Rolling bearing vibration modeling method considering non-ideal Hertz contact

Abstract

The invention relates to a rolling bearing vibration modeling method considering non-ideal Hertz contact, and belongs to the technical field of bearing vibration modeling, and the method comprises the following steps: S1, obtaining basic geometric parameters and material parameters of a rolling bearing; s2, calculating an angle range of a load area of the rolling bearing; s3, calculating contact geometric parameters of the rolling body and the healthy raceway; s4, calculating contact mechanical parameters of the rolling body and the healthy raceway; s5, calculating an angular velocity parameter of the retainer; s6, calculating the circular motion angular position and angular velocity parameter of the rolling body; s7, deformation and contact force generated when all the rolling bodies make contact with the healthy raceway of the bearing are calculated; s8, calculating time-varying mechanical parameters contained in contact between the rolling body and the defect; and S9, carrying out dynamic modeling on the defect vibration excitation mechanism of the rolling bearing.

Description

Technical Field

[0001] The invention belongs to the technical field of bearing vibration modeling, and relates to a rolling bearing vibration modeling method taking non-ideal Hertz contact into consideration. Background Art

[0002] The service health status of rolling bearings has a significant impact on the operating stability, running accuracy, working reliability, vibration and noise of such equipment. In severe cases, rolling bearing failures can cause mechanical equipment to shut down, resulting in economic losses and even casualties. Therefore, exploring its failure mechanism, clarifying its inherent fault excitation mechanism, and revealing the mapping relationship between its failure mechanism and vibration response are of great significance to the establishment of rolling bearing failure theory and effective condition monitoring methods.

[0003] The research on rolling bearing dynamics modeling based on kinematics, physics, and dynamics can partially replace the experimental research with high time and economic costs, and reduce the reliance on data under difficult experimental conditions. It can enhance the understanding of the mapping mechanism between bearing vibration response and fault excitation mechanism, consolidate the theoretical foundation of bearing fault judgment, and also make up for and establish a theoretical research system of rolling bearing fault excitation mechanism based on kinematics, collision mechanics, contact mechanics and other theories, which has important theoretical research significance and practical engineering application value.

[0004] The existing rolling bearing dynamics modeling methods all use rectangular notch faults to replace actual irregular morphology defects for modeling. That is, the model considers raceway defects as regular morphologies such as rectangular notches, which is contrary to the actual situation and is difficult to objectively and effectively reflect the intrinsic contact process between rolling elements and defects in reality and reveal the mechanical evolution mechanism contained therein. So far, there is still a lack of systematic research on more reasonable and effective modeling methods for irregular morphology defects under actual working conditions. In addition, in the existing rolling bearing dynamics modeling, the contact between rolling elements and defects is still based on the complete elasticity under the Hertz contact theory. That is, the existing dynamics models are mostly based on the Hertz complete elastic contact theory in the study of the modeling of time-varying mechanical parameters induced by rolling element-defect contact, but the actual process of collision between rolling elements and irregular morphology defects is accompanied by hysteresis damping characteristics, which is a non-ideal Hertz contact. At present, there is still a lack of research on the evolution mechanism of mechanical parameters contained in the non-ideal Hertz contact between rolling elements and irregular morphology defects. Summary of the invention

[0005] In view of this, the purpose of the present invention is to establish a rolling bearing defect model with fault atom parameterization equivalent, to replace the rolling body defect contact with the rolling body and fault atom contact equivalent, and to establish a rolling body-irregular morphology defect non-ideal Hertzian contact mechanical parameter evolution mechanism model by using hysteresis damping theory and collision mechanics. Based on the ring hypothesis theory and the rolling body-irregular morphology defect contact excitation mechanism, a rolling bearing vibration mechanism modeling method considering non-ideal Hertzian contact is proposed. This method aims to improve the accuracy of rolling bearing fault modeling and provide theoretical support for the rolling bearing fault excitation mechanism theoretical research system based on kinematics, collision mechanics, contact mechanics and other theories.

[0006] In order to achieve the above object, the present invention provides the following technical solutions:

[0007] A rolling bearing vibration modeling method considering non-ideal Hertz contact includes the following steps:

[0008] S1: Obtain the dimension parameters of each component of the rolling bearing and the bearing material parameters;

[0009] S2: According to the external radial load on the rolling bearing, the contact force balance equation is established, and the load zone angle range of the rolling bearing is calculated by the iterative method;

[0010] S3: Calculate the contact geometry parameters 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 rotation angular velocity and rotation angular velocity of the rolling body around the center of the outer ring, and calculate the circumferential angular position of all rolling bodies;

[0014] S7: Calculate the contact deformation and contact force between the rolling element and the inner and outer raceways using the Hertz 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: The concentrated spring-mass model is adopted to consider the non-ideal Hertzian contact effect between the rolling element and the defect, and the mechanical balance analysis of the rolling bearing is carried out to establish a 2-DOF rolling bearing dynamics model.

[0017] Furthermore, the dimension parameters of the rolling bearing components in step S1 include: rolling element radius Outer radius Inner circle radius Pitch radius Number of rolling elements N b, and 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] Further, step S2 specifically includes the following steps:

[0019] The contact between the rolling element and the inner and outer rings is divided into two planes perpendicular to the bearing plane V and parallel to the plane P. The principal curvatures of the contact pair formed by the rolling element and the inner ring and the contact pair formed by the rolling element and the outer ring in plane V and plane P, 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 major semi-axis parameter a* and minor semi-axis parameter b* of the contact ellipse formed by the rolling body and the raceway, the major semi-axis length a and minor semi-axis length b of the real contact ellipse and their corresponding ellipticity parameter κ respectively; Calculate the first kind elliptic integral ξ1 and the second kind elliptic integral ξ2 formed by the rolling body contacting the raceway and the outer raceway respectively.

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

[0021] The contact deformation δ between the rolling element and the inner and outer raceways is calculated based on the Hertz contact theory through the first and second elliptic integrals, ellipticity parameters, curvature and parameters, equivalent elastic modulus parameters and pi of the contact pair formed by the rolling element and the inner and outer races. bi and δ bo , and finally calculate the total equivalent contact stiffness K between the rolling element and the inner raceway and the outer raceway T :

[0022]

[0023] In the formula, K bi and K bo They 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 Hertz contact theory, the geometric representation model of the total contact deformation caused by the rolling element contacting the healthy inner and outer raceways in the load area is:

[0025]

[0026] Where X and Y represent the coordinate system of the inner ring and the rotating shaft. The displacement in the x and y directions is iis the i-th th The circumferential angle at which a rolling element contacts the inner and outer raceways.

[0027] Further, step S4 specifically includes: by a given external radial load Q E , establish its relationship with N b , K T , C r And the mathematical relationship balance between n, the effective load zone angle range of the rolling bearing under the external load is obtained by trial and error method [-Φ z ,Φ z ].

[0028] Further, step S5 specifically includes:

[0029] Through the bearing speed N s , calculate the angular velocity parameter ω of the cage circular motion cage :

[0030]

[0031] Where ω s is the bearing rotation angular velocity, expressed as:

[0032] ω s =πN s ×30 -1

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

[0034] Further, step S6 specifically includes:

[0035] Through the circumferential angular velocity of the cage, the time-varying angular position parameters of each rolling element are calculated; the angular velocity parameters of the rolling element rotating around the center of the outer ring are calculated; the angular velocity parameters of the rolling element rotating around itself are calculated;

[0036]

[0037] Where i is the i-th th Rolling element, The first rolling body in the coordinate system is the initial angular position in , and t is the time.

[0038] Further, step S7 specifically includes:

[0039] The sum of the contact forces between the bearing rolling element and the inner and outer raceways is calculated by the total equivalent contact stiffness and contact displacement between the rolling element and the inner and outer raceways:

[0040]

[0041] Where L i It represents the judgment parameter of the contact deformation of the i-th rolling element with the inner and outer raceways in the load zone, and is mathematically described as:

[0042]

[0043] Further, step S8 specifically includes:

[0044] Through the kinetic energy theorem before and after the rolling body and the fault atom collide, the equilibrium relationship is established, and the expression of the energy lost in the collision process is obtained:

[0045]

[0046] Where ΔE represents the energy lost during the rolling element-defect contact process, ΔE (a) It represents the total energy of the rolling element and the fault atom after the contact, ΔE (b) It represents the total energy of the rolling element and the fault atom before the contact. and Respectively represent the speed of the rolling body and the defect atom after the contact, and Respectively represent the speed of the rolling body and the defect atom before the contact;

[0047] The momentum theorem gives the following results before and after the rolling element collides with the fault atom:

[0048]

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

[0050]

[0051] Where V rv It represents the relative speed between the rolling element and the fault atom in the collision direction, defined as V rv =dδ×dt -1 , the simultaneous equations are solved to obtain λ d :

[0052]

[0053] Where V ra It represents the relative approach speed of rolling element fault atoms before collision, which is expressed as:

[0054]

[0055] V R represents the collision recovery coefficient between two contacting bodies and is defined as:

[0056]

[0057] Considering that the rolling body and the fault atom collide to the maximum deformation, the equivalent relationship between the equivalent mass, the contact acceleration and the contact force is established for the rolling body and the fault unit respectively by using Newton's second law; the integral of the equivalent relationship over time is calculated and combined with the initial conditions before the collision, the mathematical equations between the equivalent mass, the relative velocity, the relative contact deformation and the force-deformation index are solved;

[0058] Taking the relative speed corresponding to the maximum deformation moment of contact as the input condition, the function model of the maximum deformation of the rolling element and the fault unit in contact is solved;

[0059] At the moment of maximum contact deformation, the maximum contact force is obtained according to the force-deformation relationship;

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

[0061] Combining the above parameters, a non-ideal Hertzian contact time-varying contact force model for rolling elements with irregular morphology defects is established:

[0062]

[0063] γ i It represents the contact parameter between the rolling element and the fault atom, which is expressed as:

[0064]

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

[0066]

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

[0068]

[0069] Further, 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 used to consider the non-ideal Hertzian contact effect between the rolling element and the defect. The mechanical balance analysis of the deep groove ball bearing is carried out. The contact parameters between the rolling element and the defect and the parameters of the rolling element in the load zone are introduced. According to Newton's second law and the rigid ring hypothesis theory, a 2-DOF rolling bearing dynamics model is established:

[0071]

[0072] Where m eq Denotes the equivalent mass of the inner ring of the rolling bearing and the shaft, D f Represents the damping coefficient of the rolling bearing system, W x and W y They 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 the present invention are: to solve the problems existing in the current rolling bearing fault vibration modeling method, and to provide a rolling bearing outer ring raceway fault vibration modeling method and model with good robustness and accuracy. Considering that in the actual process, the raceway defect is an irregular morphology, the traditional modeling method assumes that the shape of such a defect is a regular morphology, and this method is difficult to accurately and effectively characterize the bearing vibration characteristics caused by the defect in the actual process. The present invention proposes a method for establishing a real defect model by parameterizing the fault atom. In the existing rolling bearing dynamics modeling method, the contact between the rolling body and the defect is still based on the complete elasticity under the Hertz contact theory. However, under actual working conditions, during the collision between the rolling body and the irregular morphology defect, accompanied by the hysteresis damping characteristics, the contact between the rolling body and the defect has a hysteresis damping force in addition to the Hertz contact force. The present invention is based on theories and methods such as collision theory, momentum conservation, and kinetic energy theorem, and establishes the kinematic and mechanical equilibrium equations formed by the contact between the rolling body and the defect atom. The relevant information such as the speed of the rolling element and the fault atom before and after the collision is obtained, and finally the time-varying contact force model of the rolling element-defect contact process is obtained, which provides a theoretical basis for accurately establishing the vibration dynamics model of rolling bearing faults.

[0074] ① The present invention uses a series of fault atoms with different radius sizes, radial angle positions and a certain number to equivalently replace the natural spalling defects of the rolling bearing raceway, and parameterizes and establishes a mathematical model of the rolling bearing raceway defects, which is beneficial to: (a) multi-parameter collaborative equivalent characterization of rolling bearing defects, which is convenient for studying the influence of defect size parameters on the bearing vibration response; (b) establishing a mathematical model of the evolution mechanism of time-varying mechanical parameters contained in the contact process between the rolling body 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 parameterized mathematical model of rolling bearing defects that is more in line with the actual situation, and ultimately improving the accuracy and reliability of the rolling bearing fault vibration mechanism modeling method.

[0075] ② The present invention studies the time-varying mechanical parameter evolution mechanism induced by rolling element-defect contact through the exploration of the physical event of rolling element-defect contact, based on the hysteresis damping theory, collision theory, momentum conservation, kinetic energy theorem and other theories and methods. It is beneficial to: (a) reveal the evolution law of mechanical parameters contained in rolling element-defect contact from the mechanism level, and clarify the mapping relationship between the rolling element defect interaction mechanism and the impact vibration response; (b) establish a mathematical model of the time-varying displacement of the inner ring of the bearing together with the rotating shaft caused by the rolling element-defect contact; (c) establish the intrinsic connection and excitation mechanism between the evolution law of time-varying mechanical parameters caused by rolling element-defect contact and the change of bearing system stiffness.

[0076] Other advantages, objectives and features of the present invention will be described in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the following examination and study, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below in conjunction with the accompanying drawings, wherein:

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

[0079] Figure 2 It is the principle diagram of the rolling element radial displacement change;

[0080] Figure 3 It is a schematic diagram of the contact between the rolling element and the defect;

[0081] Figure 4 (a) is the simulated vibration acceleration signal, and (b) is the vibration acceleration signal obtained by actual test;

[0082] Figure 5 (a) is the envelope spectrum of the simulated vibration acceleration signal, and (b) is the envelope spectrum of the vibration acceleration signal obtained by actual testing;

[0083] Figure 6 (a) is a single simulated vibration impact response, (b) is the time-frequency distribution characteristics of a single simulated vibration impact response, (c) is the measured vibration impact signal, and (d) is the time-frequency distribution characteristics of a single measured vibration impact signal. DETAILED DESCRIPTION

[0084] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways 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 only illustrate the basic concept of the present invention in a schematic manner, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0085] It should be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present invention, and thus the drawings only show components related to the present invention rather than being drawn according to the number, shape and size of components in actual implementation. In actual implementation, the type, quantity and proportion of each component may be changed arbitrarily, and the component layout may also be more complicated.

[0086] In the following description, numerous details are discussed to provide a more thorough explanation of the embodiments of the present invention. However, it is obvious to those skilled in the art that the embodiments of the present invention can be implemented without these specific details. In other embodiments, well-known structures and devices are shown in the form of block diagrams rather than in detail to avoid making the embodiments of the present invention difficult to understand.

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

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

[0089] Table 1

[0090]

[0091] Calculation of the angular range of the rolling bearing load zone: Based on the external radial load on the rolling bearing, the contact force balance equation is established, and the angular range of the rolling bearing load zone is calculated through an iterative method.

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

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

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

[0095] Calculation of the angular position and angular velocity parameters of the rolling body's circular motion: Calculate the angular velocity of rotation and the angular velocity of rotation of the rolling body around the center of the outer ring, and calculate the circumferential angular position of all rolling bodies.

[0096] Calculation of deformation and contact force caused by contact between all rolling elements and the healthy raceway of the bearing: Calculate the contact deformation and contact force between the rolling elements and the inner and outer raceways using the Hertz contact theory.

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

[0098] Dynamic modeling of vibration excitation mechanism of rolling bearing defects: Taking deep groove ball bearings as an example, 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 used to consider the non-ideal Hertzian contact between the rolling element and the defect, and the mechanical balance analysis of the deep groove ball bearing is performed. The contact parameters between the rolling element and the defect and the parameters of the rolling element in the load zone are introduced. According to Newton's second law and the rigid ring hypothesis theory, a 2-degree-of-freedom rolling bearing dynamic model is established.

[0099] Comparative analysis and verification of simulated vibration response and measured vibration response results: Based on Matlab software programming simulation, set the simulation time length, initial values ​​of vibration displacement and vibration velocity, rolling bearing system damping parameters, external horizontal and vertical radial loads on the rolling bearing, and time step. Use the ode45 differential equation solver to obtain the above-established 2-DOF differential equation to obtain the vibration displacement and vibration velocity, and obtain the vibration acceleration through differential calculation. Solve the time domain characteristics and frequency characteristics of the vibration acceleration response, and compare them with the time domain characteristics and frequency domain characteristics of the measured signal; analyze the similarities and differences of the impact response caused by rolling bearing defects in the simulated signal and the measured signal; compare and analyze the time-frequency distribution characteristics of the vibration signal under measured and simulated conditions; furthermore, compare the impact response characteristics caused by the rolling element entering and exiting the defect area in the simulated response and the measured signal. The above four aspects verify the correctness of the rolling bearing vibration modeling method considering non-Hertzian contact proposed in this patent.

[0100] Embodiment 2:

[0101] As attached Figure 1 to Figure 6 As shown in Table 1, it is basically the same as Example 1, except that:

[0102] The specific implementation steps of the basic geometric parameters and material parameters of the rolling bearing are as follows: This patent takes the 6205 bearing as an example, and its geometric dimension values ​​are listed in Table 1. For the convenience of description, the rolling element radius is defined as Outer radius Inner circle radius Pitch radius Number of rolling elements N b , and radial clearance C r ; By consulting its manufacturing materials, the elastic modulus E of the inner and outer rings of the bearing is 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 of the rolling element and healthy raceway contact geometric parameters are as follows: the contact between the rolling element and the inner and outer rings is divided into two planes perpendicular to the bearing (plane V) and parallel to the bearing (plane P), and the main curvatures of the contact pair formed by the rolling element (contact body a) and the inner ring (contact body b) and the contact pair formed by the rolling element and the outer ring (contact body b) in plane V and plane P are calculated 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 major semi-axis parameter a* and minor semi-axis parameter b* of the contact ellipse formed by the rolling body and the raceway, the major semi-axis length a and minor semi-axis length b of the real contact ellipse and their corresponding ellipticity parameter κ respectively; Calculate the first kind elliptic integral ξ1 and the second kind elliptic integral ξ2 formed by the rolling body contacting the raceway and the outer raceway respectively.

[0104] The specific implementation steps of the contact mechanical parameters between the rolling element and the healthy raceway are as follows: based on the Hertz contact theory, the contact deformation δ formed by the contact between the rolling element and the inner and outer raceways is calculated by using the first and second elliptic integrals, ellipticity parameters, curvature and 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 , and finally calculate the total equivalent contact stiffness K between the rolling element and the inner raceway and the outer raceway T .

[0105]

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

[0107] According to Hertz contact theory, based on Figure 2 The schematic diagram of rolling contact of rolling elements is shown in the figure. In the load zone, the geometric expression model of the total contact deformation caused by the rolling elements and the defect-free inner and outer raceways can be expressed as:

[0108]

[0109] Where X and Y represent the coordinate system of the inner ring and the rotating shaft. The displacement (offset) in the x and y directions in the formula is i is the i-th th The circumferential angle at which a rolling element contacts the inner and outer raceways.

[0110] The specific implementation steps of the load zone angle range are: by a given external radial load Q E , establish its relationship with N b , K T , C r And the mathematical relationship balance between n, the effective load zone angle range of the rolling bearing under the external load is obtained by trial and error method [-Φ z ,Φ z ], in order to accurately establish the rolling bearing defect vibration model in accordance with the actual constraints.

[0111] The specific implementation steps of the cage angular velocity parameter are: s , calculate the angular velocity parameter ω of the cage circular motion cage .

[0112]

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

[0114] The specific implementation steps of the rolling body circular motion angular position and angular velocity parameters are: calculating the time-varying angular position parameters of each rolling body through the circumferential angular velocity of the cage; calculating the angular velocity parameters of the rolling body rotating around the center of the outer ring; calculating the angular velocity parameters of the rolling body rotating around itself.

[0115]

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

[0117] The specific implementation steps of the contact deformation and contact force between all rolling elements and the healthy raceways of the bearing are as follows: the sum of the contact forces generated by the contact between the load-bearing rolling elements and the inner and outer raceways is calculated through the total equivalent contact stiffness and contact displacement between the rolling elements and the inner and outer raceways.

[0118]

[0119] Where L i The parameter that determines the deformation of the ith rolling element in contact with the inner and outer raceways in the load zone can be mathematically described as:

[0120]

[0121] The specific implementation steps of the time-varying mechanical parameters implied by the contact between the rolling element and the defect are as follows: In practice, the contact between the rolling element and the fault atom is a non-ideal Hertzian contact, and in addition to the Hertzian contact force, there is also the generation of a hysteresis damping force during the contact process. Figure 3 The figure shows a physical model diagram of the collision between a rolling body and a defective atom. Through the kinetic energy theorem before and after the collision between the rolling body and the defective atom, an equilibrium relationship can be established, and an expression for the energy lost during the collision can be obtained.

[0122]

[0123] Where ΔE represents the energy lost during the rolling element-defect contact process, ΔE (a) It represents the total energy of the rolling element and the fault atom after the contact, ΔE (b) It represents the total energy of the rolling element and the fault atom before the contact. and Respectively represent the speed of the rolling body and the defect atom after the contact, and Respectively represent the speeds of the rolling body and the defect atom before the contact.

[0124] The momentum theorem shows that before and after the rolling element and the fault atom collide,

[0125]

[0126] The simultaneous equations (7) and (8) can be solved to obtain ΔE.

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

[0128]

[0129] Where V rv It represents the relative speed between the rolling element and the fault atom in the collision direction, which can be defined as V rv =dδ×dt -1 , the simultaneous equations (7), (8) and (9) can be solved to obtain λ d

[0130]

[0131] Where V ra It represents the relative approach speed of the rolling element fault atom before collision, which can be expressed as:

[0132]

[0133] V R represents the collision recovery coefficient between two contacting bodies and can be defined as:

[0134]

[0135] Considering the rolling body and the fault atom contact to the maximum deformation, the equivalent relationship between equivalent mass, contact acceleration and contact force can be established by applying Newton's second law to the rolling body and the fault unit respectively. By integrating the relationship over time and combining it with the initial conditions before the collision, the mathematical equations between equivalent mass, relative velocity, relative contact deformation and force-deformation index can be solved. Taking the relative velocity corresponding to the maximum deformation moment of the contact as the input condition, the function model of the maximum deformation of the rolling body and the fault unit can be solved. At the maximum deformation moment of the contact, the maximum contact force can be obtained according to the force-deformation relationship. Based on the energy conservation and hysteresis damping theory, the entire non-completely elastic contact process is an energy loss process. The energy lost in the process from contact to maximum deformation is obtained by integrating the hysteresis damping force with the contact deformation. The time-varying contact force model of non-ideal Hertzian contact of rolling body with irregular morphology defects can be established based on the above-obtained parameters.

[0136]

[0137] γ i It represents the contact parameter between the rolling element and the fault atom, which can be expressed as:

[0138]

[0139] Then, during the entire operation of the rolling bearing, the i th The total contact force between the rolling element and the inner and outer raceways can be expressed according to formula (5) combined with formula (12) as follows:

[0140]

[0141] It can be seen that the comprehensive contact force (including the non-ideal Hertzian contact force of rolling elements and defects) generated by the contact between all rolling elements in the load zone and the inner and outer raceways of the rolling bearing can be expressed as:

[0142]

[0143] The specific implementation steps of the dynamic modeling of the rolling bearing defect vibration excitation mechanism are as follows: taking the deep groove ball bearing as an example, 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 effect between the rolling element and the defect is considered. The mechanical balance analysis of the deep groove ball bearing is performed, and the contact parameters between the rolling element and the defect and the parameters of the rolling element in the load zone are introduced. According to Newton's second law and the rigid ring hypothesis theory, a 2-degree-of-freedom rolling bearing dynamic model is established.

[0144]

[0145] Where m eq Denotes the equivalent mass of the inner ring of the rolling bearing and the shaft, D f Represents the damping coefficient of the rolling bearing system, W x and W y They 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 of the comparison and analysis of the simulated vibration response and the measured vibration response results are as follows: based on Matlab software programming simulation, the simulation time length is set to 2s, the width of the fault size along the raceway direction is 1.54mm, and the initial values ​​of the vibration displacement and vibration velocity are 1×10 -9 m and 0m / s, the damping parameter of the rolling bearing system is 900N s×m -1 The rolling bearing is subjected to external horizontal and vertical radial loads of 40 N and 0 N respectively, and the time step is 1×10 -5 s. Use the ode45 differential equation solver to solve the above-established 2-DOF differential equation to obtain the vibration displacement and vibration velocity, and then obtain the vibration acceleration through differential calculation, such as Figure 4 As shown in (a). Solve the frequency spectrum of the vibration acceleration response, as Figure 5 As shown in (a) in .

[0147] like Figure 4 (a) and (b) in the figure show the vibration acceleration response under simulation and measured conditions. It can be seen from the figure that the simulation response has obvious periodic impact vibration response and is basically consistent with the measured signal. Figure 5 (a) and (b) show the envelope spectra of the simulated and measured vibration acceleration responses. It can be seen from the figure that the characteristic frequency of the simulated vibration acceleration response of the faulty bearing is basically consistent with the measured result. The relative error of the fault characteristic frequency of the fault signal relative to the measured signal is 0.42%, and the relative errors of the 2× and 3× times relative to the fault characteristic frequency of the measured signal are 0.49% and 0.21% respectively. It can be seen that the fault characteristic frequency of the simulated vibration acceleration response is basically consistent with the measured value. Figure 6 (a) to (d) in the figure show the time-frequency distribution diagram of the simulated vibration acceleration response and the measured vibration acceleration signal. It can be seen from the figure that the simulated vibration acceleration response can simulate the low-frequency entry event and high-frequency exit event caused by the rolling bearing entering and exiting the defect area, 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-Hertzian contact proposed in this patent is verified.

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

[0149] In the above-described embodiments, although the invention has been described in conjunction with specific embodiments of the invention, many substitutions, modifications, and variations of these embodiments will be apparent to those of ordinary skill in the art based on the foregoing description. For example, other storage structures (e.g., dynamic RAM (DRAM)) may use the embodiments discussed. Embodiments of the invention are intended to encompass all such substitutions, modifications, and variations that fall within the broad scope of the appended claims.

[0150] This embodiment further provides a computer-readable storage medium on which a computer program is stored. When the program is executed by a processor, any one of the methods in this embodiment is implemented.

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

[0152] The memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory, so that the terminal executes any one of the methods in this embodiment.

[0153] The computer-readable storage medium in this embodiment can be understood by ordinary technicians in this field: all or part of the steps of implementing the above-mentioned method embodiments can be completed by hardware related to the computer program. The aforementioned computer program can be stored in a computer-readable storage medium. When the program is executed, the steps of the above-mentioned method embodiments are executed; and the aforementioned storage medium includes: ROM, RAM, magnetic disk or optical disk and other media that can store program codes.

[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 with each other. The memory is used to store computer programs, the communication interface is used to communicate, and the processor and the transceiver are used to run computer programs so that the electronic terminal executes each step of the above method.

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

[0156] The above-mentioned processor can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components.

[0157] The present invention can be used in many general or special computing system environments or configurations, such as personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronic devices, network PCs, minicomputers, mainframe computers, distributed computing environments including any of the above systems or devices, and the like.

[0158] The present invention may be described in the general context of computer-executable instructions executed by a computer, such as program modules. Generally, program modules include routines, programs, objects, components, data structures, etc. that perform specific tasks or implement specific abstract data types. The present invention may also be practiced in distributed computing environments where tasks are performed by remote processing devices connected through a communication network. In a distributed computing environment, program modules may be located 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 solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution, which should be included in the scope of the claims of the present invention.

Claims

1. A rolling bearing vibration modeling method considering non-ideal Hertzian contact, characterized by: The following steps are involved: S1: Obtain the dimension parameters of each component of the rolling bearing and the bearing material parameters; S2: According to the external radial load on the rolling bearing, the contact force balance equation is established, and the load zone angle range of the rolling bearing is calculated by the iterative method; S3: Calculate the contact geometry parameters 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 rotation angular velocity and rotation angular velocity of the rolling body around the center of the outer ring, and calculate the circumferential angular position of all rolling bodies; S7: Calculate the contact deformation and contact force between the rolling element and the inner and outer raceways using the Hertz contact theory; S8: Calculate the time-varying contact force generated by the non-ideal Hertzian contact between the rolling element and the defect; S9: The concentrated spring-mass model is adopted to consider the non-ideal Hertzian contact effect between the rolling element and the defect, and the mechanical balance analysis of the rolling bearing is carried out to establish a 2-DOF rolling bearing dynamics model.

2. The rolling bearing vibration modeling method considering non-ideal Hertzian contact according to claim 1 is characterized in that: The dimension parameters of the rolling bearing components in step S1 include: rolling element radius Outer radius Inner circle radius Pitch radius Number of rolling elements N b , and 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 .

3. The rolling bearing vibration modeling method considering non-ideal Hertzian contact according to claim 1 is characterized in that: Step S2 specifically includes the following steps: The contact between the rolling element and the inner and outer rings is divided into two planes perpendicular to the bearing plane V and parallel to the plane P. The principal curvatures of the contact pair formed by the rolling element and the inner ring and the contact pair formed by the rolling element and the outer ring in plane V and plane P, 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 major semi-axis parameter a* and minor semi-axis parameter b* of the contact ellipse formed by the rolling body and the raceway, the major semi-axis length a and minor semi-axis length b of the real contact ellipse and their corresponding ellipticity parameter κ respectively; Calculate the first kind elliptic integral ξ1 and the second kind elliptic integral ξ2 formed by the rolling body contacting the raceway and the outer raceway respectively.

4. The rolling bearing vibration modeling method considering non-ideal Hertzian contact according to claim 1 is characterized in that: Step S3 specifically includes the following steps: The contact deformation δ between the rolling element and the inner and outer raceways is calculated based on the Hertz contact theory through the first and second elliptic integrals, ellipticity parameters, curvature and parameters, equivalent elastic modulus parameters and pi of the contact pair formed by the rolling element and the inner and outer races. bi and δ bo , and finally calculate the total equivalent contact stiffness K between the rolling element and the inner raceway and the outer raceway T : In the formula, K bi and K bo They represent the contact stiffness between the rolling element and the inner and outer rings, respectively, and n represents the load deformation index; According to Hertz contact theory, the geometric representation model of the total contact deformation caused by the rolling element contacting the healthy inner and outer raceways in the load area is: Where X and Y represent the coordinate system of the inner ring and the rotating shaft. The displacement in the x and y directions is i is the i-th th The circumferential angle at which a rolling element contacts the inner and outer raceways.

5. The rolling bearing vibration modeling method considering non-ideal Hertzian contact according to claim 1, characterized in that: Step S4 specifically includes: by a given external radial load Q E , establish its relationship with N b , K T , C r And the mathematical relationship balance between n, the effective load zone angle range of the rolling bearing under the external load is obtained by trial and error method [-Φ z ,Φ z ].

6. The rolling bearing vibration modeling method considering non-ideal Hertzian contact according to claim 1, characterized in that: Step S5 specifically includes: Through the bearing speed N s , calculate the angular velocity parameter ω of the cage circular motion cage : Where ω s is the bearing rotation angular velocity, expressed as: oh s =πN s ×30 -1 Where α is the rolling bearing load angle.

7. The rolling bearing vibration modeling method considering non-ideal Hertzian contact according to claim 1, characterized in that: Step S6 specifically includes: Through the circumferential angular velocity of the cage, the time-varying angular position parameters of each rolling element are calculated; the angular velocity parameters of the rolling element rotating around the center of the outer ring are calculated; the angular velocity parameters of the rolling element rotating around itself are calculated; Where i is the i-th th Rolling element, The first rolling body in the coordinate system is the initial angular position in , and t is the time.

8. The rolling bearing vibration modeling method considering non-ideal Hertzian contact according to claim 1, characterized in that: Step S7 specifically includes: The sum of the contact forces between the bearing rolling element and the inner and outer raceways is calculated by the total equivalent contact stiffness and contact displacement between the rolling element and the inner and outer raceways: Where L i It represents the judgment parameter of the contact deformation of the i-th rolling element with the inner and outer raceways in the load zone, and is mathematically described as:

9. The rolling bearing vibration modeling method considering non-ideal Hertzian contact according to claim 1, characterized in that: Step S8 specifically includes: Through the kinetic energy theorem before and after the rolling body and the fault atom collide, the equilibrium relationship is established, and the expression of the energy lost in the collision process is obtained: Where ΔE represents the energy lost during the rolling element-defect contact process, ΔE (a) It represents the total energy of the rolling element and the fault atom after the contact, ΔE (b) It represents the total energy of the rolling element and the fault atom before the contact. and Respectively represent the speed of the rolling body and the defect atom after the contact, and Respectively represent the speed of the rolling body and the defect atom before the contact; The momentum theorem gives the following results before and after the rolling element collides with the fault atom: The energy lost due to rolling element-defect contact is expressed as: Where V rv It represents the relative speed between the rolling element and the fault atom in the collision direction, defined as V rv =dδ×dt -1 , the simultaneous equations are solved to obtain λ d : Where V ra It represents the relative approach speed of rolling element fault atoms before collision, which is expressed as: V R represents the collision recovery coefficient between two contacting bodies and is defined as: Considering that the rolling body and the fault atom collide to the maximum deformation, the equivalent relationship between the equivalent mass, the contact acceleration and the contact force is established for the rolling body and the fault unit respectively by using Newton's second law; the integral of the equivalent relationship over time is calculated and combined with the initial conditions before the collision, the mathematical equations between the equivalent mass, the relative velocity, the relative contact deformation and the force-deformation index are solved; Taking the relative velocity corresponding to the maximum deformation moment of contact as the input condition, the function model of the maximum deformation of the rolling element and the fault unit in contact is solved; At the moment of maximum contact deformation, the maximum contact force is obtained according to the force-deformation relationship; Based on the energy conservation and hysteresis damping theory, the entire non-perfectly elastic contact process is an energy loss process. The energy lost from contact to maximum deformation can be obtained by integrating the hysteresis damping force with the contact deformation. Combining the above parameters, a non-ideal Hertzian contact time-varying contact force model for rolling elements with irregular morphology defects is established: γ i It represents the contact parameter between the rolling element and the fault atom, which is expressed as: During the entire operation of the rolling bearing, the i th The total contact force between the rolling element and the inner and outer raceways is expressed as: The comprehensive contact force model generated by all rolling elements in the load zone contacting the inner and outer raceways of the rolling bearing is expressed as:

10. The rolling bearing vibration modeling method considering non-ideal Hertzian contact according to claim 1, characterized in that: Step S9 specifically includes: 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 used to consider the non-ideal Hertzian contact effect between the rolling element and the defect. The mechanical balance analysis of the deep groove ball bearing is carried out. The contact parameters between the rolling element and the defect and the parameters of the rolling element in the load zone are introduced. According to Newton's second law and the rigid ring hypothesis theory, a 2-DOF rolling bearing dynamics model is established: Where m eq Denotes the equivalent mass of the rolling bearing inner ring and the shaft, D f Represents the damping coefficient of the rolling bearing system, W x and W y They represent the external loads on the rolling bearing in the coordinate system The load components along the x and y directions.

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