CN105224792B - A kind of rolling bearing performance keeps the Forecasting Methodology of reliability - Google Patents

Abstract

The invention discloses a method for predicting the performance maintenance reliability of a rolling bearing, which includes acquiring performance data and constructing a performance sample density function during the best period of rolling bearing operating performance; obtaining the confidence degree and the confidence interval of performance random variables according to the principle of small probability events; According to the Poisson counting process, the frequency of the performance data falling outside the confidence interval of the performance random variable and the reliability of the rolling bearing performance are obtained, and then the relative reliability of the rolling bearing performance in the future is obtained, and the rolling bearing is predicted to maintain the best future time. The degree of failure of the performance posture. This method does not require any prior information of the performance density function, nor does it need to set the performance threshold in advance. It can predict the failure degree of the optimal operating performance situation of rolling bearings in the future, with high prediction accuracy, and can detect failure hazards in advance, so as to take timely intervention measures , Provide decision-making to avoid serious safety accidents.

Description

A Prediction Method for Rolling Bearing Performance Retention Reliability

technical field

The invention belongs to the technical field of rolling bearing service performance failure evaluation and performance reliability prediction, and in particular relates to a prediction method for rolling bearing performance maintenance reliability.

Background technique

Rolling bearing is a precision mechanical element that changes the sliding friction between the running shaft and the shaft seat into rolling friction, thereby reducing friction loss. Rolling bearings are generally composed of inner rings, outer rings, rolling elements and cages. The function of the inner ring is to cooperate with the shaft and rotate together with the shaft; the function of the outer ring is to cooperate with the bearing seat to play a supporting role; Roll between the ring and the outer ring to bear and transmit the load; the cage can evenly distribute the rolling elements, prevent the rolling elements from falling off and collide with each other, guide the rolling elements to rotate and improve the internal lubrication of the bearing.

Rolling bearings are one of the most important components in mechanical transmission systems, and are widely used in aerospace, ships, automobiles, and rail transit. Rolling bearings are also the easily damaged parts of the mechanical system and need regular maintenance and replacement. The maintenance and replacement of rolling bearings usually requires the disassembly and assembly of the entire mechanical system. The time, manpower and material resources consumed in the disassembly process are usually hundreds of times the cost of the bearing itself. However, untimely maintenance and replacement may cause the entire system to fail to work due to bearing failure, resulting in greater economic losses and even endangering the lives of operators. Therefore, accurate prediction of service life according to specific working conditions and bearing parameters can greatly reduce excessive maintenance, reduce its use cost and maintenance cost, and play a very important role in industrial production and technological development.

The performance of rolling bearings mainly includes vibration, noise, friction torque, temperature rise, rotation accuracy, etc. These properties have an important impact on the operation performance of mechanical systems. The performance failure of rolling bearings refers to the phenomenon that rolling bearings lose their operating performance or fail to work normally due to poor lubrication, friction and wear, damage, adhesion, corrosion, deformation and other failures of internal parts during operation. Rolling bearings maintain the best performance status operation, which is the basis for the mechanical system to achieve the best performance status operation. According to the stochastic process theory, the reliability of the rolling bearing to maintain the best performance state of operation will change in the future, which will increase the possibility of endangering the safe and reliable operation of the mechanical system. Therefore, it is of great application value to study the performance maintenance reliability of rolling bearings.

Generally speaking, the performance failure test of rolling bearings refers to: according to a certain standard, such as national standards or industry standards, a certain number of samples are randomly selected from a batch of rolling bearings, and then the samples are placed in the same test environment for reliability testing. Complete life test to obtain the life of each failed sample, and finally process the test data according to the standard GB/T24607-2009, and give the reliability indicators such as the shape parameters b, L10, characteristic life and average life of the rolling bearing. Reliability evaluation or analysis of batch bearings. However, due to the improvement of the quality of rolling bearings, it is unrealistic and unnecessary to make every sample fail during the reliability test; it is unrealistic to conduct complete tests on some expensive and small number of rolling bearings.

Existing performance reliability evaluation and prediction methods obtain performance reliability based on the prior assumption that the performance density function, performance degradation trajectory and performance failure threshold are known, and have achieved certain results. Among the existing reliability assessment methods, "Acta Astronautica Sinica" published an article entitled "Reliability Assessment Based on Performance Degradation Data" in Issue 3, 2006. This article assumes that the performance degradation trajectory is a linear function of time, considering the performance degradation value Obeying the normal distribution and given the threshold, the reliability evaluation of aerospace system performance degradation can be carried out. Among the existing methods for evaluating the reliability of rolling bearing performance, CN104318043A discloses a method for detecting the variation process of the vibration performance reliability of rolling bearings. This method relies on the time series counting process to obtain the variation intensity of the bearing vibration in a short time interval. A very small amount of original information; through self-service re-sampling of the original information of the variation intensity, a large amount of generated information of the variation intensity is simulated; the gray prediction model is used to process the generated information to obtain the estimated value of the variation intensity; the Poisson process is used to characterize the reliability function and predict in real time Variation process of bearing vibration performance reliability. Based on the time series of vibration information, the method integrates the gray bootstrap principle into the Poisson process, and proposes the gray bootstrap Poisson method to predict the variation process of the performance reliability of rolling bearings. However, this method requires a prior performance test to obtain a performance threshold, which is obtained through experiments, and the corresponding threshold is different according to the selected damage site and sensor. Therefore, in the existing reliability assessment methods, when the prior information of the performance density function is unknown and the performance threshold is not set in advance, it is impossible to predict the variation process of the performance reliability of the rolling bearing.

Contents of the invention

The purpose of the present invention is to provide a method for predicting the reliability of rolling bearing performance retention, which solves the problem of predicting the reliability of rolling bearing performance retention when the prior information of the performance density function is unknown and the performance threshold is not set in advance.

In order to achieve the above object, the technical solution adopted in the present invention is:

A method for predicting the performance maintenance reliability of rolling bearings, comprising the following steps:

1) Measure the performance of rolling bearings and obtain performance data during the period when the rolling bearings have the best operating performance;

2) According to the principle of maximum entropy, use the performance data obtained in step 1) to construct a performance sample density function;

3) Obtain the confidence degree according to the principle of small probability events, and use the quantile method to obtain the confidence interval of the performance random variable;

4) According to the Poisson counting process, the frequency at which the performance data falls outside the confidence interval of the performance random variable is obtained;

5) According to the non-failure probability of the Poisson counting process, the reliability of rolling bearing performance is obtained from the frequency that the performance data falls outside the confidence interval of the performance random variable;

6) According to the relative error concept of the measurement theory, the relative reliability of the performance of the rolling bearing in the future time is obtained, and the failure degree of the rolling bearing to maintain the best performance situation in the future is predicted according to the relative reliability of the performance maintenance.

The performance data obtained in step 1) refers to the performance data of the rolling bearing running in the evaluation time interval, and the evaluation time interval refers to a time interval after the running-in period of the rolling bearing ends, and the end time of the evaluation time interval is the current time, t=1 ; The time interval after the evaluation time interval is called the prediction time interval, t>1, each prediction time interval has the same time span as the evaluation time interval, and the end time of the prediction time interval is the future time described in step 6) . For each additional prediction time interval, the future time t is increased by 1; the unit of time t is the same as that of the evaluation time interval.

The evaluation time interval is in the best period of rolling bearing operation performance, which means that the rolling bearing operation performance situation is the best in this time interval; during the rolling bearing operation performance best period, the rolling bearing operation maintains the best performance situation, which means that there is almost no performance. Probability of failure; this period is usually located in the immediate time interval after the end of the running-in period of the rolling bearing.

The performance of rolling bearings mainly includes vibration, noise, friction torque, temperature rise, rotation accuracy, etc. In step 1), during the period when the rolling bearing has the best operating performance, a certain performance of the rolling bearing is regularly measured by the measurement system, and then the time history of the failure degree of the rolling bearing's performance in the future is predicted.

There are K performance data for constructing the performance sample density function, and the kth performance data is x _k , k=1, 2, ..., K; K≥1000;

The performance sample density function is p(x):

In formula (1), x is the performance random variable describing the performance of the rolling bearing; m is the highest origin moment order; i is the origin moment order; λ ₀ , λ ₁ ,…, λ _m are Lagrangian multipliers, and There is a first Lagrangian multiplier λ ₀ as:

In formula (2), x is the performance random variable describing the performance of the rolling bearing; S ₁ is the lower bound value of the performance random variable x feasible region; S ₂ is the upper bound value of the performance random variable x feasible region; i is the origin moment order; λ _i is the i-th Lagrangian multiplier, and the Lagrangian multipliers λ ₁ , λ ₂ ,..., λ _m are obtained from the m equations in formula (3):

In formula (3), x is the performance random variable describing the performance of the rolling bearing; x _k is the kth performance data, k represents the serial number of the performance data, and K is the number of performance data; S ₁ is the lower bound of the feasible region of the performance random variable x value, S ₂ is the upper bound value of the feasible region of the performance random variable x; i and j are the order of the origin moment, m is the highest order of the origin moment, and λ _i is the i-th Lagrangian multiplier.

In step 3), the confidence degree is a characterization of the probability of occurrence of the best operating performance situation inherent in the overall performance of the rolling bearing, and its acquisition method is: according to the statistical small probability event principle, the significance level can be 0-0.2, Such as 0.01, 0.05, 0.1, etc., the corresponding confidence level is 1~0.8, such as 0.99, 0.95, 0.9, etc.; the value of the confidence level is based on the principle of small probability events, determined through performance tests in advance, and represents the overall performance of the rolling bearing. The probability of occurrence of an inherently optimal operating performance situation.

The confidence P is based on the principle of small probability events and is determined through performance tests in advance. The specific method includes the following steps:

i) Select the same type of rolling bearing for performance test in advance, and test it when the rolling bearing’s running performance is at its best, and obtain K≥1000 performance data, where K is the number of performance data; use K performance data to construct a performance sample density function p(x ); select the 7 values of the confidence estimate P _q as 1, 0.999, 0.99, 0.95, 0.9, 0.85, 0.8, etc., and use the quantile method to find the qth performance random variable confidence interval corresponding to P _q [X _Lq , X _Uq ], record how many data among the K performance data fall outside the performance random variable confidence interval [X _Lq , X _Uq ], and thus obtain the performance data that falls within the performance random variable confidence interval [ The qth frequency value λ _q other than X _Lq , X _Uq ], where X _Lq and X _Uq are respectively the lower bound value and the upper bound value, and the serial number q=1,2,3,...,7;

ii) Continue to conduct the rolling bearing performance test and inspection until the performance fails, and obtain W≥1000 performance failure data when the performance fails, and W is the number of performance failure data; or, obtain K performance failure data when the rolling bearing operating performance is at its best. After the data is collected, the test is suspended, the rolling bearing is taken out, and the fault at the time of performance failure is constructed on the rolling surface of the raceway, and the fault at the time of performance failure is simulated. W performance failure data of W;

iii) Record how many of the W performance failure data fall outside the performance random variable confidence interval [X _Lq , X _Uq ], and thus obtain the performance failure data that fall within the performance random variable confidence interval [X _Lq , X The qth frequency value β _q other than _Uq ], where X _Lq and X _Uq are respectively the lower bound value and the upper bound value, and the serial number q=1,2,3,...,7;

iv) According to the formula d _q ={[exp(-β _q )-exp(-λ _q )]/exp(-λ _q )}×100%, calculate the relative reliability d _q of rolling bearing performance when the performance fails, and obtain the first q d _q values, where λ _q is the qth frequency value of the performance data falling outside the performance random variable confidence interval [X _Lq , X _Uq ], β _q is the performance failure data falling within the performance random variable confidence interval [X _Lq , X _Uq ], the qth frequency value other than q=1,2,3,…,7; pick the one that is less than and closest to -10% from the 7 d _q values, and mark its subscript q is q*, and the corresponding confidence estimate P _q* is the confidence P determined in advance through performance tests based on the principle of small probability events.

In the above method, the calculation methods of X _Lq and X _Uq in step i) are the same as X _L and X _U respectively; in step ii), the failure method when the performance failure is constructed on the rolling surface is to use acidic substances on the rolling surface of the raceway A total of 3 small spots visible to the naked eye were corroded at an angle of 120 degrees along the circumferential direction, simulating the failure of performance failure.

In step 3), the confidence interval of the performance random variable is [X _L , X _U ], and the lower bound value X _L is obtained by formula (4):

The upper limit value X _U is obtained by formula (5):

In formula (4) and formula (5), x is the performance random variable describing the performance of the rolling bearing; S ₁ is the lower bound value of the performance random variable x feasible domain; S ₂ is the upper bound value of the performance random variable x feasible domain; [X _L , X _U ] is the confidence interval of the performance random variable x; p(x) is the performance sample density function; P is the confidence degree.

According to the Poisson counting process, record how many data among the K performance data fall outside the confidence interval [X _L , X _U ] of the performance random variable x, and thus obtain the performance data falling within the confidence interval of the performance random variable x Frequency λ other than [X _L , X _U ].

In step 4), the frequency of the performance data falling outside the confidence interval of the performance random variable is λ:

In formula (6), λ is the frequency of the performance data falling outside the performance random variable x confidence interval [X _L , X _U ], n is the performance data falling outside the performance random variable x confidence interval [X _L , X _U ] K is the number of performance data.

In the prediction method of the present invention, the performance maintenance reliability of the rolling bearing refers to the possibility that the rolling bearing can maintain the best performance state during the test and service period. Performance maintaining reliability is expressed as a function, and the specific value of this function is called performance maintaining reliability. That is, step 5) is to obtain the performance maintenance reliability function of the rolling bearing from the frequency at which the performance data falls outside the confidence interval of the performance random variable according to the failure-free probability of the Poisson counting process, and the specific value of this function is the performance maintenance reliability.

In step 5), the rolling bearing performance maintenance reliability is R(t):

R(t)=exp(-λt); t≥1 (7),

In formula (7), t is time, t≥1; R(t) is the reliability of rolling bearing performance at time t, which is used to represent the possibility that rolling bearing operation can maintain the best performance situation at time t; λ is performance data Frequency that falls outside the confidence interval [X _L , X _U ] for the performance random variable x.

In step 6), the relative reliability of rolling bearing performance in the future is d(t):

In formula (8), R(1) is the reliability of the rolling bearing performance at the current time t=1; t is the 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 it is used to characterize the failure degree of the rolling bearing running to maintain the best performance situation at the time t in the future.

In step 6), the method for predicting the failure degree of the rolling bearing to maintain the best performance situation in the future according to the relative reliability of performance maintenance includes: according to the significance hypothesis testing principle and measurement theory, the rolling bearing operating performance is classified; according to the rolling bearing operating performance classification, Prediction of the time history of the extent of failure for optimum performance in rolling bearings.

The basic principles of rolling bearing running performance classification are as follows:

a) According to the principle of significance hypothesis testing, if the relative reliability of rolling bearing performance is not less than 0%, it means that the predicted reliability of rolling bearing performance in the future is not lower than the reliability of rolling bearing performance in the current time. Reach the best situation; otherwise, it can be rejected that the running performance of the rolling bearing has reached the best situation;

b) When the relative reliability of the rolling bearing performance is kept less than 0%, according to the measurement theory, when the absolute value of the relative error is between (0%, 5%], the error of the measured value relative to the true value is very small, and the absolute value of the relative error is in ( 5%, 10%], the error of the measured value relative to the true value is becoming larger, and the error of the measured value relative to the true value becomes larger when the absolute value of the relative error is greater than 10%.

Based on the above-mentioned significant hypothesis testing principle and measurement theory, the running performance classification of rolling bearings is carried out.

The grading of the running performance of the rolling bearing refers to dividing the running performance of the rolling bearing into four levels: S1, S2, S3, and S4:

S1: The relative reliability of the rolling bearing performance maintenance d(t)≥0%, that is, the rolling bearing has the best operating performance at the future time t, and the best performance situation has almost no possibility of failure;

S2: The rolling bearing performance maintains a relative reliability d(t) ∈ [-5%, 0%), that is, the rolling bearing has normal operating performance at the time t in the future, and the possibility of failure of the best performance situation is small;

S3: Rolling bearing performance maintains relative reliability d(t) ∈ [-10%, -5%), that is, the running performance of rolling bearing at time t in the future is getting worse, and the possibility of failure of the best performance situation is increasing;

S4: The relative reliability of the rolling bearing performance maintenance d(t)<-10%, that is, the running performance of the rolling bearing becomes worse at the future time t, and the possibility of failure of the best performance situation becomes larger.

According to the above four grades of rolling bearing operating performance classification, the time history of the failure degree of the best performance situation of rolling bearings is predicted. The relative reliability of rolling bearing performance maintenance is actually the attenuation degree of the rolling bearing performance maintenance reliability in the future relative to the best performance situation at the current time. A negative value indicates attenuation, and a positive value indicates no attenuation. The smaller the relative reliability d(t) of the rolling bearing performance is, the worse the running performance of the rolling bearing becomes, and the greater the possibility of failure of the best performance situation becomes.

The future time t corresponding to the relative reliability d(t)=-10% of the rolling bearing performance is the critical time for the performance of the rolling bearing to deteriorate. Before the critical time arrives, intervention measures are taken to maintain or replace the rolling bearing. In order to avoid serious safety accidents caused by the failure of the best performance of rolling bearings.

The method for predicting the performance maintenance reliability of the rolling bearing of the present invention is completed under the support of the National Natural Science Foundation of China (51475144). The elements included in the prediction method are confidence level, confidence interval, performance maintenance reliability, and performance maintenance relative reliability. Among them, the confidence degree is a characterization of the probability of the best operating performance situation inherent in the overall performance of the rolling bearing; the confidence interval can represent the best performance situation that the rolling bearing can maintain during the test and service; the performance maintenance reliability indicates that the rolling bearing operation can maintain The possibility of the best performance situation; the relative reliability of performance maintenance is used to characterize the failure degree of rolling bearing operation to maintain the best performance situation in the future.

The method for predicting the reliability of rolling bearing performance maintenance in the present invention is to obtain performance data during the best period of rolling bearing operating performance, construct the performance sample density function, and obtain the confidence degree and the confidence interval of the performance random variable; according to the Poisson counting process, obtain the performance The frequency of the data falling outside the confidence interval of the performance random variable and the reliability of the performance of the rolling bearing are used to obtain the relative reliability of the performance of the rolling bearing in the future, and based on this, the degree of failure of the rolling bearing to maintain the best performance situation in the future is predicted. This method does not require any prior information of the performance density function, nor does it need to set the performance threshold in advance. It can predict the failure degree of the optimal operating performance situation of rolling bearings in the future, with high prediction accuracy, and can detect failure hazards in advance, so as to take timely intervention measures , Provide decision-making to avoid serious safety accidents. The method is a method for predicting reliability of rolling bearing test and performance maintenance during service with unknown prior information of performance density function and no need to set performance threshold in advance; Intervention measures should be taken to maintain or replace rolling bearings before major accidents, so as to avoid serious safety accidents.

Description of drawings

Fig. 1 is the data distribution diagram of rolling bearing friction moment in embodiment 1;

Fig. 2 is the density function graph of rolling bearing friction moment sample in embodiment 1;

Fig. 3 is the time course diagram of the relative reliability of the rolling bearing friction torque in embodiment 1;

Fig. 4 is the distribution diagram of vibration acceleration data of rolling bearing in embodiment 2;

Fig. 5 is the density function graph of the rolling bearing vibration acceleration sample in embodiment 2;

Fig. 6 is a time course diagram of the relative reliability of the vibration acceleration of the rolling bearing in the second embodiment.

Detailed ways

The present invention will be further described below in combination with specific embodiments.

In the specific embodiment, the time for regularly measuring the performance of the rolling bearing is carried out within a time interval after the end of the running-in period of the rolling bearing; the running performance of the rolling bearing is the best in this time interval, and this time interval is the evaluation time interval, and the end of the evaluation time interval Time is the current time, t=1. The future time when forecasting refers to the time interval after the evaluation time interval, which is called the prediction time interval, and t is increased by 1 for each additional prediction time interval. The unit of time t is the same as that of the evaluation time interval. For example, the regular measurement of rolling bearing performance starts from January 1, 2015 and ends on June 30, 2015, and it is necessary to predict the possibility of failure of the best performance situation of rolling bearings between January 1 and June 30, 2017. Here, the evaluation time interval is 0.5 years (from January 1, 2015 to June 30, 2015), the current time is t=1, the future time is t=1+4=5, a total of 4 prediction time interval, each prediction time interval is 0.5 years, and it is necessary to predict the possibility of failure of the best performance situation of rolling bearings in the fifth time interval (between January 1 and June 30, 2017). Here, five time intervals total 2.5 years, and the unit of time t is 0.5 years.

Example 1

The prediction method of the rolling bearing performance maintenance reliability of the present embodiment 1 comprises the following steps:

1) During the best period of rolling bearing operation performance, the friction torque of the rolling bearing in the evaluation time interval is regularly measured by the measurement system, and K performance data of the friction torque are obtained at the current time t=1, K=20000, the kth performance data is x _k , k=1, 2, ..., 20000, and the data unit is N m; the distribution diagram of the obtained rolling bearing friction torque data is shown in Figure 1;

In this embodiment 1, the evaluation time interval is 1 year, each prediction time interval is 1 year, and the unit of time t is year; the rolling bearing performance maintenance reliability prediction method of this embodiment is used to predict the failure of the rolling bearing friction torque performance the time course of the degree in a future time;

2) According to the principle of maximum entropy, use the performance data obtained in step 1) to construct the performance sample density function p(x):

In formula (1), x is the performance random variable describing the performance of the rolling bearing; m is the highest origin moment order; i is the origin moment order; λ ₀ , λ ₁ ,…, λ _m are Lagrangian multipliers, and There is a first Lagrangian multiplier λ ₀ as:

In formula (2), x is the performance random variable describing the performance of the rolling bearing; S ₁ is the lower bound value of the performance random variable x feasible region; S ₂ is the upper bound value of the performance random variable x feasible region; i is the origin moment order; λ _i is the i-th Lagrangian multiplier, and the Lagrangian multipliers λ ₁ , λ ₂ ,..., λ _m are obtained from the m equations in formula (3):

In formula (3), x is the performance random variable describing the performance of the rolling bearing; x _k is the kth performance data, k represents the serial number of the performance data, and K is the number of performance data; S ₁ is the lower bound of the feasible region of the performance random variable x value, S ₂ is the upper bound value of the performance random variable x feasible region; i and j are the order of the origin moment, m is the highest order of the origin moment, λ _i is the i-th Lagrangian multiplier;

Use the 20,000 friction torque performance data obtained in step 1) to construct the friction torque sample density function p(x), and the results are shown in Figure 2;

3) Obtain the confidence degree according to the principle of small probability events, and use the quantile method to obtain the confidence interval of the performance random variable;

According to the principle of small probability events, the confidence degree P=0.99 is obtained through experiments in advance, and the confidence interval of random variable x of friction torque can be calculated [X _L , X _U ]=[233.329N·m, 251.897N·m]:

The lower limit value X _L is obtained by formula (4):

The upper limit value X _U is obtained by formula (5):

In formula (4) and formula (5), x is the performance random variable describing the performance of the rolling bearing; S ₁ is the lower bound value of the performance random variable x feasible domain; S ₂ is the upper bound value of the performance random variable x feasible domain; [X _L , X _U ] is the confidence interval of the performance random variable x; p(x) is the performance sample density function; P is the degree of confidence;

Wherein, the confidence P is based on the principle of small probability events, and is determined through performance tests in advance, and the specific method is as follows:

i) Select the same type of rolling bearing for performance test in advance, and test it when the rolling bearing’s running performance is at its best, and obtain K≥1000 performance data, where K is the number of performance data; use K performance data to construct a performance sample density function p(x ); select the 7 values of the confidence estimate P _q as 1, 0.999, 0.99, 0.95, 0.9, 0.85, 0.8, etc., and use the quantile method to find the qth performance random variable confidence interval corresponding to P _q [X _Lq , X _Uq ] (the calculation methods of X _Lq and X _Uq are the same as X _L and X _U ), record how many of the K performance data fall in the performance random variable confidence interval [X _Lq , X _Uq ] , and thus obtain the qth frequency value λ _q of the performance data falling outside the performance random variable confidence interval [X _Lq , X _Uq ], where X _Lq and X _Uq are the lower and upper bound values respectively, and the serial number q=1,2,3,...,7;

ii) After obtaining K pieces of performance data when the running performance of the rolling bearing is at its best, suspend the test, take out the rolling bearing, and build a fault when the performance fails on the rolling surface of the raceway, that is, use an acidic substance on the rolling surface of the raceway A total of 3 small spots visible to the naked eye are corroded at an angle of 120 degrees along the circumferential direction to simulate the failure of the performance failure. performance failure data;

iii) Record how many of the W performance failure data fall outside the performance random variable confidence interval [X _Lq , X _Uq ], and thus obtain the performance failure data that fall within the performance random variable confidence interval [X _Lq , X The qth frequency value β _q other than _Uq ], where X _Lq and X _Uq are respectively the lower bound value and the upper bound value, and the serial number q=1,2,3,...,7;

iv) According to the formula d _q ={[exp(-β _q )-exp(-λ _q )]/exp(-λ _q )}×100%, calculate the relative reliability d _q of rolling bearing performance when the performance fails, and obtain the first q d _q values, where λ _q is the qth frequency value of the performance data falling outside the performance random variable confidence interval [X _Lq , X _Uq ], β _q is the performance failure data falling within the performance random variable confidence interval [X _Lq , X _Uq ], the qth frequency value other than q=1,2,3,…,7; pick the one that is less than and closest to -10% from the 7 d _q values, and mark its subscript q is q*, and the corresponding confidence estimate value P _q* is based on the principle of small probability events, the confidence P determined through performance tests in advance; the confidence P=0.99 obtained in this embodiment;

4) According to the Poisson counting process, the frequency at which the performance data falls outside the confidence interval of the performance random variable is obtained;

Record how many of the 20,000 data fall outside the confidence interval [X _L , X _U ] of the friction torque random variable x, and obtain the friction torque data that fall within the friction torque random variable x confidence interval [X _L , X _U ] Outer frequency λ:

In formula (6), λ is the frequency of the performance data falling outside the performance random variable x confidence interval [X _L , X _U ], n is the performance data falling outside the performance random variable x confidence interval [X _L , X _U ] K is the number of performance data;

5) According to the non-failure probability of the Poisson counting process, the performance maintenance reliability of the rolling bearing is obtained from the frequency at which the performance data falls outside the confidence interval of the performance random variable, and the time history of the friction torque performance maintenance reliability R(t) of the rolling bearing is obtained;

The rolling bearing performance maintenance reliability is R(t):

R(t)=exp(-λt); t≥1 (7),

In formula (7), t is time, t≥1; R(t) is the reliability of rolling bearing performance at time t, which is used to represent the possibility that rolling bearing operation can maintain the best performance situation at time t; λ is performance data Frequency that falls outside the confidence interval [X _L , X _U ] for the performance random variable x;

6) According to the relative error concept of the measurement theory, obtain the relative reliability of the performance of the rolling bearing in the future time, and obtain the time history of the relative reliability d(t) of the friction torque of the rolling bearing;

The performance of rolling bearings in the future maintains relative reliability as d(t):

In formula (8), R(1) is the reliability of the rolling bearing performance at the current time t=1; t is the 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, which is used to represent the failure degree of the rolling bearing running at the best performance state at the time t in the future;

The time course of the relative reliability d(t) of the friction torque of the rolling bearing is shown in Fig. 3;

7) According to the principle of significant hypothesis testing and measurement theory, the running performance of rolling bearings is divided into four levels: S1, S2, S3, and S4:

S1: The relative reliability of the rolling bearing performance maintenance d(t)≥0%, that is, the rolling bearing has the best operating performance at the future time t, and the best performance situation has almost no possibility of failure;

S2: The rolling bearing performance maintains a relative reliability d(t) ∈ [-5%, 0%), that is, the rolling bearing has normal operating performance at the time t in the future, and the possibility of failure of the best performance situation is small;

S3: Rolling bearing performance maintains relative reliability d(t) ∈ [-10%, -5%), that is, the running performance of rolling bearing at time t in the future is getting worse, and the possibility of failure of the best performance situation is increasing;

S4: The relative reliability of the rolling bearing performance maintenance d(t)<-10%, that is, the running performance of the rolling bearing at the future time t becomes worse, and the possibility of failure of the best performance situation becomes larger;

8) According to the above four grades of rolling bearing operating performance classification, the time history of predicting the failure degree of the best performance situation of rolling bearings is as follows:

In Figure 3, when t=6, d(t)=-4.43%∈[-5%, 0%), and the value of d(t) is close to -5%;

When t=7, d(t)=-5.29%∈[-10%, -5%), d(t) is already less than -5%;

When t=12, d(t)=-9.47%∈[-10%, -5%), and the value of d(t) is close to -10%;

When t=13, d(t)=-10.29%<-10%, the value of d(t) is already less than -10%.

According to the above content, the failure degree of the rolling bearing to maintain the best performance situation in the future is predicted:

Based on this, it can be predicted that before the 6th year, the running performance of the rolling bearing is normal, and the possibility of failure of the best performance situation of friction torque is small; after the 7th year and before the 12th year, the running performance of the rolling bearing is getting worse, The probability of failure in the best performance state of friction torque is increasing; until the 13th year, the running performance of the rolling bearing becomes worse, and the possibility of failure in the best performance state of friction torque is high.

According to the above time course, in the 12th and 13th years, intervention measures should be taken to maintain or replace the rolling bearing, so as to avoid serious safety accidents caused by the failure of the best performance state of bearing friction torque.

Example 2

The prediction method of the rolling bearing performance maintenance reliability of the present embodiment 2 comprises the following steps:

1) During the best period of rolling bearing operation performance, the vibration acceleration of the rolling bearing in the evaluation time interval is regularly measured by the measurement system, and at the current time t=1, K performance data of vibration acceleration are obtained, K=20000, the kth performance data is x _k , k=1, 2, ..., 20000, and the unit of data is μm/s ² ; the obtained vibration acceleration data distribution diagram of the rolling bearing is shown in Figure 4;

In this embodiment 2, the evaluation time interval is 1 year, each prediction time interval is 1 year, and the unit of time t is year; the rolling bearing performance maintenance reliability prediction method of this embodiment is used to predict the failure of the rolling bearing vibration acceleration performance the time course of the degree in a future time;

2) According to the principle of maximum entropy, use the performance data obtained in step 1) to construct the performance sample density function p(x):

In formula (1), x is the performance random variable describing the performance of the rolling bearing; m is the highest origin moment order; i is the origin moment order; λ ₀ , λ ₁ ,…, λ _m are Lagrangian multipliers, and There is a first Lagrangian multiplier λ ₀ as:

In formula (2), x is the performance random variable describing the performance of the rolling bearing; S ₁ is the lower bound value of the performance random variable x feasible region; S ₂ is the upper bound value of the performance random variable x feasible region; i is the origin moment order; λ _i is the i-th Lagrangian multiplier, and the Lagrangian multipliers λ ₁ , λ ₂ ,..., λ _m are obtained from the m equations in formula (3):

In formula (3), x is the performance random variable describing the performance of the rolling bearing; x _k is the kth performance data, k represents the serial number of the performance data, and K is the number of performance data; S ₁ is the lower bound of the feasible region of the performance random variable x value, S ₂ is the upper bound value of the performance random variable x feasible region; i and j are the order of the origin moment, m is the highest order of the origin moment, λ _i is the i-th Lagrangian multiplier;

Construct the vibration acceleration sample density function p(x) with the 20,000 vibration acceleration performance data obtained in step 1), and the results are shown in Figure 5;

3) Obtain the confidence degree according to the principle of small probability events, and use the quantile method to obtain the confidence interval of the performance random variable;

According to the principle of small probability events, the confidence level P=0.99 is obtained through experiments in advance, and the confidence interval of vibration acceleration random variable x [X _L , X _U ]=[-0.0549μm/s ² , 0.0692μm/s ² ] can be calculated:

The lower limit value X _L is obtained by formula (4):

The upper limit value X _U is obtained by formula (5):

In formula (4) and formula (5), x is the performance random variable describing the performance of the rolling bearing; S ₁ is the lower bound value of the performance random variable x feasible domain; S ₂ is the upper bound value of the performance random variable x feasible domain; [X _L , X _U ] is the confidence interval of the performance random variable x; p(x) is the performance sample density function; P is the degree of confidence;

Wherein, the confidence degree P is based on the principle of small probability events, and is determined through performance tests in advance, and the specific method is the same as in Example 1; the confidence degree obtained in this embodiment is P=0.99;

4) According to the Poisson counting process, the frequency at which the performance data falls outside the confidence interval of the performance random variable is obtained;

Record how many of the 20,000 data fall outside the confidence interval [X _L , X _U ] of the vibration acceleration random variable x, and obtain vibration acceleration data that fall within the confidence interval [X _L , X _U ] of the vibration acceleration random variable x Outer frequency λ:

In formula (6), λ is the frequency of the performance data falling outside the performance random variable x confidence interval [X _L , X _U ], n is the performance data falling outside the performance random variable x confidence interval [X _L , X _U ] K is the number of performance data;

5) According to the non-failure probability of the Poisson counting process, the reliability of rolling bearing performance maintenance is obtained from the frequency at which the performance data falls outside the confidence interval of the performance random variable, and the time history of the vibration acceleration performance maintenance reliability R(t) of the rolling bearing is obtained;

The rolling bearing performance maintenance reliability is R(t):

R(t)=exp(-λt); t≥1 (7),

In formula (7), t is time, t≥1; R(t) is the reliability of rolling bearing performance at time t, which is used to represent the possibility that rolling bearing operation can maintain the best performance situation at time t; λ is performance data Frequency that falls outside the confidence interval [X _L , X _U ] for the performance random variable x;

6) According to the relative error concept of the measurement theory, obtain the relative reliability of the performance of the rolling bearing in the future time, and obtain the time history of the relative reliability d(t) of the vibration acceleration of the rolling bearing;

The performance of rolling bearings in the future maintains relative reliability as d(t):

In formula (8), R(1) is the reliability of the rolling bearing performance at the current time t=1; t is the 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, which is used to represent the failure degree of the rolling bearing running at the best performance state at the time t in the future;

The time history of the relative reliability d(t) of the vibration acceleration of the rolling bearing is shown in Figure 6;

7) According to the principle of significant hypothesis testing and measurement theory, the running performance of rolling bearings is divided into four levels: S1, S2, S3, and S4:

S1: The relative reliability of rolling bearing performance maintenance d(t) ≥ 0%, that is, the running performance of the rolling bearing at the time t in the future reaches the best, and there is almost no possibility of failure in the best performance situation;

S2: The rolling bearing performance maintains a relative reliability d(t) ∈ [-5%, 0%), that is, the rolling bearing has normal operating performance at the time t in the future, and the possibility of failure of the best performance situation is small;

S3: Rolling bearing performance maintains relative reliability d(t) ∈ [-10%, -5%), that is, the running performance of rolling bearing at time t in the future is getting worse, and the possibility of failure of the best performance situation is increasing;

S4: The relative reliability of the rolling bearing performance maintenance d(t)<-10%, that is, the running performance of the rolling bearing at the future time t becomes worse, and the possibility of failure of the best performance situation becomes larger;

8) According to the above four grades of rolling bearing operating performance classification, the time history of predicting the failure degree of the best performance situation of rolling bearings is as follows:

In Figure 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%.

According to the above content, the failure degree of the rolling bearing to maintain the best performance situation in the future is predicted:

Based on this, it can be predicted that before the 6th year, the running performance of the rolling bearing is normal, and the possibility of failure of the best vibration acceleration performance situation is small; after the 7th year and before the 12th year, the running performance of the rolling bearing is getting worse, The possibility of failure of the best performance of vibration acceleration is increasing; until the 13th year, the running performance of the rolling bearing becomes worse, and the possibility of failure of the best performance of vibration acceleration is high.

According to the above time course, in the 12th and 13th years, intervention measures should be taken to maintain or replace the rolling bearing, so as to avoid serious safety accidents caused by the failure of the best performance state of the vibration acceleration of the bearing.

The performance of the rolling bearing includes vibration, noise, friction torque, temperature rise, rotation accuracy, etc., and all performances can be predicted by the technical scheme of the present invention to maintain reliability. In other embodiments of the present invention, the prediction method of rolling bearing performance maintenance reliability of the present invention is used to predict the failure of the rolling bearing to maintain the best performance situation in the future according to the relative reliability of performance maintenance such as noise, temperature rise, and rotation accuracy. Degree; Concrete method of operation is the same as embodiment 1.

When performing intervention measures based on the prediction results of the technical solution of the present invention, if the critical time of the prediction results for different performances of the same rolling bearing is different, the intervention measures should be 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.