CN116561904A - Rolling bearing dynamics modeling and vibration characteristic analysis method - Google Patents

Abstract

The invention discloses a dynamic modeling and vibration characteristic analysis method for a rolling bearing, which comprises the following steps: s1: establishing a healthy bearing dynamics model: the rigidity and the damping of the bearing, the force between the rolling body and the retainer and the force between the rolling body and the rollaway nest are respectively calculated when the bearing is in elastohydrodynamic lubrication, and the basic physical quantity required in a healthy bearing dynamics model is determined; s2: building a bearing dynamics model with local faults: by introducing a half sine function, time-varying displacement excitation when the rolling body passes through the local fault is described, and finally, a bearing dynamics model with the local fault is established; s3: identifying a primary excitation source in a dynamic model with local faults: and determining a main excitation source by comparing the numerical value and the change trend of the basic physical quantity in the dynamic model. The invention simulates the actual working condition of the bearing in the running process more truly, and provides a theoretical basis for vibration response analysis of the rolling bearing under fault excitation.

Description

A method for dynamic modeling and vibration characteristic analysis of rolling bearings

Technical Field

The invention relates to the technical field of mechanical equipment health status assessment and fault diagnosis, and in particular to a rolling bearing dynamics modeling and vibration characteristic analysis method.

Background Art

Rolling bearings are widely used in rotating machinery, playing important roles such as supporting and transmitting power. However, they are often in harsh working environments and are prone to failure. If not handled in time, major accidents may occur. The performance of the bearing directly affects the operating accuracy and service life of the entire equipment. Therefore, bearing fault diagnosis is particularly important. Dynamic modeling and vibration analysis of rolling bearings with local defects provide a theoretical basis for analyzing the causes of faults and revealing the intrinsic relationship between system dynamic parameters and response signals in the fault state. However, the current dynamic analysis of rolling bearings often only focuses on the influence of single factors such as lubrication on vibration response, and lacks consideration of many factors in the operation process. Therefore, the existing methods cannot truly simulate the actual working conditions of the bearing during operation, and there is a large room for improvement. At the same time, the existing methods do not identify the main excitation sources in the dynamic model, resulting in a lack of theoretical basis for the vibration analysis of faulty bearings.

Summary of the invention

The purpose of the present invention is to provide a rolling bearing dynamics modeling and vibration characteristic analysis method to solve the problems in the prior art.

To achieve the above object, the present invention provides the following technical solution: a rolling bearing dynamics modeling and vibration characteristic analysis method, comprising the following steps:

S1: Establish a healthy bearing dynamics model: The stiffness and damping of the bearing, the force between the rolling element and the cage, and the force between the rolling element and the raceway when the bearing is in elastohydrodynamic lubrication are calculated, and the basic physical quantities required in the healthy bearing dynamics model are determined;

S2: Establishment of a bearing dynamics model with local faults: By introducing a half-sine function, the time-varying displacement excitation of the rolling element when it passes through a local fault is described, and finally a bearing dynamics model with local faults is established;

S3: Identification of the main excitation sources in the dynamic model with local faults: By comparing the numerical values and changing trends of the basic physical quantities in the dynamic model, the main excitation sources in the model are determined.

Preferably, S1.1: calculating bearing stiffness and damping based on elastohydrodynamic lubrication;

In the established dynamic model, the oil film in the Hertz contact area is toughened, and its oil film stiffness is much greater than the Hertz contact stiffness of the contact pair, so the oil film stiffness in the Hertz contact area is ignored;

The damping of the contact pair is composed of the structural damping of the bearing and the oil film damping in the Hertz area in series, and then in parallel with the viscous damping in the inlet area. Because the viscous damping of the oil film in the Hertz contact area is small, the damping is negligible after being connected in series with the structural damping in the Hertz contact area. Therefore, the damping of the contact pair comes from the viscous damping of the oil film in the inlet area.

The contact stiffness of the contact pair can be expressed as:

Where, E ^* is Young's modulus; μ is Poisson's ratio; Σρ is the raceway curvature; F is the first kind of complete elliptic integral, E is the second kind of complete elliptic integral; κ is the contact area ellipticity;

The viscous damping of the oil film in the inlet area can be expressed as:

Where η ₀ is the dynamic viscosity of the lubricant at room temperature; R _x is the equivalent radius of curvature along the rolling direction; a _nj is the major semi-axis length of the contact ellipse;

The viscosity given in the ISO standard is the kinematic viscosity, which is converted into dynamic viscosity by the following formula:

η ₀ =υ·ρ·10 ^-6 (Pa·s) (3)

For rolling bearings with elliptical point contact, the minimum oil film thickness and the oil film thickness at the center of the contact area are calculated using the Hamrock-Dowson film thickness formula:

h ₀ ＝2.69R _x U ^0.67 G ^0.53 W ^-0.067 (1-0.61e- ^0.73κ ) (4)

Where U, G and W are dimensionless velocity parameter, dimensionless material parameter and dimensionless load parameter respectively;

S1.2: Calculate the forces between the rolling elements and the cage;

During the operation of the bearing, the rolling elements rotate around the center of the bearing; in the non-load-bearing area, the cage drives the rolling elements to move; in the load-bearing area, the rolling elements drive the cage to move; the contact stiffness between the rolling elements and the cage is calculated using the Hertz contact theory; due to the complexity of the cage structure, the stiffness between the cages is calculated using the finite element method;

The force between the jth rolling element and the cage can be expressed as:

Where _ψr and _ψc are the rotational angular displacements of the rolling element and cage around the center of the bearing, respectively; _n is the load deformation index, which is 1 in a smaller elastic deformation range; _Krc is the connection stiffness between the rolling element and the cage; _Rm is the pitch diameter;

The friction between the jth rolling element and the cage can be expressed as:

Where, μ _c is the friction coefficient;

The internal force between the cages is expressed as:

Where _Kcc and _Ccc are the connection stiffness and connection damping between the cages, respectively; is the angular velocity of the cage rotating around the bearing center;

S1.3: Calculate the force between the rolling element and the raceway; based on Hertz nonlinear contact theory, the contact force between the rolling element and the inner/outer raceway is expressed as:

Where λ is a symbolic function, expressed as:

The contact deformation between the jth rolling element and the raceway is expressed as:

In the formula, and ^rj represent the radial displacements of the inner ring, outer ring and rolling element at the jth rolling element, respectively; e represents the radial clearance; is the displacement excitation caused by the jth rolling element entering the defect;

The radial displacement of the inner and outer rings at the jth rolling element is expressed as:

The angular position of the jth rolling element is expressed as:

In the formula, N _b represents the number of rolling elements;

The friction force between the jth rolling element and the raceway is expressed as:

The friction coefficient between the rolling element and the raceway is calculated by the following formula:

In the formula, represents the relative sliding velocity between the jth rolling element and the raceway, which is obtained by the following calculation:

ΔV _i ^j =V _ir -V _ri (23)

In the formula, and are the circumferential velocity and rotational velocity of the jth rolling body respectively, and R _r represents the radius of the rolling body.

Preferably, S2 includes 2.1: describing a local fault in a bearing raceway; for an early defect form of a bearing, the width of the fault is small, and the displacement of the rolling element when passing through the defect is smaller than the depth of the fault. In the state where the rolling element passes through the defect, L is the width of the fault, B is the depth of the fault, and H _max is the maximum displacement excitation;

When the rolling body enters and passes through the defect, the rolling body is always in contact with the I side. When the rolling body passes through the II side, the rolling body has left the defect area. This passing mode uses a half-sine function to describe the time-varying excitation of the displacement. The maximum displacement excitation H _max of the rolling body is:

The time-varying displacement excitation function of the rolling element when it passes through a defect can be expressed by the following function:

In the formula, represents the defect angle; represents the initial angle of the defect; n = i, o; It can be expressed by the following formula:

in, represents the angular position of the defect;

According to the above analysis, the dynamic equation of the bearing is as follows:

The dynamic equation of the inner circle's horizontal motion is:

The dynamic equation of the vertical motion of the inner ring is:

The dynamic equation of the cage circular motion is:

The dynamic equation of the circular motion of the rolling element:

The dynamic equation of rolling element rotation motion:

The dynamic equation of radial motion of rolling element:

In the formula, the centrifugal force of the jth rolling element can be expressed as:

F _wj =m _r R _m w _oj ² (36).

Preferably, S3 comprises the following steps:

S3.1: In order to verify the accuracy of the model, the bearing fault simulation test bench was used to conduct experiments and obtain experimental signals. At the same time, programming simulation was carried out based on MATLAB software, and the ode45 solver was used to solve the simulation signal. The envelope spectrum characteristics between the experimental signal and the simulation signal were qualitatively compared. The bearing used was SKF6205-2RS, and the grooves were processed on the inner and outer rings of the bearing respectively by wire cutting. The bearing was driven by a drive motor at a speed of 900r/min, and the sampling frequency was set to 10kHz. The acceleration of the outer ring of the bearing in the Y direction was used as the original signal of the dynamic model. The envelope spectrum of the original signal was obtained by Fourier transform and Hilbert transform.

After the above experiment verified the accuracy of the constructed dynamic model, the changes of key physical quantities in the constructed dynamic model over a certain period of time were displayed in the form of images. Finally, by analyzing and comparing the similarities between the physical quantities and the vibration responses of the bearings in terms of numerical values and change trends, it was determined that the main excitation source in the model was the contact force between the rolling elements and the raceways.

Compared with the prior art, the beneficial effects of the present invention are as follows: taking rolling bearings as the research object, a bearing dynamics model is established that takes into account cage flexibility, elasto-fluid lubrication, and time-varying displacement excitation caused by local faults. The model is more sophisticated and can more accurately simulate the vibration mechanism of the bearing; the vibration response of the constructed dynamics model is compared with the experimental signal, and after verifying the accuracy of the model, the excitation source in the model is determined through comparative analysis, providing a theoretical basis for the analysis of bearing vibration response. At the same time, the constructed fault model can simulate the vibration response of the bearing under different fault types and fault sizes, and can provide a data source for intelligent fault diagnosis of rolling bearings based on big data.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation of the present invention. In the accompanying drawings:

Figure 1 shows the contact model in the bearing dynamics model;

FIG2 is a schematic diagram of a force analysis of a cage;

FIG3 is a diagram showing a rolling element passing through a defect;

Figure 4 shows the changes in the main physical quantities in the dynamic model when the fault is in the inner ring of the bearing;

Figure 5 shows the changes of the main physical quantities in the dynamic model when the fault is in the outer ring of the bearing;

Figure 6 shows the vibration response and some physical quantities when the fault is in the inner ring of the bearing changes in

Figure 7 shows the vibration response and some physical quantities when the fault is on the outer ring of the bearing changes in

Figure 8 is a bearing dynamics model;

Figure 9 is a comparison of the envelope spectra of the simulation signal and the experimental signal under different fault conditions.

DETAILED DESCRIPTION

In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work belong to the scope of protection of the present invention. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the invention claimed for protection, but merely represents the selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work belong to the scope of protection of the present invention.

Referring to FIGS. 1-9 , in an embodiment of the present invention, a rolling bearing dynamics modeling and vibration characteristic analysis method comprises the following steps:

S1: Establish a healthy bearing dynamics model: The stiffness and damping of the bearing, the force between the rolling element and the cage, and the force between the rolling element and the raceway when the bearing is in elastohydrodynamic lubrication are calculated, and the basic physical quantities required in the healthy bearing dynamics model are determined;

S2: Establishment of a bearing dynamics model with local faults: By introducing a half-sine function, the time-varying displacement excitation of the rolling element when it passes through a local fault is described, and finally a bearing dynamics model with local faults is established;

S3: Identification of the main excitation sources in the dynamic model with local faults: By comparing the numerical values and changing trends of the basic physical quantities in the dynamic model, the main excitation sources in the model are determined.

Preferably, S1.1: calculating bearing stiffness and damping based on elastohydrodynamic lubrication;

In the established dynamic model, the oil film in the Hertz contact area is toughened, and its oil film stiffness is much greater than the Hertz contact stiffness of the contact pair, so the oil film stiffness in the Hertz contact area is ignored;

The damping of the contact pair is composed of the structural damping of the bearing and the oil film damping in the Hertz area in series, and then in parallel with the viscous damping in the inlet area. Because the viscous damping of the oil film in the Hertz contact area is small, the damping is negligible after being connected in series with the structural damping in the Hertz contact area. Therefore, the damping of the contact pair comes from the viscous damping of the oil film in the inlet area.

The contact stiffness of the contact pair can be expressed as:

Where, E ^* is Young's modulus; μ is Poisson's ratio; Σρ is the raceway curvature; F is the first kind of complete elliptic integral, E is the second kind of complete elliptic integral; κ is the contact area ellipticity;

The viscous damping of the oil film in the inlet area can be expressed as:

Where η ₀ is the dynamic viscosity of the lubricant at room temperature; R _x is the equivalent radius of curvature along the rolling direction; a _nj is the major semi-axis length of the contact ellipse;

The viscosity given in the ISO standard is the kinematic viscosity, which is converted into dynamic viscosity by the following formula:

η ₀ =υ·ρ·10 ^-6 (Pa·s) (3)

For rolling bearings with elliptical point contact, the minimum oil film thickness and the oil film thickness at the center of the contact area are calculated using the Hamrock-Dowson film thickness formula:

h ₀ ＝2.69R _x U ^0.67 G ^0.53 W ^-0.067 (1-0.61e ^-0.73κ ) (4)

Where U, G and W are dimensionless velocity parameter, dimensionless material parameter and dimensionless load parameter respectively;

S1.2: Calculate the forces between the rolling elements and the cage;

During the operation of the bearing, the rolling elements rotate around the center of the bearing; in the non-load-bearing area, the cage drives the rolling elements to move; in the load-bearing area, the rolling elements drive the cage to move; the contact stiffness between the rolling elements and the cage is calculated using the Hertz contact theory; due to the complexity of the cage structure, the stiffness between the cages is calculated using the finite element method;

The force between the jth rolling element and the cage can be expressed as:

Where _ψr and _ψc are the rotational angular displacements of the rolling element and cage around the center of the bearing, respectively; n is the load deformation index, which is 1 in a smaller elastic deformation range; _Krc is the connection stiffness between the rolling element and the cage; _Rm is the pitch diameter;

The friction between the jth rolling element and the cage can be expressed as:

Where, μ _c is the friction coefficient;

The internal force between the cages is expressed as:

Where _Kcc and _Ccc are the connection stiffness and connection damping between the cages, respectively; is the angular velocity of the cage rotating around the bearing center;

S1.3: Calculate the force between the rolling element and the raceway; based on Hertz nonlinear contact theory, the contact force between the rolling element and the inner/outer raceway is expressed as:

Where λ is a symbolic function, expressed as:

The contact deformation between the jth rolling element and the raceway is expressed as:

In the formula, r _i ^j , and ^rj represent the radial displacements of the inner ring, outer ring and rolling element at the jth rolling element, respectively; e represents the radial clearance; is the displacement excitation caused by the jth rolling element entering the defect;

The radial displacement of the inner and outer rings at the jth rolling element is expressed as:

The angular position of the jth rolling element is expressed as:

In the formula, N _b represents the number of rolling elements;

The friction force between the jth rolling element and the raceway is expressed as:

The friction coefficient between the rolling element and the raceway is calculated by the following formula:

In the formula, represents the relative sliding velocity between the jth rolling element and the raceway, which is obtained by the following calculation:

ΔV _i ^j =V _ir -V _ri (23)

In the formula, and are the circumferential velocity and rotational velocity of the jth rolling body respectively, and R _r represents the radius of the rolling body.

Preferably, S2 includes 2.1: describing a local fault in a bearing raceway; for an early defect form of a bearing, the width of the fault is small, and the displacement of the rolling element when passing through the defect is smaller than the depth of the fault. In the state where the rolling element passes through the defect, L is the width of the fault, B is the depth of the fault, and H _max is the maximum displacement excitation;

When the rolling body enters and passes through the defect, the rolling body is always in contact with the I side. When the rolling body passes through the II side, the rolling body has left the defect area. This passing mode uses a half-sine function to describe the time-varying excitation of the displacement. The maximum displacement excitation H _max of the rolling body is:

The time-varying displacement excitation function of the rolling element when it passes through a defect can be expressed by the following function:

In the formula, represents the defect angle; represents the initial angle of the defect; n = i, o; It can be expressed by the following formula:

in, represents the angular position of the defect;

According to the above analysis, the dynamic equation of the bearing is as follows:

The dynamic equation of the inner circle's horizontal motion is:

The dynamic equation of the vertical motion of the inner ring is:

The dynamic equation of the cage circular motion is:

The dynamic equation of the circular motion of the rolling element:

The dynamic equation of rolling element rotation motion:

The dynamic equation of radial motion of rolling element:

In the formula, the centrifugal force of the jth rolling element can be expressed as:

F _wj =m _r R _m w _oj ² (36).

Preferably, S3 comprises the following steps:

S3.1: In order to verify the accuracy of the model, the bearing fault simulation test bench was used to conduct experiments and obtain experimental signals. At the same time, programming simulation was carried out based on MATLAB software, and the ode45 solver was used to solve the simulation signal. The envelope spectrum characteristics between the experimental signal and the simulation signal were qualitatively compared. The bearing used was SKF6205-2RS, and the grooves were processed on the inner and outer rings of the bearing respectively by wire cutting. The bearing was driven by a drive motor at a speed of 900r/min, and the sampling frequency was set to 10kHz. The acceleration of the outer ring of the bearing in the Y direction was used as the original signal of the dynamic model. The envelope spectrum of the original signal was obtained by Fourier transform and Hilbert transform.

The changes of the main physical quantities in the dynamic model proposed by the present invention are shown in Figures 4 and 5. It can be clearly seen from the amplitude that the friction between the rolling element and the inner rolling element Friction between rolling element and outer rolling element Friction between the rolling element and the previous cage Friction between the rolling element and the next cage Much smaller than the contact force between the rolling element and the inner raceway Contact force between rolling element and outer raceway Contact force between rolling element and previous cage Contact force between rolling element and the next cage This shows that and It plays a dominant role in influencing the vibration response of the bearing.

Figure 6 shows the vibration response and main physical quantities of the inner ring when the fault is in the inner ring of the bearing. From the perspective of numerical value and change pattern, compared to, It has a great influence on the vibration response of the inner ring. Therefore, it can be judged that the contact force between the rolling element and the raceway is the main physical quantity affecting the vibration response of the bearing, which is the excitation source in the proposed dynamic model. When the fault is located in the outer ring of the bearing, the vibration response of the inner ring and the main physical quantity The change of is shown in Figure 7. From the change trend in the figure, the same conclusion can be drawn: the contact force between the rolling element and the raceway is the main physical quantity that affects the vibration response of the bearing, which is the excitation source in the proposed dynamic model.

The dynamic model of the bearing is shown in Figure 8. The present invention uses a bearing fault simulation test bench to conduct experiments, obtains experimental signals, obtains the envelope of the original experimental signal by Hilbert transform, and then performs Fourier transform on the envelope to obtain the envelope spectrum of the experimental signal as shown in Figure 9. The theoretical characteristic frequency of the bearing is shown in Table 1. The parameters used in the dynamic model are shown in Table 2. The present invention considers two defect conditions, namely, local fault of the outer ring and local fault of the inner ring.

Table 1 Fault characteristic frequency of SKF6205 deep groove ball bearing

Table 2 SKF6205 deep groove ball bearing parameters

The invention is described in detail below in conjunction with simulation signal analysis. The invention comprises the following steps:

Step 1: Establish a healthy bearing dynamics model. This step calculates the stiffness and damping of the bearing when the bearing is in elastohydrodynamic lubrication, the force between the rolling element and the cage, and the force between the rolling element and the raceway, and determines the basic physical quantities required in a healthy bearing dynamics model.

Step 2: Establish a bearing dynamics model with local faults. By introducing a half-sine function, the time-varying displacement excitation of the rolling element when it passes through a local fault is described, and finally a bearing dynamics model with local faults is established.

Step 3: After verifying the accuracy of the model through simulation signal analysis, identify the main excitation source in the dynamic model with local faults. After confirming the accuracy of the model by comparing the simulation signal with the experimental signal, this step compares the numerical values and change trends of the basic physical quantities in the dynamic model to determine the main excitation source in the model.

The step 1 comprises:

Step 1.1: Calculate the bearing stiffness and damping based on elasto-fluid lubrication. In the dynamic model established by the present invention, the contact model is shown in Figure 1. Since the oil film in the Hertz contact area is toughened, its oil film stiffness is much greater than the Hertz contact stiffness of the contact pair, so the oil film stiffness of the Hertz contact area can be ignored. The damping of the contact pair is composed of the structural damping of the bearing and the oil film damping in the Hertz area in series, and then in parallel with the viscous damping in the entrance area. Because the viscous damping of the oil film in the Hertz contact area is small, the damping can be ignored after being connected in series with the structural damping of the Hertz contact area. Therefore, the damping of the contact pair mainly comes from the viscous damping of the oil film in the entrance area. The contact stiffness of the contact pair can be expressed as:

Where, E ^* is Young's modulus; μ is Poisson's ratio; Σρ is the raceway curvature; F is the first kind of complete elliptic integral, E is the second kind of complete elliptic integral; κ is the contact area ellipticity.

The viscous damping of the oil film in the inlet area can be expressed as:

Where η ₀ is the dynamic viscosity of the lubricant at room temperature; R _x is the equivalent radius of curvature along the rolling direction; and a _nj is the length of the major semi-axis of the contact ellipse. The viscosity given in the ISO standard is the kinematic viscosity, which can be converted into the dynamic viscosity by the following formula:

η ₀ =υ·ρ·10 ^-6 (Pa·s) (3)

For rolling bearings with elliptical point contact, the most common calculation formula for the minimum oil film thickness and the oil film thickness at the center of the contact area is the Hamrock-Dowson film thickness formula:

h ₀ ＝2.69R _x U ^0.67 G ^0.53 W ^-0.067 (1-0.61e ^-0.73κ ) (4)

Where U, G and W are dimensionless velocity parameter, dimensionless material parameter and dimensionless load parameter, respectively.

Step 1.2: Calculate the force between the rolling element and the cage. During the operation of the bearing, the rolling element rotates around the center of the bearing. In the non-load-bearing area, the cage drives the rolling element to move; in the load-bearing area, the rolling element drives the cage to move. The contact stiffness between the rolling element and the cage is calculated using the Hertz contact theory. Due to the complexity of the cage structure, the stiffness between the cages is calculated using the finite element method. The force analysis of the cage is shown in Figure 2.

The force between the jth rolling element and the cage can be expressed as:

Where _ψr and _ψc are the rotational angular displacements of the rolling element and cage around the center of the bearing, respectively. n is the load deformation index, which is 1 in the smaller elastic deformation range. _Krc is the connection stiffness between the rolling element and the cage. _Rm is the pitch diameter.

The friction force between the jth rolling element and the cage can be expressed as:

Where _μc is the friction coefficient.

The internal force between the cages can be expressed as:

Where _Kcc and _Ccc are the connection stiffness and connection damping between the cages respectively; Ccc is the angular velocity of the cage rotating around the bearing center.

Step 1.3: Calculate the force between the rolling element and the raceway. Based on Hertz nonlinear contact theory, the contact force between the rolling element and the inner/outer raceway can be expressed as:

Where λ is a symbolic function, which can be expressed as:

The contact deformation between the jth rolling element and the raceway can be expressed as:

In the formula, r _i ^j , and ^rj represent the radial displacements of the inner ring, outer ring and rolling element at the jth rolling element, respectively; e represents the radial clearance; is the displacement excitation caused by the jth rolling element entering the defect, which will be explained in detail in step 2.

The radial displacement of the inner and outer rings at the jth rolling element can be expressed as:

The angular position of the jth rolling element can be expressed as:

Where _Nb represents the number of rolling elements.

The friction force between the jth rolling element and the raceway can be expressed as:

The friction coefficient between the rolling element and the raceway can be calculated by the following formula:

In the formula, represents the relative sliding velocity between the jth rolling element and the raceway, which is obtained by the following calculation:

ΔV _i ^j =V _ir -V _ri (23)

In the formula, and are the circumferential velocity and rotational velocity of the jth rolling body respectively, and R _r represents the radius of the rolling body.

The step 2 comprises:

Step 2.1: Describe the local fault in the bearing raceway. The present invention mainly studies the early defect form of the bearing. The width of this fault is small, and the displacement of the rolling element when passing through the defect is smaller than the depth of the fault. The state of the rolling element passing through the defect is shown in Figure 3, where L is the width of the fault, B is the depth of the fault, and H _max is the maximum displacement excitation.

As can be seen from Figure 3, when the rolling body enters and passes through the defect, the rolling body is always in contact with side I, and when the rolling body passes through side II, the rolling body has left the defect area. This passing mode can use a half-sine function to describe the time-varying excitation of the displacement. The maximum displacement excitation H _max of the rolling body is:

The time-varying displacement excitation function of the rolling element when it passes through a defect can be expressed by the following function:

In the formula, represents the defect angle; represents the initial angle of the defect; n = i, o; It can be expressed by the following formula:

in, Represents the angular position of the defect.

According to the above analysis, the dynamic equation of the bearing can be obtained as follows:

The dynamic equation of the inner circle's horizontal motion is:

The dynamic equation of the vertical motion of the inner ring is:

The dynamic equation of the cage circular motion is:

The dynamic equation of the circular motion of the rolling element:

The dynamic equation of rolling element rotation motion:

The dynamic equation of radial motion of rolling element:

In the formula, the centrifugal force of the jth rolling element can be expressed as:

F _wj = m _r R _m w _oj ² (36)

The step 3 comprises:

Step 3.1: In order to verify the accuracy of the model, the bearing fault simulation test bench was used to conduct experiments and obtain experimental signals. At the same time, programming simulation was performed based on MATLAB software, and the ode45 solver was used to solve and obtain the simulation signal. The envelope spectrum characteristics between the experimental signal and the simulation signal were qualitatively compared. The bearing used was SKF6205-2RS. The grooves were processed on the inner and outer rings of the bearing by wire cutting. The bearing was driven by a drive motor at a speed of 900r/min, and the sampling frequency was set to 10kHz. The acceleration of the outer ring of the bearing in the Y direction was used as the original signal of the dynamic model. The envelope spectrum of the original signal can be obtained by Fourier transform and Hilbert transform.

The present invention considers two defect conditions, namely, local fault of the outer ring and local fault of the inner ring. The comparison of the simulation and experimental signals under the two defect conditions is shown in FIG9. When the bearing is in the condition of inner ring fault, the envelope spectra of the simulation signal and the experimental signal of the bearing are shown in FIG9(a) and (b). It can be clearly seen from FIG9(a) that the fault characteristic frequency Bpfi of the inner ring and its multiples are modulated by the rotation frequency fs. A similar situation can also be clearly seen from FIG9(b).

Figure 9(c) and (d) respectively describe the envelope spectra of the simulated signal and the experimental signal in the case of a local fault in the outer race. The obvious fault characteristic frequency Bpfo and its multiples can be seen in both the simulated signal and the experimental signal.

According to the above comparison, it can be seen that under different defect conditions, the main characteristics of the simulation signal are consistent with the main characteristics of the experimental signal, thus proving the effectiveness of the proposed model.

Step 3.2: The changes of the main physical quantities in the dynamic model proposed by the present invention are shown in Figures 4 and 5. It can be clearly seen from the amplitude that the friction between the rolling element and the inner rolling element Friction between rolling element and outer rolling element Friction between the rolling element and the previous cage Friction between the rolling element and the next cage Much smaller than the contact force between the rolling element and the inner raceway Contact force between rolling element and outer raceway Contact force between rolling element and previous cage Contact force between rolling element and the next cage This shows that and It plays a dominant role in influencing the vibration response of the bearing.

Figure 6 shows the vibration response and main physical quantities of the inner ring when the fault is in the inner ring of the bearing. From the perspective of numerical value and change pattern, compared to, It has a great influence on the vibration response of the inner ring. Therefore, it can be judged that the contact force between the rolling element and the raceway is the main physical quantity affecting the vibration response of the bearing, which is the excitation source in the proposed dynamic model. When the fault is located in the outer ring of the bearing, the vibration response of the inner ring and the main physical quantity The change of is shown in Figure 7. From the change trend in the figure, the same conclusion can be drawn: the contact force between the rolling element and the raceway is the main physical quantity that affects the vibration response of the bearing, which is the excitation source in the proposed dynamic model.

In order to solve the problem that traditional models cannot truly reflect the actual state of bearings during operation, the present invention takes rolling bearings as the research object and establishes a bearing dynamics model that takes into account the flexibility of the cage, elasto-fluid lubrication, and time-varying displacement excitation caused by local faults. The model is more sophisticated and can more accurately simulate the vibration mechanism of the bearing. The vibration response of the constructed dynamics model is compared with the experimental signal. After verifying the accuracy of the model, the excitation source in the model is determined through comparative analysis, providing a theoretical basis for the analysis of bearing vibration response. At the same time, the constructed fault model can simulate the vibration response of the bearing under different fault types and fault sizes, and can provide a data source for intelligent fault diagnosis of rolling bearings based on big data.

Figure 6 Vibration response and some physical quantities when the fault is in the inner ring of the bearing Changes in: (a, c) Contact force between rolling element and inner/outer raceway in horizontal direction (b, d) Contact force between rolling element and inner/outer raceway in vertical direction (e, g) Horizontal contact force between the rolling element and the previous/next cage (f, h) Contact force between the rolling element and the previous/next cage in the vertical direction (i) Vibration response of the inner ring in the horizontal direction; (j) Vibration response of the inner ring in the vertical direction.

Figure 7 Vibration response and some physical quantities when the fault is on the outer ring of the bearing Changes in: (a, c) Contact force between rolling element and inner/outer raceway in horizontal direction (b, d) Contact force between rolling element and inner/outer raceway in vertical direction (e, g) Horizontal contact force between the rolling element and the previous/next cage (f, h) Contact force between the rolling element and the previous/next cage in the vertical direction (i) Vibration response of the inner ring in the horizontal direction; (j) Vibration response of the inner ring in the vertical direction.

Figure 9 Comparison of envelope spectra of simulated signals and experimental signals under different fault conditions: (a) envelope spectrum of simulated signal under inner ring fault condition; (b) envelope spectrum of experimental signal under inner ring fault condition; (c) envelope spectrum of simulated signal under outer ring fault condition; (d) envelope spectrum of experimental signal under outer ring fault condition.

Finally, it should be noted that the above is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or replace some of the technical features therein by equivalents. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims (4)

1. A rolling bearing dynamics modeling and vibration characteristic analysis method, characterized in that it includes the following steps: S1: Establish a healthy bearing dynamics model: The stiffness and damping of the bearing, the force between the rolling element and the cage, and the force between the rolling element and the raceway when the bearing is in elastohydrodynamic lubrication are calculated, and the basic physical quantities required in the healthy bearing dynamics model are determined; S2: Establishment of a bearing dynamics model with local faults: By introducing a half-sine function, the time-varying displacement excitation of the rolling element when it passes through a local fault is described, and finally a bearing dynamics model with local faults is established; S3: Identification of the main excitation sources in the dynamic model with local faults: By comparing the numerical values and changing trends of the basic physical quantities in the dynamic model, the main excitation sources in the model are determined. 2. A rolling bearing dynamics modeling and vibration characteristic analysis method according to claim 1, characterized in that: S1.1: calculating the bearing stiffness and damping based on elasto-fluid lubrication; In the established dynamic model, the oil film in the Hertz contact area is toughened, and its oil film stiffness is much greater than the Hertz contact stiffness of the contact pair, so the oil film stiffness in the Hertz contact area is ignored; The damping of the contact pair is composed of the structural damping of the bearing and the oil film damping in the Hertz area in series, and then in parallel with the viscous damping in the inlet area. Because the viscous damping of the oil film in the Hertz contact area is small, the damping is negligible after being connected in series with the structural damping in the Hertz contact area. Therefore, the damping of the contact pair comes from the viscous damping of the oil film in the inlet area. The contact stiffness of the contact pair can be expressed as: Where, E ^* is Young's modulus; μ is Poisson's ratio; Σρ is the raceway curvature; F is the first kind of complete elliptic integral, E is the second kind of complete elliptic integral; κ is the contact area ellipticity; The viscous damping of the oil film in the inlet area can be expressed as: Where η ₀ is the dynamic viscosity of the lubricant at room temperature; R _x is the equivalent radius of curvature along the rolling direction; a _nj is the major semi-axis length of the contact ellipse; The viscosity given in the ISO standard is the kinematic viscosity, which is converted into dynamic viscosity by the following formula: η ₀ =υ·ρ·10 ^-6 (Pa·s) (3) For rolling bearings with elliptical point contact, the minimum oil film thickness and the oil film thickness at the center of the contact area are calculated using the Hamrock-Dowson film thickness formula: h ₀ ＝2.69R _x U ^0.67 G ^0.53 W ^-0.067 (1-0.61e ^-0.73κ ) (4) Where U, G and W are dimensionless velocity parameter, dimensionless material parameter and dimensionless load parameter respectively; S1.2: Calculate the forces between the rolling elements and the cage; During the operation of the bearing, the rolling elements rotate around the center of the bearing; in the non-load-bearing area, the cage drives the rolling elements to move; in the load-bearing area, the rolling elements drive the cage to move; the contact stiffness between the rolling elements and the cage is calculated using the Hertz contact theory; due to the complexity of the cage structure, the stiffness between the cages is calculated using the finite element method; The force between the jth rolling element and the cage can be expressed as: Where _ψr and _ψc are the rotational angular displacements of the rolling element and cage around the center of the bearing, respectively; n is the load deformation index, which is 1 in a smaller elastic deformation range; _Krc is the connection stiffness between the rolling element and the cage; _Rm is the pitch diameter; The friction between the jth rolling element and the cage can be expressed as: Where, μ _c is the friction coefficient; The internal force between the cages is expressed as: Where _Kcc and _Ccc are the connection stiffness and connection damping between the cages, respectively; is the angular velocity of the cage rotating around the bearing center; S1.3: Calculate the force between the rolling element and the raceway; based on Hertz nonlinear contact theory, the contact force between the rolling element and the inner/outer raceway is expressed as: Where λ is a symbolic function, expressed as: The contact deformation between the jth rolling element and the raceway is expressed as: In the formula, and ^rj represent the radial displacements of the inner ring, outer ring and rolling element at the jth rolling element, respectively; e represents the radial clearance; is the displacement excitation caused by the jth rolling element entering the defect; The radial displacement of the inner and outer rings at the jth rolling element is expressed as: The angular position of the jth rolling element is expressed as: In the formula, N _b represents the number of rolling elements; The friction force between the jth rolling element and the raceway is expressed as: The friction coefficient between the rolling element and the raceway is calculated by the following formula: In the formula, represents the relative sliding velocity between the jth rolling element and the raceway, which is obtained by the following calculation: ΔV _i ^j =V _ir -V _ri (23) In the formula, and are the circumferential velocity and rotational velocity of the jth rolling body respectively, and R _r represents the radius of the rolling body. 3. A rolling bearing dynamics modeling and vibration characteristic analysis method according to claim 1, characterized in that: said S2 includes 2.1: describing a local fault in the bearing raceway; for the early defect form of the bearing, the width of the fault is small, and the displacement of the rolling element when passing through the defect is smaller than the depth of the fault. In the state where the rolling element passes through the defect, L is the width of the fault, B is the depth of the fault, and H _max is the maximum displacement excitation; When the rolling body enters and passes through the defect, the rolling body is always in contact with the I side. When the rolling body passes through the II side, the rolling body has left the defect area. This passing mode uses a half-sine function to describe the time-varying excitation of the displacement. The maximum displacement excitation H _max of the rolling body is: The time-varying displacement excitation function of the rolling element when it passes through a defect can be expressed by the following function: In the formula, represents the defect angle; represents the initial angle of the defect; n = i, o; It can be expressed by the following formula: in, represents the angular position of the defect; According to the above analysis, the dynamic equation of the bearing is as follows: The dynamic equation of the inner circle's horizontal motion is: The dynamic equation of the vertical motion of the inner ring is: The dynamic equation of the cage circular motion is: The dynamic equation of the circular motion of the rolling element: The dynamic equation of rolling element rotation motion: The dynamic equation of radial motion of rolling element: In the formula, the centrifugal force of the jth rolling element can be expressed as: F _wj =m _r R _m w _oj ² (36). 4. A rolling bearing dynamics modeling and vibration characteristic analysis method according to claim 1, characterized in that: said S3 comprises the following steps: S3.1: In order to verify the accuracy of the model, the bearing fault simulation test bench was used to conduct experiments and obtain experimental signals. At the same time, programming simulation was carried out based on MATLAB software, and the ode45 solver was used to solve the simulation signal. The envelope spectrum characteristics between the experimental signal and the simulation signal were qualitatively compared. The bearing used was SKF6205-2RS, and the grooves were processed on the inner and outer rings of the bearing respectively by wire cutting. The bearing was driven by a drive motor at a speed of 900r/min, and the sampling frequency was set to 10kHz. The acceleration of the outer ring of the bearing in the Y direction was used as the original signal of the dynamic model. The envelope spectrum of the original signal was obtained by Fourier transform and Hilbert transform.