CN109946077A - Fractional order damps the method that rolling bearing fault dynamics sequential model is established - Google Patents
Fractional order damps the method that rolling bearing fault dynamics sequential model is established Download PDFInfo
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Abstract
The invention discloses the methods that a kind of fractional order damping rolling bearing fault dynamics sequential model is established, on the basis of having obtained rolling bearing contact equivalent stiffness and equivalent damping, comprehensively considering has lubricant to influence to establish the rolling bearing gradual change kinetic model containing single pitting fault by influence when failure to inner ring self-deformation amount with rolling element；Fractional calculus theory is applied in rolling bearing, derives the calculation formula of fractional order damping force, establishes consider fractional order damping rolling bearing inner ring fault model, housing washer fault model and rolling bearing rolling element fault model respectively；Model proposed by the present invention have it is of overall importance, can preferably reflect the history-dependent process of system；Good effect is achieved with using less several parameters；The physical significance of expression is apparent, states more succinct；Model considers the influence of the lubricating oil between rolling element and inner ring.
Description
Technical field
The present invention relates to bearing system dynamics and fault diagnosis technology, in particular to a kind of fractional order damps rolling bearing fault
The method that dynamics sequential model is established.
Background technique
Rolling bearing is that passing movement rotor is most important part in rotating machinery in various machinery, has frictional force
The advantages that small, starting is easy, lubrication is simple and is conveniently replaceable, is widely used in precision instrument, aerospace, automobile, lathe and machine
The fields such as device people.Rolling bearing in the process of running, since insufficient lubrication, fatigue, abrasion etc. may all make bearing premature breakdown,
Statistical data shows that the 30% of rotating machinery fault is as caused by bearing.Once bearing break down will cause it is a series of
Adverse reaction, gently then leads to the machine strike even production line downtime in being currently running, and brings huge economic damage to enterprise
It loses；Life security that is heavy then jeopardizing relevant staff.Therefore it in order to ensure rotating machinery safely and smoothly runs at high speed, drops
Low vibration and noise level improve production efficiency, promote competitiveness of the enterprise in society, it is necessary to for the event of rolling bearing
Barrier is studied.
In order to effectively diagnose rolling bearing fault, many scholars are in the failure mechanism of rolling bearing and kinetic characteristics etc.
Aspect has done a large amount of research work, for example, Walters is established for the first time including rolling element, the displacement of retainer, revolving speed and interior
The equation of motion of the rolling bearings whole kinetic characteristics such as the opposite sliding of each element in portion, establishes rolling bearing kinetic simulation
Type.Harris is further furtherd investigate on the model basis of Walters, it is contemplated that rolling element stress and moment unbalance
When the inertia force that generates and moment of inertia so that the kinetic model of rolling bearing is more mature.Gupta improves rolling bearing
Dynamic (dynamical) analysis method, it is contemplated that rolling bearing establishes more perfect rolling from the entire dynamic process for starting starting
Dynamic bearing dynamic analysis model.Meeks has further developed rolling bearing dynamic analysis in the theoretical basis of Gupta
Model, the model are non-fully Elastic Contact the contact treatment between rolling element and retainer and retainer and lasso, are established
Retainer six-degree-of-freedom dynamic model.Sopanen proposes a kind of kinetic model with six degree of freedom, which examines
Hertz contact deformation and elastohydrodynamics are considered, giving can be according to the shape, material property and radial clearance of bearing
The kinetic model of calculating.Cong is based on dynamic load analysis and proposes rolling bearing fault model, considers in the model
Number of shocks, and by dynamics and kinematics analysis, obtain calculation of fault equation.Kogan is in classical dynamics and power
On the basis for learning equation, three-dimensional bearing kinetic model is proposed, which simulates frictional force using hyperbolic tangent function, make
The interaction between each element of bearing is indicated with Hertz contact spring damper model.
Although rolling bearing Dynamic Modeling obtains some progress, there are still some problems: first, spot corrosion defect
Idealization can discharge when that is, hypothesis rolling element enters and leaves faulty section and obtain all deformed amount, the process is not considered
For progressive formation.Second, in actual rotating machinery, the failure for having many rolling bearings is the situation due to lubricant
Caused by change, due to there is the presence of lubricant, one can be formed and kept between rolling element and retainer and bearing inner race
Determine the elastic hydrodynamic oil film of thickness, and generate lubricating oil viscous drag, but there is no consider lubricant in the process
Influence.Third is all seldom to consider fractional calculus based on integer rank calculus.
Summary of the invention
The technical problem to be solved by the present invention is to the analysis methods by improving rolling bearing kinetic model, it is ensured that rotation
Favourable turn tool safely and smoothly runs at high speed, and reduces vibration and noise level, improves production efficiency.
The present invention solves above-mentioned technical problem and uses following technical scheme, and fractional order damps rolling bearing fault dynamics gradually
The method that varying model is established, steps are as follows:
1) on the basis of having obtained rolling bearing contact equivalent stiffness and equivalent damping, comprehensively considering has lubricant influence
It is dynamic to establish the rolling bearing gradual change containing single pitting fault for influence when passing through failure with rolling element to inner ring self-deformation amount
Mechanical model；
2) fractional calculus theory is applied in rolling bearing, derives the calculation formula of fractional order damping force, point
Fractional order damping rolling bearing inner ring fault model, housing washer fault model and rolling bearing rolling element Jian Li not be considered
Fault model；
A) specific step is as follows for the rolling bearing inner ring fault model foundation:
Juxtaposition metamorphose amount for the bearing of damage, between j-th of rolling element and raceway are as follows:
δ=xcos θj+ysinθj-e-βjλ+Hj (1)
In formula, x is the displacement of inner ring radial direction X-direction；Y is the displacement of inner ring radial direction Y-direction；θjIt is j-th of rolling element center institute
The position angle at place；E is radial clearance；λ is the deflection of gradual change release when rolling element rolls across inner ring fault zone；HjFor oil film thickness
Degree；ωcFor the angular velocity of rotation of retainer；Z is the number of rolling element；θlFor the start bit angle setting for the rolling element that number is 1；ωi
For the angular velocity of rotation of rotor；DbFor rolling element diameter；DmFor the pitch diameter of rolling bearing；α is between rolling element and inner ring raceway
Contact angle；
βjIt is switching value, indicates when rolling element is located in the position angular spread of spot corrosion defect, there are certain contacts
Deflection；And when rolling element is not in the position angular spread of spot corrosion defect, deflection has not existed；Therefore it is defined as:
In formula,It is the position angle at inner ring pitting fault center；ΔΦsIt is the span angle of failure；bcIt is the one of failure width
Half；ΦspallIt is the position angle at pitting fault center；
When rolling element passes through inner ring defect, the deflection of release is the deflection C of rolling elementdrWith the deflection of inner ring
CdiThe sum of；When rolling element touches defect bottom, the maximum deformation quantity of release is λmaxJust it is equal to failure depth, it may be assumed that
λmax=CdrCdi (7)
In formula, riIt is inner radii；rbIt is rolling element radius；
Actual release deflection are as follows:
According to Hertz contact theory, the calculating of the contact load Q of the point contact between single rolling element and inside and outside circle raceway
Method is respectively as follows:
In formula, K is equivalent juxtaposition metamorphose coefficient, it is related rolling element and the inside and outside juxtaposition metamorphose coefficient enclosed between raceway；
Contact between rolling element and inside and outside circle raceway is indicated with one group of spring damping model；In rolling element and inside and outside circle
Under the premise of the contact angle of raceway is equal, total equivalent juxtaposition metamorphose coefficient are as follows:
In formula, ball bearing n=1.5；KoAnd KiIt is juxtaposition metamorphose coefficient；nδIt is coefficient relevant to principal curvatures difference function, it can
By tabling look-up to obtain；Σ ρ is contact principal curvatures and function, calculation method are as follows:
∑ ρ=ρII+ρIII+ρ2I+ρ2II (14)
In formula, subscript 1 and 2 respectively represents rolling element and inside and outside circle raceway；I represents the axial plane of rotor；II represent with
Perpendicular to I sagittal plane；The circular of every principal curvatures can be by tabling look-up to obtain；
nδIt is a design factor, it is related to the principal curvatures difference function of rolling bearing, is obtained by tabling look-up；Principal curvatures is poor
Function is defined as:
By all contact load Q be projected in X-axis in Y-axis both direction and be added, then obtain inner ring raceway and all
Total contact load between rolling element:
Using Newtonian fluid model, i.e., lubricant is thought of as Newtonian fluid；That is born at j-th of rolling element tangentially rubs
Wipe power are as follows:
τ=η * Q (17)
In formula, η is stiction coefficient；
By Newton's second law, the kinetics equation of rolling bearing inner ring are as follows:
In formula, m is the quality of rolling bearing；C is the equivalent damping of system；FeFor the radial load of inner ring；FrOutside for outer ring
Load lotus；
Damping force is the function for being displaced first derivative, its Fractional Derivative may be expressed as:
Fd=cx ' (t)=cDαx(t) (19)
In formula, FdIt is damping force；DαIt is the complex variable of Laplace transformation；
Inner ring kinetic model after considering damping force are as follows:
B) specific step is as follows for the housing washer fault model foundation:
The kinetics equation of foundation are as follows:
In formula,It is the angle of plus load and X-axis；
Maximum deformation quantity λmaxIt is in rolling element deflection CdrOn the basis of, subtract the deflection C of outer ringdo, it may be assumed that
λmax=Cdr-cdo (22)
In formula, roIt is outer radii；
Therefore, the improving method for calculating deformation of loess soil of actual gradual change release are as follows:
C) specific step is as follows for the rolling bearing rolling element fault model foundation:
Rolling body dynamics non-dimensional model after considering damping force are as follows:
When rolling element failure and outer ring raceway contact, maximum deformation quantity λmaxIt should be in rolling element deflection CdrBasis
On, subtract the deflection C of outer ringdo；And when rolling element failure and inner ring raceway contact, maximum deformation quantity λmaxShould roll
Body deflection CdrOn the basis of, in addition the deflection C of inner ringdiThat is:
Therefore, the improving method for calculating deformation of loess soil of actual gradual change release are as follows:
The present invention considers fractional order damping characteristic and lubricating oil effect, the mould of proposition in rolling bearing Dynamic Modeling
It is of overall importance that type has characteristics that the model that (1) proposes has, and can preferably reflect the history-dependent process of system；And it is traditional
Model has locality, and unsuitable description has history-dependent process；(2) model proposed overcomes traditional model theory and reality
It tests result to coincide bad critical defect, is achieved with good effect using less several parameters；(3) model proposed is than passing
The physical significance that model indicates of uniting is apparent, states more succinct；(4) model proposed considers the profit between rolling element and inner ring
The influence of lubricating oil, and conventional model has ignored lubricating oil viscous drag, conventional model obviously do not conform to the actual conditions conjunction.
Detailed description of the invention
Fig. 1 is Utopian transition model of the invention；
Fig. 2 is actual asymptotic model of the invention；
Fig. 3 is the single spot corrosion fault model of inner ring of the invention；
Fig. 4 is asymptotic model inner ring part pitting fault enlarged diagram of the invention；
Fig. 5 is that the vibration signal of inner ring failure of the invention is displaced time-domain diagram；
Fig. 6 is the vibration signal speed time-domain diagram of inner ring failure of the invention；
Fig. 7 is that the vibration signal of inner ring failure of the invention is displaced amplitude frequency diagram；
Fig. 8 is the vibration signal speed amplitude frequency diagram of inner ring failure of the invention；
Fig. 9 is the bifurcation graphs of the fractional order order of inner ring failure of the invention；
The Chart of axes track that Figure 10 is the fractional order order of inner ring failure of the invention when being 0.6；
The spectrogram that Figure 11 is the fractional order order of inner ring failure of the invention when being 0.6；
Figure 12 is the acceleration time domain figure of the experimental result of inner ring failure of the invention；
Figure 13 is the acceleration amplitude frequency diagram of the experimental result of inner ring failure of the invention；
Figure 14 is the single spot corrosion fault model in outer ring of the invention；
Figure 15 is asymptotic model outer ring part pitting fault enlarged diagram of the invention；
Figure 16 is that the vibration signal of outer ring failure of the invention is displaced time-domain diagram；
Figure 17 is the vibration signal speed time-domain diagram of outer ring failure of the invention；
Figure 18 is that the vibration signal of outer ring failure of the invention is displaced amplitude frequency diagram；
Figure 19 is the vibration signal speed amplitude frequency diagram of outer ring failure of the invention；
Figure 20 is the bifurcation graphs of the fractional order order of outer ring failure of the invention；
The Chart of axes track that Figure 21 is the fractional order order of outer ring failure of the invention when being 0.6；
The spectrogram that Figure 22 is the fractional order order of outer ring failure of the invention when being 0.6；
Figure 23 is the acceleration time domain figure of the experimental result of outer ring failure of the invention；
Figure 24 is the acceleration amplitude frequency diagram of the experimental result of outer ring failure of the invention；
Figure 25 is the single spot corrosion fault model of rolling element of the invention；
Figure 26 is that the vibration signal of rolling element failure of the invention is displaced time-domain diagram；
Figure 27 is the vibration signal speed time-domain diagram of rolling element failure of the invention；
Figure 28 is that the vibration signal of rolling element failure of the invention is displaced amplitude frequency diagram；
Figure 29 is the vibration signal speed amplitude frequency diagram of rolling element failure of the invention；
Figure 30 is the bifurcation graphs of the fractional order order of rolling element failure of the invention；
The Chart of axes track that Figure 31 is the fractional order order of rolling element failure of the invention when being 0.6；
The spectrogram that Figure 32 is the fractional order order of rolling element failure of the invention when being 0.6；
Figure 33 is the acceleration time domain figure of the experimental result of rolling element failure of the invention；
Figure 34 is the acceleration amplitude frequency diagram of the experimental result of rolling element failure of the invention.
Specific embodiment
The present invention will be further described below with reference to the drawings.
Rolling bearing surface damage faulty power modeling method of the invention, includes the following steps:
Current rolling bearing fault model (as shown in Figure 1), which is that failure is reduced to rectangular recess, is being rolled
The moment that body occurs with failure and disconnection contacts can just cause to deform, and the size of deflection is equal to the depth of failure.And
Actual rolling bearing fault more should be the arc-shaped defect of (as shown in Figure 2), rolling element and fault contact in a flash simultaneously
It will not be badly deformed, only when the bottom Shi Caihui that rolling element touches failure reaches maximum deflection.
1. rolling bearing inner ring fault model:
Assuming that when certain point is there are when local damage failure on inner ring, concrete condition (as shown in Figure 3).For damage
Bearing, the juxtaposition metamorphose amount between j-th of rolling element and raceway are as follows:
δ=xcos θj+ysinθj-e-βjλ+Hj (1)
In formula, x is the displacement of inner ring radial direction X-direction；Y is the displacement of inner ring radial direction Y-direction；θjIt is j-th of rolling element center institute
The position angle at place；E is radial clearance；λ is the deflection of gradual change release when rolling element rolls across inner ring fault zone；HjFor oil film thickness
Degree；ωcFor the angular velocity of rotation of retainer；Z is the number of rolling element；θ1For the start bit angle setting for the rolling element that number is 1；ωi
For the angular velocity of rotation of rotor；DbFor rolling element diameter；DmFor the pitch diameter of rolling bearing；α is between rolling element and inner ring raceway
Contact angle.
βjIt is switching value, indicates when rolling element is located in the position angular spread of spot corrosion defect, there are certain contacts
Deflection；And when rolling element is not in the position angular spread of spot corrosion defect, deflection has not existed.Therefore it is defined as:
In formula,It is the position angle at inner ring pitting fault center；ΔΦsIt is the span angle of failure；bcIt is failure width
Half；ΦspallIt is the position angle at pitting fault center, as shown in fig. 1.
Juxtaposition metamorphose amount is defined as failure depth d (as shown in Figure 4) by ideal inner ring failure spot corrosion model.But it is practical
Rolling bearing inner ring be not rigid body in complete meaning, when contacting with rolling element, inner ring can also change, therefore
When rolling element passes through inner ring defect, the deflection of release should be the deflection C of rolling elementdrWith the deflection C of inner ringdiIt
With；When rolling element touches defect bottom, the maximum deformation quantity of release ismaxJust it is equal to failure depth, it may be assumed that
λmax=Cdr+Cdi (7)
In formula, riIt is inner radii；rbIt is rolling element radius.
Due to deformation release and to regain be an asymptotic process, when rolling element is rolled in inner ring fault zone
When, juxtaposition metamorphose amount is constantly changing.Therefore, actual release Deformation calculation is considered as inner ring and the deformation of rolling element is released
The progressive formation put and obtained, the then deflection are as follows:
According to Hertz contact theory, the calculating of the contact load Q of the point contact between single rolling element and inside and outside circle raceway
Method is respectively as follows:
In formula, K is equivalent juxtaposition metamorphose coefficient, it is related rolling element and the inside and outside juxtaposition metamorphose coefficient enclosed between raceway.
Contact between rolling element and inside and outside circle raceway can be indicated with one group of spring damping model.Rolling element with it is inside and outside
Under the premise of the contact angle of circle raceway is equal, total equivalent juxtaposition metamorphose coefficient are as follows:
In formula, ball bearing n=1.5.KoAnd KiIt is juxtaposition metamorphose coefficient；nδIt is coefficient relevant to principal curvatures difference function, it can
By tabling look-up to obtain；∑ρIt is contact principal curvatures and function, its calculation method are as follows:
∑ ρ=ρII+ρ1II+ρ2I+ρ2II (14)
In formula, subscript 1 and 2 respectively represents rolling element and inside and outside circle raceway；I represents the axial plane of rotor；II represent with
Perpendicular to the sagittal plane of I.The circular of every principal curvatures can be by tabling look-up to obtain.
nδIt is a design factor, it is related to the principal curvatures difference function of rolling bearing, is obtained by tabling look-up.Principal curvatures is poor
Function is defined as:
By all contact load Q be projected in X-axis in Y-axis both direction and be added, then obtain inner ring raceway and all
Total contact load between rolling element:
Since the internal geometry and working environment of bearing are more complicated, true rolling element frictional resistance model is established
It is relatively difficult.Therefore, most of rolling bearing kinetic models handled using experience and semiempirical model rolling element and inner ring,
The oil drag resistance of outer ring.Newtonian fluid model is used herein, i.e., lubricant is thought of as Newtonian fluid.In view of rolling element
It not only rolls but also slides along plane, tangential friction force can be divided into pure rolling friction power and force of sliding friction.Consider lubricating oil viscosity,
And the elastohydrodynamic lubrication oil film that can be generated between rolling element and raceway is relatively thin, generally 0.3~1 μm, therefore j-th of rolling element
The tangential friction force that place is born are as follows:
τ=η * Q (17)
In formula, η is stiction coefficient.
By Newton's second law, the kinetics equation of rolling bearing inner ring are as follows:
In formula, m is the quality of rolling bearing；C is the equivalent damping of system；FeFor the radial load of inner ring；FrOutside for outer ring
Load lotus.
By taking 6220 profile shafts are held as an example, the major parameter of bearing are as follows: rolling element diameter be 25.4mm, pitch diameter 140mm,
Race diameter is 190.8mm, and inner ring diameter 89.2mm, rolling element quantity is 10, revolving speed 719.57rad/min, emulation
Failure is having a size of 0.3mm × 0.3mm.Primary condition when emulation are as follows: initial displacement x=y=0, initial velocity x '=y '=0,
Time from 0.2s to 0.3s, equivalent damping c=200N*s/m, rotor speed 1772r/min.
Fig. 5 and Fig. 6 is the vibration signal displacement time-domain diagram and speed time-domain diagram of inner ring failure respectively.By Fig. 6 it can be concluded that
When rolling bearing inner ring is there are when pitting fault, there are some peak values, but most of peak value is not particularly pertinent；In Fig. 5
Displacement time domain waveform in, there are quasi-periodic signal about 4~5 in 0.4s, then frequency be 10~12.5Hz, tentatively estimate
Counting this characteristic frequency is that rotor turns frequency (11.99Hz).
Fig. 7 and Fig. 8 is the vibration signal displacement amplitude frequency diagram and speed amplitude frequency diagram of inner ring failure respectively.Including main frequency
Substantially have frequency by inner ring failure when of rotor frequency (12.21Hz), rolling element and its secondary and triple-frequency harmonics (70.84Hz,
141.7 Hz and 212.5Hz) and rotor speed caused by side frequency (83.05Hz, 153.9Hz etc.) occur but in fig. 8
Inner ring fault characteristic frequency quadruple and fifth harmonic harmonic wave (288.2Hz and 354.2Hz).
Damping force is the function for being displaced first derivative, its Fractional Derivative may be expressed as:
Fd=cx ' (t)=cDax(t) (19)
In formula, FdIt is damping force；DαIt is the complex variable of Laplace transformation.
Inner ring kinetic model after considering fractional order damping force are as follows:
Fig. 9 is the bifurcation graphs of inner ring single point of failure systems.It can be seen in figure 9 that changing the rank of rolling bearing fractional order
The secondary kinetic characteristic to system has very big influence.As fractional order order α≤0.2, rolling bearing arrangement is in chaos shape
State；As α > 0.2, rolling bearing arrangement enters periodic motion state.
The inner ring Single Point of Faliure Chart of axes track of rolling bearing when Figure 10 and Figure 11 is fractional order order α=0.6 respectively
With spectrogram.It can be seen from fig. 10 that Chart of axes track is although complex, but present the movement of obvious 8 font
Characteristic illustrates that rolling bearing motion state at this time is periodic motion, this exactly corresponds to the conclusion with order bifurcation graphs.And
The abscissa range of Chart of axes track is [- 8,8] 10-7M, the range of ordinate are [- 10,10] 10-7M, the available axis of rolling
The orbit of shaft center of the inner ring Single Point of Faliure held is ellipse.From in the system spectrum figure of Figure 11 can from obtain, system occur
4 × harmonic.But account for main component is 2 × harmonic, and also occurs 6 × harmonic in frequency spectrum.
Figure 12 and Figure 13 is respectively the acceleration time domain figure and amplitude frequency diagram of the experimental result of inner ring failure.From the time domain of Figure 12
Specific available information can not be seen in waveform diagram.It can be concluded that rotational frequency (13Hz), inner ring event from the spectrogram of Figure 13
Barrier characteristic frequency and its higher hamonic wave (73Hz, 150Hz, 199Hz, 285Hz and 341Hz) and rotor turn side frequency (65 caused by frequency
Hz and 162Hz etc.).1.5 frequencys multiplication (106Hz) of inner ring fault characteristic frequency are even had also appeared in figure.
2. housing washer fault model:
Since outer ring and rack are generally tighter transition fit or interference fit, the speed of outer ring is zero.Outer ring failure
Model is as shown in figure 14:
As shown in figure 15, maximum deformation quantity λmaxIt is in rolling element deflection CdrOn the basis of, subtract the deflection of outer ring
Cdo, it may be assumed that
λmax=Cdr-Cdo (21)
In formula, roIt is outer radii.
Therefore, the improving method for calculating deformation of loess soil of actual gradual change release are as follows:
The kinetics equation of foundation are as follows:
In formula,It is the angle of plus load and X-axis.
Figure 16 and Figure 17 is the vibration signal displacement time-domain diagram and speed time-domain diagram of outer ring failure respectively.It can be obtained by Figure 17
There are when pitting fault for housing washer out, it can be seen that the fault characteristic frequency of outer ring (has 19~20 peaks in 0.4s
Value)；And the displacement time domain waveform of Figure 16 in 0.4s not there is only quasi-periodic signal about 4~5 (frequency is 10~
12.5Hz), there is also 4~5 peak values and in each periodic signal, this is just also the fault characteristic frequency of outer ring.
Figure 18 and Figure 19 is the vibration signal displacement amplitude frequency diagram and speed amplitude frequency diagram of outer ring failure respectively.Including main frequency
Rate has the frequency and its secondary and triple-frequency harmonics of rotor frequency (12.21Hz), rolling element by outer ring failure when substantially
Side frequency caused by (48.85Hz, 97.7Hz and 146.6Hz) and rotor speed (87.93Hz etc.), and have also appeared outer ring event
Hinder characteristic frequency quadruple and fifth harmonic harmonic wave and higher multiplied frequency harmonic (195.4Hz, 244.3Hz, 293.1Hz and
344.44Hz etc.).
Figure 20 is the bifurcation graphs of outer ring single point of failure systems.It can be seen in figure 20 that changing rolling bearing fractional order
Order has very big influence to the kinetic characteristic of system.As fractional order order α≤0.1, rolling bearing arrangement is in chaos
State；As α > 0.1, rolling bearing arrangement enters periodic motion state.
The outer ring Single Point of Faliure Chart of axes track of rolling bearing when Figure 21 and Figure 22 is fractional order order α=0.6 respectively
With spectrogram.It can be seen from figure 21 that Chart of axes track is although complex, but present the fortune of 8 fonts in obvious
Dynamic characteristic illustrates that rolling bearing motion state at this time is periodic motion, this exactly corresponds to the conclusion with order bifurcation graphs.And
And the abscissa range of Chart of axes track is [- 1.5,1.5] 10-4m, the range of ordinate is [- 1,1] 10-4m, available
The orbit of shaft center of the inner ring Single Point of Faliure of rolling bearing is approximate circle.From in the system spectrum figure of Figure 22 can from obtain,
What system accounted for main component is 2 × harmonic, and also occurs 1 × harmonic, 3 × harmonic equimultiple in frequency spectrum
Frequency component.
Figure 23 and Figure 24 is respectively the acceleration time domain figure and amplitude frequency diagram of the experimental result of outer ring failure.From the time domain of Figure 23
Specific available information can not be seen in waveform diagram.It can be concluded that rotational frequency (12Hz), outer ring event from the spectrogram of Figure 24
Hinder characteristic frequency and its higher hamonic wave (52Hz, 99Hz, 199Hz, 155Hz and 207Hz).
3. rolling bearing rolling element fault model:
Since there are multiple rolling elements in rolling bearing, and rolling element not only revolves in rotary course, and there is also certainly
Turn.When rolling element itself is there are when failure, can be contacted respectively with the generation of inside and outside circle raceway, therefore the failure of rolling element damages mould
Type is complex.
Assuming that concrete condition is as shown in figure 25 when there is the single pitting fault in part on rolling element.
When rolling element failure and outer ring raceway contact, maximum deformation quantity λmaxIt should be in rolling element deflection CdrBasis
On, subtract the deflection C of outer ringdo；And when rolling element failure and inner ring raceway contact, maximum deformation quantity λmaxShould roll
Body deflection CdrOn the basis of, in addition the deflection C of inner ringdiThat is:
Therefore, the improving method for calculating deformation of loess soil of actual gradual change release are as follows:
Rolling body dynamics non-dimensional model after considering damping force are as follows:
Figure 26 and Figure 27 is the vibration signal displacement time-domain diagram and speed time-domain diagram of rolling element failure respectively.By Figure 26 and figure
27 it can be concluded that rolling bearing inner ring is there are when pitting fault, and there are some same for speed time domain waveform and displacement waveform diagram
Peak value, in 0.4s exist about 4~5 peak values, then frequency be 10~12.5Hz, according to a preliminary estimate this characteristic frequency be rotor turn
Frequently (11.99 Hz).
Figure 28 and Figure 29 is the vibration signal displacement amplitude frequency diagram and speed amplitude frequency diagram of rolling element failure respectively.It is only capable of from figure
See 7.33Hz (being approximately equal to retainer rotational frequency) and 62.27Hz (characteristic frequency for being approximately equal to rolling element failure).
Figure 30 is the bifurcation graphs of rolling element single point of failure systems.As can be seen from Figure 30, change rolling bearing fractional order
Order have very big influence to the kinetic characteristic of system.As fractional order order α≤0.2, rolling bearing arrangement is in mixed
Ignorant state；As α > 0.2, rolling bearing arrangement enters periodic motion state.
The rolling element Single Point of Faliure orbit of shaft center of rolling bearing when Figure 31 and Figure 32 is fractional order order α=0.6 respectively
Figure and spectrogram.As can be seen from Figure 31, Chart of axes track is although complex, but presents the fortune of obvious ellipse
Dynamic characteristic illustrates that rolling bearing motion state at this time is periodic motion, this exactly corresponds to the conclusion with order bifurcation graphs.And
And the abscissa range of Chart of axes track is [- 1.5,1.5] 10-7m, the range of ordinate is [- 4,4] 10-7m, available
The orbit of shaft center of the rolling element Single Point of Faliure of rolling bearing is ellipse.From in the system spectrum figure of Figure 31 can from obtain,
What system accounted for main component is 2 × harmonic.
Figure 33 and Figure 34 is respectively the acceleration time domain figure and amplitude frequency diagram of the experimental result of rolling element failure.From Figure 33 when
It is difficult to find any information in domain waveform figure.It include the main features frequency such as 145.7Hz in the low-frequency range frequency domain figure of Figure 34,
Have also appeared some sidebands, such as 121.4Hz.
Claims (1)
1. fractional order damps the method that rolling bearing fault dynamics sequential model is established, which is characterized in that steps are as follows:
1) on the basis of having obtained rolling bearing contact equivalent stiffness and equivalent damping, comprehensively considering has lubricant to influence and roll
Influence when kinetoplast passes through failure to inner ring self-deformation amount, establishes the rolling bearing gradual change dynamics containing single pitting fault
Model；
2) fractional calculus theory is applied in rolling bearing, derives the calculation formula of fractional order damping force, builds respectively
It is vertical to consider fractional order damping rolling bearing inner ring fault model, housing washer fault model and rolling bearing rolling element failure
Model；
A) specific step is as follows for the rolling bearing inner ring fault model foundation:
Juxtaposition metamorphose amount for the bearing of damage, between j-th of rolling element and raceway are as follows:
In formula, x is the displacement of inner ring radial direction X-direction；Y is the displacement of inner ring radial direction Y-direction；θjIt is position locating for j-th of rolling element center
Angle setting；E is radial clearance；λ is the deflection of gradual change release when rolling element rolls across inner ring fault zone；HjFor oil film thickness；ωc
For the angular velocity of rotation of retainer；Z is the number of rolling element；θ1For the start bit angle setting for the rolling element that number is 1；ωiFor rotor
Angular velocity of rotation；DbFor rolling element diameter；DmFor the pitch diameter of rolling bearing；Contact of the α between rolling element and inner ring raceway
Angle；
βjIt is switching value, indicates when rolling element is located in the position angular spread of spot corrosion defect, there are certain juxtaposition metamorphoses
Amount；And when rolling element is not in the position angular spread of spot corrosion defect, deflection has not existed；Therefore it is defined as:
In formula,It is the position angle at inner ring pitting fault center；ΔΦsIt is the span angle of failure；bcIt is the half of failure width；
ΦspallIt is the position angle at pitting fault center；
When rolling element passes through inner ring defect, the deflection of release is the deflection C of rolling elementdrWith the deflection C of inner ringdiIt
With；When rolling element touches defect bottom, the maximum deformation quantity of release is λmaxJust it is equal to failure depth, it may be assumed that
λmax=Cdr+Cdi (7)
In formula, riIt is inner radii；rbIt is rolling element radius；
Actual release deflection are as follows:
According to Hertz contact theory, the calculation method of the contact load Q of the point contact between single rolling element and inside and outside circle raceway
It is respectively as follows:
In formula, K is equivalent juxtaposition metamorphose coefficient, it is related rolling element and the inside and outside juxtaposition metamorphose coefficient enclosed between raceway；
Contact between rolling element and inside and outside circle raceway is indicated with one group of spring damping model；In rolling element and inside and outside circle raceway
Contact angle it is equal under the premise of, total equivalent juxtaposition metamorphose coefficient are as follows:
In formula, ball bearing n=1.5；KoAnd KiIt is juxtaposition metamorphose coefficient；nδIt is coefficient relevant to principal curvatures difference function, Ke Yitong
It crosses and tables look-up to obtain；Σ ρ is contact principal curvatures and function, calculation method are as follows:
∑ ρ=ρ1I+ρ1II+ρ2I+ρ2II (14)
In formula, subscript 1 and 2 respectively represents rolling element and inside and outside circle raceway；I represents the axial plane of rotor；II represent with it is vertical
In I sagittal plane；The circular of every principal curvatures can be by tabling look-up to obtain；
nδIt is a design factor, it is related to the principal curvatures difference function of rolling bearing, is obtained by tabling look-up；Principal curvatures difference function
Is defined as:
By all contact load Q be projected in X-axis in Y-axis both direction and be added, then obtain inner ring raceway and all rollings
Total contact load between body:
Using Newtonian fluid model, i.e., lubricant is thought of as Newtonian fluid；The tangential friction force born at j-th of rolling element
Are as follows:
τ=η * Q (17)
In formula, η is stiction coefficient；
By Newton's second law, the kinetics equation of rolling bearing inner ring are as follows:
In formula, m is the quality of rolling bearing；C is the equivalent damping of system；FeFor the radial load of inner ring；FrTo be loaded outside outer ring
Lotus；
Damping force is the function for being displaced first derivative, its Fractional Derivative may be expressed as:
Fd=cx ' (t)=cDax(t) (19)
In formula, FdIt is damping force；DαIt is the complex variable of Laplace transformation；
Inner ring kinetic model after considering damping force are as follows:
B) specific step is as follows for the housing washer fault model foundation:
The kinetics equation of foundation are as follows:
In formula,It is the angle of plus load and X-axis；
Maximum deformation quantity λmaxIt is in rolling element deflection CdrOn the basis of, subtract the deflection C of outer ringdo, it may be assumed that
λmax=Cdr-Cdo (22)
In formula, roIt is outer radii；
Therefore, the improving method for calculating deformation of loess soil of actual gradual change release are as follows:
C) specific step is as follows for the rolling bearing rolling element fault model foundation:
Rolling body dynamics non-dimensional model after considering damping force are as follows:
When rolling element failure and outer ring raceway contact, maximum deformation quantity λmaxIt should be in rolling element deflection CdrOn the basis of, subtract
Remove the deflection C of outer ringdo；And when rolling element failure and inner ring raceway contact, maximum deformation quantity λmaxShould be deformed in rolling element
Measure CdrOn the basis of, in addition the deflection C of inner ringdiThat is:
Therefore, the improving method for calculating deformation of loess soil of actual gradual change release are as follows:
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