculate the rotational angular velocity and spin angular velocity of the rolling element around the center of the outer ring, and calculate the circumferential angular position of all rolling elements.

[0096] Calculation of deformation and contact force generated by the contact between all rolling elements and the bearing healthy raceway: The contact deformation and contact force between the rolling elements and the inner and outer raceways are calculated using Hertzian contact theory.

[0097] Calculation of time-varying mechanical parameters implied by the contact between the rolling element and the defect: based on Figure 3 The physical model of rolling element-defect contact is shown, and the time-varying contact force generated by the non-ideal Hertzian contact between the rolling element and the defect is calculated.

[0098] Dynamic Modeling of Vibration Excitation Mechanism of Rolling Bearing Defects: Taking a deep groove ball bearing as an example, a Cartesian coordinate system is established in the simulation with the horizontal direction as the x-axis and the vertical direction as the y-axis. A concentrated spring-mass model is adopted, considering the non-ideal Hertzian contact between the rolling elements and the defects. Mechanical equilibrium analysis is performed on the deep groove ball bearing, introducing the contact parameters between the rolling elements and the defects, as well as the parameters of the rolling elements within the load zone. Based on Newton's second law and the rigid ring assumption theory, a 2-DOF dynamic model of the rolling bearing is established.

[0099] Comparative analysis and verification of simulated and measured vibration response results: Simulation was performed using Matlab software, setting the simulation time, initial values ​​of vibration displacement and velocity, damping parameters of the rolling bearing system, external horizontal and vertical radial loads on the rolling bearing, and the time step. The ode45 differential equation solver was used to obtain the established 2-DOF differential equations, yielding the vibration displacement and velocity. Vibration acceleration was calculated through differentiation. The time-domain and frequency characteristics of the vibration acceleration response were solved and compared with those of the measured signal. The similarity and differences between the impact response caused by rolling bearing defects in the simulated and measured signals were analyzed. The time-frequency distribution characteristics of the vibration signals under measured and simulated conditions were compared. Furthermore, the impact response characteristics caused by the rolling element entering and exiting the defect area were compared between the simulated and measured signals. These four aspects verify the correctness of the rolling bearing vibration modeling method considering non-Hertzian contact proposed in this patent.

[0100] Example 2:

[0101] As attached Figures 1-6 As shown in Figure 1 and Table 1, the results are basically the same as in Example 1, except that:

[0102] The specific implementation steps for the basic geometric and material parameters of the rolling bearing are as follows: This patent takes the 6205 bearing as an example, and its geometric dimensions are listed in Table 1. For ease of description, the radius of the rolling element is defined. Outer radius Inner radius Pitch circle radius Number of rolling elements N b and radial clearance C r By examining the materials used in its manufacture, the elastic modulus E of the bearing's inner and outer rings was obtained. i / o And Poisson's ratio ρ i / o And the elastic modulus E of the rolling element b And Poisson's ratio ρ b As listed in Table 1.

[0103] The specific implementation steps for the contact geometry parameters between the rolling element and the healthy raceway are as follows: Divide the contact between the rolling element and the inner and outer rings into two planes perpendicular to the bearing (plane V) and parallel to the bearing (plane P). Calculate the principal curvatures of the contact pairs formed by the rolling element (contact a) and the inner ring (contact b) and the rolling element and the outer ring (contact b) in planes V and P, respectively, as well as the contact pair curvature and Σ. r and curvature difference S r ; Calculate the equivalent elastic modulus E of the contact between the rolling element and the raceway. q ; Calculate the dimensionless semi-major axis parameter a* and semi-minor axis parameter b* of the contact ellipse formed by the contact between the rolling element and the raceway, the length of the semi-major axis a and the length of the semi-minor axis b of the actual contact ellipse and their corresponding ellipticity parameter κ; Calculate the first-type elliptic integral ξ1 and the second-type elliptic integral ξ2 formed by the contact between the rolling element and the raceway and the outer raceway, respectively.

[0104] The specific implementation steps for the contact mechanical parameters between the rolling element and the healthy raceway are as follows: Based on Hertzian contact theory, the contact deformation δ formed between the rolling element and the inner and outer raceways is calculated using the first and second kind elliptic integrals, ellipticity parameters, curvature parameters, equivalent elastic modulus parameters, and pi of the contact pair formed by the contact between the rolling element and the inner and outer raceways. bi and δ bo Finally, the total equivalent contact stiffness K between the rolling element and the inner and outer raceways is calculated. T .

[0105]

[0106] In the formula, K bi and K bo These represent the contact stiffness between the rolling element and the inner and outer rings, respectively, and n represents the load deformation index (n = 1.5 for ball bearings).

[0107] Based on Hertzian contact theory, Figure 2 The schematic diagram of the rolling element reaching contact shown illustrates that, within the load zone, the geometric model representing the total contact deformation resulting from the contact between the rolling element and the defect-free inner and outer raceways can be expressed as follows:

[0108]

[0109] In the formula, X and Y represent the inner circle together with the axis of rotation in the coordinate system. The displacement (offset) in the x and y directions, where θ i For the i-th load region th The circumferential angle of each rolling element when it contacts the inner and outer raceways.

[0110] The specific implementation steps for the load zone angle range are as follows: Using a given external radial load Q... E Establish its relationship with N b K T C r And the mathematical balance formula between n, through trial and error, yields the effective load range angle range [-Φ] of the rolling bearing under external load. z ,Φ z To accurately establish a rolling bearing defect vibration model that conforms to actual constraints.

[0111] The specific implementation steps for the cage angular velocity parameter are as follows: By controlling the bearing rotational speed N... s Calculate the angular velocity parameter ω of the cage's circular motion. cage .

[0112]

[0113] In the formula ω s The angular velocity of the bearing rotation can be expressed as: ω s =πN s ×30 -1 α is the rolling bearing load angle (the contact angle between the bearing and the raceway), as listed in Table 1.

[0114] The specific implementation steps for the angular position and angular velocity parameters of the rolling element's circumferential motion are as follows: calculate the time-varying angular position parameters of each rolling element by using the circumferential angular velocity of the cage; calculate the angular velocity parameters of the rolling element rotating around the center of the outer ring; calculate the angular velocity parameters of the rolling element rotating around itself.

[0115]

[0116] Where i is the i-th i th Rolling body, For the first rolling body in the coordinate system The initial angle position is given by t, where t is time.

[0117] The specific implementation steps for the contact deformation and contact force between all rolling elements and the bearing healthy raceway are as follows: calculate the sum of the contact forces generated by the contact between the bearing rolling elements and the inner and outer raceways by using the total equivalent contact stiffness and contact displacement of the rolling elements and the inner and outer raceways.

[0118]

[0119] In the formula L i The parameter representing the deformation of the i-th rolling element in contact with the inner and outer raceways within the load zone can be mathematically described as follows:

[0120]

[0121] The specific implementation steps for the time-varying mechanical parameters inherent in the collision between the rolling element and the defect are as follows: In reality, the collision between the rolling element and the defective atom is a non-ideal Hertzian collision. In addition to the Hertzian contact force, a hysteresis damping force is also generated during the collision process. For example... Figure 3 The diagram shows a physical model of a rolling body colliding with a defective atom. By applying the kinetic energy theorem before and after the collision, an equilibrium relationship can be established, and the expression for the energy lost during the collision can be obtained.

[0122]

[0123] In the formula, ΔE represents the energy lost during the rolling element-defect contact process. (a) ΔE represents the total energy after the collision between the rolling element and the faulty atom. (b) This represents the total energy of the rolling element and the faulty atom before they come into contact. and These represent the velocities of the rolling element and the defect atom after the collision, respectively. and These represent the velocities of the rolling element and the defect atom before the contact.

[0124] According to the momentum theorem, the following can be determined before and after the rolling element collides with the faulty atom:

[0125]

[0126] Solving equations (7) and (8) simultaneously yields ΔE.

[0127] The energy lost due to the contact between the rolling element and the defect can also be expressed as

[0128]

[0129] In the formula V rv The relative velocity between the rolling element and the faulty atom in the collision direction can be defined as V. rv =dδ×dt -1 Solving equations (7), (8), and (9) simultaneously yields λ. d

[0130]

[0131] In the formula V ra The relative approach velocity of the atoms before the collision with the faulty atoms in the rolling element can be expressed as:

[0132]

[0133] V R The collision restitution coefficient between two contacting bodies can be defined as:

[0134]

[0135] Considering the maximum deformation when the rolling element and the faulty element collide, applying Newton's second law to both the rolling element and the faulty element allows us to establish the equivalent mass, collision acceleration, and collision force. Integrating this relationship over time and combining it with the initial conditions before the collision yields the mathematical equations for the equivalent mass, relative velocity, relative contact deformation, and force-deformation exponent. Using the relative velocity corresponding to the moment of maximum deformation at contact as input, we can obtain the functional model of the maximum deformation at contact between the rolling element and the faulty element. At the moment of maximum deformation, the maximum contact force can be calculated based on the force-deformation relationship. Based on energy conservation and hysteresis damping theory, the entire incompletely elastic collision process is an energy loss process; integrating the hysteresis damping force over the contact deformation yields the energy lost during the collision to maximum deformation. Combining the parameters obtained above, we can establish a time-varying contact force model for non-ideal Hertzian collisions involving irregularly shaped defects in the rolling element.

[0136]

[0137] γ i The contact parameters between the rolling element and the faulty atom can be expressed as:

[0138]

[0139] Therefore, during the entire operation of the rolling bearing, the i-th... th The total contact force between each rolling element and the inner and outer raceways can be expressed by formula (5) and in combination with formula (12) as follows:

[0140]

[0141] Therefore, the combined contact force (including the non-ideal Hertzian contact force between the rolling elements and the inner and outer raceways of the rolling bearing) generated by the contact between all rolling elements and the bearing within the load zone can be represented as:

[0142]

[0143] The specific implementation steps for the dynamic modeling of the vibration excitation mechanism of rolling bearing defects are as follows: Taking a deep groove ball bearing as an example, a Cartesian coordinate system is established in the simulation with the horizontal direction as the x-axis and the vertical direction as the y-axis. A concentrated spring-mass model is adopted, considering the non-ideal Hertzian contact between the rolling elements and the defects. Mechanical equilibrium analysis is performed on the deep groove ball bearing, introducing the contact parameters between the rolling elements and the defects, as well as the parameters of the rolling elements within the load zone. Based on Newton's second law and the rigid ring assumption theory, a 2-degree-of-freedom dynamic model of the rolling bearing is established.

[0144]

[0145] In the formula m eq D represents the equivalent mass of the inner ring and the shaft of the rolling bearing. f W represents the damping coefficient of a rolling bearing system. x and W y These represent the external loads on the rolling bearing in the coordinate system. The load components along the x and y directions.

[0146] The specific implementation steps for comparing and verifying the simulated vibration response with the measured vibration response results are as follows: Simulation is performed using Matlab software, with the simulation time set to 2 seconds, the fault size width along the raceway direction set to 1.54 mm, and the initial values ​​of vibration displacement and vibration velocity set to 1×10⁻⁶. -9 m and 0m / s, damping parameters of the rolling bearing system: 900N s×m -1 The rolling bearing is subjected to external horizontal and vertical radial loads of 40N and 0N respectively, with a time step of 1×10. -5 The ode45 differential equation solver is used to solve the established 2-DOF differential equation, obtaining the vibration displacement and velocity. The vibration acceleration is then calculated using differential equations. Figure 4 As shown in (a). Solve for the spectrum of the vibration acceleration response, as shown in (a). Figure 5 As shown in (a) in the figure.

[0147] like Figure 4 Figures (a) and (b) show the vibration acceleration response under simulated and measured conditions. As can be seen from the figures, the simulated response exhibits a clear periodic impact vibration response, which is basically consistent with the measured signal. Figure 5 Figures (a) and (b) show the envelope spectra of the simulated and measured vibration acceleration responses. It can be seen from the figures that the characteristic frequencies of the simulated vibration acceleration response of the faulty bearing are basically consistent with the measured results. The relative error of the simulated frequency to the measured fault characteristic frequency is 0.42%. The relative errors of the 2× and 3× harmonic frequencies to the measured fault characteristic frequencies are 0.49% and 0.21%, respectively. In summary, the simulated vibration acceleration response fault characteristic frequencies are basically consistent with the measured values. Figure 6 Figures (a) to (d) show the time-frequency distribution diagrams of the simulated vibration acceleration response and the measured vibration acceleration signal. It can be seen from the figures that the simulated vibration acceleration response can simulate the low-frequency entry event and high-frequency exit event excited when the rolling bearing enters and exits the defect zone, which is basically consistent with the time-frequency distribution diagram of the measured signal. Based on the above results, the correctness of the rolling bearing vibration modeling method considering non-Hertz contact proposed in this patent is verified.

[0148] In the above embodiments, the reference to "this embodiment" in the specification indicates that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least some embodiments, but not necessarily all embodiments. Multiple appearances of "this embodiment" do not necessarily all refer to the same embodiment.

[0149] In the above embodiments, although the invention has been described in conjunction with specific embodiments thereof, many substitutions, modifications, and variations of these embodiments will be apparent to those skilled in the art from the foregoing description. For example, other memory structures (e.g., dynamic RAM (DRAM)) may be used with the embodiments discussed. The embodiments of the invention are intended to cover all such substitutions, modifications, and variations falling within the broad scope of the appended claims.

[0150] This embodiment also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements any of the methods in this embodiment.

[0151] This embodiment also provides an electronic terminal, including: a processor and a memory;

[0152] The memory is used to store computer programs, and the processor is used to execute the computer programs stored in the memory to cause the terminal to perform any of the methods in this embodiment.

[0153] As will be understood by those skilled in the art, the computer-readable storage medium described in this embodiment allows for the implementation of all or part of the steps in the above method embodiments by computer program-related hardware. The aforementioned computer program can be stored in a computer-readable storage medium. When executed, the program performs the steps of the above method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0154] The electronic terminal provided in this embodiment includes a processor, a memory, a transceiver, and a communication interface. The memory and the communication interface are connected to the processor and the transceiver and complete communication between them. The memory is used to store computer programs, the communication interface is used to perform communication, and the processor and the transceiver are used to run the computer programs, so that the electronic terminal performs the steps of the above method.

[0155] In this embodiment, the memory may include random access memory (RAM) and may also include non-volatile memory, such as at least one disk storage device.

[0156] The processors mentioned above can be general-purpose processors, including central processing units (CPUs), network processors (NPs), etc.; they can also be digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0157] This invention can be used in a wide range of general-purpose or special-purpose computing system environments or configurations. Examples include: personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronics, network PCs, minicomputers, mainframe computers, and distributed computing environments including any of the above systems or devices, etc.

[0158] This invention can be described in the general context of computer-executable instructions, such as program modules, that are executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, etc., that perform a specific task or implement a specific abstract data type. This invention can also be practiced in distributed computing environments where tasks are performed by remote processing devices connected via a communication network. In distributed computing environments, program modules can reside in local and remote computer storage media, including storage devices.

[0159] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for modeling the vibration of rolling bearings considering non-ideal Hertzian contact, characterized in that: Includes the following steps: S1: Obtain the dimensional parameters of each component of the rolling bearing, as well as the bearing material parameters; S2: Based on the external radial load on the rolling bearing, establish the contact force balance equation, and calculate the load zone angle range of the rolling bearing through an iterative method; S3: Calculate the contact geometry parameters formed by the contact between the rolling element and the healthy raceway; S4: Calculate the contact mechanical parameters between the rolling element and the inner and outer raceways; S5: Calculate the angular velocity of the cage rotation; S6: Calculate the rotational angular velocity and spin angular velocity of the rolling elements around the center of the outer ring, and calculate the circumferential angular position of all rolling elements; S7: Calculate the contact deformation and contact force between the rolling element and the inner and outer raceways using Hertzian contact theory; S8: Calculate the time-varying contact force generated by the non-ideal Hertzian contact between the rolling element and the defect; Step S8 specifically includes: By applying the kinetic energy theorem before and after the collision between the rolling element and the faulty atom, an equilibrium equation is established, yielding an expression for the energy lost during the collision: In the formula Δ E Δ represents the energy lost during the rolling element-defect contact process. E (a) Δ represents the total energy after the collision between the rolling element and the faulty atom. E (b) This represents the total energy of the rolling element and the faulty atom before they come into contact. and These represent the velocities of the rolling element and the defect atom after the collision, respectively. These represent the velocities of the rolling element and the defect atom before the collision, respectively. The momentum theorem states the following before and after the rolling element collides with the faulty atom: The energy lost due to the contact between the rolling element and the defect is expressed as: In the formula V rv The relative velocity between the rolling element and the faulty atom in the collision direction is defined as follows: V rv =d δ d t -1 Solving the simultaneous equations yields λ d : In the formula The relative approach velocity of the atoms before the collision of the rolling element fault atoms is expressed as: V R The collision restitution coefficient between two contacting bodies is defined as: Considering the maximum deformation when the rolling element and the faulty atom come into contact, Newton's second law is applied to the rolling element and the faulty atom to establish the equivalent mass, contact acceleration, and contact force. The integral of the equivalent relationship over time is obtained and combined with the initial conditions before the collision to solve the mathematical equations between the equivalent mass, relative velocity, relative contact deformation, and force-deformation exponent. Using the relative velocity corresponding to the moment of maximum deformation upon contact as input, the functional model of the maximum deformation upon contact between the rolling element and the faulty unit is obtained. At the moment of maximum deformation upon contact, the maximum contact force is obtained based on the force-deformation relationship; Based on the theory of energy conservation and hysteresis damping, the entire non-perfectly elastic contact process is an energy loss process. The energy lost during the process from contact to maximum deformation is obtained by integrating the hysteresis damping force with respect to the contact deformation. Based on the parameters obtained above, a time-varying contact force model for non-ideal Hertzian collision involving irregularly shaped defects of rolling elements is established: γ i The contact parameters between the rolling element and the faulty atom are expressed as: in i Indicates the first [unit] within the load region i th The circumferential angle of each rolling element when it contacts the inner and outer raceways; During the entire operation of the rolling bearing, the first... i th The total contact force between each rolling element and the inner and outer raceways is expressed as: Where L i Indicates the first i The parameter K is used to determine the deformation of a rolling element in contact with the inner and outer raceways within the load zone. T It represents the total equivalent contact stiffness between the rolling element and the inner and outer raceways; The combined contact force model generated by the contact between all rolling elements and the inner and outer raceways of the rolling bearing within the load zone is expressed as follows: Where N b Indicates the number of rolling elements; S9: Using a concentrated spring-mass model, considering the non-ideal Hertzian contact between the rolling elements and defects, a mechanical equilibrium analysis of the rolling bearing is performed to establish a 2-DOF rolling bearing dynamic model; Step S9 specifically includes: Taking deep groove ball bearings as the research object, the simulation uses the horizontal direction as the... x The axis is in the vertical direction. y A Cartesian coordinate system is established for the axis. A concentrated spring-mass model is adopted, and the non-ideal Hertzian contact between the rolling elements and defects is considered. Mechanical equilibrium analysis is performed on the deep groove ball bearing. Contact parameters between the rolling elements and defects, as well as parameters of the rolling elements within the load zone, are introduced. Based on Newton's second law and the rigid ring assumption theory, a 2-DOF rolling bearing dynamic model is established: In the formula m eq This indicates the equivalent mass of the inner ring of the rolling bearing and the shaft. D f This represents the damping coefficient of the rolling bearing system. W x and W y These represent the external loads on the rolling bearing in the coordinate system. ( x , o, y (middle) x and y Load components in the direction.

2. The rolling bearing vibration modeling method considering non-ideal Hertzian contact as described in claim 1, characterized in that: The dimensional parameters of each component of the rolling bearing mentioned in step S1 include: rolling element radius. b Outer radius o Inner radius i Pitch circle radius p Number of rolling elements N b and radial clearance C r The bearing material parameters include the elastic modulus of the inner and outer rings of the bearing. E i / o Compared to Poisson ρ i / o and the elastic modulus of the rolling elements E b Compared to Poisson ρ b .

3. The rolling bearing vibration modeling method considering non-ideal Hertzian contact according to claim 2, characterized in that: Step S2 specifically includes the following steps: The contact area between the rolling element and the inner and outer rings is divided into two planes: a plane V perpendicular to the bearing and a plane P parallel to the bearing. The principal curvatures of the contact pairs formed by the rolling element and the inner ring, and the rolling element and the outer ring, are calculated in planes V and P, respectively. The contact pair curvature and Σ are also calculated. r and curvature difference S r ; Calculate the equivalent elastic modulus of the contact between the rolling element and the raceway. E q Calculate the dimensionless semi-major axis parameters of the contact ellipse formed by the contact between the rolling element and the raceway. a and short half-axis parameters b The actual contact ellipse semi-axis length a and short half axis length b and its corresponding ellipticity parameters κ ; Calculate the first kind of elliptic integral formed by the rolling element in contact with the raceway and the outer raceway, respectively. ξ 1. Elliptic integral of the second kind ξ 2.

4. The rolling bearing vibration modeling method considering non-ideal Hertzian contact according to claim 3, characterized in that: Step S3 specifically includes the following steps: Based on Hertzian contact theory, the contact deformation between the rolling element and the inner and outer raceways is calculated using the first and second kind elliptic integrals, ellipticity parameters, curvature parameters, equivalent elastic modulus parameters, and pi of the contact pair formed by the contact between the rolling element and the inner and outer raceways. δ bi and δ bo Finally, the total equivalent contact stiffness between the rolling element and the inner and outer raceways is calculated. K T : In the formula, K bi and K bo These represent the contact stiffness between the rolling element and the inner ring and the outer ring, respectively. n Indicates the load deformation index; According to Hertzian contact theory, the geometric characterization model of the total contact deformation generated by the contact between the rolling element and the healthy inner and outer raceways within the load zone is as follows: In the formula X and Y These represent the inner circle along with the axis of rotation in the coordinate system. ( x , o, y In ) x and y Displacement in the direction, where θ i For the first in the load region i th The circumferential angle of each rolling element when it contacts the inner and outer raceways.

5. The rolling bearing vibration modeling method considering non-ideal Hertzian contact as described in claim 4, characterized in that: Step S4 specifically includes: applying a given external radial load Q E Establish its relationship with N b , K T , C r as well as n The mathematical relationship between them is a balance equation. The effective load range angle of the rolling bearing under external load is obtained by solving this equation using a trial-and-error method. Φ z , Φ z ].

6. The rolling bearing vibration modeling method considering non-ideal Hertzian contact according to claim 5, characterized in that: Step S5 specifically includes: bearing speed N s Calculate the angular velocity parameters of the cage's circular motion. ω cage : In the formula ω s The bearing's rotational angular velocity is expressed as: ω s = πN s 30 -1 in α This refers to the load angle of the rolling bearing.

7. The rolling bearing vibration modeling method considering non-ideal Hertzian contact according to claim 6, characterized in that: Step S6 specifically includes: Calculate the time-varying angular position parameters of each rolling element using the cage circumferential angular velocity; calculate the angular velocity parameters of the rolling element rotating about the outer ring center; calculate the angular velocity parameters of the rolling element rotating about itself; where the first rolling element in the load zone... i th The circumferential angle when the rolling element contacts the inner and outer raceways θ i Calculated using the following formula: in i For the first i th A rolling element, For the first rolling body in the coordinate system ( x , o, y The initial angle position in ) t For time.

8. The rolling bearing vibration modeling method considering non-ideal Hertzian contact according to claim 7, characterized in that: Step S7 specifically includes: Calculate the sum of contact forces generated by the contact between the rolling element and the inner and outer raceways using the total equivalent contact stiffness and contact displacement of the rolling element and the inner and outer raceways: In the formula L i Indicates the first i The parameters for determining the deformation of a rolling element in contact with the inner and outer raceways within the load zone are mathematically described as follows: 。

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