CN103927414B - Vibration response simulation analyzing method for rolling bearing with single-point failures - Google Patents

Abstract

The invention relates to a vibration response simulation analyzing method for a rolling bearing with single-point failures. On the basis of a Hertz contact theory, related knowledge about kinematics and kinetics are utilized to establish a five-degree-of-freedom nonlinear vibration mode of a rolling bearing and kinetic differential equations of the rolling bearing while influencing factors like slipping of rolling balls, oil slick rigidity and the like are taken into consideration, according to that the rolling balls change due to contact deformation is caused when the rolling balls roll through partial failures, a partial failure model of the rolling bearing is introduced into the kinetic differential equations of the rolling bearing, and the single-point failures of the rolling bearing are classified according to length-width ratios of the failures and size ratios between the failures and the rolling balls so as to establish different failure shape functions; the differential equations are solved by an ode solver in MATLAB (matrix laboratory) software, and vibration responses of the rolling bearing are simulated when an inner ring, an outer ring and the rolling balls of the rolling bearing are suffered from the single-point failures. By the aid of the vibration response simulation analyzing method, vibration responses of the bearings with failures in different sizes can be simulated. Compared with traditional methods for acquiring vibration responses of failed bearings, the vibration response simulation analyzing method has the advantages that an experimental period is short and experimental cost is saved. The computation for the vibration responses for the failed rolling bearings can lay the foundation of late failure diagnosis for the rolling bearings.

Description

Bearing vibration response simulating analysis containing Single Point of Faliure

Technical field

The invention belongs to simulation analysis field is and in particular to arrive a kind of Response Analysis method, particularly one kind contains The bearing vibration response simulating analysis of inner ring, outer ring or rolling element Single Point of Faliure.

Background technology

Rolling bearing is conventional universal component in rotating machinery, and its dynamic behavior affects the kinetics of whole system Behavior, when it produces fault, will induce whole system and produce fault.According to statistics, the 30% of rotating machinery fault is by bearing event Barrier causes, and therefore, carries out condition monitoring and fault diagnosis research for rolling bearing non-for the normal operation of maintained equipment The normally off key, but, because mechanism is unclear, have using the mistaken diagnosis that reason causes such as technology is improper and feature is inconspicuous with when failing to pinpoint a disease in diagnosis and throwing away Occur.The fault of research rolling bearing produces has important engineering and theory with the mechanism of transmission and Fault monitoring and diagnosis technology It is worth.

The response signal obtaining bearing is basis and the key of bearing failure diagnosis.Traditional method is to be arranged by artificial Fault carries out testing and obtains vibration signal or the naturally-occurring that waits middle fault to be produced, experimental period length, experiment spend big.For Promote the diagnosis of variable working condition heavy-duty gear fault and the development of Predicting Technique in real system, set up and produce and actual condition phase The phantom of the specific fault signal of rolling bearing of symbol is necessary.Set up effective bearing fault Simulation Engineering model, no With etc. middle fault to be produced naturally-occurring, can directly produce variety classes fault as needed, further investigate its fault machine Reason can provide more accurate diagnostic method for detecting the bearing fault under different running statuses with behavioral characteristics.Additionally, fault The signal that phantom produces can also be used to train neutral net or is applied to the intelligent diagnostics algorithm such as support vector machine, from Dynamic identification and prediction bearing fault type, reduce the dependency that cannot obtain a large amount of fault samples in actual production process, favorably Development in bearing failure diagnosis new method.

For the mechanism of rolling bearing fault, set up the kinetics model of vibration of object of study, and adopt numerical simulation skill It is method commonly used in the world at present that art launches further investigation.In bearing failure diagnosis, rolling bearing local surfaces are damaged Hinder evoked system unit dither frequencies typically in more than 5KHz, the present invention is in non-linear Hertz contact power and radial force Under effect, combining unit resonator, simulate, by adjusting its rigidity and damped coefficient, the bearing being ignited when bearing occurs and damages The high frequency intrinsic vibration of Internal and external cycle, sensor or other element, it is considered to the factor such as ball sliding, oil film rigidity, is set up and is rolled The outer ring of bearing, inner ring and rolling element

Content of the invention

The present invention in order to more efficiently and accurately emulation rolling bearing Single Point of Faliure vibratory response it is proposed that one Plant Single Point of Faliure rolling bearing simulating analysis, served with the method emulation rolling bearing Single Point of Faliure vibration signal permissible Emulate any position, any big glitch, save the beneficial effect of experimental cost, carry for the emulation of rolling bearing combined failure simultaneously For thinking.

For achieving the above object, technical scheme is as follows：

A kind of response simulating analysis of bearing vibration containing Single Point of Faliure comprise the following steps：

Step 1 sets up rolling bearing model of nonlinear and dynamic differential equation group

Based on Hertzian contact theory, with kinesiology and kinetics relevant knowledge, consider ball sliding, oil film rigidity Establish 5DOF rolling bearing model of nonlinear with influence factors such as bearing nonlinear time-varying rigidity.

Fault is incorporated in rolling bearing model of nonlinear step 2

Can be changed according to the juxtaposition metamorphose of the ball when rolling bearing is faulty, touching defect, arrange one Breakdown switch function, fault is incorporated in ball contact deformation formula, and according to Hertz theory, solves contact by deformation Power, contact force is updated in rolling bearing kinetics equation group, completes the introducing of fault.

Step 3 sets up the fault shape function of different faults

All failure conditions that can occur are classified, according to the difference of classification, is set up different defect shape functions To represent different defect faults.

Step 4 solves differential equation group and draws bear vibration acceleration responsive figure

Using the ode solver in Matlab software, program, solve the differential equation, finally try to achieve outer ring, inner ring, Rolling element contains the bear vibration acceleration responsive curve chart of Single Point of Faliure respectively；

The described bearing vibration response simulating analysis containing Single Point of Faliure it is characterised in that：Described step 1） In consider the ball sliding of rolling bearing, the factor such as oil film rigidity, and introduce unit resonator and damage simulating bearing The high frequency intrinsic vibration of the bearing internal external circle, sensor or other element that are ignited when hindering, so closer to the actual work of bearing Condition.

The described bearing vibration response simulating analysis containing Single Point of Faliure it is characterised in that：Described step 2） Defined in breakdown switch function, using this function, fault is incorporated in bearing vibration model, completes rolling The mathematical expression of bearing Single Point of Faliure, simple and convenient.

The described bearing vibration response simulating analysis containing Single Point of Faliure it is characterised in that：Described step 3） The middle difference according to defect shape represents defect using different defect functions, with conventional, fault is set to a definite value Compare, so can emulate the vibratory response of the rolling bearing containing variously-shaped defect, make simulation result closer to operating mode and not There is limitation more simultaneously closer to practical situation.

The invention has the beneficial effects as follows：Consider the factors such as ball sliding, oil film rigidity, introduce unit resonator, and according to The difference of flaw size adopts different defect functions, and defect is incorporated into rolling bearing 5DOF by ball contact deformation In model of nonlinear and dynamic differential equation group, the ode solver in MATLAB is finally utilized to solve differential equation group, Emulation bearing vibration response.This lays the foundation for the study mechanism of rolling bearing combined failure, and is rolling bearing event Barrier diagnosis algorithm provides data, solve traditional by experiment obtain fault vibration signal cycle long, the problem of high cost.

Brief description

The invention will be further described with reference to the accompanying drawings and detailed description.

Fig. 1 is the flow chart of method involved by the present invention.

Fig. 2 is the 5DOF model of nonlinear of the present invention.

Fig. 3 becomes flexibility vibration and load distribution schematic diagram for bearing.

Schematic diagram during Single Point of Faliure for housing washer in Fig. 4.

Fig. 5 is the failure modes situation carrying out according to different fault sizes.

Fig. 6 is fault side schematic view and corresponding fault shape letter in the case of different faults proposed by the invention Number.

Fig. 7 is ball contact to schematic diagram during defect and some geometrical relationships.

Fig. 8 is using 1205 bearings as specific embodiment, the outer ring fault vibration response being simulated using the present invention when Domain figure and frequency domain figure.

Fig. 9 is using 1205 bearings as specific embodiment, the inner ring fault vibration response being simulated using the present invention when Domain figure and frequency domain figure.

Figure 10 is using 1205 bearings as specific embodiment, the rolling element fault vibration response being simulated using the present invention Time-domain diagram and frequency domain figure.

Specific embodiment

Lower mask body combines accompanying drawing, and the present invention is further illustrated with embodiment.

Fig. 1 is a kind of flow chart of bearing vibration response simulating analysis containing Single Point of Faliure of the present invention.This The specific implementation step of invention is as follows：

Step 1 sets up rolling bearing model of nonlinear and dynamic differential equation group

Initially set up the 5DOF model of nonlinear of rolling bearing as shown in Fig. 2 this model lower left introduces one Unit resonator, simulates, by the rigidity and damped coefficient of adjustment unit resonator, the bearing being ignited when bearing occurs and damages The high frequency intrinsic vibration of Internal and external cycle, sensor or other element.

Based on this model, in rolling bearing it is considered to after sliding, the angular position φ of j-th ball_jIt is expressed as：

Wherein,φ₀Represent the initial angle position of retainer, ω_cRepresent retainer angular velocity, ω_s Represent the angular velocity of axle.When rolling element is located at supporting region, ξ_jFor+1；When rolling element is located at non-bearing area, ξ_jFor -1.Δff_m× 100% expression mean exposure frequency mutation percentage rate, typically its value between 1% and 2%, so Corresponding φ_slipValue (0.01rad～0.02rad).

Rolling bearing, in running, by rolling element number and Radial Loads power range effects, leads to bearing Support stiffness cyclically-varying, produces and becomes flexibility vibration, as shown in figure 3, the ball being in supporting region can come in contact deformation, the Total juxtaposition metamorphose of j ball can be expressed as：

δ_j=(x_s-x_p)cosφ_j+(y_s-y_p)sinφ_j- cj=1,2 ... n_b. （2）

Wherein, c represents bearing clearance, n_bRepresent ball number

Known by Hertzian contact theory, j-th ball is expressed as with the contact force of raceway：

By formula（2）With（3）Can release, total nonlinear contact power in x and y direction for the bearing can be expressed as：

Wherein, γ_jIt is a switch function, only when ball is located at supporting region, ball just has deformation, just can produce and connect Touch.Expression formula as follows：

Finally, according to kinesiology and dynamic method, analysis time bearing model of vibration draws rolling bearing motion side Cheng Wei：

Fault is incorporated in rolling bearing model of nonlinear step 2

When the inside and outside circle of rolling bearing or rolling element have local fault, when ball rolls across local fault, one can be discharged Fixed deflection, now enters the deflection δ of j-th rolling element of defect_jIt is changed into

δ_j=(x_s-x_p)cosφ_j+(y_s-y_p)sinφ_j-c-β_jc_d. （8）

Wherein, β_jIt is a breakdown switch function, when ball is located at fault, β_jIt is worth for 1, ball is not exposed to defect During fault, β_jIt is worth for 0.

When there is local fault in inside and outside circle（Fig. 4 gives schematic diagram and some geometrical relationships of outer ring fault model）, Across the angle delta φ of failure definition_d, fault angular position φ_d, now switch function β_jCan be expressed as：

When bearing has outer ring fault, fault occurs in supporting region, and position is fixing, now φ_dIt is a definite value. When inner ring has fault, abort situation rotates with inner ring and changes, now φ_dIt is a variate, φ_d=ω_st+φ_d0, φ_d0 It is primary fault Angle Position.

When rolling element has local defect, have defective rolling element during turn around can respectively with inside and outside Circle contact is once.Because Internal and external cycle raceway radius of curvature is different, across the angle delta φ of the fault contacting with Internal and external cycle_dWill be different, When ball is contacted with Internal and external cycle, the greatest drawback depth touching is also different, so when rolling element is faulty, for β_jDetermine Justice adjustment is as follows：

Wherein,

（Outer ring touches the depth capacity of ball fault）（11）

（Inner ring touches the depth capacity of ball fault）（12）

（Maximum contact loss amount when ball fault is contacted with inner ring）（13）

In above-mentioned formula, outer radiiInner radiiD_pRepresent pitch diameter, D_bTable Show ball diameter.

Step 3 sets up the failure function of different faults

When rolling bearing has local defect, when ball rolls across at this, certain deflection can be discharged, existing with regard to office Faulty bearings dynamic (dynamical) research in portion's is nearly all simply the deflection of release to be set to the definite value that value is depth of defect, and The deflection of actual release is different and different from ball size ratio with it according to defect shape.

The ratio of ball size and flaw size is defined as：

The length-width-ratio of defect itself is defined as：

Wherein, L and B represents length and the width of defect.

According to ratio itself length-width-ratio also defective of defect and ball size, defect can be divided into 5 shown in Fig. 5 kind Situation：（1）It is that ball size is far longer than flaw size that defect is only a crackle, such as shown in Fig. 5 (a), now η_bd＞ ＞ 1； （2）Quite, defect width is more than length such as Fig. 5 for ball size and flaw size（b）Shown, now η_bd＞ 1and η_d＜ 1；（3） Quite, defect width is equal to length such as Fig. 5 for ball size and flaw size（c）Shown, now η_bd＞ 1and η_d=1；（4）Ball Quite, defect width is equal to length such as Fig. 5 for size and flaw size（d）Shown, now η_bd＞ 1and η_d＞ 1；（5）Ball size Far smaller than flaw size such as Fig. 5（e）Shown, now η_bd≤1.

According to the defect of above five types, the depth of defect that ball can touch when rolling across defect can be divided into Lower three kinds of situations：（1）When defect is the first type, ball rolls across side view such as Fig. 6 during defect（a）Shown, ball is firm One contact deficiency just immediately have left defect, now can use Fig. 6（b）Rectangular function representing depth of defect, that is, defect is deep Degree is always maintained at a definite value；（2）When defect type is second and the third defect, the side that ball rolls across during defect shows It is intended to such as Fig. 6（c）Shown, during rolling across defect, depth of defect that ball can touch is with the rolling of ball for ball Moving slowly increases, and depth of defect slowly reduces after reaching maximum again, now can use Fig. 6（d）Shown semisinusoidal function comes Represent depth of defect；（3）When defect type is the 4th kind and five defective, ball rolls across schematic diagram such as Fig. 6 during defect （e）Shown, with the rolling of ball, the depth of defect that ball can touch slowly increases, and keeps constant after reaching maximum For a period of time, and slowly reduce, now can use Fig. 6（f）Shown piecewise function represents the depth of defect that ball contact arrives

To sum up, the depth of defect function that ball can touch can be expressed as：

Wherein, H₁Represent Fig. 6（b）Shown rectangular function

H₁=cd'（17）

H₂Represent Fig. 6（d）Shown semisinusoidal function

H₃Represent Fig. 6（f）Shown piecewise function

Wherein, φ represents the angle that ball rolls across after entering defect, and its scope is [0 Δ φ_d], meanwhile, by the geometry of Fig. 7 Relation understands,

H_d=0.5d- ((0.5d)²-(0.5B)²)^0.5（20）

Therefore, cd' can be expressed as：

Contact force after step 2, the 3 introducing faults obtained is brought into equation group by step 4（1）In.Using Ode solver in MATLAB software, Program equation group（1）Numerical solution, for emulating the vibration of Single Point of Faliure bearing Response.The present invention adopts 1205 rolling bearings as specific embodiment, ball number n of 1205 bearings_b=12, ball diameter D_b =7.12mm, pitch diameter D_p=38.5mm.Some physical parameters of 1205 bearings are shown in Table 1, and Fig. 8-10 is respectively outer ring, inner ring Contain the vibration acceleration response curve chart of the rolling bearing of Single Point of Faliure with rolling element.

Some physical parameters of table 11205 bearing

Claims (4)

1. a kind of containing Single Point of Faliure bearing vibration response simulating analysis it is characterised in that：The method includes as follows Step：

Step 1 sets up rolling bearing model of nonlinear and dynamic differential equation group；

Based on Hertzian contact theory, with kinesiology and kinetics relevant knowledge, consider ball sliding, oil film rigidity and axle Hold nonlinear time-varying stiffness effect factor and establish 5DOF rolling bearing model of nonlinear；

Fault is incorporated in rolling bearing model of nonlinear step 2；

Can be changed according to the juxtaposition metamorphose of the ball when rolling bearing is faulty, touching defect, a fault is set Switch function, fault is incorporated in ball contact deformation formula, and according to Hertz theory, solves contact force by deformation, will Contact force is updated in rolling bearing kinetics equation group, completes the introducing of fault

Step 3 sets up the fault shape function of different faults；

All defect situation that can occur are classified, according to the difference of classification, sets up different defect shape functions and carry out generation The different defect fault of table；

Step 4 solves differential equation group and draws bear vibration acceleration responsive figure；

Using the ode solver in Matlab software, program, solve the differential equation, finally try to achieve outer ring, inner ring, rolling Body contains the bear vibration acceleration responsive curve chart of Single Point of Faliure respectively；

Specific implementation step is as follows,

Step 1 sets up rolling bearing model of nonlinear and dynamic differential equation group

Initially set up the 5DOF model of nonlinear of rolling bearing, this model lower left introduces a unit resonator, lead to Cross the rigidity of adjustment unit resonator and damped coefficient to simulate the bearing internal external circle being ignited when bearing occurs and damages, sensor Or the high frequency intrinsic vibration of other element；

Based on this model, in rolling bearing it is considered to after sliding, the angular position φ of j-th ball_jIt is expressed as：

${\mathrm{\φ}}_j=\frac{2\mathrm{\π}(j-1)}{n_b}+{\mathrm{\ω}}_{c}dt+{\mathrm{\φ}}_0+{\mathrm{\ξ}}_j\left(0.5rand\right)\×{\mathrm{\φ}}_{slip}---\left(1\right)$

Wherein,φ₀Represent the initial angle position of retainer, ω_cRepresent retainer angular velocity, ω_sRepresent The angular velocity of axle；When rolling element is located at supporting region, ξ_jFor+1；When rolling element is located at non-bearing area, ξ_jFor -1；Δ f/f_mThe mutation percentage rate of × 100% expression mean exposure frequency, typically its value between 1% and 2%, so corresponding φ_slipValue (0.01rad～0.02rad)；

Rolling bearing, in running, by rolling element number and Radial Loads power range effects, leads to the support of bearing Rigidity cyclically-varying, produces and becomes flexibility vibration, and the ball being in supporting region can come in contact deformation, j-th ball total Juxtaposition metamorphose is expressed as：

δ_j=(x_s-x_p)cosφ_j+(y_s-y_p)sinφ_j- c j=1,2 ... n_b. (2)

Wherein, c represents bearing clearance, n_bRepresent ball number

Known by Hertzian contact theory, j-th ball is expressed as with the contact force of raceway：

$f_j=k_b{\mathrm{\δ}}_j^{1.5}---\left(3\right)$

Can be released by formula (2) and (3), total nonlinear contact power in x and y direction for the bearing is expressed as：

$f_x=k_b\Σ{\mathrm{\γ}}_j{\mathrm{\δ}}_j^{1.5}{\mathrm{cos\φ}}_j---\left(4\right)$

$f_y=k_b\Σ{\mathrm{\γ}}_j{\mathrm{\δ}}_j^{1.5}{\mathrm{sin\φ}}_j---\left(5\right)$

Wherein, γ_jIt is a switch function, only when ball is located at supporting region, ball just has deformation, just can produce contact force； Expression formula as follows：

${\mathrm{\γ}}_j=\left\{\begin{array}{cc}1& {\mathrm{\δ}}_j>0\\ 0& oherwise\end{array}\right.---\left(6\right)$

Finally, according to kinesiology and dynamic method, analysis time bearing model of vibration show that rolling bearing differential equation of motion is：

$\left\{\begin{array}{c}{m}_s{\stackrel{\·\·}{x}}_s+c_s{\stackrel{\·}{x}}_s+k_s{x}_s+f_x=0\\ m_s{\stackrel{\·\·}{y}}_s+c_s{\stackrel{\·}{y}}_s+k_s{y}_s+f_y=F_r\\ m_p{\stackrel{\·\·}{x}}_p+c_p{\stackrel{\·}{x}}_p+k_p{x}_p-f_x=0\\ m_p{\stackrel{\·\·}{y}}_p+(c_p+c_r){\stackrel{\·}{y}}_p+(k_p+k_r)y_p-k_r{y}_b-c_r{\stackrel{\·}{y}}_b-f_y=0\\ m_r{\stackrel{\·\·}{y}}_b+c_r({\stackrel{\·}{y}}_b-{\stackrel{\·}{y}}_p)+k_r(y_b-y_p)=0\end{array}\right.---\left(7\right)$

Fault is incorporated in rolling bearing model of nonlinear step 2

When the inside and outside circle of rolling bearing or rolling element have local fault, when ball rolls across local fault, can discharge certain Deflection, now enters the deflection δ of j-th rolling element of defect_jIt is changed into

δ_j=(x_s-x_p)cosφ_j+(y_s-y_p)sinφ_j-c-β_jc_d. (8)

Wherein, β_jIt is a breakdown switch function, when ball is located at fault, β_jIt is worth for 1, ball is not exposed to defect fault When, β_jIt is worth for 0；

(Fig. 4 gives schematic diagram and some geometrical relationships of outer ring fault model), definition when inside and outside circle has local fault Across the angle delta φ of fault_d, fault angular position φ_d, now switch function β_jIt is expressed as：

${\mathrm{\&beta;}}_j=\left\{\begin{array}{cc}1& {\mathrm{\&phi;}}_d<{\mathrm{\&phi;}}_j<{\mathrm{\&phi;}}_d+{\mathrm{\&Delta;\&phi;}}_d\\ 0& otherwise\end{array}\right.---\left(9\right)$

When bearing has outer ring fault, fault occurs in supporting region, and position is fixing, now φ_dIt is a definite value；When interior When circle has fault, abort situation rotates with inner ring and changes, now φ_dIt is a variate, φ_d=ω_st+φ_d0, φ_d0It is just Beginning fault Angle Position；

When rolling element has local defect, have defective rolling element and can connect with inside and outside circle respectively from during turn around Touch once；Because Internal and external cycle raceway radius of curvature is different, across the angle delta φ of the fault contacting with Internal and external cycle_dWill be different, ball When contacting with Internal and external cycle, the greatest drawback depth touching is also different, so when rolling element is faulty, for β_jDefinition adjust Whole as follows：

${\mathrm{\&beta;}}_j=\left\{\begin{array}{cc}0& j\&NotEqual;k\\ \left.\begin{array}{cc}1& 0<{\mathrm{\&phi;}}_s<{\mathrm{\&Delta;\&phi;}}_{do}\\ \frac{c_{dr}+c_{di}}{c_{dr}-c_{do}}& \mathrm{\&pi;}<{\mathrm{\&phi;}}_s<\mathrm{\&pi;}+{\mathrm{\&Delta;\&phi;}}_{di}\end{array}\right\}& j=k\\ 0& else\end{array}\right.---\left(10\right)$

Wherein,

(outer ring touches the depth capacity of ball fault) (11)

(inner ring touches the depth capacity of ball fault) (12)

(maximum contact loss amount when ball fault is contacted with inner ring) (13)

In above-mentioned formula, outer radiiInner radiiD_pRepresent pitch diameter, D_bRepresent rolling Pearl diameter；

Step 3 sets up the failure function of different faults

When rolling bearing has local defect, when ball rolls across at this, certain deflection can be discharged, existing former with regard to local The research of barrier bearing system dynamics is nearly all simply the deflection of release to be set to the definite value that value is depth of defect, and actual The deflection of release is different and different from ball size ratio with it according to defect shape；

The ratio of ball size and flaw size is defined as：

${\mathrm{\&eta;}}_{bd}=\frac{d}{min(L,B)}---\left(14\right)$

The length-width-ratio of defect itself is defined as：

${\mathrm{\&eta;}}_d=\frac{L}{B}---\left(15\right)$

Wherein, L and B represents length and the width of defect；

According to ratio itself length-width-ratio also defective of defect and ball size, defect is divided into 5 kinds of situations：(1) defect is only One crackle is that ball size is far longer than flaw size, now η_bd＞ ＞ 1；(2) ball size and flaw size are suitable, defect Width is more than shown in length, now η_bd＞ 1and η_d＜ 1；(3) quite, defect width is equal to length for ball size and flaw size Degree, now η_bd＞ 1and η_d=1；(4) quite, defect width is equal to length, now η for ball size and flaw size_bd＞ 1and η_d＞ 1；(5) ball size is far smaller than flaw size, now η_bd≤1；

According to the defect of above five types, the depth of defect that ball can touch when rolling across defect is divided into following three kinds of feelings Condition：(1) when defect is the first type, ball rolls across side during defect, and ball just immediately have left upon contact deficiency Defect, now represents depth of defect with rectangular function, and that is, depth of defect is always maintained at a definite value；(2) when defect type is Second and during the third defect, ball rolls across side schematic view during defect, ball during rolling across defect, ball institute The depth of defect that can touch slowly increases with the rolling of ball, and depth of defect slowly reduces, now after reaching maximum again Represent depth of defect with semisinusoidal function；(3) when defect type is the 4th kind and five defective, when ball rolls across defect Schematic diagram, with the rolling of ball, the depth of defect that ball can touch slowly increases, and keeps constant after reaching maximum For a period of time, and slowly reduce, piecewise function now represents the depth of defect that ball contact arrives；

To sum up, the depth of defect function representation that ball can touch is：

$cd=\left\{\begin{array}{cc}{H}_1& {\mathrm{\&eta;}}_{bd}>>1\\ H_2& {\mathrm{\&eta;}}_{bd}>1{\mathrm{and\&eta;}}_d\&le;1\\ H_3& {\mathrm{\&eta;}}_{bd}>1{\mathrm{and\&eta;}}_d>1\\ H_3& {\mathrm{\&eta;}}_{bd}\&le;1\end{array}\right.---\left(16\right)$

Wherein, H₁Represent the rectangular function shown in Fig. 6 (b)

H₁=cd'(17)

H₂Represent the semisinusoidal function shown in Fig. 6 (d)

H₃The piecewise function representing

Wherein, φ represents the angle that ball rolls across after entering defect, and its scope is [0 Δ φ_d], meanwhile, from geometrical relationship,

H_d=0.5d- ((0.5d)²-(0.5B)²)^0.5(20)

Therefore, cd' is expressed as：

${\mathrm{cd}}^{\&prime;}=\left\{\begin{array}{cc}H& H<H_d\\ H_d& H\&GreaterEqual;H_d\end{array}\right.---\left(21\right)$

Step 4 will be brought in equation group (1) by step 2,3 contact forces being introduced into after fault obtained；Soft using MATLAB Ode solver in part, the numerical solution of Program equation group (1), for emulating the vibratory response of Single Point of Faliure bearing；This Bright adopt 1205 rolling bearings as specific embodiment, ball number n of 1205 bearings_b=12, ball diameter D_b=7.12mm, Pitch diameter D_p=38.5mm.

2. according to claim 1 containing Single Point of Faliure bearing vibration response simulating analysis it is characterised in that： Above-mentioned steps 1) in consider the ball sliding of rolling bearing, the factor such as oil film rigidity, and introduce unit resonator to simulate There is the high frequency intrinsic vibration of bearing internal external circle, sensor or other element being ignited when damaging in bearing, so closer to Bearing actual condition.

3. according to claim 1 containing Single Point of Faliure bearing vibration response simulating analysis it is characterised in that： Above-mentioned steps 2) defined in a breakdown switch function, using this function, fault is incorporated in bearing vibration model, Complete the mathematical expression of rolling bearing Single Point of Faliure, simple and convenient.

4. according to claim 1 containing Single Point of Faliure bearing vibration response simulating analysis it is characterised in that： Above-mentioned steps 3) in defect is represented using different defect functions according to the difference of defect shape, with conventional, fault is arranged Compare for a definite value, so can emulate containing variously-shaped defect rolling bearing vibratory response, make simulation result closer to Operating mode and no longer have limitation simultaneously closer to practical situation.