CN110619179B - Mechanical seal reliability analysis method and system - Google Patents
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Abstract
The invention discloses a method and a system for analyzing the reliability of mechanical seal. The method comprises the following steps: respectively acquiring at least two performance index degradation data of a plurality of mechanical seal samples of the same model; respectively intercepting a plurality of continuous intervals from the degradation data of each performance index, and enabling intervals corresponding to the serial numbers intercepted from the degradation data of different performance indexes to be overlapped in time; calculating degradation increment on each interval; calculating a distribution function of the degradation increment; and calculating the correlation of each performance index and calculating the comprehensive mechanical seal reliability. By intercepting a plurality of continuous intervals, the intervals corresponding to the intercepted serial numbers in different performance indexes are ensured to have overlapping relation in time, and the correlation among the performance indexes is calculated by the distribution function of the degradation increment, so that the reliability of the mechanical seal can be accurately analyzed when different performance index detection time points are selected to be different, and the accuracy of the reliability analysis result of the mechanical seal is improved.
Description
Technical Field
The invention relates to the technical field of mechanical seal, in particular to a method and a system for analyzing the reliability of mechanical seal.
Background
The liquid lubrication mechanical seal is widely applied to various hydraulic systems. The mechanical seal mainly comprises a movable ring assembly and a static ring assembly, wherein the movable ring assembly is arranged on a rotating shaft and is kept static relative to the rotating shaft, and the static ring assembly is arranged on a shell.
The mechanical seal is mainly characterized in that high-speed relative motion exists between the moving ring and the static ring, an oil film is formed between the moving ring and the static ring, the friction rate is reduced, the service life is prolonged, and the service life is ensured while the low leakage rate is met. Under the working condition of the mechanical seal, various key performance indexes highly related to the reliability of the mechanical seal have degradation phenomena along with the progress of tests, such as: and (3) judging that the mechanical seal fails when any one of the performance indexes exceeds a threshold value. Mechanical seals generate higher temperature concentration and stress concentration at high rotating speed, and the failure of the mechanical seals directly causes the hydraulic system to be incapable of working normally. The high reliability of the mechanical seal is of great significance for reducing various hydraulic system faults, reducing the occurrence of safety accidents, improving the labor productivity and the like.
At present, the reliability analysis of the mechanical seal generally only involves the analysis of a certain performance index, and the performance indexes are regarded as independent, and the correlation among the performance indexes is ignored, so that the reliability analysis performed in such a way has errors. In recent years, a Copula function has been introduced into the field of reliability analysis from statistics, and more people have started to study this, but in the past, when reliability analysis is performed on correlation modeling by using a Copula function, the measurement time points of data of a plurality of performance indexes selected are all the same. When the measurement time points of the performance indexes are different, the conventional method performs approximation processing on the measurement time points of the performance indexes, and the measurement time points after the approximation processing are considered to be the same, so that the error of the analysis result of the sealing reliability is easily caused to be larger.
Disclosure of Invention
The invention aims to provide a method and a system for analyzing the reliability of mechanical seal, which solve the problem that the error of the analysis result of the reliability of the seal is larger when the measurement time points of selecting a plurality of performance index degradation data are different in the existing method.
In order to achieve the purpose, the invention provides the following scheme:
a method of mechanical seal reliability analysis, the method comprising:
respectively acquiring at least two performance index degradation data of a plurality of mechanical seal samples of the same model; at least two performance indexes have correlation with each other, and the degradation data is the degradation amount of the performance indexes corresponding to each time point in 0-T time;
respectively intercepting a plurality of continuous intervals in the degradation data of each performance index, and enabling intervals corresponding to the intercepted serial numbers in the degradation data of different performance indexes to be overlapped in time;
respectively calculating the degradation increment of each performance index in each section; the degradation increment is the difference value of the degradation amount of the termination endpoint and the degradation amount of the starting endpoint of the selected section;
respectively calculating the distribution function of the degradation increment corresponding to each performance index according to the degradation increment;
Calculating the correlation of each performance index according to the distribution function to obtain a correlation function with unknown parameters;
estimating the unknown parameters of the correlation function with the unknown parameters by adopting a leaf-Bayesian method to obtain a specific correlation function;
and calculating the reliability of the comprehensive mechanical seal according to the specific correlation function to obtain a reliability analysis result of the mechanical seal.
Optionally, the respectively obtaining multiple performance index degradation data of a plurality of mechanical seal samples of the same model specifically includes:
and respectively obtaining degradation data of two performance indexes of a plurality of mechanical seal samples of the same model, wherein the two performance indexes are friction torque and leakage rate.
Optionally, after obtaining the degradation data of a plurality of performance indicators of a plurality of mechanical seal samples of the same model, the method further includes:
with { Xki(tkj)；tkj≧ 0} indicates the kth performance index of the ith mechanical seal sample at the jth measurement time point tkjAmount of temporal degradation, i>0, j is not less than 0, wherein Xki(tkj)＝μkΛ(tkj)+σkW(Λ(tkj) W (-) is standard Brownian motion,
as a function of time scale, qkBeing coefficients of a time scale function, mukAs a drift coefficient in the wiener process, σkIs the diffusion coefficient in the wiener process.
Optionally, the calculating the degradation increment of the degradation data of each performance index in each section specifically includes:
according to the formula Δ Xki(tkj)＝Xki(tkj)-Xki(tk(j-1)) Calculating the k individual performance index of the ith mechanical seal sample in the time interval tk(j-1)，tkj]An increase in degradation within, and
wherein
qkBeing coefficients of a time scale function, mukAs a drift coefficient in the wiener process, σkIs the diffusion coefficient in the Venn Process, Xki(tkj) K-th performance index representing ith mechanical seal sample at j-th measurement time point tkjAmount of temporal degradation, Xki(tk(j-1)) The k-th performance index of the ith mechanical seal sample at the j-1 st measurement time point tk(j-1)The amount of degradation in time.
Optionally, the calculating, according to the degradation increments, distribution functions of the degradation increments corresponding to the performance indexes respectively specifically includes:
according to the formula
Calculating a degradation delta DeltaXki(tkj) Distribution function of, Δ Xki(tkj) For the kth performance indicator of the ith mechanical seal sample at time interval tk(j-1)，tkj]The amount of the degradation increase in the inner layer,
qkbeing coefficients of a time scale function, mukAs a drift coefficient in the wiener process, σkIs the diffusion coefficient in the wiener process.
Optionally, the calculating the correlation of each performance index according to the distribution function to obtain the correlation function with unknown parameters specifically includes:
According to the formula F (Δ X)1i(t1j),ΔX2i(t2j))＝C(F1(ΔX1i(t1j)),F2(ΔX2i(t2j) ); theta) calculating the correlation of each of said performance indicators to obtain a correlation function with unknown parameters, wherein X1i(t1j) Representing the friction torque of the ith mechanical seal sample at the jth measurement time point t1jIncrement of degradation at time, Δ X1i(t1j) Representing the friction torque of the ith mechanical seal sample at time interval t1(j-1)，t1j]Increment of internal degradation, X2i(t2j) Indicating the leak rate of the ith mechanical seal sample at the jth measurement time point t2jIncrement of degradation at time, Δ X2i(t2j) Indicating the leak rate of the ith mechanical seal sample at time interval t2(j-1)，t2j]The amount of the degradation increase in the inner layer,
u＝F1(·)，v＝F2(. theta) is a two-variable DeltaX1i(t1j) And Δ X2i(t2j) Linear correlation coefficient between; the unknown parameter is mu1,σ1,q1,μ2,σ2,q2。
Optionally, the estimating the unknown parameters of the correlation function with the unknown parameters by using the bayesian method to obtain the specific correlation function specifically includes:
according to the formula
Obtaining the value of the band unknown parameter mu1,σ1,q1,μ2,σ2,q2A log-likelihood function of;
and adopting a Bayesian method to fuse prior information to estimate unknown parameters in the log-likelihood function to obtain the specific correlation function.
Optionally, the calculating the reliability of the integrated mechanical seal according to the specific correlation function to obtain the reliability analysis result of the mechanical seal specifically includes:
According to the formula Rk(t)＝1-Gk(t) calculating the single mechanical seal reliability taking the friction torque as a performance index and the single mechanical seal reliability taking the leakage rate as a performance index respectively; wherein G isk(t) is a cumulative distribution function, and
Tkbased on a degeneration process { Xk(t); t is not less than 0} and T isk＝inf{t|Xk(t)≥ωk}，ωkA threshold value corresponding to the performance index;
according to the formula R (t) ═ C (R)1(t),R2(t), theta) calculating the comprehensive mechanical seal reliability; r1(t) Single mechanical seal reliability for Friction Torque, R2(t) single mechanical seal reliability for leak rate.
A mechanical seal reliability analysis system, the system comprising:
the degradation data acquisition module is used for respectively acquiring at least two performance index degradation data of a plurality of mechanical seal samples of the same model; at least two performance indexes have correlation with each other, and the degradation data is the degradation amount of the performance indexes corresponding to each time point in 0-T time;
the interval intercepting module is used for respectively intercepting a plurality of continuous intervals in the degradation data of each performance index, and the intervals corresponding to the serial numbers intercepted in the degradation data of different performance indexes are overlapped in time;
the degradation increment calculation module is used for calculating the degradation increment of each performance index on each section respectively; the degradation increment is the difference value of the degradation amount of the termination endpoint and the degradation amount of the starting endpoint of the selected section;
The distribution function calculation module is used for respectively calculating the distribution function of the degradation increment corresponding to each performance index according to the degradation increment;
the first correlation calculation module is used for calculating the correlation of each performance index according to the distribution function to obtain a correlation function with unknown parameters;
the second correlation calculation module is used for estimating the unknown parameters of the correlation function with the unknown parameters by adopting a Bayesian method to obtain a specific correlation function;
and the reliability calculation module is used for calculating the reliability of the comprehensive mechanical seal according to the specific correlation function to obtain the reliability analysis result of the mechanical seal.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the method comprises the steps of obtaining degradation data of at least two performance indexes, respectively intercepting a plurality of continuous intervals from the degradation data of each performance index, enabling intervals corresponding to serial numbers intercepted from the degradation data of different performance indexes to be overlapped in time, respectively calculating degradation increments of each performance index, calculating a distribution function of the degradation increments, calculating the correlation of each performance index, and finally calculating the reliability of mechanical seal to obtain an analysis result of the reliability of the mechanical seal.
The method has the advantages that the plurality of continuous sections are intercepted from the degradation data of each selected performance index, the overlapping relation of the sections corresponding to the intercepted serial numbers in different performance indexes in time is guaranteed, the correlation among the performance indexes is calculated through the distribution function of the degradation increment, the reliability of the mechanical seal can be accurately analyzed when different performance indexes are selected and the detection time points are different, and the accuracy of the reliability analysis result of the mechanical seal is improved.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without creative efforts.
Fig. 1 is a flowchart of a method for analyzing reliability of a mechanical seal according to an embodiment of the present invention;
FIG. 2 is an exploded view of a dynamic ring and a static ring of a mechanical seal sample provided by an embodiment of the invention;
FIG. 3 is a graph illustrating the friction torque degradation of a mechanical seal sample provided by an embodiment of the present invention;
FIG. 4 is a graph illustrating the degradation in leakage rate for a sample mechanical seal provided in accordance with an embodiment of the present invention;
FIG. 5 is a graph of a mechanical seal reliability function provided by an embodiment of the present invention;
fig. 6 is a structural diagram of a mechanical seal reliability analysis system according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide a method and a system for analyzing the reliability of mechanical seal, which solve the problem that the error of the analysis result of the reliability of the seal is larger when the measurement time points of selecting a plurality of performance index degradation data are different in the existing method.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Fig. 1 is a flowchart of a method for analyzing reliability of a mechanical seal according to an embodiment of the present invention, and as shown in fig. 1, the method for analyzing reliability of a mechanical seal includes:
S101: respectively acquiring at least two performance index degradation data of a plurality of mechanical seal samples of the same model; at least two performance indexes have correlation with each other, and the degradation data is the degradation amount of the performance indexes corresponding to each time point in 0-T time;
s102: respectively intercepting a plurality of continuous intervals in the degradation data of each performance index, and enabling intervals corresponding to the intercepted serial numbers in the degradation data of different performance indexes to be overlapped in time;
s103: respectively calculating the degradation increment of each performance index in each section; the degradation increment is the difference value of the degradation amount of the termination endpoint and the degradation amount of the starting endpoint of the selected section;
s104: respectively calculating the distribution function of the degradation increment corresponding to each performance index according to the degradation increment;
s105: calculating the correlation of each performance index according to the distribution function to obtain a correlation function with unknown parameters;
s106: estimating the unknown parameters of the correlation function with the unknown parameters by adopting a leaf-Bayesian method to obtain a specific correlation function;
s107: and calculating the reliability of the comprehensive mechanical seal according to the specific correlation function to obtain a reliability analysis result of the mechanical seal.
The step S101: the step of respectively acquiring a plurality of performance index degradation data of a plurality of mechanical seal samples of the same model specifically comprises: and respectively obtaining degradation data of two performance indexes of a plurality of mechanical seal samples of the same model, wherein the two performance indexes are friction torque and leakage rate.
The step S101: after a plurality of performance index degradation data of a plurality of mechanical seal samples of the same model are obtained respectively, the method further comprises the following steps:
with { Xki(tkj)；tkj≧ 0} indicates the kth performance index of the ith mechanical seal sample at the jth measurement time point tkjAmount of temporal degradation, i>0, j is not less than 0, wherein Xki(tkj)＝μkΛ(tkj)+σkW(Λ(tkj) W (-) is standard Brownian motion,
as a function of time scale, qkBeing coefficients of a time scale function, mukAs a drift coefficient in the wiener process, σkIs the diffusion coefficient in the wiener process.
The above step S103: specifically, the step of calculating the degradation increment of the degradation data of each performance index in each section includes:
according to the formula Δ Xki(tkj)＝Xki(tkj)-Xki(tk(j-1)) Calculating the k individual performance index of the ith mechanical seal sample in the time interval tk(j-1)，tkj]An increase in degradation within, and
wherein
qkBeing coefficients of a time scale function, mukAs a drift coefficient in the wiener process, σkIs the diffusion coefficient in the Venn Process, X ki(tkj) K-th performance index representing ith mechanical seal sample at j-th measurement time point tkjAmount of temporal degradation, Xki(tk(j-1)) The k-th performance index of the ith mechanical seal sample at the j-1 st measurement time point tk(j-1)The amount of degradation in time.
The step S104: the step of calculating the distribution function of the degradation increment corresponding to each performance index according to the degradation increment specifically includes:
according to the formula
Calculating a degradation delta DeltaXki(tkj) Distribution function of, Δ Xki(tkj) For the kth performance indicator of the ith mechanical seal sample at time interval tk(j-1)，tkj]The amount of the degradation increase in the inner layer,
qkbeing coefficients of a time scale function, mukAs a drift coefficient in the wiener process, σkIs the diffusion coefficient in the wiener process.
The above step S105: calculating the correlation of each performance index according to the distribution function, and obtaining the correlation function with unknown parameters specifically comprises the following steps:
according to the formula F (Δ X)1i(t1j),ΔX2i(t2j))＝C(F1(ΔX1i(t1j)),F2(ΔX2i(t2j) ); theta) calculating the correlation of each of said performance indicators to obtain a correlation function with unknown parameters, wherein X1i(t1j) Representing the friction torque of the ith mechanical seal sample at the jth measurement time point t1jIncrement of degradation at time, Δ X1i(t1j) Representing the friction torque of the ith mechanical seal sample at time interval t1(j-1)，t1j]Increment of internal degradation, X 2i(t2j) Indicating the leak rate of the ith mechanical seal sample at the jth measurement time point t2jIncrement of degradation at time, Δ X2i(t2j) Indicating the leak rate of the ith mechanical seal sample at time interval t2(j-1)，t2j]The amount of the degradation increase in the inner layer,
u＝F1(·)，v＝F2(. theta) is a two-variable DeltaX1i(t1j) And Δ X2i(t2j) Linear correlation coefficient between; the unknown parameter isμ1,σ1,q1,μ2,σ2,q2。
The above step S106: estimating the unknown parameters of the correlation function with the unknown parameters by adopting a Bayesian method to obtain a specific correlation function, wherein the specific correlation function specifically comprises the following steps:
according to the formula
Obtaining the value of the band unknown parameter mu1,σ1,q1,μ2,σ2,q2A log-likelihood function of;
and adopting a Bayesian method to fuse prior information to estimate unknown parameters in the log-likelihood function to obtain the specific correlation function.
The above step S107: the calculating the reliability of the comprehensive mechanical seal according to the specific correlation function to obtain the reliability analysis result of the mechanical seal specifically comprises:
according to the formula Rk(t)＝1-Gk(t) calculating the single mechanical seal reliability taking the friction torque as a performance index and the single mechanical seal reliability taking the leakage rate as a performance index respectively; wherein G isk(t) is a cumulative distribution function, and
Tkbased on a degeneration process { Xk(t); t is not less than 0} and T is k＝inf{t|Xk(t)≥ωk}，ωkA threshold value corresponding to the performance index;
according to the formula R (t) ═ C (R)1(t),R2(t), theta) calculating the comprehensive mechanical seal reliability; r1(t) Single mechanical seal reliability for Friction Torque, R2(t) single mechanical seal reliability for leak rate.
Specifically, in this embodiment, the mechanical seal sample is as shown in fig. 2, and the mechanical seal sample includes a stationary ring component and a moving ring, where the stationary ring component includes a mounting sleeve 1, a leather cup 2, a retaining ring 3, a spring 4 and a stationary ring 5, and the stationary ring and the moving ring are made of carbon graphite and structural steel, respectively. When the mechanical seal operates, the main shaft drives the movable ring to rotate together at high speed, and the static ring component keeps still.
In this embodiment, two performance indexes which are highly related to the reliability of the mechanical seal and have a correlation therebetween are specifically selected, and are respectively friction torque and leakage rate, and when any one of the two performance indexes exceeds a set threshold, the mechanical seal is considered to be failed.
After the friction torque and the leakage rate data of a plurality of mechanical seal samples of the same model are obtained, the degradation data are drawn into curves, and the degradation curves of the friction torque and the leakage rate are respectively shown in fig. 3 and fig. 4.
In this embodiment, a wiener process in a random process is used to perform two performance indexes: modeling the degradation process of the friction torque and the leakage rate;
Specifically, a wiener process with a time scale function is used for modeling degradation processes of two performance indexes, namely friction torque and leakage rate: let { Xk(t); t is more than or equal to 0, represents the degradation amount of the kth individual performance index at the time t, and the kth individual performance index obeys the wiener process, so that the kth individual performance index comprises the following steps:
Xk(t)＝μkΛ(t)+σkW(Λ(t))
wherein W (-) is a standard Brownian motion,
as a function of time scale, qkCoefficients that are a function of time scale; mu.skIs the drift coefficient in the wiener process; sigmakIs the diffusion coefficient in the wiener process.
From the nature of the wiener process, at time intervals [ t, t + Δ t ]]Inner, degradation increment Δ Xk(t)＝Xk(t+Δt)-Xk(t) satisfies:
where Δ Λ (t) ═ Λ (t + Δ t) - Λ (t).
Delta of degradation Δ Xk(t) distribution function Fk(ΔXk(t)) may be described as:
where Φ (·) is a standard normal distribution function.
Specifically, 10 mechanical seal samples of the same model are selected to be tested simultaneously, the two performance indexes of the friction torque and the leakage rate of the 10 samples are respectively increased by 8 sections, and the friction torque and the leakage rate selected on the same mechanical seal sample are overlapped with the sections of the same serial number in time.
In the invention, the sections with the friction torque and the leakage rate corresponding to the same serial number selected on the same sample are mutually overlapped and staggered in time, namely the two performance index measurement time points are different from each other.
Let Xki(tkj) K-th performance indicator expressed as ith mechanical seal sample at j-th measurement time point tkjWhen the time is the amount of degeneration and k is 1, X1i(t1j) Expressed as friction torque, when k is 2, X2i(t2j) Expressed as leak rate. Let the degradation increment be expressed as:
ΔXki(tkj)＝Xki(tkj)-Xki(tk(j-1))
wherein k is 1,2, i is 1,2, 10, j is 1,2, 8, and X iski(tk0)＝0。
For i 1, 2.., 10, the degradation increment Δ Xki(tkj)＝Xki(tkj)-Xki(tk(j-1)) All satisfy:
wherein,
for i 1, 2.., 10, the degradation increment Δ Xki(tkj) Distribution function F ofk(ΔXki(tkj) Can be described as:
then, determining a Copula function describing the correlation between the two performance indexes;
in the present embodiment, Copula function is used as a function describing the correlation between two performance indexes of friction torque and leak rate. The Copula function is described as:
F(ΔX1i(t1j),ΔX2i(t2j))＝C(F1(ΔX1i(t1j)),F2(ΔX2i(t2j))；θ)
here, a GaussianCopula function is selected, and the expression is as follows:
wherein u is F1(·)，v＝F2(. theta) is the parameter value of the Copula function, here two variables Δ X1i(t1j) And Δ X2i(t2j) Linear correlation coefficient therebetween.
When two variables Δ X1i(t1j) And Δ X2i(t2j) Time increment interval t1(j-1),t1j]And [ t2(j-1),t2j]Are identical, i.e. t1(j-1)＝t2(j-1),t1j＝t2jWhen theta is equal to thetaj，θjHas a value range of [ -1,1 [)]，θjRepresenting two variables Δ X1i(t1j) And Δ X2i(t2j) Time increment interval t1(j-1),t1j]And [ t2(j-1),t2j]The parameter values of the Copula function are identical.
According to the parameter theta jIs given by the parameter θjThe expression of (a) is:
wherein alpha is two variables Δ X1i(t1j) And Δ X2i(t2j) Time increment interval t1(j-1),t1j]And [ t2(j-1),t2j]Are identical, i.e. t1(j-1)＝t2(j-1),t1j＝t2jLinear correlation coefficient of time.
Carrying out joint estimation on parameters in the two performance degradation process models and parameters in a Copula function for describing the correlation between the two performance indexes by using Openbugs software;
in each case determining the distribution u of the friction torque degradation incrementsij＝F1(ΔX1i(t1j) And the distribution value v of the leak rateij＝F2(ΔX2i(t2j) After (u), mixingij,vij) Substituting into the GaussianCopula function yields:
wherein,
the log-likelihood function is then obtained as follows:
the unknown parameters in the likelihood function are estimated by fusing the prior information and the sample data information by a Bayes method, wherein the Openbugs software is adopted to calculate the posterior distribution by a Markov chain Monte Carlo method, the prior distribution is the prior distribution without information, and the parameter mu in the likelihood function1,σ1,q1,μ2,σ2,q2The results of the estimated values of α are shown in table 1:
TABLE 1 likelihood function estimation results
And after the parameters of the performance index degradation model and the correlation function are obtained, calculating the mechanical seal reliability of the binary correlation degradation at unequal time intervals.
When the degradation amount of any one of the two performance indexes, namely the friction torque and the leakage rate, exceeds a failure threshold value, the system is considered to be failed, and a system reliability function R (t) under the binary correlation degradation model at the moment can be represented as follows:
R(t)＝P{X1(t)≤ω1,X2(t)≤ω2}
Wherein, ω is1,ω2Respectively representing the thresholds for the degradation of the two performance indicators.
Based on the degradation process { Xk(t); t is not less than 0%kCan be defined as:
Tk＝inf{t|Xk(t)≥ωk}
wherein, TkObeying an inverse Gaussian distribution with a cumulative distribution function Gk(t) is:
at this time, a single reliability function R of the systemk(t) can be expressed as:
Rk(t)＝1-Gk(t)
then according to R (t) ═ C (R)1(t),R2(t)) calculating to obtain the comprehensive reliability of the system. Where C (-) is a Gaussiancopula function describing the correlation between two performance indicators, R1(t),R2And (t) is a single reliability function of the system based on performance indexes such as friction torque and leakage rate.
Diffusion coefficients in two performance degradation models are preferred in this embodiment
And the comprehensive reliability of the system obtained by calculation is more accurate.
In this embodiment, the friction torque threshold is set to be 2.2Nm, the leakage rate threshold is set to be 2ml/h, and the mechanical seal reliability of unequal interval binary correlation performance degradation is calculated, with the result shown in fig. 5.
Fig. 6 is a structural diagram of a mechanical seal reliability analysis system according to an embodiment of the present invention, and as shown in fig. 6, the embodiment further provides a mechanical seal reliability analysis system, where the system includes:
the degradation data acquisition module 7 is used for respectively acquiring at least two performance index degradation data of a plurality of mechanical seal samples of the same model; at least two performance indexes have correlation with each other, and the degradation data is the degradation amount of the performance indexes corresponding to each time point in 0-T time;
The section intercepting module 8 is used for respectively intercepting a plurality of continuous sections from the degradation data of each performance index, and enabling the sections corresponding to the serial numbers intercepted from the degradation data of different performance indexes to be overlapped in time;
a degradation increment calculation module 9, configured to calculate degradation increments of the performance indicators in the respective block sections respectively; the degradation increment is the difference value of the degradation amount of the termination endpoint and the degradation amount of the starting endpoint of the selected section;
a distribution function calculation module 10, configured to calculate, according to the degradation increments, distribution functions of degradation increments corresponding to the performance indicators respectively;
a first correlation calculation module 11, configured to calculate a correlation between the performance indicators according to the distribution function to obtain a correlation function with unknown parameters;
the second correlation calculation module 12 is configured to estimate the unknown parameters of the correlation function with the unknown parameters by using a bayesian method to obtain a specific correlation function;
and the reliability calculation module 13 is used for calculating the reliability of the comprehensive mechanical seal according to the specific correlation function to obtain a reliability analysis result of the mechanical seal.
According to the specific embodiment provided by the invention, the technical effects of the invention are as follows:
(1) By intercepting a plurality of continuous intervals in the degradation data of each selected performance index, ensuring that the intervals corresponding to the intercepted serial numbers in different performance indexes have overlapping relation in time (staggered with each other in time), and calculating the correlation among the performance indexes by using the distribution function of degradation increment, the reliability of the mechanical seal can be accurately analyzed when different detection time points of different performance indexes are selected, and the accuracy of the reliability analysis result of the mechanical seal is improved.
(2) The method and the system can be used for measuring the mechanical seal reliability of at least two performance indexes with correlation when the time points are different, and can also be used for selecting the mechanical seal reliability of two performance indexes with the same measurement time points in the prior art, namely, the method and the system have more flexibility.
(3) The method adopts a random process to model the degradation quantity of two performance indexes, and the commonly used random process comprises a wiener process, an inverse Gaussian process and a gamma process, and has higher calculation efficiency than a degradation orbit model and a reaction theory model on the premise of ensuring the precision.
(4) The method lays a theoretical foundation for the optimization design and reliability improvement of the mechanical seal, and promotes the development of the core technology of the mechanical seal, thereby improving the situation that the domestic seal industry depends heavily on import at present.
For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (8)
1. A method for analyzing reliability of a mechanical seal, the method comprising:
respectively acquiring at least two performance index degradation data of a plurality of mechanical seal samples of the same model; at least two performance indexes have correlation with each other, and the degradation data is the degradation amount of the performance indexes corresponding to each time point in 0-T time;
respectively intercepting a plurality of continuous intervals in the degradation data of each performance index, and enabling intervals corresponding to the intercepted serial numbers in the degradation data of different performance indexes to be overlapped in time;
Respectively calculating the degradation increment of each performance index in each section; the degradation increment is the difference value of the degradation amount of the termination endpoint and the degradation amount of the starting endpoint of the selected section;
respectively calculating the distribution function of the degradation increment corresponding to each performance index according to the degradation increment;
calculating the correlation of each performance index according to the distribution function to obtain a correlation function with unknown parameters;
estimating the unknown parameters of the correlation function with the unknown parameters by adopting a Bayesian method to obtain a specific correlation function, wherein the specific correlation function comprises the following steps:
according to the formula
Obtaining the value of the band unknown parameter mu1,σ1,q1,μ2,σ2,q2A log-likelihood function of;
estimating unknown parameters in the log-likelihood function by fusing prior information by a Bayesian method to obtain the specific correlation function; wherein
As a function of time scale, qkBeing coefficients of a time scale function, mukAs a drift coefficient in the wiener process, σkFor diffusion coefficient in wiener process, C (-) is Gaussian Copula function describing correlation between two performance indexes, phi (-) is standard normal distribution function, theta (-) isjRepresenting two variables Δ X1i(t1j) And Δ X2i(t2j) Time increment interval t1(j-1),t1j]And [ t 2(j-1),t2j]The parameter values of the Copula function are identical,
α is t1(j-1)＝t2(j-1),t1j＝t2jLinear correlation coefficient of time;
and calculating the reliability of the comprehensive mechanical seal according to the specific correlation function to obtain a reliability analysis result of the mechanical seal.
2. The method of claim 1, wherein the mechanical seal reliability analysis is performed by a computer,
the step of respectively acquiring multiple performance index degradation data of a plurality of mechanical seal samples of the same model specifically comprises:
and respectively obtaining degradation data of two performance indexes of a plurality of mechanical seal samples of the same model, wherein the two performance indexes are friction torque and leakage rate.
3. The method of claim 1, wherein the mechanical seal reliability analysis is performed by a computer,
after a plurality of performance index degradation data of a plurality of mechanical seal samples of the same model are respectively obtained, the method further comprises the following steps:
with { Xki(tkj)；tkj≧ 0} indicates the kth performance index of the ith mechanical seal sample at the jth measurement time point tkjAmount of temporal degradation, i>0, j is not less than 0, wherein Xki(tkj)＝μkΛ(tkj)+σkW(Λ(tkj) W (-) is standard Brownian motion,
as a function of time scale, qkBeing coefficients of a time scale function, mukAs a drift coefficient in the wiener process, σkIs the diffusion coefficient in the wiener process.
4. The method of claim 1, wherein the mechanical seal reliability analysis is performed by a computer,
the step of calculating the degradation increment of the degradation data of each performance index in each section specifically includes:
according to the formula Δ Xki(tkj)＝Xki(tkj)-Xki(tk(j-1)) Calculating the k individual performance index of the ith mechanical seal sample in the time interval tk(j-1)，tkj]An increase in degradation within, and
wherein
qkBeing coefficients of a time scale function, mukAs a drift coefficient in the wiener process, σkIs the diffusion coefficient in the Venn Process, Xki(tkj) K-th performance index representing ith mechanical seal sample at j-th measurement time point tkjAmount of temporal degradation，Xki(tk(j-1)) The k-th performance index of the ith mechanical seal sample at the j-1 st measurement time point tk(j-1)The amount of degradation in time.
5. The method of claim 1, wherein the mechanical seal reliability analysis is performed by a computer,
the step of calculating the distribution function of the degradation increments corresponding to the performance indexes according to the degradation increments specifically includes:
according to the formula
Calculating a degradation delta DeltaXki(tkj) Distribution function of, Δ Xki(tkj) For the kth performance indicator of the ith mechanical seal sample at time interval tk(j-1)，tkj]The amount of the degradation increase in the inner layer,
qkbeing coefficients of a time scale function, mukAs a drift coefficient in the wiener process, σ kIs the diffusion coefficient in the wiener process.
6. The method of claim 2, wherein the mechanical seal reliability analysis is performed by a computer,
the calculating the correlation of each performance index according to the distribution function to obtain the correlation function with unknown parameters specifically includes:
according to the formula F (Δ X)1i(t1j),ΔX2i(t2j))＝C(F1(ΔX1i(t1j)),F2(ΔX2i(t2j) ); theta) calculating the correlation of each of said performance indicators to obtain a correlation function with unknown parameters, wherein X1i(t1j) Representing the friction torque of the ith mechanical seal sample at the jth measurement time point t1jIncrement of degradation at time, Δ X1i(t1j) Representing the friction torque of the ith mechanical seal sample at that timeInterval between (t)1(j-1)，t1j]Increment of internal degradation, X2i(t2j) Indicating the leak rate of the ith mechanical seal sample at the jth measurement time point t2jIncrement of degradation at time, Δ X2i(t2j) Indicating the leak rate of the ith mechanical seal sample at time interval t2(j-1)，t2j]The amount of the degradation increase in the inner layer,
7. The method according to claim 1, wherein the calculating a comprehensive mechanical seal reliability according to the specific correlation function to obtain the reliability analysis result of the mechanical seal specifically includes:
According to the formula Rk(t)＝1-Gk(t) calculating the single mechanical seal reliability taking the friction torque as a performance index and the single mechanical seal reliability taking the leakage rate as a performance index respectively; wherein G isk(t) is a cumulative distribution function, and
，Tkbased on a degeneration process { Xk(t); t is not less than 0} and T isk＝inf{t|Xk(t)≥ωk}，ωkA threshold value corresponding to the performance index;
according to the formula R (t) ═ C (R)1(t),R2(t), theta) calculating the comprehensive mechanical seal reliability; r1(t) Single mechanical seal reliability for Friction Torque, R2(t) single mechanical seal reliability for leak rate.
8. A mechanical seal reliability analysis system, the system comprising:
the degradation data acquisition module is used for respectively acquiring at least two performance index degradation data of a plurality of mechanical seal samples of the same model; at least two performance indexes have correlation with each other, and the degradation data is the degradation amount of the performance indexes corresponding to each time point in 0-T time;
the interval intercepting module is used for respectively intercepting a plurality of continuous intervals in the degradation data of each performance index, and the intervals corresponding to the serial numbers intercepted in the degradation data of different performance indexes are overlapped in time;
The degradation increment calculation module is used for calculating the degradation increment of each performance index on each section respectively; the degradation increment is the difference value of the degradation amount of the termination endpoint and the degradation amount of the starting endpoint of the selected section;
the distribution function calculation module is used for respectively calculating the distribution function of the degradation increment corresponding to each performance index according to the degradation increment;
the first correlation calculation module is used for calculating the correlation of each performance index according to the distribution function to obtain a correlation function with unknown parameters;
the second correlation calculation module is configured to estimate the unknown parameters of the correlation function with the unknown parameters by using a bayesian method to obtain a specific correlation function, and specifically includes:
according to the formula
To obtainWith unknown parameter mu1,σ1,q1,μ2,σ2,q2A log-likelihood function of;
estimating unknown parameters in the log-likelihood function by fusing prior information by a Bayesian method to obtain the specific correlation function; wherein
As a function of time scale, qkBeing coefficients of a time scale function, mukAs a drift coefficient in the wiener process, σkFor diffusion coefficient in wiener process, C (-) is Gaussiancopula function describing correlation between two performance indexes, phi (-) is standard normal distribution function, theta (-) is jRepresenting two variables Δ X1i(t1j) And Δ X2i(t2j) Time increment interval t1(j-1),t1j]And [ t2(j-1),t2j]The parameter values of the Copula function are identical, 
and the reliability calculation module is used for calculating the reliability of the comprehensive mechanical seal according to the specific correlation function to obtain the reliability analysis result of the mechanical seal.
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