CN109992926A - Bearing outer ring defect Angle Position quantitative estimation method - Google Patents

Bearing outer ring defect Angle Position quantitative estimation method Download PDF

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CN109992926A
CN109992926A CN201910328362.6A CN201910328362A CN109992926A CN 109992926 A CN109992926 A CN 109992926A CN 201910328362 A CN201910328362 A CN 201910328362A CN 109992926 A CN109992926 A CN 109992926A
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outer ring
ring defect
angle position
defect
bearing
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CN109992926B (en
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张飞斌
褚福磊
王天杨
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Tsinghua University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M13/00—Testing of machine parts
    • G01M13/04—Bearings
    • G01M13/045—Acoustic or vibration analysis
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/06—Power analysis or power optimisation

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  • Engineering & Computer Science (AREA)
  • General Physics & Mathematics (AREA)
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  • Acoustics & Sound (AREA)
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Abstract

The present invention relates to a kind of bearing outer ring defect Angle Position quantitative estimation methods.This method passes through outer ring defect bearing touch load distribution quasi static analysis first, defines outer ring defect two dimension fusion excitation value and has obtained the mapping relations of it and defect Angle Position.It is analyzed then in conjunction with outer ring defect bearing touch load distribution dynamic, obtains the analytical expression that outer ring defect motivates lower vibration acceleration response.Based on this, then maintenance data fusion thought successively constructed two bearing outer ring defect Angle Position quantizating index: two dimension fusion peak value and two dimension fusion root-mean-square value.Ideal relationship formula and actual measurement reference point are finally integrated, the actual function relational expression of two dimension fusion root-mean-square value and outer ring defect Angle Position is established, for the quantitative evaluation of outer ring defect Angle Position, there is important theory significance and application value.

Description

Bearing outer ring defect Angle Position quantitative estimation method
Technical field
The invention belongs to rolling bearing fault diagnosis fields, and in particular to a kind of bearing outer ring defect Angle Position quantitative evaluation Method.
Background technique
Core component of the rolling bearing as mechanical system is widely used in aerospace, energy source and power, ship naval vessels, work During industry lathe, mining metallurgy etc. large size, precision, high value are equipped.Rolling bearing once breaks down, and will cause a series of tight Weight accident, causes heavy economic losses, or even jeopardize personal safety.Therefore, status monitoring, Accurate Prediction are carried out to rolling bearing Its health status and remaining life are the core demands of modern industry.And Quantitative Diagnosis is then the premise item for carrying out life prediction Part lacks the life prediction of failure quantitative information like " water without a source and a tree without roots ".Outer ring defect Angle Position is as rolling One of quantitative information of bearing fault, there has been no mature quantitative evaluation technology and methods, and main cause is exactly quantizating index Missing.
Summary of the invention
The object of the present invention is to provide a kind of bearing outer ring defect Angle Position quantitative estimation methods.Inventor is based on the axis of rolling The analysis of multimer contact nonlinear kinetics approximate analysis, high-precision numerical simulation and experimental signal analysis are held, with multidimensional signal Fusion thought has constructed a kind of bearing outer ring defect Angle Position quantizating index --- two dimension fusion root-mean-square value, and propose base It is Quantitative Diagnosis and the residue longevity of rolling bearing local defect in the bearing outer ring defect Angle Position quantitative estimation method of the index Life prediction provides theoretical basis and technical support.
To achieve the above object, technical scheme is as follows:
A kind of bearing outer ring defect Angle Position quantizating index construction and application method, comprising the following specific steps
1) outer ring defect bearing touch load is distributed quasi static analysis:
Using bearing axial end face as reference planes, axle center is origin, is horizontally to the right x-axis, is vertically downward that y-axis establishes ginseng Examine coordinate system；Ball quantity is set as Nb, the angle of the 1st ball center and x-axis is φ1, the folder at jth ball center and x-axis Angle is φj=φ1+360°(j-1)/Nb, outer ring defect angular spread is Δ φf, outer ring defect Angle Position is φf, define outer ring and lack Fall into two dimension fusion excitation value
Wherein,WithThe quasi- Static Contact of x and the direction y when respectively any one ball passes through defect area Impact force.
2) outer ring defect bearing touch load distribution dynamic is analyzed:
It is analysis object with bearing outer ring, establishes its single-degree-of-freedom kinetics equation, is outer with quasi- Static Contact impact force The excitation of portion's momentum, obtains the vibration acceleration response analytical expression of outer ring:
Wherein, ax(t) and ay(t) be respectively outer ring the direction x vibration acceleration signal and the direction y vibration acceleration signal, ωnFor the undamped natural frequency of a mechanical system of outer ring, ξ is damped coefficient, ωdThere is damped natural frequency m for outer ringoOutside for rolling bearing Quality is enclosed, t is time variable；QxAnd QyThe respectively contact force momentum in the direction x and the direction y, may be expressed as:
Wherein, Δ t is the duration of quasi- Static Contact impact force.
3) outer ring defect Angle Position quantizating index and φ are establishedfIdeal mappings relationship:
A. first outer ring defect Angle Position quantizating index is constructed: two dimension fusion peak value Pxy, it is defined as two not Tongfangs To acceleration signal peak value between ratio；Two dimension fusion peak value P is obtained in conjunction with formula (1), formula (2) and formula (3)xy With outer ring defect angular position φfIdeal relationship formula:
B. second outer ring defect Angle Position quantizating index is reconstructed: two dimension fusion root-mean-square value Rxy, it is defined as two Ratio between the root-mean-square value of the acceleration signal of different directions；In conjunction with the peak value of formula (4) and decaying exponential function and Linear relationship between root obtains two dimension fusion root-mean-square value RxyWith outer ring defect angular position φfIdeal relationship formula:
Rxy=| cot φf| (5)
4) R is establishedxyWith φfActual function relational expression:
Defect bearing in outer ring is placed in bearing block, and outer ring defect Angle Position is adjusted to vertically downward；In bearing block The first vibration acceleration sensor is installed in upper surface center, and as reference, according to the right-hand rule in bearing block side Face center is installed by the second vibration acceleration sensor；It is sensed by the first vibration acceleration sensor and the second vibration acceleration Device measures the vibration acceleration signal a that data points are N simultaneously1(i) and a2(i), the two dimension fusion for calculating real system is square Root initial value R:
Wherein,WithRespectively a1(i) and a2(i) mean value；Formula (5) is transformed using R as initial value, is obtained outer Enclose defect R in any Angle PositionxyWith φfActual function relational expression:
Rxy=| cot φf|+R (7)
5) go out outer ring defect Angle Position using two dimension fusion root-mean-square value quantitative evaluation:
In the bearing block upper surface center of outer ring defect bearing arrangement to be assessed, installation third vibration acceleration is passed Sensor, and as reference, the 4th vibration acceleration sensor is installed in bearing block side end face center according to the right-hand rule； The vibration acceleration that data points are N is measured simultaneously by third vibration acceleration sensor and the 4th vibration acceleration sensor to believe Number a3(i) and a4(i), the two dimension fusion root-mean-square value R ' of outer ring defect bearing arrangement to be assessed is calculatedxy:
Wherein,WithRespectively a3(i) and a4(i) mean value；Formula (8) is brought into formula (7), can quantify to comment Estimate the angular position φ of outer ring defect outf:
The present invention has the following advantages that and the technical effect of high-lighting: constructing a kind of bearing outer ring defect Angle Position quantization Index two dimension merges root-mean-square value, under the guide of faulty power mechanism, establishes two dimension fusion root-mean-square value and outer ring defect The functional relation of Angle Position, and the bearing outer ring defect Angle Position quantitative estimation method based on the index is proposed, have aobvious The theory significance and application value of work.
Detailed description of the invention
Work flow diagram Fig. 1 of the invention.
Fig. 2 a and Fig. 2 b are benchmark bearing arrangement vibration acceleration waveform diagram.
Fig. 3 a and Fig. 3 b are bearing arrangement vibration acceleration waveform diagram to be assessed.
Fig. 4 is with RxyFor the outer ring defect angular position φ of independent variablefChange curve.
Specific embodiment
Quantitative estimation method of the invention is described in detail in lower mask body combination attached drawing and embodiment, but of the invention Protection scope be not limited to the embodiment.
As shown in Figure 1, being the work of a kind of bearing outer ring defect Angle Position quantizating index construction and application method of the invention Make flow chart.Specific implementation process is as follows:
1) outer ring defect bearing touch load is distributed quasi static analysis:
Using bearing axial end face as reference planes, axle center is origin, is horizontally to the right x-axis, is vertically downward that y-axis establishes ginseng Examine coordinate system；In the present embodiment, bearing ball quantity is NbThe angle of=8, the 1st ball center and x-axis is φ1, jth rolling The angle of pearl center and x-axis is φj=φ1+360°(j-1)/Nb, outer ring defect angular spread is Δ φf, outer ring defect Angle Position For φf, define outer ring defect two dimension and merge excitation value
Wherein,WithThe quasi- Static Contact of x and the direction y when respectively any one ball passes through defect area Impact force；
2) outer ring defect bearing touch load distribution dynamic is analyzed:
It is analysis object with bearing outer ring, is the excitation of external momentum with quasi- Static Contact impact force, establishes the direction x and the side y To single-degree-of-freedom kinetics equation:
Wherein, x and y is respectively offset variable of the bearing outer ring in the direction x and the direction y, moFor bearing outer ring quality, c is Damped coefficient, k are support stiffness, QxAnd QyThe respectively contact force momentum in the direction x and the direction y, may be expressed as:
Wherein, Δ t is the duration of quasi- Static Contact impact force；Bearing outer ring is obtained in conjunction with formula (2) and formula (3) Vibration acceleration response analytical expression:
Wherein, ax(t) and ay(t) be respectively outer ring the direction x vibration acceleration signal and the direction y vibration acceleration signal, ωnFor the undamped natural frequency of a mechanical system of outer ring, ξ is damped coefficient, ωdFor the damped natural frequency that has of outer ring, t is time variable.
3) outer ring defect Angle Position quantizating index and φ are establishedfIdeal mappings relationship:
A. first outer ring defect Angle Position quantizating index is constructed: two dimension fusion peak value Pxy, it is defined as two not Tongfangs To acceleration signal peak value between ratio；Two dimension fusion peak value P is obtained in conjunction with formula (1) and formula (4)xyIt is lacked with outer ring Fall into angular position φfIdeal relationship formula:
B. second outer ring defect Angle Position quantizating index is reconstructed: two dimension fusion root-mean-square value Rxy, it is defined as two Ratio between the root-mean-square value of the acceleration signal of different directions；In conjunction with the peak value of formula (5) and decaying exponential function and Linear relationship between root obtains two dimension fusion root-mean-square value RxyWith outer ring defect angular position φfIdeal relationship formula:
Rxy=| cot φf| (6)
4) R is establishedxyWith φfActual function relational expression:
Defect bearing in outer ring is placed in bearing block, and outer ring defect Angle Position is adjusted to vertically downward；In bearing block The first vibration acceleration sensor is installed in upper surface center, and as reference, according to the right-hand rule in bearing block side Face center is installed by the second vibration acceleration sensor；It is sensed by the first vibration acceleration sensor and the second vibration acceleration Device measures the vibration acceleration signal a that data points are N=131072 simultaneously1(i) and a2(i), respectively as shown in Fig. 2 a, 2b；Meter Calculate the two dimension fusion root mean square initial value R of real system:
Wherein,WithRespectively a1(i) and a2(i) mean value；Formula (6) is transformed using R as initial value, is obtained outer Enclose defect R in any Angle PositionxyWith φfActual function relational expression:
Rxy=| cot φf|+R (8)
5) go out outer ring defect Angle Position using two dimension fusion root-mean-square value quantitative evaluation:
In the bearing block upper surface center of outer ring defect bearing arrangement to be assessed, installation third vibration acceleration is passed Sensor, and as reference, the 4th vibration acceleration sensor is installed in bearing block side end face center according to the right-hand rule； The vibration acceleration that data points are N is measured simultaneously by third vibration acceleration sensor and the 4th vibration acceleration sensor to believe Number a3(i) and a4(i), respectively as best shown in figures 3 a and 3b；The two dimension fusion for calculating outer ring defect bearing arrangement to be assessed is square Root R 'xy:
Wherein,WithRespectively a3(i) and a4(i) mean value；Formula (9) is brought into formula (8), outer ring is obtained and lacks Fall into angular position φfCalculation formula:
Fig. 4 gives in the present embodiment with RxyFor the outer ring defect angular position φ of independent variablefChange curve.In conjunction with formula (8) the outer ring defect angular position φ in the present embodiment can be obtained in-(10) and Fig. 4f=270 ° ± 17.7 °.In other words, pass through this Inventive method quantitative evaluation has gone out the distance between outer ring defect Angle Position and loading ability of bearing center, can be directly as core parameter For failure reason analysis and predicting residual useful life, the significance and application value of the method for the present invention have been absolutely proved.

Claims (1)

1. a kind of bearing outer ring defect Angle Position quantitative estimation method, which comprises the following steps:
1) outer ring defect bearing touch load is distributed quasi static analysis:
Using bearing axial end face as reference planes, axle center is origin, is horizontally to the right x-axis, is vertically downward that y-axis is established with reference to seat Mark system；Ball quantity is set as Nb, the angle of the 1st ball center and x-axis is φ1, the angle of jth ball center and x-axis is φj=φ1+360°(j-1)/Nb, outer ring defect angular spread is Δ φf, outer ring defect Angle Position is φf, define outer ring defect two Dimension fusion excitation value
Wherein,WithThe quasi- Static Contact impact of x and the direction y when respectively any one ball passes through defect area Power；
2) outer ring defect bearing touch load distribution dynamic is analyzed:
It is analysis object with bearing outer ring, establishes its single-degree-of-freedom kinetics equation, is external punching with quasi- Static Contact impact force Amount excitation, obtains the vibration acceleration response analytical expression of outer ring:
Wherein, ax(t) and ay(t) be respectively outer ring the direction x vibration acceleration signal and the direction y vibration acceleration signal, ωn For the undamped natural frequency of a mechanical system of outer ring, ξ is damped coefficient, ωdFor the damped natural frequency that has of outer ring, moFor housing washer Quality, t are time variable；QxAnd QyThe respectively contact force momentum in the direction x and the direction y, may be expressed as:
Wherein, Δ t is the duration of quasi- Static Contact impact force；
3) outer ring defect Angle Position quantizating index and φ are establishedfIdeal mappings relationship:
A. first outer ring defect Angle Position quantizating index is constructed: two dimension fusion peak value Pxy, it is defined as two different directions Ratio between the peak value of acceleration signal；Two dimension fusion peak value P is obtained in conjunction with formula (1), formula (2) and formula (3)xyWith it is outer Enclose defect angular position φfIdeal relationship formula:
B. second outer ring defect Angle Position quantizating index is reconstructed: two dimension fusion root-mean-square value Rxy, it is defined as two differences Ratio between the root mean square of the acceleration signal in direction；In conjunction with the peak value of formula (4) and decaying exponential function and root mean square it Between linear relationship, obtain two dimension fusion root-mean-square value RxyWith outer ring defect angular position φfIdeal relationship formula:
Rxy=| cot φf| (5)
4) R is establishedxyWith φfActual function relational expression:
Defect bearing in outer ring is placed in bearing block, and outer ring defect Angle Position is adjusted to vertically downward；In bearing block upper end The first vibration acceleration sensor is installed in face center, and as reference, according to the right-hand rule in bearing block side end face Heart position is installed by the second vibration acceleration sensor；It is same by the first vibration acceleration sensor and the second vibration acceleration sensor When measure data points be N vibration acceleration signal a1(i) and a2(i), at the beginning of calculating the two dimension fusion root mean square of real system Value R:
Wherein,WithRespectively a1(i) and a2(i) mean value；Formula (5) is transformed using R as initial value, is obtained
Outer ring defect R in any Angle PositionxyWith φfActual function relational expression:
Rxy=| cot φf|+R (7)
5) go out outer ring defect Angle Position using two dimension fusion root-mean-square value quantitative evaluation:
Third vibration acceleration sensor is installed in the bearing block upper surface center of outer ring defect bearing arrangement to be assessed, And as reference, the 4th vibration acceleration sensor is installed in bearing block side end face center according to the right-hand rule；By Three vibration acceleration sensors and the 4th vibration acceleration sensor measure the vibration acceleration signal a that data points are N simultaneously3 (i) and a4(i), the two dimension fusion root-mean-square value R ' of outer ring defect bearing arrangement to be assessed is calculatedxy:
Wherein,WithRespectively a3(i) and a4(i) mean value；Formula (8) is brought into formula (7), can quantitative evaluation go out The angular position φ of outer ring defectf:
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
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Publication number Priority date Publication date Assignee Title
US20120116734A1 (en) * 2010-10-11 2012-05-10 Centre National D'etudes Spatiales Method of characterizing an electrical defect affecting an electronic circuit, related device and information recording medium
CN103927414A (en) * 2014-04-04 2014-07-16 北京工业大学 Vibration response simulation analyzing method for rolling bearing with single-point failures
US20180075170A1 (en) * 2016-01-13 2018-03-15 International Business Machines Corporation Dynamic fault model generation for diagnostics simulation and pattern generation
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115597863A (en) * 2022-09-07 2023-01-13 安徽家瑞轴承有限公司（Cn） Bearing surface defect regionalization high-precision detection method based on data analysis
CN115597863B (en) * 2022-09-07 2023-05-30 安徽家瑞轴承有限公司 Bearing surface defect regionalization high-precision detection method based on data analysis

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