CN106126850A - A kind of rolling bearing surface damage faulty power modeling method - Google Patents

Abstract

The invention discloses a kind of rolling bearing surface damage faulty power modeling method, comprise the steps: 1) on the basis of obtaining rolling bearing contact equivalent stiffness and equivalent damping, consider rolling bearing clearance and supporting region change, set up rolling bearing spring damped vibration model；2) impulse function of surface damage trouble point is loaded on outer ring, inner ring and rolling element respectively, sets up housing washer fault model, rolling bearing inner ring fault model and roller bearing rolling element fault model respectively.The impulse function of surface damage trouble point is loaded on outer ring, inner ring and rolling element by the present invention respectively, set up housing washer fault model, rolling bearing inner ring fault model and roller bearing rolling element fault model, more conforming to practical situation, the result calculated is the most accurate.

Description

A kind of rolling bearing surface damage faulty power modeling method

Technical field

The present invention relates to a kind of rolling bearing fault dynamic modeling method, particularly to a kind of rolling bearing surface damage Faulty power modeling method.

Background technology

The one of the main reasons of rolling bearing fault diagnosis application poor effect is a lack of rolling bearing fault study mechanism. Set up key effective, that rolling bearing fault kinetic model that is that tally with the actual situation is rolling bearing fault study mechanism, Also it is the technical foundation of rolling bearing fault diagnosis.

For rolling bearing fault Dynamic Modeling problem, numerous scholars have carried out fruitful research.Zhang Genyuan Deng based on single edge contact and Elastic fluid lubrication theory model, the response characteristic of point defect rolling bearing is analyzed, used many bodies Dynamic method establishes point defect rolling bearing kinetic model.Xu Dong etc. are by supporting roll in rolling bearing operation process The analysis of subnumber Changing Pattern, establishes piecewise function and defect impulse function model.Zhao Lianchun etc. are right with deep groove ball bearing As, establish the Elastic Contact model of bear vibration, and demonstrate notional result with custom-designed test method.Old what etc. Establish early defect Non-Linear Vibration rolling bearing model.East Asia is refined etc. establishes the equivalent model of faulty bearing. Zeki Kiral etc. simulate the faulty bearings fixed by bearing spider by mechanics model structure, and consider that diverse location defect is to shaking Dynamic impact.Matej Tadin etc. considers the bear vibration characteristic analyzing different damage position in overall situation two-freedom.Lee The prosperous contact load waiting consideration lubricating oil film and deformation, use ADAMS software that rolling bearing has been carried out dynamic virtual emulation.But It is to fail effectively fault impact to be dissolved into rolling bearing nonlinear dynamical equation in rolling bearing fault Dynamic Modeling In, rolling bearing fault the model calculation has greater difference with emulation and experimental result simultaneously, it is impossible to be well applied to rolling Dynamic bearing fault diagnosis.

Summary of the invention

In order to solve above-mentioned technical problem, the present invention provides a kind of high-efficiency high-accuracy, result of calculation rolling bearing accurately Surface damage faulty power modeling method, it can well provide technical support for rolling bearing fault diagnosis.

The present invention solves the technical scheme of above-mentioned technical problem: a kind of rolling bearing surface damage faulty power modeling Method, step is as follows:

1) on the basis of obtaining rolling bearing contact equivalent stiffness and equivalent damping, it is considered to rolling bearing clearance and Supporting region changes, and sets up rolling bearing spring damped vibration model；

2) impulse function of surface damage trouble point is loaded on outer ring, inner ring and rolling element respectively, sets up rolling respectively Dynamic bearing outer ring fault model, rolling bearing inner ring fault model and roller bearing rolling element fault model.

In above-mentioned rolling bearing surface damage faulty power modeling method, step 2) in, rolling bearing inner ring fault What model was set up specifically comprises the following steps that

According to formula (1), the shape calculating i-th rolling element position becomes δ_i,

δ_i=x cos θ_i+y sinθ_i-γ (1)

In formula: γ is the initial diametrical clearance of rolling bearing, θ_iIt is the angle of i-th rolling element and world coordinates x direction, X is inner ring radially x direction displacement, and y is inner ring radially y direction displacement；

Act on the external force of inner ring along x Yu y direction, by formula (2), formula (3) calculates；

$F_x=K_n\underset{i=1}{\overset{z}{\Σ}}{\mathrm{\λ}}_i{\mathrm{\δ}}_i^{1.5}{\mathrm{cos\θ}}_i---\left(2\right)$

$F_y=K_n\underset{i=1}{\overset{z}{\Σ}}{\mathrm{\λ}}_i{\mathrm{\δ}}_i^{1.5}{\mathrm{sin\θ}}_i---\left(3\right)$

K_nEquivalence nominal rigidity, λ is contacted for single rolling element and Internal and external cycle_iFor i-th rolling element in the control of load area Parameter processed, Z is rolling element quantity；

Shown in the equation of motion of inner ring such as formula (4):

$\left\{\begin{array}{c}m\stackrel{\·\·}{y}+c\stackrel{\·}{y}+F_y=w_y+I_d\left(t\right)sin\mathrm{\ψ}\\ m\stackrel{\·\·}{x}+c\stackrel{\·}{x}+F_x=w_x+I_d\left(t\right)cos\mathrm{\ψ}\end{array}\right.---\left(4\right)$

M be inner ring with the quality of rotating shaft and, c is the overall equivalent damping of rolling element and Internal and external cycle interaction, w_x、w_yFor Load acts on the radial force on rotary body, I_dT () is parameterized impulse function.In the case of given excitation, equation (4) It is the Second Order Nonlinear Differential Equations of two couplings, by its nondimensionalization, shown in the reduced equation of rolling bearing such as formula (5):

$\left\{\begin{array}{c}\stackrel{\·\·}{\stackrel{\‾}{x}}=\frac{1}{K_n{\mathrm{\γ}}^{1.5}}\left(W+I_d\left(t\right)\cos \mathrm{\Ω}\mathrm{\τ}\right)-\frac{c}{{\mathrm{mv}}_n}\stackrel{\·}{\stackrel{\‾}{x}}-f_x(\stackrel{\‾}{x},\stackrel{\‾}{y},\mathrm{\Ω},\mathrm{\τ})\\ \stackrel{\·\·}{\stackrel{\‾}{y}}=\frac{1}{K_n{\mathrm{\γ}}^{1.5}}{I}_d\left(t\right)\sin \mathrm{\Ω}\mathrm{\τ}-\frac{c}{{\mathrm{mw}}_n}\stackrel{\·}{\stackrel{\‾}{y}}-f_y(\stackrel{\‾}{x},\stackrel{\‾}{y},\mathrm{\Ω},\mathrm{\τ})\end{array}\right.---\left(5\right)$

Change, when the position of impaired loci is in bearing owing to the position of inner peripheral surface impaired loci rotates with inner ring During non-bearing district, rolling element can be ignored by the vibration effect of impaired loci；When impaired loci is in supporting region diverse location, roll Body is varied in size by the produced impulsive force of impaired loci；

Rolling element is 2arcsin (l/R by the angle of impaired loci_I), R_IFor inner ring raceway diameter, l is that injured surface is straight Footpath；The rolling element angle that contacts with impaired loci surface is 2arcsin (l/R_I), set up rolling element and cross the segmentation pulse letter of impaired loci Number, as shown in formula (6):

$\mathrm{\&lambda;}\left(\mathrm{\&upsi;}\right)=\left\{\begin{array}{cc}1& \left|\mathrm{\&upsi;}\right|<arcsin(l/R_I)\\ 0& \left|\mathrm{\&upsi;}\right|\&GreaterEqual;arcsin(l/R_I)\end{array}\right.---\left(6\right)$

When impaired loci is in supporting region and contacts with rolling element, generation is impacted, if be in non-bearing district, do not produce Raw impact, sets up the segmentation impulse function of supporting region, as shown in formula (7):

$s\left(v\right)=\left\{\begin{array}{cc}1& \left|s\right|<L\\ 0& \left|s\right|\&GreaterEqual;L\end{array}\right.---\left(7\right)$

S is the angle of axle center direction of displacement and impaired loci, and L is 1/2nd of roller carrying field angle；For difference Damage have different expression, the size of pulse amplitude is determined by the speed loaded with contact point and can be passed through supporting region Relative motion carry out function.Rolling element is the shortest with the time of contact of surface damage, and therefore the damage on raceway is long Degree must be suitable with the ratio of raceway length, and such impulsive force could be consistent with actual, is substituted into by impulse function and rolls In the vibration equation (5) of bearing；

By the produced impulse function of inner ring damage, shown in its expression formula such as formula (8):

$I_d\left(t\right)=A_{id}(h_{id},L,\mathrm{\&omega;})\underset{i=1}{\overset{z}{\&Sigma;}}{\mathrm{\&alpha;}}_{id}\left(i\right)\&CenterDot;s\left(f\right(\mathrm{\&psi;},p\left(x\right)+arctan(y/|x\left|\right)\left)\right)\&CenterDot;\mathrm{\&lambda;}\left(f\right(\mathrm{\&psi;},{\mathrm{\&phi;}}_i\left)\right)---\left(8\right)$

Wherein: h_idFor the impaired loci degree of depth, φ_iFor the angle of i-th rolling element barycenter Yu x-axis positive direction, ψ is bearing inner race The position of upper impaired loci and the angle of x-axis positive direction, ω is angular velocity of rotation；A_id(h_id, L, ω) and it is deep about injured surface Degree, the pulse amplitude functional relation of length and angular velocity, a_idI () is the amplitude modulation parameter of i-th rolling element；

$f(\mathrm{\&psi;},p(x)+\arctan (y/\left|x\right|\left)\right)=\left\{\begin{array}{cc}\mathrm{mod}\left(\right|\mathrm{\&psi;}-\arctan \left(y/\left|x\right|\right)|,2\mathrm{\&pi;})& \mathrm{mod}\left(\right|\mathrm{\&psi;}-\arctan \left(y/\left|x\right|\right)|,2\mathrm{\&pi;})\&le;\mathrm{\&pi;}\\ 2\mathrm{\&pi;}-\mathrm{mod}\left(\right|\mathrm{\&psi;}-\arctan \left(y/\left|x\right|\right)|,2\mathrm{\&pi;})& \mathrm{mod}\left(\right|\mathrm{\&psi;}-\arctan \left(y/\left|x\right|\right)|,2\mathrm{\&pi;})>\mathrm{\&pi;}\end{array}\right.,$

In formula: mod function is MOD function；

In formula: F_rFor rolling bearing radial load,It is the 1st Individual rolling element barycenter and the angle of x-axis positive direction,ε is end-play.

In above-mentioned rolling bearing surface damage faulty power modeling method, step 2) in, housing washer fault What model was set up specifically comprises the following steps that

Set up rolling element and cross the piecewise function pulse of impaired loci, as shown in formula (10):

$\mathrm{\&lambda;}\left(\mathrm{\&upsi;}\right)=\left\{\begin{array}{cc}1& \left|\mathrm{\&upsi;}\right|<arcsin(l/R_o)\\ 0& \left|\mathrm{\&upsi;}\right|\&GreaterEqual;arcsin(l/R_o)\end{array}\right.---\left(10\right)$

υ is the minimum angle at rolling element center and impaired loci center；

By the produced impulse function of outer peripheral surface damage, as shown in formula (11):

$I_d\left(t\right)=A_{id}(h_{id},L,\mathrm{\&omega;})\underset{i=1}{\overset{z}{\&Sigma;}}{\mathrm{\&alpha;}}_{id}\left(i\right)\&CenterDot;\mathrm{\&lambda;}\left(f\right(\mathrm{\&psi;},{\mathrm{\&phi;}}_i\left)\right)---\left(11\right).$

In above-mentioned rolling bearing surface damage faulty power modeling method, step 2) in, the event of rolling bearing rolling element What barrier model was set up specifically comprises the following steps that

According to formula (12), calculate the impaired loci of rolling element and the angle of x-axis positive direction,

ψ=ψ₁-ω_bt (12)

ψ₁For initial angle, ω_bFor the rotational velocity of rolling element, t is the time；

According to formula (13), calculate the angle between moving axes x-axis positive direction and absolute coordinate x-axis positive direction,

θ_x=θ_x0+ω_ct (13)

θ_x0For initial angle, ω_cFor rolling element rotating speed in absolute coordinate, t is the time；

According to formula (14), calculate the angle that on rolling element, impaired loci contacts with outer ring,

ψ_o=ψ-θ_x (14)

According to formula (15), calculate the angle that on rolling element, impaired loci contacts with inner ring,

ψ_i=ψ-θ_x-180° (15)

According to formula (16), calculate and have the rolling element barycenter of impaired loci and the angle of x-axis positive direction；

φ=ω_ct+φ₀ (16)

In formula: φ₀For first rolling element angle that x-axis under bearing original state is positive with bearing；

With x, y-coordinate axle is reference, according to formula (17), calculates roller and presss from both sides with the real-time of bearing displacement in a counterclockwise direction Angle；

Wherein:

Set up rolling element and cross the piecewise function pulse of impaired loci, as shown in formula (18):

$\mathrm{\&lambda;}\left(\mathrm{\&upsi;}\right)=\left\{\begin{array}{cc}1& \left|\mathrm{\&upsi;}\right|<arcsin(l/r)\\ 0& \left|\mathrm{\&upsi;}\right|\&GreaterEqual;arcsin(l/r)\end{array}\right.---\left(18\right)$

Set up the piecewise function pulse of supporting region, as shown in formula (19):

$s\left(v\right)=\left\{\begin{array}{cc}1& \left|s\right|<L\\ 0& \left|s\right|\&GreaterEqual;L\end{array}\right.---\left(19\right)$

Set up by the produced impulse function of rolling element damage, as shown in formula (19):

Wherein:

Compared with prior art, the method have the advantages that

(1) impulse function of surface damage trouble point is loaded on outer ring, inner ring and rolling element by the present invention respectively, sets up Housing washer fault model, rolling bearing inner ring fault model and roller bearing rolling element fault model, more conform to reality Border situation, the result calculated is the most accurate.

(2) the surface damage modeling of the present invention, introduces the piecewise function of supporting region and each rolling element through damage table The piecewise function in face, characterizes impaired loci when being in supporting region diverse location, and rolling element is by the produced impulsive force of impaired loci Vary in size, have simple and practical, calculate advantage accurately.

Accompanying drawing explanation

Fig. 1 is the inner ring fault model of the present invention.

Fig. 2 is the vibration signal time-domain diagram in the inner ring fault x direction of the present invention.

Fig. 3 is the vibration amplitude frequency diagram in the inner ring fault x direction of the present invention.

Fig. 4 is the outer ring fault model of the present invention.

Fig. 5 is the vibration signal time-domain diagram in the fault x direction, outer ring of the present invention.

Fig. 6 is the vibration amplitude frequency diagram in the fault x direction, outer ring of the present invention.

Fig. 7 is the rolling element fault model of the present invention.

Fig. 8 is the vibration signal time-domain diagram in the rolling element fault x direction of the present invention.

Fig. 9 is the vibration amplitude frequency diagram in the rolling element fault x direction of the present invention.

Figure 10 is the inner ring fault x direction vibration acceleration signal of the present invention.

Figure 11 is the inner ring fault x direction acceleration of vibration spectrum analysis figure of the present invention.

Figure 12 is fault x direction, the outer ring vibration acceleration signal figure of the present invention.

Figure 13 is fault x direction, the outer ring vibration acceleration signal spectrum analysis figure of the present invention.

Figure 14 is the rolling element fault x direction vibration acceleration signal figure of the present invention.

Figure 15 is the rolling element fault x direction vibration acceleration signal spectrum analysis figure of the present invention.

Figure 16 is the inner ring fault x direction analysis of vibration signal figure of the present invention.

Figure 17 is the analysis of vibration signal figure in the fault x direction, outer ring of the present invention.

Figure 18 is the analysis of vibration signal figure in the rolling element fault x direction of the present invention.

Detailed description of the invention

The present invention is further illustrated below in conjunction with the accompanying drawings.

The rolling bearing surface damage faulty power modeling method of the present invention, comprises the steps:

1. rolling bearing inner ring fault model

In the case of considering rolling bearing clearance, rolling element can be because of damage by the size of the produced impulsive force of impaired loci Point is in the diverse location of supporting region and different, ignores the relative slip of contact surface, can be transported by inner ring by simplifying The dynamic quality spring-damp system being considered as two-freedom.

As it is shown in figure 1, load produced by the effect power being carried on inner ring by axle and the damage of bearing local surfaces Impulsive force is accordingly to be regarded as external applied load and acts on inner ring, and the shape of i-th rolling element position becomes δ_i, computing formula such as formula (1) shown in.

δ_i=x cos θ_i+y sinθ_i-γ (1)

In formula: γ is the initial diametrical clearance of rolling bearing, θ_iIt is the angle of i-th rolling element and world coordinates x direction, X is inner ring radially x direction displacement, and y is inner ring radially y direction displacement.

The external force of inner ring is acted on equal to loading ability of bearing distributed force sum, computing formula such as formula (2), public affairs along x Yu y direction Shown in formula (3).

$F_x=K_n\underset{i=1}{\overset{z}{\&Sigma;}}{\mathrm{\&lambda;}}_i{\mathrm{\&delta;}}_i^{1.5}{\mathrm{cos\&theta;}}_i---\left(2\right)$

$F_y=K_n\underset{i=1}{\overset{z}{\&Sigma;}}{\mathrm{\&lambda;}}_i{\mathrm{\&delta;}}_i^{1.5}{\mathrm{sin\&theta;}}_i---\left(3\right)$

K_nEquivalence nominal rigidity, λ is contacted for single rolling element and Internal and external cycle_iFor i-th rolling element in the control of load area Parameter processed, Z is rolling element quantity.

Shown in the equation of motion of inner ring such as formula (4):

$\left\{\begin{array}{c}m\stackrel{\&CenterDot;\&CenterDot;}{y}+c\stackrel{\&CenterDot;}{y}+F_y=w_y+I_d\left(t\right)sin\mathrm{\&psi;}\\ m\stackrel{\&CenterDot;\&CenterDot;}{x}+c\stackrel{\&CenterDot;}{x}+F_x=w_x+I_d\left(t\right)cos\mathrm{\&psi;}\end{array}\right.---\left(4\right)$

M be inner ring with the quality of rotating shaft and, c is the overall equivalent damping of rolling element and Internal and external cycle interaction, w_x、w_yFor Load acts on the radial force on rotary body, I_dT () is parameterized impulse function.In the case of given excitation, equation (4) It it is the Second Order Nonlinear Differential Equations of two couplings^[13], by its nondimensionalization, the reduced equation of rolling bearing is as shown in (5):

$\left\{\begin{array}{c}\stackrel{\&CenterDot;\&CenterDot;}{\stackrel{\&OverBar;}{x}}=\frac{1}{K_n{\mathrm{\&gamma;}}^{1.5}}\left(W+I_d\left(t\right)\cos \mathrm{\&Omega;}\mathrm{\&tau;}\right)-\frac{c}{{\mathrm{mv}}_n}\stackrel{\&CenterDot;}{\stackrel{\&OverBar;}{x}}-f_x(\stackrel{\&OverBar;}{x},\stackrel{\&OverBar;}{y},\mathrm{\&Omega;},\mathrm{\&tau;})\\ \stackrel{\&CenterDot;\&CenterDot;}{\stackrel{\&OverBar;}{y}}=\frac{1}{K_n{\mathrm{\&gamma;}}^{1.5}}{I}_d\left(t\right)\sin \mathrm{\&Omega;}\mathrm{\&tau;}-\frac{c}{{\mathrm{mw}}_n}\stackrel{\&CenterDot;}{\stackrel{\&OverBar;}{y}}-f_y(\stackrel{\&OverBar;}{x},\stackrel{\&OverBar;}{y},\mathrm{\&Omega;},\mathrm{\&tau;})\end{array}\right.---\left(5\right)$

The position of inner peripheral surface impaired loci rotates with inner ring and changes, and holds when the position of impaired loci is in the non-of bearing When carrying district, rolling element can be ignored by the vibration effect of impaired loci.When impaired loci is in supporting region diverse location, rolling element leads to Cross varying in size of the produced impulsive force of impaired loci.Piecewise function and each rolling element that so can introduce supporting region pass through damage The piecewise function on surface.

Rolling element is 2arcsin (l/R by the angle of impaired loci_I), R_IFor inner ring raceway diameter, l is that injured surface is straight Footpath.The rolling element angle that contacts with impaired loci surface is 2arcsin (l/R_I), set up rolling element and cross the segmentation pulse letter of impaired loci Number, as shown in (6).

$\mathrm{\&lambda;}\left(\mathrm{\&upsi;}\right)=\left\{\begin{array}{cc}1& \left|\mathrm{\&upsi;}\right|<arcsin(l/R_I)\\ 0& \left|\mathrm{\&upsi;}\right|\&GreaterEqual;arcsin(l/R_I)\end{array}\right.---\left(6\right)$

When impaired loci is in supporting region and contacts with rolling element, generation is impacted, if be in non-bearing district, do not produce Raw impact, sets up the segmentation impulse function of supporting region, as shown in (7).

$s\left(v\right)=\left\{\begin{array}{cc}1& \left|s\right|<L\\ 0& \left|s\right|\&GreaterEqual;L\end{array}\right.---\left(7\right)$

In formula: s is the angle of axle center direction of displacement and impaired loci, L is 1/2nd of roller carrying field angle.For Different damages has different expression, and the size of pulse amplitude is determined by the speed loaded with contact point and can be by holding The relative motion carrying district carrys out function.Rolling element is the shortest with the time of contact of surface damage, the therefore damage on raceway Hindering length must be suitable with the ratio of raceway length, and such impulsive force could be consistent with actual, is substituted into by impulse function In the vibration equation (5) of rolling bearing.

By the produced impulse function of inner ring damage, shown in its expression formula such as formula (8).

$I_d\left(t\right)=A_{id}(h_{id},L,\mathrm{\&omega;})\underset{i=1}{\overset{z}{\&Sigma;}}{\mathrm{\&alpha;}}_{id}\left(i\right)\&CenterDot;s\left(f\right(\mathrm{\&psi;},p\left(x\right)+arctan(y/|x\left|\right)\left)\right)\&CenterDot;\mathrm{\&lambda;}\left(f\right(\mathrm{\&psi;},{\mathrm{\&phi;}}_i\left)\right)---\left(8\right)$

Wherein: h_idFor the impaired loci degree of depth, φ_iFor the angle of i-th rolling element barycenter Yu x-axis positive direction, ψ is bearing inner race The position of upper impaired loci and the angle of x-axis positive direction, ω is angular velocity of rotation；A_id(h_id, L, ω) and it is deep about injured surface Degree, the pulse amplitude functional relation of length and angular velocity, a_idI () is the amplitude modulation parameter of i-th rolling element；

$f(\mathrm{\&psi;},p(x)+\arctan (y/\left|x\right|\left)\right)=\left\{\begin{array}{cc}\mathrm{mod}\left(\right|\mathrm{\&psi;}-\arctan \left(y/\left|x\right|\right)|,2\mathrm{\&pi;})& \mathrm{mod}\left(\right|\mathrm{\&psi;}-\arctan \left(y/\left|x\right|\right)|,2\mathrm{\&pi;})\&le;\mathrm{\&pi;}\\ 2\mathrm{\&pi;}-\mathrm{mod}\left(\right|\mathrm{\&psi;}-\arctan \left(y/\left|x\right|\right)|,2\mathrm{\&pi;})& \mathrm{mod}\left(\right|\mathrm{\&psi;}-\arctan \left(y/\left|x\right|\right)|,2\mathrm{\&pi;})>\mathrm{\&pi;}\end{array}\right.,$

In formula: mod function is MOD function.

In formula: F_rFor rolling bearing radial load,It is the 1st Individual rolling element barycenter and the angle of x-axis positive direction,ε is end-play.

Take parameter K_n=8.5941 × 10⁹, m=924.9g, γ=0.00127mm, c=484.026Ns/m, W=9.06N, Axle rotating speed is 600rpm, initial value takes Use fourth order Runge-Kutta computational methods to solve, inner ring x direction time domain vibration signal and width thereof can be obtained Frequently signal is respectively such as Fig. 2, shown in 3.

As can be seen from Figure 3 inner ring turns frequency is 10.38Hz, and 1 frequency multiplication of inner ring failure-frequency is 49.85Hz.

Introduce rolling bearing and become flexibility frequency f_vcI.e. frequency during rolling element fixed point a certain by outer ring is as rolling bearing The fundamental frequency of inner ring radial vibration, computing formula is as shown in (9).

$f_{vc}=\frac{z}{2}\left(1-\frac{d}{D}cos\mathrm{\&alpha;}\right)f_s---\left(9\right)$

D is rolling element diameter, and D is pitch diameter, and α is contact angle, f_sFor the speed of inner ring, by rolling bearing parameter Data substitute into can try to achieve change flexibility frequency f_vc=3.05f_s。

Rotating speed is Theoretical Calculation f obtained during 600rpm as seen from Figure 3_vc=30.5Hz, single order to that indicated in the drawings The frequency of peak value is essentially identical, and occurs in that frequency multiplication relation.Frequency spectrum from inner ring x direction can find fundamental frequency 30.46Hz with Theoretical Calculation f_vcAlmost consistent, and there are two frequency multiplication relations, may thereby determine that the correctness that model is set up.

2. housing washer fault model

Outer ring fault model is as shown in Figure 4.Position ability when the supporting region of outer ring contacts with rolling element when impaired loci Can produce vibratory impulse, therefore impaired loci is once be not on supporting region, and bearing will not be produced impulsive force.Is produced from outer ring Raw impaired loci is typically at its supporting region, therefore outer ring raceway surface damage point produces the frequency of impulsive force with rolling element through outer ring The frequency of raceway impaired loci is equal.

Set up rolling element and cross the piecewise function pulse of impaired loci, as shown in formula (10):

$\mathrm{\&lambda;}\left(\mathrm{\&upsi;}\right)=\left\{\begin{array}{cc}1& \left|\mathrm{\&upsi;}\right|<\arcsin (l/R_o)\\ 0& \left|\mathrm{\&upsi;}\right|\&GreaterEqual;\arcsin (l/R_o)\end{array}\right.---\left(10\right)$

υ is the minimum angle at rolling element center and impaired loci center.

By the outer peripheral surface produced impulse function of damage, as shown in formula (11), x direction, outer ring time domain vibration signal and Its amplitude-frequency signal is respectively such as Fig. 5, shown in 6.

$I_d\left(t\right)=A_{id}(h_{id},L,\mathrm{\&omega;})\underset{i=1}{\overset{z}{\&Sigma;}}{\mathrm{\&alpha;}}_{id}\left(i\right)\&CenterDot;\mathrm{\&lambda;}\left(f\right(\mathrm{\&psi;},{\mathrm{\&phi;}}_i\left)\right)---\left(11\right)$

As can be seen from Figure 6 its outer ring failure-frequency is 30.46Hz.

3. rolling bearing rolling element fault model

The rolling element fault model of rolling bearing is as shown in Figure 7.Assume not produce when rolling element contacts with Internal and external cycle relatively Sliding, its rolling element only makees the impaired loci of rotation and translation, so its surface the most respectively with interior in xoy plane Circle, outer ring respectively contacts once.

According to formula (12), the impaired loci of calculating rolling element and the angle of x-axis positive direction:

ψ=ψ₁-ω_bt (12)

In formula: ψ₁For initial angle, ω_bFor the rotational velocity of rolling element, t is the time.

According to formula (13), the angle calculated between moving axes x-axis positive direction and absolute coordinate x-axis positive direction is,

θ_x=θ_x0+ω_ct (13)

In formula: θ_x0For initial angle, ω_cFor rolling element rotating speed in absolute coordinate, t is the time.

According to formula (14), calculate the angle that on rolling element, impaired loci contacts with outer ring.

ψ_o=ψ-θ_x (14)

According to formula (15), calculate the angle that on rolling element, impaired loci contacts with inner ring.

ψ_i=ψ-θ_x-180° (15)

According to formula (16), calculate and have the rolling element barycenter of impaired loci and the angle of x-axis positive direction.

φ=ω_ct+φ₀ (16)

In formula: φ₀For first rolling element angle that x-axis under bearing original state is positive with bearing.

So with x, y-coordinate axle is reference, according to formula (17), calculate roller in a counterclockwise direction with the reality of bearing displacement Time angle.

Wherein:

The piecewise function pulse of impaired loci crossed by rolling element,

$\mathrm{\&lambda;}\left(\mathrm{\&upsi;}\right)=\left\{\begin{array}{cc}1& \left|\mathrm{\&upsi;}\right|<arcsin(l/r)\\ 0& \left|\mathrm{\&upsi;}\right|\&GreaterEqual;arcsin(l/r)\end{array}\right.---\left(18\right)$

Set up the piecewise function pulse of supporting region,

$s\left(v\right)=\left\{\begin{array}{cc}1& \left|s\right|<L\\ 0& \left|s\right|\&GreaterEqual;L\end{array}\right.---\left(19\right)$

By the produced impulse function of rolling element damage it is,

Wherein

Vibration signal time-domain diagram and the amplitude frequency diagram thereof that in like manner can obtain rolling bearing inner ring x direction are distinguished the most as shown in Figure 8,9.

As can be seen from Figure 91 frequency multiplication of rolling element fault characteristic frequency is 39.46Hz.

4. rolling bearing fault Dynamics Simulation checking

Rolling bearing three-dimensional entity model is set up as shown in Figure 10 according to actual rolling bearing size.By rolling bearing bearing Being reduced to spring-damper structure for supporting outer ring, rolling element is contacted with Internal and external cycle respectively by the contact force set, rolling Being arranged by parameter between kinetoplast and rolling element makes it be kept at an angle each other, respectively in outer ring, inner ring and rolling The surface damage impact shock of impaired loci three kinds of single faults of simulation is set on kinetoplast.

4.1 rolling bearing inner ring fault simulations

Inner ring starts to rotate from resting state, reaches 3600rad/s stabilized (steady-state) speed, it is carried out 3 seconds at 0.3 second Emulation, the barycenter acceleration time domain figure in inner ring x direction and amplitude frequency diagram are as shown in figure 11.

The time-domain diagram of inner ring x direction vibration acceleration signal analyzed by resonance and demodulation after as shown in figure 11, can from figure To find out that inner ring turns frequently as 10.09Hz, it is 0.29Hz with the deviation of model calculation value 10.38Hz, the fault of rolling bearing inner ring The fundamental frequency of frequency is 50.06Hz, is 0.46Hz with model calculation value 49.5Hz deviation, and the existence of deviation is primarily due to axle Hold play, and the impact of impulse function.

4.2 housing washer fault simulations

Inner ring starts to rotate from resting state, reaches 3600rad/s stabilized (steady-state) speed, carry out 1 second imitating to it at 0.3 second Very, inner ring x direction barycenter acceleration time domain figure and amplitude frequency diagram such as Figure 12, shown in 13.

It can clearly be seen that frequency multiplication relation from Figure 13, the fundamental frequency of housing washer fault characteristic frequency is 30.15Hz, It is 0.35Hz with model calculation value 30.5 deviation.

4.3 rolling bearing rolling element fault simulations

Inner ring starts to rotate from resting state, reaches 3600rad/s stabilized (steady-state) speed, carry out 5 seconds imitating to it at 0.3 second Very, the barycenter acceleration time domain figure in inner ring x direction and amplitude frequency diagram are such as Figure 14, shown in 15.

Fundamental frequency 39.56Hz and the model calculation value of the fault characteristic frequency of rolling element can be significantly seen from Figure 15 39.62Hz deviation is 0.06Hz, and adjacent peaks difference is 3.70Hz, with the model calculation value 3.81Hz deviation of rolling element revolution frequency For 0.11Hz.

5. bearing vibration model experiment checking

Experimental provision uses the resultant fault simulated experiment platform of Spectra Quest company (U.S.), to band inner ring fault Rexnord ER10k rolling bearing carries out vibration signals collecting.Acquisition instrument is Br ü el&The PULSE of company LabShop platform.When rolling bearing rotating speed is 600rpm, to x radially degree of being accelerated vibration signals collecting, former to gather Beginning vibration signal directly carries out FFT, and such spectrum signal will not make its intrinsic feature because of signal processing modes such as de-noisings Signal adds artificial interference.The inner ring fault vibration spectrogram in x direction, outer is drawn respectively by the frequency spectrum processing of experimental signal Circle fault vibration spectrogram, rolling element fault vibration spectrogram, respectively as shown in Figure 18,19,20.

Becoming soft frequency as can see from Figure 16 into 30.4Hz and outer ring fault fundamental frequency 30.46Hz deviation is 0.06Hz.In Circle fault fundamental frequency is that in 50.07Hz, with Fig. 3, the inner ring fault fundamental frequency 49.85Hz deviation of model calculating is 0.22Hz, its 2 frequency multiplication For 100.4Hz.Owing to inner ring failure response is more weak relative to the transmission of the energy of outer ring failure response, therefore its signal to noise ratio is relatively Low, it can be seen that it all has substantial amounts of noise peak in addition to characteristic frequency peak value.

The fault signature fundamental frequency of its outer ring is the feature base that in 30.2Hz, with Fig. 6, model calculates as can see from Figure 17 Frequency value 30.46Hz deviation is 0.26Hz, and 2 especially prominent frequencys multiplication 60Hz occurs simultaneously, and in figure, 3 frequencys multiplication 90.6Hz are almost made an uproar Sound is flooded.Relative to inner ring fault, the signal to noise ratio of outer ring fault spectrum feature is that comparison is high in 100Hz.

The fundamental frequency that can significantly see rolling element fault characteristic frequency from Figure 18 is model meter in 39.56Hz, with Fig. 9 The fundamental frequency 39.62Hz deviation calculated is 0.02Hz, and its adjacent crest difference is 3.7Hz, with the model meter of its rolling element revolution frequency Calculation value 3.81Hz deviation is 0.11Hz.

Claims (4)

1. a rolling bearing surface damage faulty power modeling method, comprises the steps: 1) obtaining rolling bearing On the basis of contact equivalent stiffness and equivalent damping, it is considered to rolling bearing clearance and supporting region change, set up rolling bearing bullet Spring damped vibration model；

2) impulse function of surface damage trouble point is loaded on outer ring, inner ring and rolling element respectively, sets up the axis of rolling respectively Bearing outer-ring fault model, rolling bearing inner ring fault model and roller bearing rolling element fault model.

Rolling bearing surface damage faulty power modeling method the most according to claim 1, step 2) in, rolling bearing What inner ring fault model was set up specifically comprises the following steps that

The shape of i-th rolling element position becomes δ_i, shown in computing formula such as formula (1):

δ_i=xcos θ_i+ysinθ_i-γ (1)

In formula: γ is the initial diametrical clearance of rolling bearing, θ_iBeing the angle of i-th rolling element and world coordinates x direction, x is interior Circle radially x direction displacement, y is inner ring radially y direction displacement；

Act on the external force of inner ring along x Yu y direction, by formula (2), formula (3) calculates；

$F_x=K_n\underset{i=1}{\overset{z}{\&Sigma;}}{\mathrm{\&lambda;}}_i{\mathrm{\&delta;}}_i^{1.5}{\mathrm{cos\&theta;}}_i---\left(2\right)$

$F_y=K_n\underset{i=1}{\overset{z}{\&Sigma;}}{\mathrm{\&lambda;}}_i{\mathrm{\&delta;}}_i^{1.5}{\mathrm{sin\&theta;}}_i---\left(3\right)$

K_nEquivalence nominal rigidity, λ is contacted for single rolling element and Internal and external cycle_iJoin in the control of load area for i-th rolling element Number, Z is rolling element quantity；

Shown in the equation of motion of inner ring such as formula (4):

$\left\{\begin{array}{c}m\stackrel{\&CenterDot;\&CenterDot;}{y}+c\stackrel{\&CenterDot;}{y}+F_y=w_y+I_d\left(t\right)sin\mathrm{\&psi;}\\ m\stackrel{\&CenterDot;\&CenterDot;}{x}+c\stackrel{\&CenterDot;}{x}+F_x=w_x+I_d\left(t\right)cos\mathrm{\&psi;}\end{array}\right.---\left(4\right)$

M be inner ring with the quality of rotating shaft and, c is the overall equivalent damping of rolling element and Internal and external cycle interaction, w_x、w_yFor load Act on the radial force on rotary body, I_dT () is parameterized impulse function；In the case of given excitation, equation (4) is two The Second Order Nonlinear Differential Equations of individual coupling, by its nondimensionalization, shown in the reduced equation of rolling bearing such as formula (5):

$\left\{\begin{array}{c}\stackrel{\&CenterDot;\&CenterDot;}{\stackrel{\&OverBar;}{x}}=\frac{1}{K_n{\mathrm{\&gamma;}}^{1.5}}(W+I_d(t\left)cos\mathrm{\&Omega;}\mathrm{\&tau;}\right)-\frac{c}{{\mathrm{mw}}_n}\stackrel{\&CenterDot;}{\stackrel{\&OverBar;}{x}}-f_x(\stackrel{\&OverBar;}{x},\stackrel{\&OverBar;}{y},\mathrm{\&Omega;},\mathrm{\&tau;})\\ \stackrel{\&CenterDot;\&CenterDot;}{\stackrel{\&OverBar;}{y}}=\frac{1}{K_n{\mathrm{\&gamma;}}^{1.5}}{I}_d\left(t\right)sin\mathrm{\&Omega;}\mathrm{\&tau;}-\frac{c}{{\mathrm{mw}}_n}\stackrel{\&CenterDot;}{\stackrel{\&OverBar;}{y}}-f_y(\stackrel{\&OverBar;}{x},\stackrel{\&OverBar;}{y},\mathrm{\&Omega;},\mathrm{\&tau;})\end{array}\right.---\left(5\right)$

Change owing to the position of inner peripheral surface impaired loci rotates with inner ring, hold when the position of impaired loci is in the non-of bearing When carrying district, rolling element can be ignored by the vibration effect of impaired loci；When impaired loci is in supporting region diverse location, rolling element leads to Cross varying in size of the produced impulsive force of impaired loci；

Rolling element is 2arcsin (l/R by the angle of impaired loci_I), R_IFor inner ring raceway diameter, l is injured surface diameter；Rolling The kinetoplast angle that contacts with impaired loci surface is 2arcsin (l/R_I), set up rolling element and cross the segmentation impulse function of impaired loci, as Shown in formula (6):

$\mathrm{\&lambda;}\left(\mathrm{\&upsi;}\right)=\left\{\begin{array}{cc}1& \left|\mathrm{\&upsi;}\right|<\arcsin (l/R_I)\\ 0& \left|\mathrm{\&upsi;}\right|\&GreaterEqual;\arcsin (l/R_I)\end{array}\right.---\left(6\right)$

When impaired loci is in supporting region and contacts with rolling element, generation is impacted, if be in non-bearing district, do not produce punching Hit, set up the segmentation impulse function of supporting region, as shown in formula (7):

$s\left(v\right)=\left\{\begin{array}{cc}1& \left|s\right|<L\\ 0& \left|s\right|\&GreaterEqual;L\end{array}\right.---\left(7\right)$

S is the angle of axle center direction of displacement and impaired loci, and L is 1/2nd of roller carrying field angle；For different damages Wound has different expression, and the size of pulse amplitude is determined by the speed loaded with contact point and can be by the phase of supporting region Motion is carried out function.The time of contact of rolling element and surface damage is the shortest, therefore the damaged length on raceway with The ratio of raceway length must be suitable, and such impulsive force could be consistent with actual, and impulse function is substituted into rolling bearing Vibration equation (5) in；

By the produced impulse function of inner ring damage, shown in its expression formula such as formula (8):

$I_d\left(t\right)=A_{id}(h_{id},L,\mathrm{\&omega;})\underset{i=1}{\overset{z}{\&Sigma;}}{\mathrm{\&alpha;}}_{id}\left(i\right)\&CenterDot;s\left(f\right(\mathrm{\&psi;},p\left(x\right)+\arctan \left(y/\left|x\right|\right)\left)\right)\&CenterDot;\mathrm{\&lambda;}\left(f\right(\mathrm{\&psi;},{\mathrm{\&phi;}}_i\left)\right)---\left(8\right)$

Wherein: h_idFor the impaired loci degree of depth, φ_iFor the angle of i-th rolling element barycenter Yu x-axis positive direction, ψ is to damage on bearing inner race The position of wound point and the angle of x-axis positive direction, ω is angular velocity of rotation；A_id(h_id, L, ω) and it is about the injured surface degree of depth, long Degree and the pulse amplitude functional relation of angular velocity, a_idI () is the amplitude modulation parameter of i-th rolling element；

$f(\mathrm{\&psi;},p(x)+\arctan (y/\left|x\right|\left)\right)=\left\{\begin{array}{cc}\mathrm{mod}\left(\right|\mathrm{\&psi;}-\arctan \left(y/\left|x\right|\right)|,2\mathrm{\&pi;})& \mathrm{mod}\left(\right|\mathrm{\&psi;}-\arctan \left(y/\left|x\right|\right)|,2\mathrm{\&pi;})\&le;\mathrm{\&pi;}\\ 2\mathrm{\&pi;}-\mathrm{mod}\left(\right|\mathrm{\&psi;}-\arctan \left(y/\left|x\right|\right)|,2\mathrm{\&pi;})& \mathrm{mod}\left(\right|\mathrm{\&psi;}-\arctan \left(y/\left|x\right|\right)|,2\mathrm{\&pi;})>\mathrm{\&pi;}\end{array}\right.,$

In formula: mod function is MOD function；

In formula: F_rFor rolling bearing radial load,It is the 1st rolling Kinetoplast barycenter and the angle of x-axis positive direction,ε is end-play.

Rolling bearing surface damage faulty power modeling method the most according to claim 2, step 2) in, rolling bearing What outer ring fault model was set up specifically comprises the following steps that

Set up rolling element and cross the piecewise function pulse of impaired loci, as shown in formula (10):

$\mathrm{\&lambda;}\left(\mathrm{\&upsi;}\right)=\left\{\begin{array}{cc}1& \left|\mathrm{\&upsi;}\right|<\arcsin (l/R_o)\\ 0& \left|\mathrm{\&upsi;}\right|\&GreaterEqual;\arcsin (l/R_o)\end{array}\right.---\left(10\right)$

υ is the minimum angle at rolling element center and impaired loci center；

By the produced impulse function of outer peripheral surface damage, as shown in formula (11):

$I_d\left(t\right)=A_{id}(h_{id},L,\mathrm{\&omega;})\underset{i=1}{\overset{z}{\&Sigma;}}{\mathrm{\&alpha;}}_{id}\left(i\right)\&CenterDot;\mathrm{\&lambda;}\left(f\right(\mathrm{\&psi;},{\mathrm{\&phi;}}_i\left)\right)---\left(11\right).$

Rolling bearing surface damage faulty power modeling method the most according to claim 3, step 2) in, rolling bearing What rolling element fault model was set up specifically comprises the following steps that

According to formula (12), calculate the impaired loci of rolling element and the angle of x-axis positive direction,

ψ=ψ₁-ω_bt (12)

ψ₁For initial angle, ω_bFor the rotational velocity of rolling element, t is the time；

According to formula (13), calculate the angle between moving axes x-axis positive direction and absolute coordinate x-axis positive direction,

θ_x=θ_x0+ω_ct (13)

θ_x0For initial angle, ω_cFor the rotating speed of rolling element in absolute coordinate, t is the time；

According to formula (14), calculate the angle that on rolling element, impaired loci contacts with outer ring,

ψ_o=ψ-θ_x (14)

According to formula (15), calculate the angle that on rolling element, impaired loci contacts with inner ring,

ψ_i=ψ-θ_x-180° (15)

According to formula (16), calculate and have the rolling element barycenter of impaired loci and the angle of x-axis positive direction；

φ=ω_ct+φ₀ (16)

In formula: φ₀For first rolling element angle that x-axis under bearing original state is positive with bearing；

With x, y-coordinate axle is reference, according to formula (17), calculate roller in a counterclockwise direction with the real-time angle of bearing displacement；

Wherein:

Set up rolling element and cross the piecewise function pulse of impaired loci, as shown in formula (18):

$\mathrm{\&lambda;}\left(\mathrm{\&upsi;}\right)=\left\{\begin{array}{cc}1& \left|\mathrm{\&upsi;}\right|<arcsin(l/r)\\ 0& \left|\mathrm{\&upsi;}\right|\&GreaterEqual;arcsin(l/r)\end{array}\right.---\left(18\right)$

Set up the piecewise function pulse of supporting region, as shown in formula (19):

$s\left(v\right)=\left\{\begin{array}{cc}1& \left|s\right|<L\\ 0& \left|s\right|\&GreaterEqual;L\end{array}\right.---\left(19\right)$

Set up by the produced impulse function of rolling element damage, as shown in formula (19):

I_d(t)=A_id(h_id,L,ω)·α_id·s(f(φ,f(x)+arctan(y/|x|)))

·(λ(f(ψ,θ_x))+λ[f(ψ,θ_x+180°)]) (20)

Wherein: