CN116561904A - Rolling bearing dynamics modeling and vibration characteristic analysis method - Google Patents
Rolling bearing dynamics modeling and vibration characteristic analysis method Download PDFInfo
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- 238000002474 experimental method Methods 0.000 claims description 6
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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
Technical Field
The invention relates to the technical field of mechanical equipment health state evaluation and fault diagnosis, in particular to a rolling bearing dynamic modeling and vibration characteristic analysis method.
Background
Rolling bearings are widely used in rotary machinery and play important roles in supporting, transmitting power and the like, but are often in a severe working environment, faults are easy to occur, if the faults are not timely processed, serious accidents can be caused, the running precision and the service life of the whole equipment are directly influenced by the performance of the bearings, and therefore, the rolling bearings are particularly important for fault diagnosis of the bearings. The dynamic modeling and vibration analysis of the rolling bearing with the local defects provide a theoretical basis for analyzing the fault cause and revealing the internal connection between the system dynamic parameters and response signals in the fault state. Then, at present, the dynamic analysis of the rolling bearing usually only pays attention to the influence of single factors such as lubrication and the like on vibration response, and consideration of a plurality of factors in the running process is lacking, so that the existing method cannot truly simulate the actual working condition of the bearing in the running process, and a large improvement space exists, and meanwhile, the existing method does not identify a main excitation source in a dynamic model, so that the vibration analysis of the fault bearing lacks a certain theoretical basis.
Disclosure of Invention
The invention aims to provide a dynamic modeling and vibration characteristic analysis method for a rolling bearing, which aims to solve the problems in the prior art.
In order to achieve the above purpose, the present invention provides the following technical solutions: a method for dynamic modeling and vibration signature analysis of a rolling bearing, comprising the steps of:
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: the main excitation source in the dynamic model is determined by comparing the magnitude and the change trend of the basic physical quantity in the model.
Preferably, S1.1: calculating bearing rigidity and damping based on elastic fluid lubrication;
in the established dynamic model, oil film tempering is carried out in a Hertz contact area, and the oil film rigidity of the oil film tempering is far greater than the Hertz contact rigidity of a contact pair, so that the oil film rigidity of the Hertz contact area is ignored;
the damping of the contact pair is formed by connecting the structural damping of the bearing and the oil film damping of the Hertz region in series and then connecting the structural damping and the viscous damping of the inlet region in parallel; because the oil film viscosity damping value of the Hertz contact area is smaller, the damping is negligible after the oil film viscosity damping value is connected in series with the structure damping of the Hertz contact area, so that the damping of the contact pair comes from the viscosity damping of the oil film of the inlet area;
the contact stiffness of a contact pair can be expressed as:
in the formula ,E* Is Young's modulus; μ is poisson's ratio; Σρ is the sum of the raceways curves; f is a first type of complete elliptic integral, E is a second type of complete elliptic integral; kappa is the ellipticity of the contact area;
viscous damping of the inlet zone oil film can be expressed as:
in the formula ,η0 Is the dynamic viscosity of the lubricant at room temperature; r is R x Is the equivalent radius of curvature in the rolling direction; a, a nj A long half-axis length which is the contact ellipse;
the viscosity given in the ISO standard is the kinematic viscosity, which is converted to the dynamic viscosity by the following formula:
η 0 ＝υ·ρ·10 -6 (Pa·s) (3)
for an elliptic point contact rolling bearing, the most calculation formula of the minimum oil film thickness and the contact area center oil film thickness is a 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)
wherein U, G and W are a dimensionless speed parameter, a dimensionless material parameter, and a dimensionless load parameter, respectively;
s1.2: calculating a force between the rolling bodies and the cage;
during the working process of the bearing, the rolling bodies rotate around the center of the bearing; in the non-bearing area, the cage drives the rolling bodies to move; in the bearing area, the rolling bodies drive the retainer to move; the contact rigidity of the rolling body and the retainer is calculated by adopting a Hertz contact theory; due to the complexity of the cage structure, the stiffness between the cage and the cage is calculated using a finite element method;
the force between the j-th rolling element and the cage can be expressed as:
wherein ,ψr and ψc Rotational angular displacements of the rolling bodies and the cage around the center of the bearing are respectively; n is a load deformation index, 1 in a smaller elastic deformation range; k (K) rc Is the connection rigidity between the rolling bodies and the cage; r is R m Is the pitch diameter;
friction between the j-th rolling element and the cage can be expressed as:
wherein ,μc Is the coefficient of friction;
the internal force between the retainers is expressed as:
in the formula ,Kcc and CCC The connection rigidity and the connection damping between the retainers are respectively; is the angular velocity at which the cage rotates about the bearing center;
s1.3: calculating the force between the rolling bodies and the rollaway nest; based on the theory of Hertz nonlinear contact, the contact force between the rolling bodies and the inner/outer raceways is expressed as:
where λ is a sign function expressed as:
the contact deformation between the j-th rolling element and the raceway is expressed as:
in the formula , and rj Respectively representing radial displacement of the inner ring, the outer ring and the rolling bodies at the j-th rolling body; e represents a radial gap;Is displacement excitation caused by the defect of the jth rolling element;
the radial displacement of the inner and outer races at the j-th rolling element is expressed as:
the angular position of the j-th rolling element is expressed as:
in the formula ,Nb Representing the number of rolling bodies;
the friction between the j-th rolling element and the raceway is expressed as:
wherein the coefficient of friction between the rolling elements and the raceway is calculated by the following formula:
in the formula ,representing the relative sliding speed between the jth rolling element and the raceway, by the following calculation:
ΔV i j ＝V ir -V ri (23)
in the formula , andThe circumferential speed and the rotation speed of the jth rolling element are respectively R r Representing the radius of the rolling elements.
Preferably, the S2 includes 2.1: describing a partial fault in the bearing race; for the early defect form of the bearing, the width of the fault is smaller, the descending displacement of the rolling element passing through the defect is smaller than the depth of the fault, L is the width of the fault in the state that the rolling element passes through the defect, B is the depth of the fault, H max Is the maximum displacement excitation;
when the rolling bodies enter and pass through the defect, the rolling bodies are always contacted with the side I, and when the rolling bodies pass through the side II, the rolling bodies leave the defect area; this pass-through approach employs a half-sine function to describe the time-varying excitation of displacement; maximum displacement excitation H of rolling bodies max The method comprises the following steps:
the time-varying displacement excitation function of the rolling element passing through the defect can be expressed as follows:
in the formula ,representing a defect angle;An initial angle representing a defect; n=i, o;The expression can be represented by the following formula:
wherein ,an angular position representing a defect;
from the above analysis, the kinetic equation for this bearing is obtained as follows:
kinetic equation of horizontal movement of inner ring:
kinetic equation of vertical motion of inner ring:
kinetic equation of cage circular motion:
kinetic equation of rolling element circular motion:
kinetic equation of rolling element rotation motion:
kinetic equation of radial movement of rolling bodies:
in the formula, the centrifugal force of the j-th rolling element can be expressed as:
F wj ＝m r R m w oj 2 (36)。
preferably, the step S3 includes the steps of:
s3.1: in order to verify the accuracy of the model, a bearing fault simulation test bed is adopted for carrying out experiments to obtain an experimental signal; meanwhile, programming simulation is carried out based on MATLAB software, and an ode45 solver is adopted for solving, so that simulation signals are obtained; qualitatively comparing the envelope spectrum characteristics between the experimental signal and the simulation signal; the bearing is SKF6205-2RS, grooves are respectively processed on the inner ring and the outer ring of the bearing in a linear cutting mode, the bearing is driven by a driving motor at the rotating speed of 900r/min, and the sampling frequency is set to be 10kHz; the acceleration of the outer ring of the bearing in the Y direction is used as an original signal of a dynamic model; the envelope spectrum of the original signal is obtained by fourier transform and hilbert transform.
After the accuracy of the built dynamic model is verified by the experiment, the change condition of key physical quantity in the built dynamic model in a certain time is displayed in an image mode, and finally, the similarity of the vibration response of the physical quantity and the bearing in the numerical value and the change trend is analyzed and compared, so that the contact force of the main vibration source in the model between the rolling body and the rolling path is determined.
Compared with the prior art, the invention has the beneficial effects that: the rolling bearing is taken as a research object, a dynamic bearing model which considers the flexibility of the retainer, the lubrication of elastic fluid and the time-varying displacement excitation caused by local faults is established, the model is finer, and the vibration mechanism of the bearing can be simulated more accurately; and comparing the vibration response of the built dynamic model with an experimental signal, and determining an excitation source in the model through comparison analysis after verifying the accuracy of the model, so as to provide a theoretical basis for bearing vibration response analysis. Meanwhile, the built 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 the rolling bearing based on big data.
Drawings
The accompanying drawings are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate the invention and together with the embodiments of the invention, serve to explain the invention. In the drawings:
FIG. 1 is a contact model in a dynamic model of a bearing;
FIG. 2 is a schematic diagram of a force analysis of a cage;
FIG. 3 is a diagram of a rolling element passing defect state;
FIG. 4 shows the change of main physical quantity in the dynamic model when the fault is in the bearing inner ring;
FIG. 5 is a graph showing the change of the main physical quantity in the dynamic model when the fault is in the outer ring of the bearing;
FIG. 6 shows the vibration response and some of the physical quantities when the fault is in the bearing inner race Is a change in conditions of (2);
FIG. 7 shows the vibration response and partial physical quantity of a bearing outer race when a fault is present Is a change in conditions of (2);
FIG. 8 is a dynamic model of a bearing;
fig. 9 is a comparison of envelope spectra of simulated and experimental signals for different fault conditions.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments, based on the embodiments of the invention, which are apparent to those of ordinary skill in the art without inventive faculty, are intended to be within the scope of the invention. Thus, the following detailed description of the embodiments of the invention, as presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, based on the embodiments of the invention, which are apparent to those of ordinary skill in the art without inventive faculty, are intended to be within the scope of the invention.
Referring to fig. 1-9, in an embodiment of the present invention, a method for modeling rolling bearing dynamics and vibration characteristics includes the steps of:
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: the main excitation source in the dynamic model is determined by comparing the magnitude and the change trend of the basic physical quantity in the model.
Preferably, S1.1: calculating bearing rigidity and damping based on elastic fluid lubrication;
in the established dynamic model, oil film tempering is carried out in a Hertz contact area, and the oil film rigidity of the oil film tempering is far greater than the Hertz contact rigidity of a contact pair, so that the oil film rigidity of the Hertz contact area is ignored;
the damping of the contact pair is formed by connecting the structural damping of the bearing and the oil film damping of the Hertz region in series and then connecting the structural damping and the viscous damping of the inlet region in parallel; because the oil film viscosity damping value of the Hertz contact area is smaller, the damping is negligible after the oil film viscosity damping value is connected in series with the structure damping of the Hertz contact area, so that the damping of the contact pair comes from the viscosity damping of the oil film of the inlet area;
the contact stiffness of a contact pair can be expressed as:
in the formula ,E* Is Young's modulus; μ is poisson's ratio; Σρ is the sum of the raceways curves; f is a first type of complete elliptic integral, E is a second type of complete elliptic integral; kappa is the ellipticity of the contact area;
viscous damping of the inlet zone oil film can be expressed as:
in the formula ,η0 Is the dynamic viscosity of the lubricant at room temperature; r is R x Is the equivalent radius of curvature in the rolling direction; a, a nj A long half-axis length which is the contact ellipse;
the viscosity given in the ISO standard is the kinematic viscosity, which is converted to the dynamic viscosity by the following formula:
η 0 ＝υ·ρ·10 -6 (Pa·s) (3)
for an elliptic point contact rolling bearing, the most calculation formula of the minimum oil film thickness and the contact area center oil film thickness is a 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)
wherein U, G and W are a dimensionless speed parameter, a dimensionless material parameter, and a dimensionless load parameter, respectively;
s1.2: calculating a force between the rolling bodies and the cage;
during the working process of the bearing, the rolling bodies rotate around the center of the bearing; in the non-bearing area, the cage drives the rolling bodies to move; in the bearing area, the rolling bodies drive the retainer to move; the contact rigidity of the rolling body and the retainer is calculated by adopting a Hertz contact theory; due to the complexity of the cage structure, the stiffness between the cage and the cage is calculated using a finite element method;
the force between the j-th rolling element and the cage can be expressed as:
wherein ,ψr and ψc Rotational angular displacements of the rolling bodies and the cage around the center of the bearing are respectively; n is the load deformation index, 1 in the smaller elastic deformation range; k (K) rc Is the connection rigidity between the rolling bodies and the cage; r is R m Is the pitch diameter;
friction between the j-th rolling element and the cage can be expressed as:
wherein ,μc is the coefficient of friction;
the internal force between the retainers is expressed as:
in the formula ,Kcc and CCC The connection rigidity and the connection damping between the retainers are respectively; is the angular velocity at which the cage rotates about the bearing center;
s1.3: calculating the force between the rolling bodies and the rollaway nest; based on the theory of Hertz nonlinear contact, the contact force between the rolling bodies and the inner/outer raceways is expressed as:
where λ is a sign function expressed as:
the contact deformation between the j-th rolling element and the raceway is expressed as:
in the formula ,ri j 、 and rj Respectively representing radial displacement of the inner ring, the outer ring and the rolling bodies at the j-th rolling body; e represents a radial gap;Is displacement excitation caused by the defect of the jth rolling element;
the radial displacement of the inner and outer races at the j-th rolling element is expressed as:
the angular position of the j-th rolling element is expressed as:
in the formula ,Nb Representing the number of rolling bodies;
the friction between the j-th rolling element and the raceway is expressed as:
wherein the coefficient of friction between the rolling elements and the raceway is calculated by the following formula:
in the formula ,representing the relative sliding speed between the jth rolling element and the raceway, by the following calculation:
ΔV i j ＝V ir -V ri (23)
in the formula , andThe circumferential speed and the rotation speed of the jth rolling element are respectively R r Representing the radius of the rolling elements.
Preferably, the S2 includes 2.1: describing a partial fault in the bearing race; for the early defect form of the bearing, the width of the fault is smaller, the descending displacement of the rolling element passing through the defect is smaller than the depth of the fault, L is the width of the fault in the state that the rolling element passes through the defect, B is the depth of the fault, H max Is the maximum displacement excitation;
when the rolling bodies enter and pass through the defect, the rolling bodies are always contacted with the side I, and when the rolling bodies pass through the side II, the rolling bodies leave the defect area; this pass-through approach employs a half-sine function to describe the time-varying excitation of displacement; maximum displacement excitation H of rolling bodies max The method comprises the following steps:
the time-varying displacement excitation function of the rolling element passing through the defect can be expressed as follows:
in the formula ,representing a defect angle;An initial angle representing a defect; n=i, o;The expression can be represented by the following formula:
wherein ,an angular position representing a defect;
from the above analysis, the kinetic equation for this bearing is obtained as follows:
kinetic equation of horizontal movement of inner ring:
kinetic equation of vertical motion of inner ring:
kinetic equation of cage circular motion:
kinetic equation of rolling element circular motion:
kinetic equation of rolling element rotation motion:
kinetic equation of radial movement of rolling bodies:
in the formula, the centrifugal force of the j-th rolling element can be expressed as:
F wj ＝m r R m w oj 2 (36)。
preferably, the step S3 includes the steps of:
s3.1: in order to verify the accuracy of the model, a bearing fault simulation test bed is adopted for carrying out experiments to obtain an experimental signal; meanwhile, programming simulation is carried out based on MATLAB software, and an ode45 solver is adopted for solving, so that simulation signals are obtained; qualitatively comparing the envelope spectrum characteristics between the experimental signal and the simulation signal; the bearing is SKF6205-2RS, grooves are respectively processed on the inner ring and the outer ring of the bearing in a linear cutting mode, the bearing is driven by a driving motor at the rotating speed of 900r/min, and the sampling frequency is set to be 10kHz; the acceleration of the outer ring of the bearing in the Y direction is used as an original signal of a dynamic model; the envelope spectrum of the original signal is obtained by fourier transform and hilbert transform.
The change of main physical quantity in the dynamic model of the invention is shown in fig. 4 and 5, and the friction between the rolling body and the inner rolling can be obviously seen from the amplitudeFriction between rolling element and outer rolling>Friction between rolling element and previous cage +.>Friction between rolling element and subsequent cage>Far less than the contact force between the rolling bodies and the inner raceway +.>Contact force between the rolling element and the outer raceway>Contact force between rolling element and previous cage +>Contact force between a rolling element and a subsequent cage>This indicates that-> andPlays a dominant role in influencing the bearing vibration response.
FIG. 6 shows the vibration response and the main physical quantity of the inner ring when the fault is in the inner ring of the bearingIs a variation of (2). From the point of view of the value and the law of variation, and +.>In contrast to this, the method comprises,the vibration response to the inner ring is greatly affected. Therefore, the contact force between the rolling body and the roller path can be judged to be the main physical quantity affecting the vibration response of the bearing, namely the vibration excitation in the dynamic modelA source. When the fault is located in the bearing outer ring, the vibration response of the inner ring and the main physical quantity +.> The variation of (2) is shown in fig. 7. From the trend of the change in the figures, the same conclusion can be drawn as well: the contact force between the rolling body and the rollaway nest is the main physical quantity affecting the vibration response of the bearing, namely the excitation source in the dynamic model.
The dynamic model of the bearing is shown in fig. 8. The invention adopts a bearing fault simulation test bed to carry out experiments to obtain an experimental signal, obtains an envelope curve of an original experimental signal through Hilbert transformation, and carries out Fourier transformation on the envelope curve to obtain an envelope spectrum of the experimental signal as shown in figure 9. The theoretical characteristic frequencies of the bearings are shown in table 1. The parameters used in the kinetic model are shown in table 2. The invention considers two defect situations, namely the local failure of the outer ring and the local failure of the inner ring.
TABLE 1 failure characteristic frequency of SKF6205 deep groove ball bearing
TABLE 2SKF6205 deep groove ball bearing parameters
The invention is described in detail below in connection with simulated signal analysis, and includes the steps of:
step 1: and establishing a healthy bearing dynamics model. The rigidity and damping of the bearing, the force between the rolling body and the retainer and the force between the rolling body and the raceway are calculated when the bearing is in elastohydrodynamic lubrication, and the basic physical quantity required in a healthy bearing dynamic model is determined.
Step 2: a dynamic model of the bearing with local faults is built. By introducing a half sine function, time-varying displacement excitation of the rolling bodies when the rolling bodies pass through the local faults is described, and finally, a dynamic bearing model with the local faults is established.
Step 3: after the accuracy of the model is verified through simulation signal analysis, the main excitation source in the dynamic model with local faults is identified. The method comprises the steps of comparing the simulation signal with the experimental signal to determine the accuracy of the model, and comparing the numerical value and the change trend of the basic physical quantity in the dynamic model to determine the main excitation source in the model.
The step 1 comprises the following steps:
step 1.1: bearing stiffness and damping based on elastohydrodynamic lubrication were calculated. In the dynamic model established by the invention, the contact model is shown in figure 1. The oil film rigidity of the Hertz contact area can be ignored because the oil film rigidity of the Hertz contact area is far greater than the Hertz contact rigidity of the contact pair. The damping of the contact pair is formed by connecting the structural damping of the bearing and the oil film damping of the Hertz region in series and then connecting the structural damping and the viscous damping of the inlet region in parallel. Because the oil film viscosity damping value of the Hertz contact area is smaller, the damping is negligible after the damping is connected in series with the Hertz contact area structure damping, so the damping of the contact pair is mainly from the viscosity damping of the oil film of the inlet area. The contact stiffness of a contact pair can be expressed as:
in the formula ,E* Is Young's modulus; μ is poisson's ratio; Σρ is the sum of the raceways curves; f is a first type of complete elliptic integral, E is a second type of complete elliptic integral; kappa is the contact area ellipticity.
Viscous damping of the inlet zone oil film can be expressed as:
in the formula ,η0 Is the dynamic viscosity of the lubricant at room temperature; r is R x Is the equivalent radius of curvature in the rolling direction; a, a nj For the long half-axis length of the contact ellipse. The viscosities given in the ISO standard are kinematic viscosities, which can be converted into dynamic viscosities by the following formula:
η 0 ＝υ·ρ·10 -6 (Pa·s) (3)
for an elliptic point contact rolling bearing, the most common calculation formula of the minimum oil film thickness and the central oil film thickness of a contact area is a 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)
wherein U, G and W are a dimensionless speed parameter, a dimensionless material parameter, and a dimensionless load parameter, respectively.
Step 1.2: the force between the rolling bodies and the cage is calculated. During operation of the bearing, the rolling elements rotate about the bearing center. In the non-bearing area, the cage drives the rolling bodies to move; in the bearing region, the rolling bodies drive the cage in motion. The contact rigidity of the rolling bodies and the retainer is calculated by adopting the Hertz contact theory. Due to the complexity of the cage structure, the stiffness between the cage and the cage is calculated using a finite element method. The force analysis of the cage is shown in figure 2.
The force between the j-th rolling element and the cage can be expressed as:
wherein ,ψr and ψc The rotational angular displacement of the rolling bodies and the cage, respectively, about the bearing center. n is the load deformation index and is 1 in the smaller elastic deformation range. K (K) rc Between rolling bodies and cagesConnection stiffness. R is R m Is the pitch diameter.
The friction between the j-th rolling element and the cage can be expressed as:
wherein ,μc Is the coefficient of friction.
The internal force between the retainers can be expressed as:
in the formula ,Kcc and CCC The connection rigidity and the connection damping between the retainers are respectively; is the angular velocity at which the cage rotates about the bearing center.
Step 1.3: the force between the rolling elements and the raceway is calculated. Based on the theory of Hertz nonlinear contact, the contact force between the rolling bodies and the inner/outer raceways can be expressed as:
where λ is a sign function, which can be expressed as:
the contact deformation between the j-th rolling element and the raceway can be expressed as:
in the formula ,ri j 、 and rj Respectively representing radial displacement of the inner ring, the outer ring and the rolling bodies at the j-th rolling body; e represents a radial gap;Is the displacement excitation caused by the entry of the jth rolling element into the defect, which will be described in detail in step 2.
The radial displacement of the inner and outer races at the j-th rolling element can be expressed as:
the angular position of the j-th rolling element can be expressed as:
in the formula ,Nb Representing the number of rolling elements.
The friction between the j-th rolling element and the raceway can be expressed as:
wherein the coefficient of friction between the rolling elements and the raceway can be calculated by the following formula:
in the formula ,representing the relative sliding speed between the jth rolling element and the raceway, by the following calculation:
ΔV i j ＝V ir -V ri (23)
in the formula , andThe circumferential speed and the rotation speed of the jth rolling element are respectively R r Representing the radius of the rolling elements.
The step 2 comprises the following steps:
step 2.1: a partial fault in the bearing race is described. The invention mainly researches the early defect form of the bearing, the width of the fault is smaller, the descending displacement of the rolling element 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, L is the width of the fault, B is the depth of the fault, H max Is at maximumAnd (5) displacement excitation.
As can be seen from fig. 3, the rolling elements are always in contact with the I-side when they enter and pass the defect, and the rolling elements have left the defect zone when they pass the II-side. This approach may employ a half-sine function to describe the time-varying excitation of the displacement. Maximum displacement excitation H of rolling bodies max The method comprises the following steps:
the time-varying displacement excitation function of the rolling element passing through the defect can be expressed as follows:
in the formula ,representing a defect angle;An initial angle representing a defect; n=i, o;The expression can be represented by the following formula:
wherein ,representing the angular position of the defect.
From the above analysis, the kinetic equation of the bearing can be obtained as follows:
kinetic equation of horizontal movement of inner ring:
kinetic equation of vertical motion of inner ring:
kinetic equation of cage circular motion:
kinetic equation of rolling element circular motion:
kinetic equation of rolling element rotation motion:
kinetic equation of radial movement of rolling bodies:
in the formula, the centrifugal force of the j-th rolling element can be expressed as:
F wj ＝m r R m w oj 2 (36)
the step 3 comprises the following steps:
step 3.1: in order to verify the accuracy of the model, a bearing fault simulation test bed is adopted for carrying out experiments, and experimental signals are obtained. Meanwhile, programming simulation is carried out based on MATLAB software, and an ode45 solver is adopted for solving, so that simulation signals are obtained. Qualitative comparisons are made of the envelope spectral characteristics between the experimental and simulated signals. The used bearing is SKF6205-2RS, grooves are respectively processed on the inner ring and the outer ring of the bearing in a linear cutting mode, the bearing is driven by a driving motor at the rotating speed of 900r/min, and the sampling frequency is set to be 10kHz. The acceleration of the bearing outer race in the Y direction is used as the original signal for the dynamic model. The envelope spectrum of the original signal may be obtained by fourier transform and hilbert transform.
The invention considers two defect situations, namely the local failure of the outer ring and the local failure of the inner ring. A comparison of the simulated and experimental signals for both defect cases is shown in fig. 9. The envelope spectra of the analog and experimental signals of the bearing when the bearing is in the case of an inner ring failure are shown in fig. 9 (a) and (b). From fig. 9 (a), it is apparent that the fault characteristic frequency Bpfi of the inner ring and its multiple are modulated by the switching frequency fs. A similar situation is also evident from fig. 9 (b).
Fig. 9 (c) and (d) depict the envelope spectra of an analog signal and an experimental signal, respectively, in the case of a partial fault of the outer ring. The obvious fault characteristic frequency Bpfo and the frequency multiplication thereof can be seen in both the analog signal and the experimental signal.
From the above comparison, it can be seen that the main features of the analog signal and the main features of the experimental signal are consistent in different defect cases, and thus the effectiveness of the proposed model is demonstrated.
Step 3.2: the change of main physical quantity in the dynamic model of the invention is shown in fig. 4 and 5, and the friction between the rolling body and the inner rolling can be obviously seen from the amplitudeFriction between rolling element and outer rolling>Friction between rolling element and previous cage +.>Friction between rolling element and subsequent cage>Far smaller than the space between the rolling body and the inner roller pathContact force of->Contact force between the rolling element and the outer raceway>Contact force between rolling element and previous cage +>Contact force between a rolling element and a subsequent cage>This indicates that->Andplays a dominant role in influencing the bearing vibration response.
FIG. 6 shows the vibration response and the main physical quantity of the inner ring when the fault is in the inner ring of the bearingIs a variation of (2). From the point of view of the value and the law of variation, and +.>In contrast to this, the method comprises,the vibration response to the inner ring is greatly affected. Therefore, the contact force between the rolling body and the roller path can be judged to be the main physical quantity affecting the vibration response of the bearing, namely the vibration excitation source in the dynamic model. When the fault is located in the bearing outer ring, the vibration response of the inner ring and the main physical quantity +.> The variation of (2) is shown in fig. 7. Trend of change from graphFrom this point of view, the same conclusion can be reached as well: the contact force between the rolling body and the rollaway nest is the main physical quantity affecting the vibration response of the bearing, namely the excitation source in the dynamic model.
In order to solve the problem that the traditional model cannot truly reflect the real state of the bearing in the running process, the invention takes the rolling bearing as a research object, establishes a dynamic bearing model which considers the flexibility of the retainer, the lubrication of the elastic fluid and the time-varying displacement excitation caused by local faults, has finer model and can simulate the vibration mechanism of the bearing more accurately. And comparing the vibration response of the built dynamic model with an experimental signal, and determining an excitation source in the model through comparison analysis after verifying the accuracy of the model, so as to provide a theoretical basis for bearing vibration response analysis. Meanwhile, the built 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 the rolling bearing based on big data.
FIG. 6 vibration response and partial physical quantity when failure is in bearing inner race Is the case for the change in (a): (a, c) contact force between the rolling elements and the inner/outer raceways in the horizontal direction ∈ ->(b, d) contact force of the rolling elements with the inner/outer raceways in the vertical direction +.>(e, g) contact force between the rolling element and the preceding/following cage in the horizontal direction +.>(f, h) contact force between the rolling element and the preceding/following cage in the vertical direction +.>(i) In the horizontal directionThe vibration response of the upper inner ring; (j) vibration response of the inner race in the vertical direction.
FIG. 7 vibration response and partial physical quantity when failure is in bearing outer race Is the case for the change in (a): (a, c) contact force between the rolling elements and the inner/outer raceways in the horizontal direction ∈ ->(b, d) contact force of the rolling elements with the inner/outer raceways in the vertical direction +.>(e, g) contact force between the rolling element and the preceding/following cage in the horizontal direction +.>(f, h) contact force between the rolling element and the preceding/following cage in the vertical direction +.>(i) Vibration response of the inner ring in the horizontal direction; (j) vibration response of the inner race in the vertical direction.
Comparison of envelope spectra of analog and experimental signals for different fault conditions in fig. 9: (a) an envelope spectrum of the analog signal in the event of an inner ring failure; (b) an envelope spectrum of the experimental signal in the event of an inner ring failure; (c) an envelope spectrum of the analog signal in the event of an outer ring failure; (d) envelope spectrum of the experimental signal in case of failure of the outer ring.
Finally, it should be noted that: the foregoing description is only a preferred embodiment of the present invention, and the present invention is not limited thereto, but it is to be understood that modifications and equivalents of some of the technical features described in the foregoing embodiments may be made by those skilled in the art, although the present invention has been described in detail with reference to the foregoing embodiments. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (4)
1. A dynamic modeling and vibration characteristic analysis method for a rolling bearing is characterized in that: the method 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: the main excitation source in the dynamic model is determined by comparing the magnitude and the change trend of the basic physical quantity in the model.
2. A rolling bearing dynamics modeling and vibration signature analysis method according to claim 1, characterized in that: s1.1: calculating bearing rigidity and damping based on elastic fluid lubrication;
in the established dynamic model, oil film tempering is carried out in a Hertz contact area, and the oil film rigidity of the oil film tempering is far greater than the Hertz contact rigidity of a contact pair, so that the oil film rigidity of the Hertz contact area is ignored;
the damping of the contact pair is formed by connecting the structural damping of the bearing and the oil film damping of the Hertz region in series and then connecting the structural damping and the viscous damping of the inlet region in parallel; because the oil film viscosity damping value of the Hertz contact area is smaller, the damping is negligible after the oil film viscosity damping value is connected in series with the structure damping of the Hertz contact area, so that the damping of the contact pair comes from the viscosity damping of the oil film of the inlet area;
the contact stiffness of a contact pair can be expressed as:
in the formula ,E* Is Young's modulus; μ is poisson's ratio; Σρ is the sum of the raceways curves; f is a first type of complete elliptic integral, E is a second type of complete elliptic integral; kappa is the ellipticity of the contact area;
viscous damping of the inlet zone oil film can be expressed as:
in the formula ,η0 Is the dynamic viscosity of the lubricant at room temperature; r is R x Is the equivalent radius of curvature in the rolling direction; a, a nj A long half-axis length which is the contact ellipse;
the viscosity given in the ISO standard is the kinematic viscosity, which is converted to the dynamic viscosity by the following formula:
η 0 ＝υ·ρ·10 -6 (Pa·s) (3)
for an elliptic point contact rolling bearing, the most calculation formula of the minimum oil film thickness and the contact area center oil film thickness is a 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)
wherein U, G and W are a dimensionless speed parameter, a dimensionless material parameter, and a dimensionless load parameter, respectively;
s1.2: calculating a force between the rolling bodies and the cage;
during the working process of the bearing, the rolling bodies rotate around the center of the bearing; in the non-bearing area, the cage drives the rolling bodies to move; in the bearing area, the rolling bodies drive the retainer to move; the contact rigidity of the rolling body and the retainer is calculated by adopting a Hertz contact theory; due to the complexity of the cage structure, the stiffness between the cage and the cage is calculated using a finite element method;
the force between the j-th rolling element and the cage can be expressed as:
wherein ,ψr and ψc Rotational angular displacements of the rolling bodies and the cage around the center of the bearing are respectively; n is the load deformation index, 1 in the smaller elastic deformation range; k (K) rc Is the connection rigidity between the rolling bodies and the cage; r is R m Is the pitch diameter;
friction between the j-th rolling element and the cage can be expressed as:
wherein ,μc Is the coefficient of friction;
the internal force between the retainers is expressed as:
in the formula ,Kcc and CCC The connection rigidity and the connection damping between the retainers are respectively; is the angular velocity at which the cage rotates about the bearing center;
s1.3: calculating the force between the rolling bodies and the rollaway nest; based on the theory of Hertz nonlinear contact, the contact force between the rolling bodies and the inner/outer raceways is expressed as:
where λ is a sign function expressed as:
the contact deformation between the j-th rolling element and the raceway is expressed as:
in the formula , and rj Respectively representing radial displacement of the inner ring, the outer ring and the rolling bodies at the j-th rolling body; e represents a radial gap;Is displacement excitation caused by the defect of the jth rolling element;
the radial displacement of the inner and outer races at the j-th rolling element is expressed as:
the angular position of the j-th rolling element is expressed as:
in the formula ,Nb Representing the number of rolling bodies;
the friction between the j-th rolling element and the raceway is expressed as:
wherein the coefficient of friction between the rolling elements and the raceway is calculated by the following formula:
in the formula ,representing the relative sliding speed between the jth rolling element and the raceway, by the following calculation:
ΔV i j ＝V ir -V ri (23)
in the formula , andThe circumferential speed and the rotation speed of the jth rolling element are respectively R r Representing the radius of the rolling elements.
3. A rolling bearing dynamics modeling and vibration signature analysis method according to claim 1, characterized in that: the S2 includes 2.1: describing a partial fault in the bearing race; for the early defect form of the bearing, the width of the fault is smaller, the descending displacement of the rolling element passing through the defect is smaller than the depth of the fault, L is the width of the fault in the state that the rolling element passes through the defect, B is the depth of the fault, H max Is the maximum displacement excitation;
when the rolling bodies enter and pass through the defect, the rolling bodies are always contacted with the side I, and when the rolling bodies pass through the side II, the rolling bodies leave the defect area; this pass-through approach employs a half-sine function to describe the time-varying excitation of displacement; maximum displacement excitation H of rolling bodies max The method comprises the following steps:
the time-varying displacement excitation function of the rolling element passing through the defect can be expressed as follows:
in the formula ,representing a defect angle;An initial angle representing a defect; n=i, o;The expression can be represented by the following formula:
wherein ,an angular position representing a defect;
from the above analysis, the kinetic equation for this bearing is obtained as follows:
kinetic equation of horizontal movement of inner ring:
kinetic equation of vertical motion of inner ring:
kinetic equation of cage circular motion:
kinetic equation of rolling element circular motion:
kinetic equation of rolling element rotation motion:
kinetic equation of radial movement of rolling bodies:
in the formula, the centrifugal force of the j-th rolling element can be expressed as:
F wj ＝m r R m w oj 2 (36)。
4. a rolling bearing dynamics modeling and vibration signature analysis method according to claim 1, characterized in that: the step S3 comprises the following steps:
s3.1: in order to verify the accuracy of the model, a bearing fault simulation test bed is adopted for carrying out experiments to obtain an experimental signal; meanwhile, programming simulation is carried out based on MATLAB software, and an ode45 solver is adopted for solving, so that simulation signals are obtained; qualitatively comparing the envelope spectrum characteristics between the experimental signal and the simulation signal; the bearing is SKF6205-2RS, grooves are respectively processed on the inner ring and the outer ring of the bearing in a linear cutting mode, the bearing is driven by a driving motor at the rotating speed of 900r/min, and the sampling frequency is set to be 10kHz; the acceleration of the outer ring of the bearing in the Y direction is used as an original signal of a dynamic model; the envelope spectrum of the original signal is obtained by fourier transform and hilbert transform.
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| CN117313446B (en) * | 2023-08-16 | 2024-06-11 | 中国船舶重工集团公司第七0三研究所 | Rolling bearing raceway defect expansion fault diagnosis method and system |
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