CN105224792B - A kind of rolling bearing performance keeps the Forecasting Methodology of reliability - Google Patents
A kind of rolling bearing performance keeps the Forecasting Methodology of reliability Download PDFInfo
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Abstract
The invention discloses the Forecasting Methodology that a kind of rolling bearing performance keeps reliability, it is included in rolling bearing runnability best period, obtains performance data, builds performance sample rate function；The confidential interval of confidence level and performance stochastic variable is obtained according to Little Probability Event Princiole；According to Poisson counting process, acquisition performance data falls the frequency and rolling bearing performance holding reliability outside performance stochastic variable confidential interval, and then property retention Relative Reliability of the rolling bearing in future time is obtained, predicted roll bearing keeps the failure degree of optimum performance situation in future time accordingly.Any prior information of this method without Properties: Density function, without performance threshold is previously set, the failure degree of future time rolling bearing optimum performance situation can be predicted, prediction accuracy is high, the hidden danger that fails can be found in advance, to take intervening measure in time, avoiding generation severe safety accident from providing decision-making.
Description
Technical Field
The invention belongs to the technical field of rolling bearing service performance failure evaluation and performance reliability prediction, and particularly relates to a prediction method for rolling bearing performance maintaining reliability.
Background
A rolling bearing is a precision mechanical element that reduces friction loss by changing sliding friction between a running shaft and a shaft seat into rolling friction. The rolling bearing generally comprises an inner ring, an outer ring, a rolling body, a retainer and the like, wherein the inner ring is used for being matched with a shaft and rotating together with the shaft; the outer ring is matched with the bearing seat to play a supporting role; the rolling body rolls between the inner ring and the outer ring to bear and transmit load; the retainer can enable the rolling bodies to be uniformly distributed, prevent the rolling bodies from falling off and colliding with each other, guide the rolling bodies to rotate and improve the internal lubrication of the bearing.
The rolling bearing is one of the most important parts in a mechanical transmission system, and has wide application in the fields of aerospace, ships, automobiles and rail traffic. The rolling bearings are also a vulnerable part of the mechanical system, requiring regular maintenance and replacement. Maintenance and replacement of the rolling bearing generally need to disassemble and assemble the whole mechanical system, and the cost of time, manpower and material resources consumed in the disassembling and assembling process is usually hundreds of times of the cost of the bearing. However, the lack of time for maintenance and replacement may render the entire system inoperable due to failure of the bearings, resulting in greater economic loss and even endangering the life safety of the operators. Therefore, the service life is accurately predicted according to specific working conditions and bearing parameters, excessive maintenance can be greatly reduced, the use cost and the maintenance cost are reduced, and the method plays an important role in industrial production and technological development.
The performance of the rolling bearing mainly comprises vibration, noise, friction torque, temperature rise, rotation precision and the like, and the performance has important influence on the operation performance of a mechanical system. The performance failure of the rolling bearing refers to the phenomenon that the rolling bearing loses the running performance or cannot normally work due to the faults of poor lubrication, friction and abrasion, damage, adhesion, corrosion, deformation and the like of internal parts in the running process. The rolling bearing keeps the best performance potential state operation, and is the basis for realizing the best performance potential state operation of a mechanical system. According to the stochastic process theory, the reliability of the rolling bearing to maintain optimum performance potential operation will change in the future, which increases the possibility of compromising the safe and reliable operation of the mechanical system. Therefore, the research on the performance maintaining reliability of the rolling bearing has important application value.
In general, the performance failure test of a rolling bearing refers to: according to a certain standard, such as a national standard or an industrial standard, a certain number of samples are randomly extracted from a batch of rolling bearings, then the extracted samples are placed in the same test environment for a complete reliability life test to obtain the life of each failure sample, finally, test data are processed according to the standard GB/T24607-2009, reliability indexes such as shape parameters b and L10, characteristic life and average life of the rolling bearings are given, and accordingly reliability evaluation or analysis is carried out on the batch of rolling bearings. However, due to the improvement of the quality of the rolling bearing, it is unrealistic and unnecessary to ensure that each sample fails in the reliability test process; it is not practical to fully test some expensive, low volume rolling bearings.
The existing performance reliability evaluation and prediction method obtains the performance reliability based on the assumption that a performance density function, a performance degradation track and a performance failure threshold are known in advance, and has obtained a certain effect. In the existing reliability evaluation method, an article entitled "reliability evaluation based on performance degradation data" is published in "astronavigation science newspaper" 3 rd year, and the article assumes that a performance degradation trajectory is a linear function of time, considers that a performance degradation value obeys normal distribution and gives a threshold value, and can perform reliability evaluation of performance degradation of an astronavigation system. In the existing rolling bearing performance reliability evaluation method, CN104318043A discloses a rolling bearing vibration performance reliability variation process detection method, which obtains a very small amount of original information of variation strength expressed by bearing vibration in a short time interval by means of a counting process of a time sequence; simulating a large amount of generated information of the variation intensity by self-help resampling of the original information of the variation intensity; processing the generated information by using a gray prediction model to obtain a variation intensity estimated value; and (3) representing a reliability function by using a Poisson process, and predicting a variation process of the vibration performance reliability of the bearing in real time. The method is based on the time sequence of vibration information, a gray self-help principle is integrated into a poisson process, and a gray self-help poisson method is provided to predict the variation process of the performance reliability of the rolling bearing. However, this method requires a performance test to obtain a performance threshold value, which is obtained through the test, and the corresponding threshold value is different according to the selected damage part and the sensor. Therefore, in the conventional reliability evaluation method, when the prior information of the performance density function is unknown and the performance threshold is not set in advance, the variation process of the performance reliability of the rolling bearing cannot be predicted.
Disclosure of Invention
The invention aims to provide a prediction method for the performance maintaining reliability of a rolling bearing, which solves the problem of the performance maintaining reliability prediction of the rolling bearing under the condition that the prior information of a performance density function is unknown and a performance threshold value is not set in advance.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows:
a method for predicting the performance retention reliability of a rolling bearing comprises the following steps:
1) Measuring the performance of the rolling bearing to obtain performance data when the running performance of the rolling bearing is optimal;
2) Constructing a performance sample density function by using the performance data obtained in the step 1) according to a maximum entropy principle;
3) Obtaining confidence coefficient according to a small probability event principle, and obtaining a confidence interval of the performance random variable by using a quantile method;
4) According to the Poisson counting process, acquiring the frequency of the performance data falling outside a performance random variable confidence interval;
5) According to the non-failure probability of the Poisson counting process, the reliability of the performance of the rolling bearing is kept by the frequency of the performance data falling outside the confidence interval of the performance random variable;
6) And according to a relative error concept of a measurement theory, acquiring the performance maintaining relative reliability of the rolling bearing at the future time, and predicting the failure degree of the rolling bearing maintaining the optimal performance potential at the future time according to the performance maintaining relative reliability.
The performance data obtained in the step 1) is performance data of the rolling bearing running in an evaluation time interval, wherein the evaluation time interval is a time interval after the running-in period of the rolling bearing is ended, the end time of the evaluation time interval is the current time, and t =1; the time interval after the evaluation time interval is called a prediction time interval, t >1, each prediction time interval has the same time span with the evaluation time interval, and the end time of the prediction time interval is the future time in the step 6). Adding 1 to the future time t every time 1 prediction time interval is added; the unit of time t coincides with the unit of the evaluation time interval.
The evaluation time interval is in the optimal running performance period of the rolling bearing, and the optimal running performance potential state of the rolling bearing in the time interval is indicated; in the period of the optimal running performance of the rolling bearing, the rolling bearing keeps the optimal performance potential state in running, which means that the possibility of performance failure is almost eliminated; this period is usually located in a time interval immediately after the end of the running-in period of the rolling bearing.
The rolling bearing performance mainly comprises vibration, noise, friction torque, temperature rise, rotation precision and the like. In the step 1), a certain performance of the rolling bearing is periodically measured by a measuring system in the optimal running performance period of the rolling bearing, and the time history of the performance failure degree of the rolling bearing in the future time is predicted.
K performance data for constructing a performance sample density function, and x individual performance data k ，k＝1，2，…，K；K≥1000；
The performance sample density function is p (x):
in the formula (1), x is a performance random variable for describing the performance of the rolling bearing; m is the highest origin moment order; i is the origin moment order; lambda [ alpha ] 0 ，λ 1 ，…，λ m Is a Lagrange multiplier, and has a first Lagrange multiplier lambda 0 Comprises the following steps:
in the formula (2), x is a performance random variable for describing the performance of the rolling bearing; s 1 A lower bound value of a feasible domain of a performance random variable x; s 2 The performance random variable x is the upper bound value of the feasible region; i is the origin moment order; lambda i For the ith Lagrangian multiplier, lagrangian multiplier λ 1 ，λ 2 ，…，λ m Obtained from the m equation sets of equation (3):
in the formula (3), x is a performance random variable for describing the performance of the rolling bearing; x is the number of k The performance data is kth individual performance data, K represents the serial number of the performance data, and K is the number of the performance data; s 1 Is the lower bound value, S, of the feasible domain of the performance random variable x 2 The performance random variable x is the upper bound value of the feasible region; i and j are both the order of origin moment, m is the highest order of origin moment, λ i Is the ith lagrange multiplier.
In step 3), the confidence coefficient is the representation of the potential state occurrence probability of the inherent optimal operation performance of the rolling bearing performance totality, and the acquisition method comprises the following steps: according to the statistical small probability event principle, the significance level can be 0-0.2, such as 0.01, 0.05, 0.1 and the like, and the corresponding confidence coefficient is 1-0.8, such as 0.99, 0.95, 0.9 and the like; the value of the confidence coefficient is determined in advance through a performance test on the basis of a small probability event principle, and the occurrence probability of the inherent optimal operation performance potential state of the whole performance of the rolling bearing is represented.
The confidence P is determined in advance through a performance test by taking a small probability event principle as a basis, and the specific method comprises the following steps:
i) Selecting the same rolling bearing in advance for a performance test, and detecting the rolling bearing when the running performance is in the best period to obtain K which is more than or equal to 1000 performance data, wherein K is the number of the performance data; constructing a performance sample density function p (x) by using the K individual performance data; selecting a confidence estimate P q Respectively, sequentially obtaining 7 values of 1, 0.999, 0.99, 0.95, 0.9, 0.85, 0.8, etc., and determining the corresponding P value by quantile method q Q-th individual-performance random variable confidence interval [ X ] Lq ，X Uq ]Recording how many data among the K individual performance data fall within a performance random variable confidence interval [ X ] Lq ，X Uq ]In addition, and thus obtaining that the performance data falls within a performance random variable confidence interval [ X ] Lq ，X Uq ]Outer q frequency value lambda q Where X is Lq And X Uq The serial numbers q =1,2,3, …,7 are respectively a lower bound value and an upper bound value;
ii) continuing to perform the performance test and detection of the rolling bearing until the performance fails, and obtaining more than or equal to 1000 performance failure data when the performance fails, wherein W is the number of the performance failure data; or after the rolling bearing operation performance is in the best period to obtain the K individual performance data, suspending the test, taking out the rolling bearing, constructing a fault when the performance is invalid on the rolling surface of the raceway of the rolling bearing, simulating the fault when the performance is invalid, and detecting the rolling bearing with the fault when the simulated performance is invalid to obtain the W individual performance invalid data when the performance is invalid;
iii) Recording how many data in W individual performance failure data fall within a performance random variable confidence interval [ X ] Lq ，X Uq ]And obtaining therefrom a confidence interval [ X ] that the performance failure data falls within the performance random variable Lq ，X Uq ]Other q-th frequency value beta q Where X is Lq And X Uq Lower and upper bound values, respectively, serial numbers q =1,2,3, …,7;
iv) according to formula d q ＝{[exp(-β q )-exp(-λ q )]/exp(-λ q ) Maintaining relative reliability d of rolling bearing performance when computation performance of 100% fails q To obtain the qth d q Value, here λ q For performance data falling within a performance random variable confidence interval [ X ] Lq ，X Uq ]Q frequency value of other, beta q For the performance failure data falling within the performance random variable confidence interval [ X ] Lq ，X Uq ]The q-th frequency value of the other, index q =1,2,3, …,7; from 7 d q The one with the index q of less than and closest to-10% of the values is selected, and the corresponding confidence measure P is assigned q* The confidence P is determined in advance through a performance test based on the principle of the small probability event.
In the above process, X in step i) Lq And X Uq Are respectively the same as X L And X U (ii) a In step ii), inThe failure method when the rolling surface is constructed to have performance failure is that acid substances are used for corroding 3 small and macroscopic spots on the rolling surface of the raceway at angles of 120 degrees in the circumferential direction, and the failure when the performance failure occurs is simulated.
In step 3), the confidence interval of the random variable of the performance is [ X ] L ，X U ]Lower bound value X L The following equation (4) is used to determine:
upper bound value X U The following equation (5) is used to determine:
in the formulas (4) and (5), x is a performance random variable for describing the performance of the rolling bearing; s 1 A lower bound value of a feasible domain of a performance random variable x; s 2 The performance random variable x is the upper bound value of the feasible region; [ X ] L ，X U ]Is the confidence interval of the performance random variable x; p (x) is a performance sample density function; p is the confidence.
According to the Poisson counting process, the confidence interval [ X ] of how many data fall in the random variable X of the performance in the K performance data is recorded L ，X U ]In addition, and thus obtaining that the performance data falls within a performance random variable X confidence interval [ X [ ] L ，X U ]And an outer frequency lambda.
In step 4), the frequency of the performance data falling outside the confidence interval of the performance random variable is lambda:
in the formula (6), lambda is the confidence interval [ X ] of the performance data falling in the performance random variable X L ，X U ]Outside frequencies, n is the confidence interval [ X ] that the performance data falls within the performance random variable X L ，X U ]The number of the other, K, is the number of the performance data.
In the prediction method of the invention, the reliability of the performance of the rolling bearing is the possibility that the rolling bearing can keep the optimal performance potential during the test and the service period. The performance retention reliability is expressed as a function, and the specific value of the function is called performance retention reliability. Namely, step 5) is to obtain a rolling bearing performance maintaining reliability function according to the non-failure probability of the Poisson counting process and the frequency of the performance data falling outside the performance random variable confidence interval, wherein the specific value of the function is the performance maintaining reliability.
In step 5), the reliability of the performance maintenance of the rolling bearing is R (t):
R(t)＝exp(-λt)；t≥1 (7)，
in the formula (7), t is time, and t is more than or equal to 1; r (t) is the reliability of the performance maintenance of the rolling bearing at the time t and is used for representing the possibility that the rolling bearing can maintain the optimal performance potential during the operation at the time t; lambda is the confidence interval [ X ] that the performance data falls in the performance random variable X L ，X U ]And (c) other frequencies.
And 6), keeping the relative reliability of the performance of the rolling bearing at the future time as d (t):
in the formula (8), R (1) is the rolling bearing performance retention reliability at the current time t =1; t is future time, t >1; r (t) is the reliability of the rolling bearing performance at the future time t; d (t) is the relative reliability of the performance of the rolling bearing, and is used for representing the failure degree of the rolling bearing in the best performance potential state during the future time t.
In step 6), the method for predicting the failure degree of the rolling bearing for keeping the optimal performance potential in the future time according to the relative reliability of the performance maintenance comprises the following steps: grading the running performance of the rolling bearing according to a significance hypothesis testing principle and a measurement theory; and predicting the time history of the potential failure degree of the optimal performance of the rolling bearing according to the rolling bearing operation performance grading.
The basic principle of the classification of the running performance of the rolling bearing is as follows:
a) According to the significance hypothesis testing principle, if the relative reliability of the rolling bearing performance is not less than 0%, the predicted rolling bearing performance maintaining reliability at the future time is not lower than the rolling bearing performance maintaining reliability at the current time, the rolling bearing operation performance cannot be refused to reach the optimal potential state; otherwise, the running performance of the rolling bearing can be refused to reach the optimal potential state;
b) When the rolling bearing performance is kept less than 0%, according to the theory of measurement, the error of the measured value with respect to the true value is small when the absolute value of the relative error is between (0%, 5% >), the error of the measured value with respect to the true value is becoming large when the absolute value of the relative error is between (5%, 10% >), and the error of the measured value with respect to the true value becomes large when the absolute value of the relative error is greater than 10%.
And classifying the running performance of the rolling bearing based on the significance hypothesis testing principle and the measurement theory.
The classification of the running performance of the rolling bearing refers to that the running performance of the rolling bearing is divided into 4 grades of S1, S2, S3 and S4:
s1: the performance of the rolling bearing keeps the relative reliability d (t) more than or equal to 0 percent, namely the running performance of the rolling bearing at the future time t reaches the best, and the best performance potential state almost has no possibility of failure;
s2: the performance of the rolling bearing keeps relative reliability d (t) within the range of-5 percent and 0 percent, namely the running performance of the rolling bearing at the future time t is normal, and the possibility of potential failure of the optimal performance is low;
s3: the performance of the rolling bearing keeps relative reliability d (t) E < -10%, -5%), namely the running performance of the rolling bearing at the future time t is deteriorating, and the possibility of failure of the optimal performance potential state is increasing;
s4: the performance of the rolling bearing keeps the relative reliability d (t) < -10%, namely the running performance of the rolling bearing at the future time t is deteriorated, and the possibility of potential failure of the optimal performance is increased.
And predicting the time history of the potential failure degree of the optimal performance of the rolling bearing according to the 4 grades of the rolling bearing operation performance grading. The relative reliability of the performance of the rolling bearing is actually the attenuation degree of the reliability of the performance of the rolling bearing at the future time relative to the optimal performance potential at the current time, wherein a negative value represents attenuation, and a positive value represents no attenuation. The smaller the rolling bearing performance retention relative reliability d (t), the worse the rolling bearing running performance becomes and the greater the possibility of optimum performance potential failure becomes.
The future time t corresponding to the rolling bearing performance keeping relative reliability d (t) = -10% is the critical time of the rolling bearing performance deterioration, and before the critical time comes, intervention measures are taken to maintain or replace the rolling bearing, so that serious safety accidents caused by potential failure of the optimal performance of the rolling bearing are avoided.
The method for predicting the performance maintaining reliability of the rolling bearing is completed under the subsidy of the national science foundation (51475144). The prediction method comprises the following elements of confidence degree, confidence interval, performance maintaining reliability and performance maintaining relative reliability. The confidence coefficient is the representation of the potential state occurrence probability of the inherent optimal operation performance of the rolling bearing performance; the confidence interval can represent the optimum performance potential state which can be kept when the rolling bearing operates during the test and the service period; the performance maintaining reliability represents the possibility that the rolling bearing can maintain the optimal performance potential during operation; the performance maintaining relative reliability is used for representing the failure degree of the rolling bearing in the best performance potential state in the future.
The invention relates to a prediction method for maintaining reliability of rolling bearing performance, which is characterized in that performance data are obtained in the optimal period of the rolling bearing running performance, a performance sample density function is constructed, and a confidence interval of a confidence coefficient and a performance random variable is obtained; according to the Poisson counting process, the frequency of performance data falling outside a performance random variable confidence interval and the performance maintaining reliability of the rolling bearing are obtained, the performance maintaining relative reliability of the rolling bearing at the future time is further obtained, and accordingly the failure degree of the rolling bearing maintaining the optimal performance potential state at the future time is predicted. The method does not need any prior information of a performance density function or a preset performance threshold, can predict the failure degree of the optimum running performance potential of the rolling bearing at the future time, has high prediction accuracy, can discover failure hidden dangers in advance, and provides a decision for taking intervention measures in time and avoiding serious safety accidents. The method is a rolling bearing test and service period performance keeping reliability prediction method with unknown prior information of a performance density function and without setting a performance threshold in advance; according to the method provided by the invention, intervention measures can be taken before the possibility of potential failure of the optimal performance of the rolling bearing is increased, the rolling bearing is maintained or replaced, and serious safety accidents are avoided.
Drawings
FIG. 1 is a friction torque data distribution diagram of a rolling bearing in example 1;
FIG. 2 is a graph showing a density function of a sample of a friction torque of the rolling bearing in example 1;
FIG. 3 is a time chart of the maintenance of the relative reliability of the friction torque of the rolling bearing in embodiment 1;
FIG. 4 is a graph showing a vibration acceleration data distribution of a rolling bearing in example 2;
FIG. 5 is a graph of density function of samples of vibration acceleration of the rolling bearing in example 2;
fig. 6 is a time chart showing how the vibration acceleration of the rolling bearing maintains a relative reliability in embodiment 2.
Detailed Description
The present invention will be further described with reference to the following embodiments.
In a specific embodiment, the time for periodically measuring the performance of the rolling bearing is carried out in a time interval after the running-in period of the rolling bearing is ended; the running performance potential of the rolling bearing in the time interval is optimal, the time interval is an evaluation time interval, the end time of the evaluation time interval is the current time, and t =1. The future time in prediction refers to a time interval after the evaluation time interval, which is called a prediction time interval, and t is added by 1 every time 1 prediction time interval is added. The unit of time t coincides with the unit of the evaluation time interval. For example, the rolling bearing performance is periodically measured from 1/2015 to 30/6/2015, and the possibility of potential failure of the optimum performance of the rolling bearing between 1/2017 and 30/6/20157 is predicted. Here, the evaluation time interval is 0.5 years (starting from 1/2015 and ending at 30/2015/6/2015), the current time is t =1, the future time is t =1+4=5, a total of 4 prediction time intervals are passed, each prediction time interval is 0.5 years, and the possibility of potential failure of the optimum performance of the rolling bearing at the 5 th time interval (between 1/2017 and 30/6/2015) is predicted. Here, the 5 time intervals amount to 2.5 years, and the unit of the time t is 0.5 year.
Example 1
The method for predicting the performance retention reliability of the rolling bearing of embodiment 1 includes the steps of:
1) In the optimal running performance period of the rolling bearing, the friction torque of the rolling bearing in the evaluation time interval is regularly measured through a measuring system, K individual performance data of the friction torque is obtained at the current time t =1, K =20000, and the K individual performance data is x k K =1,2, …,20000, and the data unit is N · m; the obtained friction torque data distribution diagram of the rolling bearing is shown in FIG. 1;
in this example 1, the evaluation time interval is 1 year, each prediction time interval is 1 year, and the unit of time t is year; the time history of the failure degree of the friction torque performance of the rolling bearing in the future time is predicted by adopting the prediction method of the performance maintaining reliability of the rolling bearing;
2) Constructing a performance sample density function p (x) by using the performance data obtained in the step 1) according to the maximum entropy principle:
in the formula (1), x is a performance random variable for describing the performance of the rolling bearing; m is the highest origin moment order; i is the origin moment order; lambda [ alpha ] 0 ，λ 1 ，…，λ m Is a Lagrange multiplier, and has a first Lagrange multiplier lambda 0 Comprises the following steps:
in the formula (2), x is a performance random variable for describing the performance of the rolling bearing; s 1 A lower bound value of a feasible domain of a performance random variable x; s 2 The performance random variable x is the upper bound value of the feasible region; i is the origin moment order; lambda [ alpha ] i For the ith Lagrangian multiplier, lagrangian multiplier λ 1 ，λ 2 ，…，λ m Obtained from the m equation sets of equation (3):
in the formula (3), x is a performance random variable for describing the performance of the rolling bearing; x is a radical of a fluorine atom k The performance data is kth individual performance data, K represents the serial number of the performance data, and K is the number of the performance data; s 1 Is the lower bound value, S, of the feasible domain of the performance random variable x 2 The performance random variable x is the upper bound value of the feasible region; i and j are both the order of origin moment, m is the highest order of origin moment, λ i Is the ith Lagrangian multiplier;
constructing a friction torque sample density function p (x) by using 20000 friction torque performance data obtained in the step 1), wherein the result is shown in FIG. 2;
3) Obtaining confidence coefficient according to a small probability event principle, and obtaining a confidence interval of the performance random variable by using a quantile method;
according to the principle of small probability events, the confidence coefficient P =0.99 is obtained in advance through experiments, and the random variable x position of the friction torque can be calculatedSignal interval [ X L ，X U ]＝[233.329N·m，251.897N·m]：
Lower bound value X L The following equation (4) is used to determine:
upper bound value X U The following equation (5) is used to determine:
in the formulas (4) and (5), x is a performance random variable for describing the performance of the rolling bearing; s 1 A lower bound value of a feasible domain of a performance random variable x; s. the 2 The performance random variable x is the upper bound value of the feasible region; [ X ] L ，X U ]A confidence interval of a performance random variable x; p (x) is a performance sample density function; p is a confidence coefficient;
the confidence P is determined in advance through a performance test based on a small probability event principle, and the specific method comprises the following steps:
i) Selecting the same rolling bearing in advance to carry out a performance test, and detecting when the running performance of the rolling bearing is in the best period to obtain K which is more than or equal to 1000 performance data, wherein K is the number of the performance data; constructing a performance sample density function p (x) by using the K individual performance data; selecting a confidence estimate P q Respectively, sequentially obtaining 7 values of 1, 0.999, 0.99, 0.95, 0.9, 0.85, 0.8, etc., and determining the corresponding P value by quantile method q Q-th individual-performance random variable confidence interval [ X ] Lq ，X Uq ](X Lq And X Uq Are respectively the same as X L And X U ) Recording how many data among the K individual performance data fall within a performance random variable confidence interval [ X ] Lq ，X Uq ]In addition, and thus obtaining that the performance data falls within a performance random variable confidence interval [ X ] Lq ，X Uq ]Other q-th frequency value lambda q Where X is Lq And X Uq Lower and upper bound values, respectively, with the number q =1,2,3,…,7；
ii) after obtaining K individual performance data when the running performance of the rolling bearing is in the best period, pausing the test, taking out the rolling bearing, constructing a fault when the performance is failed on the rolling surface of the raceway, namely corroding 3 small and visible spots on the rolling surface of the raceway at angles of 120 degrees at intervals along the circumferential direction by using an acidic substance, simulating the fault when the performance is failed, and detecting the rolling bearing with the fault when the simulated performance is failed to obtain W individual performance failure data when the performance is failed;
iii) Recording how many data in the W individual performance failure data fall within the performance random variable confidence interval [ X ] Lq ，X Uq ]And obtaining therefrom a confidence interval [ X ] that the performance failure data falls within the performance random variable Lq ，X Uq ]Other q-th frequency value beta q Where X is Lq And X Uq The serial numbers q =1,2,3, …,7 are respectively a lower bound value and an upper bound value;
iv) according to formula d q ＝{[exp(-β q )-exp(-λ q )]/exp(-λ q ) Maintaining relative reliability d of rolling bearing performance when computation performance of 100% fails q Obtaining the qth d q Value, here λ q For performance data falling within a performance random variable confidence interval [ X ] Lq ，X Uq ]Q-th frequency value, beta q For the performance failure data falling within the performance random variable confidence interval [ X ] Lq ，X Uq ]The q-th frequency value from the series q =1,2,3, …,7; from 7 d q The one with the index q of less than and closest to-10% of the values is selected, and the corresponding confidence measure P is assigned q* The confidence P is determined in advance through a performance test based on a small probability event principle; the confidence P =0.99 obtained in this example;
4) According to the Poisson counting process, acquiring the frequency of the performance data falling outside a performance random variable confidence interval;
record how many of the 20000 data fall within the X confidence interval [ X ] of the random variable of friction torque L ，X U ]Besides, the friction torque is obtainedThe data falls in a confidence interval [ X ] of a friction torque random variable X L ，X U ]Frequency λ outside:
in the formula (6), lambda is the confidence interval [ X ] of the performance data falling in the performance random variable X L ，X U ]Outside frequencies, n is the confidence interval [ X ] that the performance data falls within the performance random variable X L ，X U ]The number of the other, K is the number of the performance data;
5) According to the non-failure probability of the Poisson counting process, obtaining the performance maintaining reliability of the rolling bearing from the frequency of the performance data falling outside the performance random variable confidence interval, and obtaining the time history of the performance maintaining reliability R (t) of the friction torque performance of the rolling bearing;
the reliability of rolling bearing performance maintenance is R (t):
R(t)＝exp(-λt)；t≥1 (7)，
in the formula (7), t is time, and t is more than or equal to 1; r (t) is the reliability of the performance maintenance of the rolling bearing at the time t and is used for representing the possibility that the rolling bearing can maintain the optimal performance potential during the operation at the time t; lambda is the confidence interval [ X ] that the performance data falls in the performance random variable X L ，X U ]A frequency other than the frequency;
6) According to a relative error concept of a measurement theory, acquiring performance maintaining relative reliability of the rolling bearing in future time, and acquiring a time history of maintaining relative reliability d (t) of friction torque of the rolling bearing;
the performance of the rolling bearing at the future time keeps relative reliability d (t):
in the formula (8), R (1) is the rolling bearing performance retention reliability at the current time t =1; t is future time, t >1; r (t) is the reliability of the rolling bearing performance at the future time t; d (t) is the relative reliability of the performance of the rolling bearing, and is used for representing the failure degree of the rolling bearing in the best performance potential state during the future time t;
the time history of the relative reliability d (t) of the friction torque maintaining of the rolling bearing is shown in FIG. 3;
7) According to the significance hypothesis testing principle and the measurement theory, the operation performance of the rolling bearing is divided into 4 levels including S1, S2, S3 and S4:
s1: the performance of the rolling bearing keeps the relative reliability d (t) more than or equal to 0 percent, namely the running performance of the rolling bearing at the future time t reaches the best, and the best performance potential state almost has no possibility of failure;
s2: the performance of the rolling bearing keeps relative reliability d (t) E [ -5%, 0%), namely the running performance of the rolling bearing at the future time t is normal, and the possibility of potential failure of the optimal performance is low;
s3: the performance of the rolling bearing keeps relative reliability d (t) E < -10%, -5%), namely the running performance of the rolling bearing at the future time t is deteriorating, and the possibility of failure of the optimal performance potential state is increasing;
s4: the performance of the rolling bearing keeps the relative reliability d (t) < -10 percent, namely the running performance of the rolling bearing at the future time t is deteriorated, and the possibility of potential failure of the optimal performance is increased;
8) According to the 4 grades of the rolling bearing operation performance grading, the time history for predicting the potential failure degree of the optimal performance of the rolling bearing is as follows:
in fig. 3, when t =6, d (t) = -4.43% ∈ [ -5%, 0%), and the value of d (t) approaches-5%;
when t =7, d (t) = -5.29% ∈ [ -10%, -5%), d (t) already being less than-5%;
when t =12, d (t) = -9.47% ∈ [ -10%, -5%), the value of d (t) approaches-10%;
when t =13, d (t) = -10.29% < -10%, the value of d (t) is already less than-10%.
Predicting the failure degree of the rolling bearing for keeping the optimal performance potential in the future according to the contents:
therefore, the running performance of the rolling bearing is normal by the 6 th year, and the possibility of potential failure of the optimal performance of the friction torque is low; the running performance of the rolling bearing is deteriorating and the potential failure of the friction torque optimum performance is increasing from 7 years later to 12 years earlier; until 13 th year, the running performance of the rolling bearing is deteriorated, and the possibility of potential failure of the optimum performance of the friction torque is high.
According to the time history, intervention measures should be taken between the 12 th year and the 13 th year to maintain or replace the rolling bearing, so that serious safety accidents caused by potential failure of the best performance of the friction torque of the bearing are avoided.
Example 2
The method for predicting the performance retention reliability of the rolling bearing of embodiment 2 comprises the following steps:
1) In the period of optimal running performance of the rolling bearing, periodically measuring the vibration acceleration of the rolling bearing in the evaluation time interval by using a measuring system, and acquiring K individual performance data of the vibration acceleration at the current time t =1, wherein K =20000 and K individual performance data is x k K =1,2, …,20000, data unit is μm/s 2 (ii) a The obtained vibration acceleration data distribution diagram of the rolling bearing is shown in FIG. 4;
in this example 2, the evaluation time interval is 1 year, each prediction time interval is 1 year, and the unit of time t is year; predicting the time history of the failure degree of the vibration acceleration performance of the rolling bearing in the future time by adopting the prediction method of the performance maintaining reliability of the rolling bearing;
2) Constructing a performance sample density function p (x) by using the performance data obtained in the step 1) according to the maximum entropy principle:
in the formula (1), x is a performance random variable for describing the performance of the rolling bearing; m is the highest origin moment order(ii) a i is the origin moment order; lambda [ alpha ] 0 ，λ 1 ，…，λ m Is a Lagrange multiplier, and has a first Lagrange multiplier lambda 0 Comprises the following steps:
in the formula (2), x is a performance random variable for describing the performance of the rolling bearing; s. the 1 A lower bound value of a feasible domain of a performance random variable x; s. the 2 The performance random variable x is the upper bound value of the feasible region; i is the origin moment order; lambda [ alpha ] i For the ith Lagrangian multiplier, lagrangian multiplier λ 1 ，λ 2 ，…，λ m Obtained from the m equation sets of equation (3):
in the formula (3), x is a performance random variable for describing the performance of the rolling bearing; x is a radical of a fluorine atom k K is the kth individual performance data, K represents the serial number of the performance data, and K is the number of the performance data; s 1 Is the lower bound value, S, of the feasible domain of the performance random variable x 2 The performance random variable x is the upper bound value of the feasible region; i and j are both the order of origin moment, m is the highest order of origin moment, λ i Is the ith Lagrangian multiplier;
constructing a vibration acceleration sample density function p (x) by using 20000 vibration acceleration performance data obtained in the step 1), wherein the result is shown in figure 5;
3) Obtaining confidence coefficient according to a small probability event principle, and obtaining a confidence interval of the performance random variable by using a quantile method;
according to the principle of small probability event, the confidence coefficient P =0.99 is obtained in advance through experiments, and the confidence interval [ X ] of the vibration acceleration random variable X can be calculated L ，X U ]＝[-0.0549μm/s 2 ，0.0692μm/s 2 ]：
Lower bound value X L The following equation (4) was used to determine:
upper bound value X U The following equation (5) is used to determine:
in the formulas (4) and (5), x is a performance random variable for describing the performance of the rolling bearing; s 1 A lower bound value of a feasible domain of a performance random variable x; s. the 2 The performance random variable x is the upper bound value of the feasible region; [ X ] L ，X U ]A confidence interval of a performance random variable x; p (x) is a performance sample density function; p is a confidence coefficient;
the confidence P is determined in advance through a performance test according to a small probability event principle, and the specific method is the same as that of the embodiment 1; the confidence P =0.99 obtained in this example;
4) According to the Poisson counting process, acquiring the frequency of the performance data falling outside a performance random variable confidence interval;
record how many of the 20000 data fall within the vibration acceleration random variable X confidence interval [ X [ ] L ，X U ]Besides, acquiring that the vibration acceleration data falls in a vibration acceleration random variable X confidence interval [ X ] L ，X U ]Frequency of the outer part λ:
in the formula (6), λ is the confidence interval [ X ] of the performance data falling in the performance random variable X L ，X U ]Outside frequencies, n is the confidence interval [ X ] that the performance data falls within the performance random variable X L ，X U ]The number of the other, K is the number of the performance data;
5) According to the non-failure probability of the Poisson counting process, obtaining the performance maintaining reliability of the rolling bearing from the frequency of the performance data falling outside the performance random variable confidence interval, and obtaining the time history of the performance maintaining reliability R (t) of the vibration acceleration of the rolling bearing;
the reliability of rolling bearing performance maintenance is R (t):
R(t)＝exp(-λt)；t≥1 (7)，
in the formula (7), t is time, and t is more than or equal to 1; r (t) is the reliability of the performance maintenance of the rolling bearing at the time t and is used for representing the possibility that the rolling bearing can maintain the optimal performance potential during the operation at the time t; lambda is the confidence interval [ X ] that the performance data falls in the performance random variable X L ，X U ]A frequency other than the frequency;
6) According to a relative error concept of a measurement theory, acquiring the performance maintaining relative reliability of the rolling bearing at the future time, and acquiring the time history of the vibration acceleration maintaining relative reliability d (t) of the rolling bearing;
the performance of the rolling bearing at the future time keeps relative reliability d (t):
in the formula (8), R (1) is the rolling bearing performance retention reliability at the current time t =1; t is future time, t >1; r (t) is the reliability of the rolling bearing performance at the future time t; d (t) is the relative reliability of the performance of the rolling bearing, and is used for representing the failure degree of the rolling bearing in the best performance potential state during the future time t;
the time history of the vibration acceleration of the rolling bearing maintaining the relative reliability d (t) is shown in FIG. 6;
7) According to the significance hypothesis testing principle and the measurement theory, the operation performance of the rolling bearing is divided into 4 levels including S1, S2, S3 and S4:
s1: the performance of the rolling bearing keeps the relative reliability d (t) more than or equal to 0 percent, namely the running performance of the rolling bearing at the future time t reaches the best, and the best performance potential state almost has no possibility of failure;
s2: the performance of the rolling bearing keeps relative reliability d (t) within the range of-5 percent and 0 percent, namely the running performance of the rolling bearing at the future time t is normal, and the possibility of potential failure of the optimal performance is low;
s3: the performance of the rolling bearing keeps relative reliability d (t) E < -10%, -5%), namely the running performance of the rolling bearing at the future time t is deteriorating, and the possibility of failure of the optimal performance potential state is increasing;
s4: the performance of the rolling bearing keeps the relative reliability d (t) < -10 percent, namely the running performance of the rolling bearing at the future time t is deteriorated, and the possibility of potential failure of the optimal performance is increased;
8) According to the 4 grades of the rolling bearing operation performance grading, the time history for predicting the potential failure degree of the optimal performance of the rolling bearing is as follows:
in fig. 6, when t =6, d (t) = -4.66% ∈ [ -5%, 0%), the value of d (t) is very close to-5%;
when t =7, d (t) = -5.57% ∈ 10%, -5%), d (t) is already less than-5%;
when t =12, d (t) = -9.97% ∈ [ -10%, -5%), the value of d (t) is very close to-10%;
when t =13, d (t) = -10.83% < -10%, the value of d (t) is already less than-10%.
And predicting the failure degree of the rolling bearing for keeping the optimal performance potential in the future according to the contents:
therefore, the running performance of the rolling bearing is normal by the 6 th year, and the possibility of potential failure of the optimal performance of the vibration acceleration is low; the running performance of the rolling bearing is deteriorating and the potential failure of the optimum performance of the vibration acceleration is increasing from 7 years later to 12 years earlier; until 13 th year, the running performance of the rolling bearing is deteriorated, and the possibility of potential failure of the optimum performance of the vibration acceleration is high.
According to the time history, intervention measures should be taken between 12 th year and 13 th year to maintain or replace the rolling bearing, so that serious safety accidents caused by the potential failure of the best performance of the vibration acceleration of the bearing are avoided.
The performance of the rolling bearing comprises vibration, noise, friction torque, temperature rise, rotation precision and the like, and all the performances can be subjected to performance maintaining reliability prediction by adopting the technical scheme of the invention. In other embodiments of the invention, the method for predicting the performance maintaining reliability of the rolling bearing is adopted to maintain the relative reliability according to the performances of noise, temperature rise, rotation precision and the like, and predict the failure degree of the rolling bearing for maintaining the optimal performance potential in the future time; the specific procedure was the same as in example 1.
When the intervention measures are carried out according to the prediction results of the technical scheme of the invention, if the critical time of the prediction results of different performances of the same rolling bearing is different, the intervention measures are taken before the shortest critical time.
Claims (10)
1. A method for predicting the performance retention reliability of a rolling bearing, characterized by: comprises the following steps:
1) Measuring the performance of the rolling bearing to obtain performance data when the running performance of the rolling bearing is optimal;
2) Constructing a performance sample density function by using the performance data obtained in the step 1) according to a maximum entropy principle;
3) Obtaining confidence coefficient according to a small probability event principle, and obtaining a confidence interval of the performance random variable by using a quantile method;
4) According to the Poisson counting process, acquiring the frequency of the performance data falling outside a performance random variable confidence interval;
5) According to the non-failure probability of the Poisson counting process, the reliability of the performance maintenance of the rolling bearing is obtained from the frequency of the performance data falling outside the confidence interval of the performance random variable;
6) According to a relative error concept of a measurement theory, obtaining the performance maintaining relative reliability of the rolling bearing in the future time, and predicting the failure degree of the rolling bearing for maintaining the optimal performance potential state in the future time according to the performance maintaining relative reliability;
the step 3) of determining the confidence level comprises the following steps:
i) Selecting the same rolling bearing in advance for performance test, and testing the rolling bearing when the running performance is at the bestDetecting to obtain K which is more than or equal to 1000 performance data, wherein K is the number of the performance data; constructing a performance sample density function p (x) by using the K individual performance data; selecting a confidence estimate P q Respectively sequentially obtaining 7 values of 1, 0.999, 0.99, 0.95, 0.9, 0.85 and 0.8, and determining the corresponding P value by quantile method q Q-th individual-performance random variable confidence interval [ X ] Lq ，X Uq ]Recording how many data among the K individual performance data fall within a performance random variable confidence interval [ X ] Lq ，X Uq ]In addition, and thus obtaining that the performance data falls within a performance random variable confidence interval [ X ] Lq ，X Uq ]Other q-th frequency value lambda q Where X is Lq And X Uq The serial numbers q =1,2,3, …,7 are respectively a lower bound value and an upper bound value;
ii) continuing to perform the performance test and detection of the rolling bearing until the performance is invalid, and acquiring W which is more than or equal to 1000 performance invalid data when the performance is invalid, wherein W is the number of the performance invalid data; or after the rolling bearing operation performance is in the best period and K individual performance data is obtained, pausing the test, taking out the rolling bearing, constructing a fault when the performance is invalid on the rolling surface of a raceway of the rolling bearing, simulating the fault when the performance is invalid, and detecting the rolling bearing with the fault when the simulated performance is invalid to obtain W individual performance invalid data when the performance is invalid;
iii) Recording how many data in the W individual performance failure data fall within the performance random variable confidence interval [ X ] Lq ，X Uq ]Out of, and thus obtaining that the performance failure data falls within a performance random variable confidence interval [ X ] Lq ，X Uq ]Other q-th frequency value beta q Where X is Lq And X Uq The serial numbers q =1,2,3, …,7 are respectively a lower bound value and an upper bound value;
iv) according to formula d q ＝{[exp(-β q )-exp(-λ q )]/exp(-λ q ) Maintaining relative reliability d of rolling bearing performance when computation performance of 100% fails q Obtaining the qth d q Value, here λ q For performance data falling within a performance random variable confidence interval [ X ] Lq ，X Uq ]Q-th frequency value, beta q For the performance failure data falling within the performance random variable confidence interval [ X ] Lq ，X Uq ]The q-th frequency value from the series q =1,2,3, …,7; from 7 d q The one with the index q of less than and closest to-10% of the values is selected, and the corresponding confidence measure P is assigned q* Is the confidence of the determination.
2. The rolling bearing performance retention reliability prediction method according to claim 1, characterized in that: the performance data obtained in the step 1) refers to performance data of a rolling bearing running in an evaluation time interval, wherein the evaluation time interval refers to a time interval after the running-in period of the rolling bearing is ended, and the end time of the evaluation time interval is the current time; and (3) a time interval after the evaluation time interval is called a prediction time interval, each prediction time interval has the same time span with the evaluation time interval, and the end time of the prediction time interval is the future time in the step 6).
3. The prediction method of the rolling bearing performance retention reliability according to claim 1 or 2, characterized in that: k performance data for constructing a performance sample density function, and x individual performance data k ，k＝1，2，…，K；K≥1000；
The performance sample density function is p (x):
in the formula (1), x is a performance random variable for describing the performance of the rolling bearing; m is the highest origin moment order; i is the origin moment order; lambda [ alpha ] 0 ，λ 1 ，…，λ m Is a Lagrange multiplier, and has a first Lagrange multiplier lambda 0 Comprises the following steps:
in the formula (2), x is the description of scrollingRandom variation in performance of bearing performance; s 1 A lower bound value of a feasible domain of a performance random variable x; s 2 The performance random variable x is the upper bound value of the feasible region; i is the origin moment order; lambda [ alpha ] i For the ith Lagrangian multiplier, lagrangian multiplier λ 1 ，λ 2 ，…，λ m Obtained from the m equation sets of equation (3):
in the formula (3), x is a performance random variable for describing the performance of the rolling bearing; x is a radical of a fluorine atom k The performance data is kth individual performance data, K represents the serial number of the performance data, and K is the number of the performance data; s 1 Is the lower bound value, S, of the feasible region of the performance random variable x 2 The performance random variable x is the upper bound value of the feasible region; i and j are both the order of origin moment, m is the highest order of origin moment, λ i Is the ith lagrange multiplier.
4. The rolling bearing performance retention reliability prediction method according to claim 1, characterized in that: in step 3), the confidence interval of the random variable of the performance is [ X ] L ，X U ]Lower bound value X L The following equation (4) is used to determine:
upper bound value X U The following equation (5) is used to determine:
in the formulas (4) and (5), x is a performance random variable for describing the performance of the rolling bearing; s. the 1 A lower bound value of a feasible domain of a performance random variable x; s 2 The performance random variable x is the upper bound value of the feasible region; [ X ] L ，X U ]A confidence interval of a performance random variable x; p (x) is a performance sample density function; p isAnd (7) reliability.
5. The rolling bearing performance retention reliability prediction method according to claim 1 or 4, characterized in that: in step 4), the frequency of the performance data falling outside the confidence interval of the performance random variable is lambda:
in the formula (6), lambda is the confidence interval [ X ] of the performance data falling in the performance random variable X L ，X U ]Outside frequencies, n is the confidence interval [ X ] that the performance data falls within the performance random variable X L ，X U ]The number of the other, K, is the number of the performance data.
6. The rolling bearing performance retention reliability prediction method according to claim 5, characterized in that: in the step 5), the reliability of the rolling bearing performance is R (t):
R(t)＝exp(-λt)；t≥1 (7)，
in the formula (7), t is time, and t is more than or equal to 1; r (t) is the reliability of the performance maintenance of the rolling bearing at the time t and is used for representing the possibility that the rolling bearing can maintain the optimal performance potential during the operation at the time t; lambda is the confidence interval [ X ] that the performance data falls in the performance random variable X L ，X U ]And (c) other frequencies.
7. The method of predicting the rolling bearing performance retention reliability according to claim 6, characterized in that: step 6), the performance of the rolling bearing in the future keeps the relative reliability d (t):
in the formula (8), R (1) is the rolling bearing performance retention reliability at the current time t =1; t is future time, t >1; r (t) is the reliability of the rolling bearing performance at the future time t; d (t) is the relative reliability of the rolling bearing performance, and is used for representing the failure degree of the rolling bearing in the best performance potential state during the future time t.
8. The rolling bearing performance retention reliability prediction method according to claim 7, characterized in that: in step 6), the method for predicting the failure degree of the rolling bearing for keeping the optimal performance potential in the future time according to the relative reliability of the performance maintenance comprises the following steps: grading the running performance of the rolling bearing according to a significance hypothesis testing principle and a measurement theory; and predicting the time history of the potential failure degree of the optimal performance of the rolling bearing according to the rolling bearing operation performance grading.
9. The rolling bearing performance retention reliability prediction method according to claim 8, characterized in that: the classification of the running performance of the rolling bearing refers to that the running performance of the rolling bearing is divided into 4 grades of S1, S2, S3 and S4:
s1: the performance of the rolling bearing keeps the relative reliability d (t) more than or equal to 0 percent, namely the running performance of the rolling bearing at the future time t reaches the best, and the best performance potential state almost has no possibility of failure;
s2: the performance of the rolling bearing keeps relative reliability d (t) within the range of-5 percent and 0 percent, namely the running performance of the rolling bearing at the future time t is normal, and the possibility of potential failure of the optimal performance is low;
s3: the performance of the rolling bearing keeps relative reliability d (t) E < -10%, -5%), namely the running performance of the rolling bearing at the future time t is deteriorating, and the possibility of failure of the optimal performance potential state is increasing;
s4: the performance of the rolling bearing keeps the relative reliability d (t) < -10%, namely the running performance of the rolling bearing at the future time t is deteriorated, and the possibility of potential failure of the optimal performance is increased.
10. The rolling bearing performance retention reliability prediction method according to claim 9, characterized in that: the future time t corresponding to the rolling bearing performance keeping relative reliability d (t) = -10% is the critical time of the rolling bearing performance deterioration, and before the critical time comes, intervention measures are taken for avoiding serious safety accidents caused by potential failure of the rolling bearing optimal performance.
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