CN106597992B - A kind of numerically-controlled machine tool component importance analysis - Google Patents
A kind of numerically-controlled machine tool component importance analysis Download PDFInfo
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Abstract
The invention belongs to numerical control machine tool technique fields, are related to a kind of numerically-controlled machine tool component importance analysis, include the following steps: 1, establish corresponding relationship and inter-module failure transitive relation between various components and fault time；2, component transitive relation is established in analysis, is described with logm control machine tool system component faults transitive relation；3, failure Email Filtering structural model is converted by failure transitive relation, determines level of the system component in fault- traverse technique；4, the numerically-controlled machine tool system component faults rate modeling based on time correlation；5, numerically-controlled machine tool system component faults related coefficient is calculated；6, numerically-controlled machine tool system component faults rate models under failure rate correlation；7, numerically-controlled machine tool system assembly reliability dynamic different degree model and core different degree model are established, component Significance Analysis is carried out.The present invention and tradition ignore fault time it is related or leave out of consideration the modeling of the system components fail rate in fault propagation direction than it is more reasonable, more meet reality.
Description
Technical field
The invention belongs to numerical control machine tool technique fields, are related to a kind of numerically-controlled machine tool component importance analysis, specifically relate to
And failure causation analysis, failure transmitting digraph are established, the system components fail rate modeling based on time correlation, inter-module failure
Related coefficient is calculated, is modeled based on the relevant component faults rate modeling of failure rate and dynamic different degree and core different degree, herein
On the basis of carry out component Significance Analysis, determining influences crucial component to system reliability and is promoted to system reliability important
Component.
Background technique
Numerically-controlled machine tool is complication system, and the complexity of system structure causes its failure linksystem；Meanwhile in numerically-controlled machine tool
In use, each numerically-controlled machine tool component failure can all cause numerically-controlled machine tool machine failure, and work as numerically-controlled machine tool system failure
When, faulty components can generate one itself fault time and make the time truncation of every other component；Therefore, numerically-controlled machine tool
System component Reliability modeling needs combination failure direction of propagation property to be unfolded with fault time correlation with assessment, and current numerical control machine
Fault propagation directionality is ignored in the modeling of bed assembly reliability, or ignores fault time correlation, so that numerically-controlled machine tool system group
There are deviations for part reliability model, and then cause the assessment of component different degree, Reliability Distribution and maintenance time and reality obvious not
Symbol.
Brinbaum most proposed the concept of " reliability importance " early in 1969, wherein unreliable comprising reflection component
Degree variation causes " probabilistic compct " of system dependability variation degree, and reflection component improves complexity and economy is excellent
Bad " criticality importance ", but because ignoring component faults temporal correlation and failure dependency, so that result and engineering are practical not
Symbol.J.S.Hong indicates joint failure function with node or the failure function on side based on series-parallel Undirected networks structure,
Joint effected reliably degree is proposed on the basis of probabilistic compct, combines failure effect degree, edge effected reliably degree, and edge loses
Disturbance degree is imitated, and discusses four relationship, but because ignoring component nodes fault propagation directionality, so that component different degree is assessed
There are deviations.Vanderlei da Costa Bueno is based on Static fault tree analysis and static failure Tree-structure Model proposes
Other different degree concepts such as cut set disturbance degree, mortality different degree, differential disturbance degree because of component faults rule and influence to be dynamic
Variation, therefore these three models are helpless for the importance of dynamic evaluation component.Yao Chengyu is in T-S Fuzzy fault tree analysis
On the basis of algorithm, influence of the crash rate of comprehensive all malfunctions of component to system significance level determines T-S Fuzzy importance,
It because the acquisition of Fuzzy Number Valued has certain subjectivity, therefore analyzes result and varies with each individual, confidence level is not high.Wang Xiaofeng et al. is by portion
The ratio between the part number of stoppages and system total failare number indicate component reliability importance；The parts for maintenance time is always tieed up with system
Repairing the ratio between time indicates component maintainability different degree；Because ignoring the randomness of component faults, therefore it is important to be only capable of static evaluation component
Property.He Yu establishes each subsystem Reliability Function of lathe on the basis of failure is independently assumed, then leads under Cascade System hypothesis
It crosses and local derviation method is asked to carry out each subsystem dynamic reliability different degree modeling, and carry out core different degree modeling, but because ignoring group
Part fault time correlation and failure dependency influence the credibility of result.
Numerically-controlled machine tool building block is numerous, and operation mechanism is complicated, the single consideration component faults correlation of tradition or component event
The component faults rate model of Downtime correlation is not suitable for component Significance Analysis.
Summary of the invention
Group for the prior art because ignoring the time correlation of numerically-controlled machine tool system component faults or the foundation of fault propagation direction
Part failure rate model and cause component different degree model to have the defects that deviation, the present invention provide a kind of consideration component faults time
The modeling of numerically-controlled machine tool component faults rate and importance analysis, utilize this under correlation is related to the failure rate in fault propagation direction
Method analyzes numerically-controlled machine tool system component different degree, more meets reality.
In order to solve the above technical problems, the present invention is achieved by the following technical scheme:
A kind of numerically-controlled machine tool component importance analysis, includes the following steps:
Step 1: entire numerically-controlled machine tool system component is divided into n component；According to the numerically-controlled machine tool field failure of acquisition
Information is calculated by means of data, the correlation experience in terms of failure causation analysis and system structure function determines fault time, foundation
Corresponding relationship and inter-module failure transitive relation between various components and fault time；
Step 2: establishing component transitive relation according to failure causation analysis, and former with logm control machine tool system component
Barrier transitive relation is described；
Step 3: application decision laboratory (Decision making trial and evaluation
Laboratory, DEMATEL) method converted numerically-controlled machine tool system inter-module failure transitive relation to using graph theory and matrix tool
Failure Email Filtering structural model determines level of the system component in fault- traverse technique；
Step 4: the numerically-controlled machine tool system component faults rate based on time correlation models；
Step 5: the numerically-controlled machine tool system component faults rate function based on failure Email Filtering model, time correlation, draws
Enter Copula theory, carries out numerically-controlled machine tool system component faults related coefficient and calculate；
Step 6: numerically-controlled machine tool system component faults rate, system group based on failure Email Filtering model, time correlation
Part failure related coefficient, the numerically-controlled machine tool system component faults rate under failure rate correlation that carries out model；
Step 7: being based on Cascade System it is assumed that by asking local derviation method to establish numerically-controlled machine tool system assembly reliability dynamic
Different degree model and core different degree model, line number of going forward side by side control machine tool assembly Significance Analysis.
Numerically-controlled machine tool system component faults transitive relation Description Matrix is established described in technical scheme steps two to refer to:
With direct relation matrix Y=[yij]n×nComponent faults transitive relation is described；
Wherein: yijIt is component i to the failure degree of transitivity of component j；When i=j, yij=0.
Level of the system component described in technical scheme steps three in failure TRANSFER MODEL determines, refers to according to following step
It is rapid to calculate the numerically-controlled machine tool system inter-module failure degree of correlation:
(1) direct relation matrix is standardized as the following formula, obtains normalized matrix X；
(2) combined influence matrix T is calculated using formula (2)；
I is unit matrix in formula.
(3) each component degree of correlation is calculated
Every a line and each column to combined influence matrix T are summed respectively as the following formula, obtain disturbance degree D and degree of being affected B.
Wherein D value indicates the component directly or indirectly to the influence degree of other assemblies, and B value indicates that the component is direct by other assemblies
Or indirect influence degree.
Calculate centrad (di+bj) indicate inter-module strength of association, reason degree (di-bj) indicate component influences or by shadow
Loud degree.If (di-bj) be positive value when, indicate the component tendency influence class；(di-bj) be negative value when indicate the component be inclined to
It is affected class.
The size of each component disturbance degree, degree of being affected, centrad and the reason degree that are determined according to DEMATEL method, specifies group
Part directly or indirectly influences relationship, establishes attached system components fail biography shown in Fig. 2 in conjunction with the failure transport mechanism of each inter-module
Pass hierarchy Model.
Numerically-controlled machine tool system component faults rate modeling based on time correlation refers to using Johnson method to system component
The failure serial number of fault time is modified, and is carried out parameter Estimation using maximum-likelihood method, is carried out with linearly dependent coefficient method
Hypothesis testing, in the hope of model initial parameter, for component faults information small sample feature, the parameter obtained to maximum-likelihood method
Estimated result carries out drift correction, to determine component faults rate model.
Numerically-controlled machine tool system component faults rate modeling procedure described in technical scheme steps four based on time correlation is as follows:
(1) it is directed to the right censored data of fixed time test bring, according to the n component faults time of numerically-controlled machine tool system,
It is calculated using failure serial number of the Johnson method to fault time；
By all k numbers such as fault of numerical control machine tool data and right truncation according to arranging from small to large by integer, this column number is remembered
For j (1≤j≤k)；Integer arrangement is pressed to numerically-controlled machine tool m fault data of the component from small to large, remembers that this column number is i (1≤i
≤ m), then the serial number r of i-th of fault data of the componentiIt is calculated with formula (5):
ri=ri-1+(k+1-ri-1)/(k+2-j) (5)
In formula: r0=0；
(2) numerically-controlled machine tool component faults rate model parameter estimation；
If numerically-controlled machine tool component faults data obey distribution functionFailure rate is λ0(t)
=β θβ(t)β-1Two parameter Weibull model；If t1,t2,…,tkFor a component faults interval time order statistic, then shape
Shape estimates of parametersWith dimensional parameters estimated valueEstimated using formula (6):
Newton-Raphson iterative method row numerical solution can be used to above formula；
For component faults information small sample feature, using formula (7), with repairing parital coefficient γβ(k) to form parameter's
Drift correction:
Using formula (8) to the carry out drift correction of scale parameter α:
γβ(k) calculation method are as follows: as sample size k >=4,As sample size k=3,
Accordingly, available Weibull model estimates of parameters；
(3) numerically-controlled machine tool component faults rate model hypothesis is examined；
Using K-S method of inspection, according to formula (9), (10) computation model test value Dk, according to fault time data volume k and
Level of significance α calculates K-S and examines critical value Dk,α, work as Dk< Dk,αWhen, then it is assumed that fault data, which is obeyed, assumes distribution, otherwise
Refusal is assumed；
Wherein: F0(x) --- assuming that distribution function；
Fk(x) --- sample size is the empirical distribution function of k, it may be assumed that
The calculating of numerically-controlled machine tool component faults related coefficient refers to based on failure Email Filtering model, with the number of time correlation
Control machine tool system component faults rate function is edge distribution, introduces Copula contiguous function, constructs joint distribution function, passes through meter
It calculates and solves failure related coefficient.
Steps are as follows for the calculating of numerically-controlled machine tool system component faults related coefficient described in technical scheme steps five:
(1) suitable Copula function is chosen；
Copula function is " contiguous function ", it is that its one-dimensional edge distribution connects the Joint Distribution of multiple random variables
Pick up the function come.The component of Weibull distribution is obeyed for time between failures, is chosen in Archimedes family of functions
Gumbel Copula function.
(2) joint distribution function is established；
If reliability is R under the fault time correlation of system componentsi(t), i=1,2 ... n, then with Gumbel
Copula is the joint distribution function R of k associated component of contiguous function1 ..., k(t) are as follows:
Wherein, related coefficient θ ∈ (0,1], when θ=1, component faults are mutually indepedent between indicating level；As θ → 0, indicate
Component faults are intended to perfectly correlated between level.
(3) failure related coefficient calculates；
The modeling of numerically-controlled machine tool system component faults rate refers under failure rate correlation determines according to failure Email Filtering model
Failure direction of transfer, the relevant numerically-controlled machine tool system component faults rate of binding time and system components fail related coefficient, building
Component resultant fault rate model.For the failure of the composition of three layer assemblies shown in the attached drawing 2 passs hierarchical model.Three layer assemblies composition
System components fail transitive relation is as shown in Fig. 3.
Then the comprehensive reliability function R of bottom component and middle layer assembly is obtained by formula (12)12(t), and Matlab is used
Software is programmed, and calls maximum likelihood function that can acquire correlativity coefficient θ.
Similarly, system comprehensive reliability function R is obtained by formula (13)123(t), and correlativity coefficient θ is acquired2。
The modeling of numerically-controlled machine tool system component faults rate is as follows under failure rate correlation described in technical scheme steps six:
Bottom component resultant fault rate are as follows:
Middle layer assembly resultant fault rate are as follows:
It is obtained by formula (11), R12(t)=C (R1(t),R2(t)), then
Skin assemblies resultant fault rate are as follows:
It is obtained under failure rate correlation after each hierarchy component failure rate function, based on formula (18) according to formula (14) to (17)
Calculate the corresponding Reliability Function of each level
The modeling of numerically-controlled machine tool system component different degree refers to system component series connection to be it is assumed that by asking under failure rate correlation
The method of local derviation seeks each level assembly dynamic different degree model, on this basis, with the product of component unreliable degree and dynamic different degree
Core disturbance degree is defined, carrys out evaluation component reliability Improvement.
Specific step is as follows for numerically-controlled machine tool component Significance Analysis described in technical scheme steps seven:
(1) System reliability modeling
If any one of system component failure just directly causes whole system failure, which is regarded as by several
The train that component is constituted.Three component system Reliability Function shown in attached drawing 3 can be obtained in correlation according to this structure
Are as follows:
(2) reliability dynamic different degree models
The system dependability model lower component Reliability Model related to failure rate obtained by formula (19), according to formula
(20) it carries out assembly reliability dynamic different degree and builds type:
In formula: IjFor the reliability dynamic importance functions of j component.
Formula (20) indicates that reliability importance is change rate of the system dependability to component reliability, if two component i and j
It is I in the different degree relationship of moment ti(t) > Ij(t), then illustrating that the unfailing performance of lifting assembly i more significantly improves system can
Horizontal by degree, component i is more important than component j at this time for side light.
(3) reliability core different degree models
The modeling of assembly reliability core different degree is as shown in formula (21):
Kj=(1-Rj(t))×Ij (21)
In formula: KjFor component j core different degree；IjFor component j dynamic different degree；RjIt (t) is component j Reliability Function.
Core different degree is the amendment to dynamic different degree, avoids the occurrence of the problem that different degree is high but promotion effect is low.Group
Part reliability dynamic different degree model considers component to the size of system reliability influence degree, if but certain moment component can
Very high by property level, continuing to lift up the component reliability will become extremely difficult.On the contrary, at this time promoted a reliability compared with
Low component promotes system reliability level can be more economical.Therefore core different degree model mentions for measuring assembly reliability level
Potentiality are risen, i.e. the big component of core different degree, improved potentiality are also big.
Compared with prior art the beneficial effects of the present invention are:
Invention components reliability importance analysis method considers the event of system component in the true centering member of component faults rate
Downtime correlation, it is also contemplated that system components fail propagates hierarchical relationship, fault propagation direction, and it is quasi- to improve the modeling of component faults rate
True property, and traditional to ignore fault time related or leave the system components fail rate in fault propagation direction modeling ratio out of consideration more
Rationally, more meet reality.
Detailed description of the invention
The present invention will be further described below with reference to the drawings:
Fig. 1 is Cnc ReliabilityintelligeNetwork Network importance analysis flow chart of the present invention；
The system failure Email Filtering model that Fig. 2 is made of three layer assemblies；
The system failure transitive relation model that Fig. 3 is made of three layer assemblies；
Fig. 4 is numerically-controlled machine tool system failure Email Filtering model；
Fig. 5 a is three layer assembly reliability curves under numerically-controlled machine tool system failure rate correlation；
Fig. 5 b is three layer assembly dynamic different degree curve under numerically-controlled machine tool system failure rate correlation；
Fig. 5 c is three layer assembly core different degree curve under numerically-controlled machine tool system failure rate correlation；
Fig. 6 a is three layer assembly reliability curves under numerically-controlled machine tool system time correlation；
Fig. 6 b is three layer assembly dynamic different degree curve under numerically-controlled machine tool system time correlation；
Fig. 6 c is three layer assembly core different degree curve under numerically-controlled machine tool system time correlation；
Specific embodiment
The present invention is explained in detail with reference to the accompanying drawing:
As shown in fig.1, numerically-controlled machine tool assembly reliability importance analysis of the invention include the following steps: will be
System is divided into n component；System components fail data divide and trouble correlation analytic；Fault propagation digraph is established and matrix is retouched
It states；Component faults rate modeling based on time correlation；Inter-module failure related coefficient calculates；Based on the relevant component event of failure rate
The modeling of barrier rate；System component reliability importance models under failure rate correlation.
One, the division of system components fail data and trouble correlation analytic
To carry out the modeling of component faults transmittance process and failure rate modeling, realization system component reliability importance is modeled,
The present invention is divided using failure causation analysis to fault data and trouble correlation analytic.
1, system components fail data divide
System component divides: entire numerically-controlled machine tool system component being divided into n according to structure of numerically controlled machine-tool and working principle
A component；
Component faults data: it for the numerically-controlled machine tool field failure information of acquisition, is calculated by means of data, combination failure causes
Fault time is determined because analyzing, and establishes corresponding relationship between various components and fault time；
2, system components fail association analysis
According to the numerically-controlled machine tool field failure information of acquisition, according to the correlation experience in terms of system structure function, using event
Barrier causation analysis determines component faults incidence relation.
Two, system components fail transfer matrix describes
To carry out component faults transmitting modeling, the analysis of system component reliability importance is realized, the present invention uses direct square
The direct transitive relation of component faults is described in battle array.
Failure transitive relation is mainly the field failure data and trouble correlation analytic according to acquisition, and combination failure diagnoses hand
Volume is determined.System components fail transitive relation n × n rank direct matrix Y=[yij]n×nIt is described；
Wherein: yijIt is component i to the failure degree of transitivity of component j；When i=j, yij=0；
Direct matrix can inter-module failure transmitting direct relation express with a matrix type, but between node
Connecing influence relationship can not portray.The failure of some elements is to be transmitted to other component by certain intermediate members in system, into
It also must be considered that into when row outage correlation.
Three, numerically-controlled machine tool system component faults Email Filtering model foundation
Because direct matrix Y can only describe the direct transitive relation of component faults, for the description of indirect transfer relationship need by
Direct relation matrix Y standardization, after obtaining normalized matrix X, calculates combined influence matrix T, calculates disturbance degree accordingly, is affected
Degree, centrad and reason degree determine therefrom that component is that tendency influences class or is affected class, and combination failure influences relationship and determines group
Level of the part in failure Email Filtering model, i.e. bottom, middle layer and surface layer.System components fail Email Filtering model foundation
It is that meter carries out according to the following steps:
(1) direct relation matrix Y is standardized as the following formula, obtains normalized matrix X；
(2) combined influence matrix T is calculated using following formula；
I is unit matrix in formula.
(3) each component degree of correlation is calculated
Every a line and each column to combined influence matrix T are summed respectively as the following formula, obtain disturbance degree D and degree of being affected B.
Wherein D value indicates the component directly or indirectly to the influence degree of other assemblies, and B value indicates that the component is direct by other assemblies
Or indirect influence degree.
Calculate centrad (di+bj) indicate inter-module strength of association, reason degree (di-bj) indicate component influences or by shadow
Loud degree.If (di-bj) be positive value when, indicate the component tendency influence class；(di-bj) be negative value when indicate the component be inclined to
It is affected class.
The size of each component disturbance degree, degree of being affected, centrad and the reason degree that are determined according to DEMATEL method, specifies group
Part directly or indirectly influences relationship, establishes attached system components fail biography shown in Fig. 2 in conjunction with the failure transport mechanism of each inter-module
Pass hierarchy Model.
Four, the system components fail modeling based on time correlation
To consider that system components fail time correlation carries out component faults modeling, system component reliability importance point is realized
Analysis, present invention introduces Johnson methods to correct system components fail chronological order.
1. system components fail chronological order is corrected；Data ks all to fault of numerical control machine tool data and right truncation etc. are from small
To arranging by integer greatly, remember that this column number is j (1≤j≤k)；Then, only to k fault data of the numerically-controlled machine tool component from small
To arranging by integer greatly, remember that this column number is i (1≤i≤m), then the serial number r of i-th of fault datai=ri-1+(k+1-
ri-1)/(k+2-j), enable r0=0.
2, numerically-controlled machine tool component faults rate models；If numerically-controlled machine tool component faults data obey distribution functionFailure rate is λ0(t)=β θβ(t)β-1Two parameter Weibull model；If t1,t2,…,tkFor
One component faults interval time order statistic, then form parameter estimated valueDimensional parameters estimation
ValueNewton-Raphson iterative method row numerical solution can be used to it；For component faults information sample
This feature, using repairing parital coefficient γβ(k) to form parameter estimated valueCarry out drift correction, form parameter estimated value after amendment
ForScale parameter estimated valueDrift correction value be
γβ(k) calculation method are as follows: as sample size k >=4,As sample size k < 4,
So far, Weibull model parameter Estimation is completed；Using K-S method of inspection, calculates and assume to divide
Cloth function F0(x) empirical distribution function for being k with sample sizeAbsolute value of the difference
Maximum value Dk, according to fault time data volume k and level of significance α, calculate K-S and examine critical value Dk,α, work as Dk< Dk,αWhen, then
Think that fault data is obeyed and assume distribution, otherwise refusal is assumed；
Five, the system components fail related coefficient based on Copula function calculates
The calculating of numerically-controlled machine tool component faults related coefficient refers to based on failure Email Filtering model, with the number of time correlation
Control machine tool system component faults rate function is edge distribution, introduces Copula contiguous function, constructs joint distribution function, passes through fortune
It is programmed with Matlab software, calls maximum likelihood function to be solved, computation module failure related coefficient.
The component of Weibull distribution is obeyed for time between failures, chooses the Gumbel in Archimedes family of functions
Copula function establishes joint distribution function；If reliability is R under the fault time correlation of system componentsi(ti), i=1,
2 ... k, the then joint distribution function of k associated component
Wherein, related coefficient θ ∈ (0,1], when θ=1, component faults are mutually indepedent between indicating level；As θ → 0, group between level is indicated
Part failure is intended to perfectly correlated.It is programmed with Matlab software, calls maximum likelihood function to be solved, can calculate
To related coefficient θ；
Six, based on the relevant system components fail rate modeling of failure rate
The modeling of numerically-controlled machine tool system component faults rate refers under failure rate correlation determines according to failure Email Filtering model
Failure direction of transfer, the relevant numerically-controlled machine tool system component faults rate of binding time and system components fail related coefficient, building
Component resultant fault rate model.For the failure of the composition of three layer assemblies shown in the attached drawing 2 passs hierarchical model.Three layer assemblies composition
System components fail transitive relation is as shown in Fig. 3.
The modeling of three layer assembly failure rates is as follows under failure rate correlation:
Bottom component resultant fault rate are as follows:According to contiguous function, bottom component, middle layer assembly can be obtained
The joint Reliability Model of the subsystem of composition is R12(t)=C (R1(t),R2(t)) the related coefficient θ that is out of order is calculated accordingly1, then
Middle layer assembly resultant fault rate are as follows:According to contiguous function, bottom component, middle layer can be obtained
The subsystem of component composition is R with the Reliability Model of combining of skin assemblies(12)3(t)=C (R12(t),R3(t)) it calculates accordingly
Failure related coefficient θ2, due toTherefore skin assemblies resultant fault rate are as follows:
Seven, numerically-controlled machine tool system assembly reliability different degree models under failure rate correlation
The modeling of numerically-controlled machine tool system component different degree refers to system component series connection to be it is assumed that by asking under failure rate correlation
The method of local derviation seeks each level assembly dynamic different degree model, on this basis, with the product of component unreliable degree and dynamic different degree
To define core disturbance degree.
In the case where obtaining failure rate correlation after each hierarchy component failure rate function, pressIt calculates each
The corresponding Reliability Function of hierarchy componentAssuming that component system is series model, then three components shown in attached drawing 3 can be obtained
System dependability function isAccording to system dependability function to each component reliability
The method that function seeks local derviation establishes j assembly reliability dynamic importance functionsThe unreliable degree function of definitions component with
The product of assembly reliability dynamic importance functions is assembly reliability core importance functions K, j assembly reliability core different degree
Function Kj=(1-Rj(t))×Ij。
Application reliability dynamic different degree model evaluation component is to the size of system reliability influence degree, with reliability core
The horizontal Improvement of heart different degree model evaluation assembly reliability.
Embodiment
Numerically-controlled machine tool component Significance Analysis
Accident analysis is carried out to 5 of acquisition 13, scene of certain numerically-controlled machine tool relevant fault data, discovery shares 7 components
Relevant fault occurs, 7 component liaison fault information analysis of numerically-controlled machine tool are as shown in table 1.
1 numerically-controlled machine tool system component liaison accident analysis table of table
The influence relationship that relevant fault occurs according to 1 inter-module of table obtains direct relation matrix Y are as follows:
According to formula (2), (3) respectively obtain normalized matrix X and combined influence matrix T is respectively as follows:
By calculating, disturbance degree, degree of being affected and the centrad and reason degree of each component are obtained, as shown in table 2.
2 disturbance degree of table, degree of being affected, centrad, reason degree table
The type numerically-controlled machine tool component can be divided by three levels by table 2.Because both J and K centrad and reason degree are overlapped, and
Degree of being affected is equal to 0, is determined as the source of trouble, therefore J and K is bottom component；Because both S and M disturbance degree are equal to 0, therefore are determined as
Skin assemblies, i.e. S and M are skin assemblies；Remaining V, D, F are all middle layer assembly.It is digitally controlled machine failure transmitting level accordingly
Model, as shown in Fig. 4.
5 certain type fault of numerical control machine tool information are as shown in table 3.
3 component faults interval time of table
Note: band " * " is bottom component faults data in table, and band " # " is skin assemblies fault data, remaining is middle layer assembly
Fault data.
With bottom component faults time data instance, test data is ranked up using formula (5), correction result such as table
Shown in 4.
The amendment of 4 bottom component faults order of table
Assuming that component faults interval time obeys Weibull distribution, according to obtaining revised failure rank in table 4, according to
Formula (6)~(10), obtaining level assembly reliability model parameter on earth is α*=370.879, β*=1.149, DK=6=0.4708,
As k=6 and level of significance α=0.10 when Dk,α=0.498, because of Dk< Dk,α, therefore model passes through the test of fitness of fot, the type number
Control lathe bottom level Reliability Function and failure rate function are as follows:
Bottom component:
Middle layer and skin assemblies Reliability Function can similarly be obtained and failure rate function is respectively as follows:
Middle layer assembly:
Skin assemblies:
Hierarchical relationship is transmitted according to system shown in Figure 4 component faults, establishes Joint Distribution using Gumbel Copula function
Model is programmed with Matlab software, is called maximum likelihood function to be solved, is obtained θ1=0.254, equally to parameter
Estimated value is fitted inspection using K-S method of inspection, because of DK=19=0.111, D19,0.1=0.280, meet Dk< Dk,α, therefore model
Pass through the test of fitness of fot.
Therefore the joint distribution function of bottom component, middle layer assembly composition subsystem and skin assemblies can be established, i.e. system is comprehensive
Close Reliability Function are as follows:
θ is acquired with same method2=0.198.
The relevant each hierarchy component reliability dynamic importance functions of failure rate and core can be established according to formula (20), (21)
Heart importance functions draw corresponding different degree curve as shown in Fig. 5 b and Fig. 5 c using software.It can similarly draw under time correlation
Each component different degree curve is as shown in Fig. 5 b and Fig. 5 c.
(1) by Fig. 6 a it is found that time correlation bottom layer assembly reliability curves fall off rate is the largest；Generate this difference
It is other the reason is that by bottom component Reliability Function form parameter be greater than 1 caused by；By Fig. 5 a it is found that failure rate correlation lower component can
In line of writing music, bottom component reliability fall off rate is less than the reliability fall off rate in middle layer and surface layer；Generate this difference
The reason of be caused by ignoring failure direction of transfer in Fig. 6 a, because of the presence of failure related coefficient, middle layer and skin assemblies therefore
Barrier rate can significantly rise, and reliability is decreased obviously, this is consistent with failure transfer principle.
(2) comprehensive it is found that the time interval and different degree of each hierarchy component reliability variation changed by Fig. 6 a, 6b, 6c
Time interval is consistent, and the low component dynamic different degree of reliability and core different degree are high；It is obtained by Fig. 5 a, 5b, 5c synthesis, respectively
The time interval of hierarchy component reliability variation and the time interval of different degree variation, which exist, to be deviated, and deviant is related to failure
Coefficient positive correlation, also meets the low component dynamic different degree of reliability and core different degree is high, illustrates assembly reliability
Different degree cannot directly determine that this is really to match with engineering according to the time interval of reliability variation.
(3) present invention considers influence of the system components fail to studied component faults rank, is obtained by rank amendment
The failure rate model of system component, and combination failure Email Filtering model and failure related coefficient were obtained, failure rate correlation is established
Lower numerically-controlled machine tool component faults rate model establishes different degree model accordingly and carries out Significance Analysis, overcomes existing because ignoring
System components fail time correlation ignores failure direction of transfer and leads to the deviation of component faults rate model.Finally, with certain
For seven class component of domestic numerical control machine tool system, the validity of proposed method is demonstrated.When this is for rationally carrying out modular repair
Between plan and Reliability Distribution, improve system designed reliability, ensure machine tool system safe operation have certain guidance
Meaning.
Claims (7)
1. a kind of numerically-controlled machine tool component importance analysis, which is characterized in that include the following steps:
Step 1: entire numerically-controlled machine tool system component is divided into n component；Believed according to the numerically-controlled machine tool field failure of acquisition
Breath determines fault time by means of the correlation experience in terms of data calculating, failure causation analysis and system structure function, determines each
A component and corresponding relationship and inter-module failure transitive relation between fault time；
Step 2: establish component transitive relation according to failure causation analysis, and with logm control machine tool system inter-module failure
Transitive relation is described；
Step 3: application decision D. Lab ecision making trial and evaluation laboratory method benefit
Failure Email Filtering structural model is converted by numerically-controlled machine tool system inter-module failure transitive relation with graph theory and matrix tool, really
Determine level of the system component in failure Email Filtering structural model；
Step 4: the numerically-controlled machine tool system component faults rate based on time correlation models；
Step 5: the numerically-controlled machine tool system component faults rate function based on failure Email Filtering structural model, time correlation, introduces
Copula is theoretical, carries out numerically-controlled machine tool system component faults related coefficient and calculates；
Step 6: based on failure Email Filtering structural model, the numerically-controlled machine tool system component faults rate of time correlation, system component
Failure related coefficient, the numerically-controlled machine tool system component faults rate under failure rate correlation that carries out model；
Step 7: being based on Cascade System it is assumed that important by asking local derviation method to establish numerically-controlled machine tool system assembly reliability dynamic
Spend model and core different degree model, line number of going forward side by side control machine tool assembly Significance Analysis.
2. numerically-controlled machine tool component importance analysis according to claim 1, it is characterised in that:
The matrix that numerically-controlled machine tool system inter-module failure transitive relation is described in step 2 refers to direct relation matrix Y=
[yij]n×n:
Wherein: yijIt is component i to the failure degree of transitivity of component j；When i=j, yij=0.
3. numerically-controlled machine tool component importance analysis according to claim 2, it is characterised in that:
Level of the system component described in step 3 in failure Email Filtering structural model determines, refers to and counts according to the following steps
Calculate the numerically-controlled machine tool system inter-module failure degree of correlation:
(1) direct relation matrix Y is handled as the following formula (2), obtains normalized matrix X；
(2) combined influence matrix T is calculated using formula (3)；
I is unit matrix in formula；tij--- component i is including direct with indirect influence to the combined influence of component j；
(3) each component degree of correlation is calculated；
Every a line and each column to combined influence matrix T are summed respectively as the following formula, obtain disturbance degree D and degree of being affected B；Wherein
D value indicates the component directly or indirectly to the influence degree of other assemblies, and B value indicates that the component is direct or indirect by other assemblies
Influence degree；
Centrad (di+bj) indicate inter-module correlation degree, reason degree (di-bj) indicate component influences or the degree that is affected；
If (di-bj) be positive value when, indicate the component tendency influence class；(di-bj) be negative value when indicate the component tendency be affected class；
Wherein diIt indicates i-th of element in disturbance degree matrix D, is added up by combined influence matrix T the i-th row all elements
It arrives；bjIt indicates j-th of element in degree of being affected matrix B, is obtained by the way that combined influence matrix T jth column all elements are cumulative；
According to the size of each component disturbance degree, degree of being affected, centrad and reason degree, specifying component directly or indirectly influences to close
System, establishes failure Email Filtering structural model in conjunction with the failure transport mechanism of each inter-module.
4. numerically-controlled machine tool component importance analysis according to claim 1, it is characterised in that:
Numerically-controlled machine tool system component faults rate modeling procedure described in step 4 based on time correlation is as follows:
(1) it is adopted for the right censored data of fixed time test bring according to the fault time of n component of numerically-controlled machine tool system
It is calculated with failure serial number of the Johnson method to fault time；
By fault of numerical control machine tool data and all k numbers of right truncation according to being arranged from small to large by integer, remember this column number be j (1≤
j≤k)；Integer arrangement is pressed to numerically-controlled machine tool m fault data of the component from small to large, remembers that this column number is i (1≤i≤m), then
The serial number r of i-th of fault data of the componentiIt is calculated with formula (5):
ri=ri-1+(k+1-ri-1)/(k+2-j) (5)
In formula: r0=0；
(2) numerically-controlled machine tool component faults rate model parameter estimation；
If numerically-controlled machine tool component faults data obey two parameter Weibull model；If t1,t2,…,tkWhen for a component faults interval
Between order statistic, then form parameter estimated valueWith dimensional parameters estimated valueEstimated using formula (6):
Newton-Raphson iterative method row numerical solution is used to above formula；
For component faults information small sample feature, with repairing parital coefficient γβ(k) to form parameterDeviation be modified, correct
Form parameter is β afterwards*It is calculated using formula (7):
With repairing parital coefficient γα(k,β*) to scale parameterDeviation be modified, after amendment scale parameter be α*Using formula (8)
It calculates:
γβ(k) calculation method are as follows: as sample size k >=4,As sample size k=3,
Wherein,Referred to as gamma function；
Accordingly, available Weibull model estimates of parameters；
(3) numerically-controlled machine tool component faults rate model hypothesis is examined；
Using K-S method of inspection, according to formula (9), (10) computation model test value Dk, according to fault time data volume k and conspicuousness
Horizontal α calculates K-S and examines critical value Dk,α, work as Dk< Dk,αWhen, then it is assumed that fault data, which is obeyed, assumes distribution, and otherwise refusal is false
If；
Wherein: F0(x) --- assuming that distribution function；
Fk(x) --- sample size is the empirical distribution function of k, it may be assumed that
5. numerically-controlled machine tool component importance analysis according to claim 1, it is characterised in that:
Steps are as follows for the calculating of the related coefficient of numerically-controlled machine tool system component faults described in step 5:
(1) suitable Copula function is chosen；
Copula function is the function that the Joint Distribution of multiple random variables is connected with its one-dimensional edge distribution；For event
The component for hindering interval time obedience Weibull distribution, chooses the Gumbel Copula function in Archimedes family of functions；
(2) joint distribution function is established；
If reliability is R under the fault time correlation of system componentsi(t), i=1,2 ..., k are then with Gumbel Copula
The joint distribution function R of k associated component of contiguous function1 ..., k(t) are as follows:
Wherein, related coefficient θ ∈ (0,1], when θ=1, component faults are mutually indepedent between indicating level；As θ → 0, level is indicated
Between component faults be intended to it is perfectly correlated；
(3) failure related coefficient calculates；
The comprehensive reliability function R of bottom component and middle layer assembly is obtained by formula (12)12(t)；System is obtained by formula (13)
Comprehensive reliability function R123(t)；
It is programmed with Matlab software, maximum likelihood function is called to acquire correlativity coefficient θ1、θ2。
6. numerically-controlled machine tool component importance analysis according to claim 5, it is characterised in that:
The modeling of numerically-controlled machine tool system component faults rate, which refers to, under failure rate correlation determines event according to failure Email Filtering structural model
Hinder direction of transfer, the relevant numerically-controlled machine tool system component faults rate of binding time and system components fail related coefficient, building group
Part resultant fault rate model；
The modeling of numerically-controlled machine tool system component faults rate is as follows under failure rate correlation described in step 6:
Bottom component resultant fault rate are as follows:
Middle layer assembly resultant fault rate are as follows:
The comprehensive reliability function R of bottom component and middle layer assembly is obtained by formula (12)12(t), then bottom component and middle layer assembly
Form the resultant fault rate λ of subsystem12(t) it is calculated by formula (16)；
Skin assemblies resultant fault rate are as follows:
λ1(t) bottom component faults rate is indicated；λ2(t) middle layer component faults rate is indicated；λ3(t) skin assemblies failure rate is indicated；
R′12It (t) is R12(t) derivative；
It is obtained under failure rate correlation after each hierarchy component resultant fault rate function, based on formula (18) according to formula (14) to (17)
Calculate each hierarchy component Reliability Function
7. numerically-controlled machine tool component importance analysis according to claim 5, it is characterised in that:
Specific step is as follows for the Significance Analysis of numerically-controlled machine tool component described in step 7:
(1) System reliability modeling
If any one of system component failure just directly causes whole system failure, which is regarded as by several components
The train of composition；Correlation according to this structure obtains three component system Reliability Functions are as follows:
(2) reliability dynamic different degree models
The system dependability model obtained by formula (19), combination failure rate correlation lower component Reliability Model, according to formula
(20) modeling of assembly reliability dynamic different degree is carried out:
In formula: IjFor the reliability dynamic importance functions of j component；
By formula (20) it is found that if two component i and j moment t different degree relationship be Ii(t) > Ij(t), then illustrate promotion group
The unfailing performance of part i more significantly improves system dependability level, and component i is more important than component j at this time for side light；
(3) reliability core different degree models
The modeling of assembly reliability core different degree is as shown in formula (21):
Kj=(1-Rj(t))×Ij (21)
In formula: KjFor component j core different degree；IjFor component j dynamic different degree；RjIt (t) is component j Reliability Function；
So far component different degree curve is obtained, realizes numerically-controlled machine tool component Significance Analysis.
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