CN106845050A - Rolling bearing reliability assessment scheme - Google Patents
Rolling bearing reliability assessment scheme Download PDFInfo
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- CN106845050A CN106845050A CN201510878179.5A CN201510878179A CN106845050A CN 106845050 A CN106845050 A CN 106845050A CN 201510878179 A CN201510878179 A CN 201510878179A CN 106845050 A CN106845050 A CN 106845050A
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Abstract
The present invention relates to a kind of reliability assessment scheme, more particularly to a kind of efficient, reliability rolling bearing reliability assessment scheme high.Rolling bearing reliability assessment scheme, it is characterised in that：Including the double stress Step-stress tests of rolling bearing, the Reliability Evaluation Model based on competing failure model, Poisson process intensity function and acceleration model, set up acceleration degradation model.Rolling bearing reliability assessment scheme proposed by the present invention shortens the reliability growth process of rolling bearing newly developed, with very strong operability.
Description
Technical field
The present invention relates to a kind of reliability assessment scheme, more particularly to a kind of efficient, reliability rolling bearing high can
By property evaluation scheme.
Background technology
The reliability of rolling bearing is one of great general character and critical problem of restriction rolling bearing industry development.As
Work of the indexs such as the important component of industrial robot joint supporting, precision, life-span, the reliability of rolling bearing to industrial robot
Vital effect is played as performance.Therefore, whether meet reliability to analyze and assess the rolling bearing of new research and development to refer to
Mark is required, it is necessary to which reliability test data is estimated.
The rapid evaluation of rolling bearing reliability is realized, can be launched from following several respects：One is research quick obtaining
The test method of sample fail data, i.e. accelerated test；Two is that research completes reliability assessment by less sample fail data
Method, i.e. small sample appraisal procedure；Three is to study the reliability information for how making full use of and being included in process of the test.
Utilization in reliability assessment work to Test Information, can only utilize one-dimension information, i.e. time；Can also be used two
Dimension information, i.e. time, failure mode or amount of degradation.Can expand statistical information amount using failure mode or amount of degradation information, enrich
Reliability assessment data, shorten the acquisition time of information.Therefore, it is highly desirable to the reliability assessment of research and utilization two-dimensional signal
Method.
Competing failure occasion accelerating experiment technology is that accelerated test should from simple structure product to complex structure product popularization
Basis.Usually assume that product only has a kind of failure mode in traditional accelerated test statistical analysis.But at work, roll
Bearing there may be Multiple Failure Modes, and any failure mode occurs cause it to fail, i.e. rolling bearing failure is
The result of Multiple Failure Modes competition.For competing failure occasion, the accelerated test statistical method of traditional single failure mode is simultaneously
It is improper.Existing correlation scholar establishes the competing failure model Sum Maximum Likelihood Estimate of competing failure occasion ALT（MLE）Side
Method.But the statistical method based on MLE is, it is necessary to larger sample size could obtain excellent essential behaviour.
Need to pass through when carrying out rolling bearing (acceleration) life test, when fail data is less or occurs without failure at all
Increase sample size or increase test period to obtain the fail data of abundance so that experimentation cost and test period are difficult to hold
Receive.
The content of the invention
The technical problems to be solved by the invention are, it is proposed that it is a kind of efficiently, the axis of rolling under reliability degradation experiment high
Hold reliability RES(rapid evaluation system).
The technical solution adopted in the present invention mainly comprises the following steps：
1. double stress Step-stress tests of rolling bearing
FMECA analyses based on early stage understand that stress and vibration are the essential environmental factors for influenceing rolling bearing reliability.Cause
This, the present invention carries out double stress Step-stress tests to rolling bearing using the double stress of stress-vibration.During further to shorten experiment
Between, the rapid evaluation of rolling bearing reliability is realized, with regard to the double stress design problems of stress-vibration in step-stress life testing, according to
The criterion and method of the accelerated life test plan optimization design of proposition, with rolling bearing in normal work stress level the life-span
The minimum target of variance of estimate, under it is determined that each stress level is combined, with the proof stress level of each accelerated factor, respectively
The sample allocation proportion of secondary experiment and each truncated time of experiment are design variable, theoretical using Maximum-likelihood estimation, are set up
The Mathematical Modeling of the double stress step-stress life testing scheme optimization designs of stress-vibration.To improving reliability assessment precision, reducing
Test number (TN), shortening test period.
The matter of utmost importance for analyzing accelerated test data is the determination of acceleration model.With reference to the working environment and group of rolling bearing
Into, the accelerated life test of the double stress of stress-vibration is implemented to it, acceleration model uses Peck models.Can for fail data
The incomplete sex chromosome mosaicism that can occur, is first modeled to test data；Again for every kind of failure mode data have complete data,
The situation of censored data, Peck model parameters are estimated using Diversity data regression method.
2. the Reliability Evaluation Model of competing failure model is based on
For the not single problem of rolling bearing failure mode, competing failure model is set up.Accelerate for competing failure occasion
Testing data of life-span partial data that may be present, censored data and failure mode do not determine data this several types, basic to think
Lu Shi：Prior distribution form is selected first, prior distribution expression formula is determined, Bayes points is carried out to partial data and censored data
Analysis, obtains Posterior distrbutionp expression formula；Then the Posterior distrbutionp for being obtained using the last time as prior distribution, one by one to failure mode
Do not determine that data point carries out Bayes estimations, obtain Posterior distrbutionp and its expression formula；Finally, extrapolated by acceleration model and normally should
Parameter evaluation value under power level.
Posteriority is calculated using the Gibbs methods of samplings to count, and then obtain the estimate of parameter.The iteration from the distribution of full condition
Be sampled, when iterations is sufficiently large, so that it may obtain the sample from joint posterior distribution, and then also come from
The sample of edge distribution.How it is critical only that from each full condition distribution sampling for Gibbs sampling, is not mark when full condition is distributed
During quasi-distribution function, it is sampled and there is certain difficulty, full condition distribution sample value can be obtained using standard Adaptive rejection sampling.
During the double stress steps of stress-vibration plus accelerated test, both there is unexpected loss, there is also degradation failure.
Accelerated life test data analysing method above-mentioned is used to unexpected loss.For degradation failure, based on random
Process and the double stress acceleration models of stress-vibration are set up and accelerate degradation model, determine failure threshold, then during the failure of rolling bearing
Between reach the time T of failure threshold first for performance degradation amount, will amount of degradation distributed model be converted into the distribution of T, then with it is prominent
Competing failure model is set up in the fail data combination of hair property.
3. Poisson process intensity function and acceleration model
Acceleration equation under the double stress Step-stress tests of stress-vibration uses Peck models：
To partial data, the situation of censored data mixing under the double stress synergy of stress-vibration, using Diversity data
Regression analysis.For three-parameter weibull distribution situation, be converted into the extreme value distribution by logarithmic transformation carries out polynary mixing again
Data regression is closed to be processed.
If y is the stochastic variable for obeying the extreme value distribution, its distribution function is：
In formulaIt is location parameter,It is scale parameter.IfWithBetween there is linear relationship,
Then regression equation is represented by：
4. set up and accelerate degradation model
Rolling bearing characteristic quantity under cyclic loading effect is gradually degenerated, and a duty cycle is regarded as a chronomere,
The product degradation fractional increments di caused in i-th duty cycle is a stochastic variable, and load effect is received in its distribution.Assuming that should
Random variable values are, variance is, then after n duty cycle, the accumulation amount of degradation of rolling bearing.According to
Central-limit theorem, when n is very big, there is stochastic variable（）Convergence in distribution in standardized normal distribution, then arrive
T, amount of degradationMean value function and variance function be,。
When degradation failure threshold values is l, the failure probability of product t：
Order,, have：
Analyzed more than again, the degeneration increment that high stress level causes within the unit interval is big, i.e. affected by force, when
Accelerated stress has when being stress-vibration pair stress, the acceleration degeneration equation of B-S distributions：
(a, b are unknown preset parameter)
Under the double stress Step-stress tests of stress-vibration, rolling bearing both there is also degradation failure in the presence of burst failure, then need to consider
Competing failure problem of the burst failure to degenerative process when related.Without loss of generality, if rolling bearing performance increasing over time
Plus and gradually degenerate, performance degradation amount is designated as x (t), and it is the stochastic variable of Time Continuous, degradation failure threshold values be l, that is, work as x
T during () >=l there is degradation failure in product；In addition, rolling bearing also has multiple burst failure modes, burst failure may be produced
The influence of product amount of degradation, generally, a certain moment amount of degradation is bigger, and the possibility that burst failure occurs is also bigger.
Obviously, the size of t amount of degradation x is a stochastic variable, if its distribution function is G (x;T), it is corresponding close
Degree function is g (x;t).The time that rolling bearing occurs degradation failure is designated as Td, according to the failure criteria of degradation failure, only examines
It is in the failure probability of t when worry is degenerated：
It is a family of distributions with time-varying parameter, if the family of distributions of its unknown time-varying parameter is
If the burst out-of-service time is Tt, the probability that burst failure at a time occurs is influenceed by amount of degradation x, therefore burst is lost
The effect time dangerous function of Tt is represented by, then its condition survival function and condition failure distribution function are respectively：
Rolling bearing failure is burst failure and the result of degradation failure, various according to more than, and t its reliability is：
Then the competing failure distribution function of rolling bearing is：
Rolling bearing reliability assessment scheme proposed by the present invention shortens the reliability growth process of rolling bearing newly developed, tool
There is very strong operability.
Brief description of the drawings
Accompanying drawing is overall structure block diagram of the invention.
Specific embodiment
With reference to accompanying drawing, the quick Bayes evaluation system of rolling bearing reliability is used under the present invention to be proposed degradation experiment
Technical scheme mainly comprise the following steps：
1. double stress Step-stress tests of rolling bearing
FMECA analyses based on early stage understand that stress and vibration are the essential environmental factors for influenceing rolling bearing reliability.Cause
This, the present invention carries out double stress Step-stress tests to rolling bearing using the double stress of stress-vibration.During further to shorten experiment
Between, the rapid evaluation of rolling bearing reliability is realized, with regard to the double stress design problems of stress-vibration in step-stress life testing, according to
The criterion and method of the accelerated life test plan optimization design of proposition, with rolling bearing in normal work stress level the life-span
The minimum target of variance of estimate, under it is determined that each stress level is combined, with the proof stress level of each accelerated factor, respectively
The sample allocation proportion of secondary experiment and each truncated time of experiment are design variable, theoretical using Maximum-likelihood estimation, are set up
The Mathematical Modeling of the double stress step-stress life testing scheme optimization designs of stress-vibration.To improving reliability assessment precision, reducing
Test number (TN), shortening test period.
The matter of utmost importance for analyzing accelerated test data is the determination of acceleration model.With reference to the working environment and group of rolling bearing
Into, the accelerated life test of the double stress of stress-vibration is implemented to it, acceleration model uses Peck models.Can for fail data
The incomplete sex chromosome mosaicism that can occur, is first modeled to test data；Again for every kind of failure mode data have complete data,
The situation of censored data, Peck model parameters are estimated using Diversity data regression method.
2. the Reliability Evaluation Model of competing failure model is based on
For the not single problem of rolling bearing failure mode, competing failure model is set up.Accelerate for competing failure occasion
Testing data of life-span partial data that may be present, censored data and failure mode do not determine data this several types, basic to think
Lu Shi：Prior distribution form is selected first, prior distribution expression formula is determined, Bayes points is carried out to partial data and censored data
Analysis, obtains Posterior distrbutionp expression formula；Then the Posterior distrbutionp for being obtained using the last time as prior distribution, one by one to failure mode
Do not determine that data point carries out Bayes estimations, obtain Posterior distrbutionp and its expression formula；Finally, extrapolated by acceleration model and normally should
Parameter evaluation value under power level.
Posteriority is calculated using the Gibbs methods of samplings to count, and then obtain the estimate of parameter.The iteration from the distribution of full condition
Be sampled, when iterations is sufficiently large, so that it may obtain the sample from joint posterior distribution, and then also come from
The sample of edge distribution.How it is critical only that from each full condition distribution sampling for Gibbs sampling, is not mark when full condition is distributed
During quasi-distribution function, it is sampled and there is certain difficulty, full condition distribution sample value can be obtained using standard Adaptive rejection sampling.
During the double stress steps of stress-vibration plus accelerated test, both there is unexpected loss, there is also degradation failure.
Accelerated life test data analysing method above-mentioned is used to unexpected loss.For degradation failure, based on random
Process and the double stress acceleration models of stress-vibration are set up and accelerate degradation model, determine failure threshold, then during the failure of rolling bearing
Between reach the time T of failure threshold first for performance degradation amount, will amount of degradation distributed model be converted into the distribution of T, then with it is prominent
Competing failure model is set up in the fail data combination of hair property.
3. Poisson process intensity function and acceleration model
Acceleration equation under the double stress Step-stress tests of stress-vibration uses Peck models：
To partial data, the situation of censored data mixing under the double stress synergy of stress-vibration, using Diversity data
Regression analysis.For three-parameter weibull distribution situation, be converted into the extreme value distribution by logarithmic transformation carries out polynary mixing again
Data regression is closed to be processed.
If y is the stochastic variable for obeying the extreme value distribution, its distribution function is：
In formulaIt is location parameter,It is scale parameter.IfWithBetween there is linear relationship,
Then regression equation is represented by：
4. set up and accelerate degradation model
Rolling bearing characteristic quantity under cyclic loading effect is gradually degenerated, and a duty cycle is regarded as a chronomere,
The product degradation fractional increments di caused in i-th duty cycle is a stochastic variable, and load effect is received in its distribution.Assuming that should
Random variable values are, variance is, then after n duty cycle, the accumulation amount of degradation of rolling bearing.Root
According to central-limit theorem, when n is very big, there is stochastic variable（）Convergence in distribution in standardized normal distribution, then
To t, amount of degradationMean value function and variance function be,。
When degradation failure threshold values is l, the failure probability of product t：
Order,, have：
Analyzed more than again, the degeneration increment that high stress level causes within the unit interval is big, i.e. affected by force, when
Accelerated stress has when being stress-vibration pair stress, the acceleration degeneration equation of B-S distributions：
(a, b are unknown preset parameter)
Under the double stress Step-stress tests of stress-vibration, rolling bearing both there is also degradation failure in the presence of burst failure, then need to consider
Competing failure problem of the burst failure to degenerative process when related.Without loss of generality, if rolling bearing performance increasing over time
Plus and gradually degenerate, performance degradation amount is designated as x (t), and it is the stochastic variable of Time Continuous, degradation failure threshold values be l, that is, work as x
T during () >=l there is degradation failure in product；In addition, rolling bearing also has multiple burst failure modes, burst failure may be produced
The influence of product amount of degradation, generally, a certain moment amount of degradation is bigger, and the possibility that burst failure occurs is also bigger.
Obviously, the size of t amount of degradation x is a stochastic variable, if its distribution function is G (x;T), it is corresponding close
Degree function is g (x;t).The time that rolling bearing occurs degradation failure is designated as Td, according to the failure criteria of degradation failure, only examines
It is in the failure probability of t when worry is degenerated：
It is a family of distributions with time-varying parameter, if the family of distributions of its unknown time-varying parameter is。
If the burst out-of-service time is Tt, the probability that burst failure at a time occurs is influenceed by amount of degradation x, therefore prominent
The dangerous function for sending out out-of-service time Tt is represented by, then its condition survival function and condition failure distribution function are respectively：
Rolling bearing failure is burst failure and the result of degradation failure, various according to more than, and t its reliability is：
Then the competing failure distribution function of rolling bearing is：
。
Claims (1)
1. rolling bearing reliability assessment scheme, it is characterised in that：Step is including the double stress Step-stress tests of rolling bearing, based on competing
Reliability Evaluation Model, Poisson process intensity function and acceleration model, the foundation for striving failure model accelerate degradation model.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201510878179.5A CN106845050A (en) | 2015-12-04 | 2015-12-04 | Rolling bearing reliability assessment scheme |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201510878179.5A CN106845050A (en) | 2015-12-04 | 2015-12-04 | Rolling bearing reliability assessment scheme |
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107991095A (en) * | 2017-12-28 | 2018-05-04 | 哈工大机器人（合肥）国际创新研究院 | The life test apparatus and method of robot precision cycloid decelerator |
| CN108052720A (en) * | 2017-12-07 | 2018-05-18 | 沈阳大学 | A kind of bearing performance degradation assessment method based on migration cluster |
-
2015
- 2015-12-04 CN CN201510878179.5A patent/CN106845050A/en active Pending
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108052720A (en) * | 2017-12-07 | 2018-05-18 | 沈阳大学 | A kind of bearing performance degradation assessment method based on migration cluster |
| CN107991095A (en) * | 2017-12-28 | 2018-05-04 | 哈工大机器人（合肥）国际创新研究院 | The life test apparatus and method of robot precision cycloid decelerator |
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| WD01 | Invention patent application deemed withdrawn after publication |
Application publication date: 20170613 |
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