CN103971025A - Failure correlativity dynamic change analysis method of numerically-controlled machine tool - Google Patents

Abstract

The invention discloses a failure correlativity dynamic change analysis method of a numerically-controlled machine tool, aiming to overcome the problem that the degree of correlation among a plurality of systems with an intricate correlativity in a failure chain of mutual interference failure (I.F) cannot be determined by the prior art. The failure correlativity dynamic change analysis method comprises the steps: 1, processing failure data by using an FMECA (Failure Mode Effects and Criticality Analysis) analysis technology, dividing failure parts of all subsystems of the machine tool, settling data of correlation failures among all subsystems; 2, analyzing correlation data, summarizing interaction forms among the relevant subsystems, and defining types and elements of failure chains; 3, specific to different correlation failure chains, solving a comprehensive failure rate of correlation failure subsystems by using a dependency relationship of independent failure rates, correlation failure rates and comprehensive failure rates, respectively establishing a correlation coefficient computing model of all failure chains, and forming a correlation coefficient model system of correlation failures; 4, considering the analysis of a maintenance policy of correlation failures.

Description

A kind of fault of numerical control machine tool correlationship Dynamic Variation Analysis method

Technical field

The invention belongs to numerical control machine tool technique field, relate to a kind of numerically-controlled machine dependent failure analytical approach, especially relate to a kind of fault of numerical control machine tool correlationship Dynamic Variation Analysis method.

Technical background

The existence of numerical control equipment dependent failure has caused the variation of its indigenous fault rate, if reliability design and allocated phase have been ignored the failure dependency between subsystem, the design load of reliability is inevitable produces larger error with the actual occurrence value of production.The simultaneously existence of dependent failure, if carry out predictive maintenance with the fiduciary level of independent failure, also caused node servicing time after prolong.In the system failure, there are 4 kinds of most typical dependent failures: series connection fault, negative correlation fault, common cause failure and phase mutual interference fault.The present invention relates to phase mutual interference fault type (Interactive failures, be called for short I.F), the common feature of this class dependent failure is: components A can accelerate or cause the generation of the fault of part B in the time breaking down, and this destruction is sometimes mutual.This interactional result has caused the failure rate of failure system to rise, and between the amplitude of rising and subsystem, interactional degree is relevant.Design, processing and manufacturing, installation and the misoperation of lathe all may cause the generation of this class dependent failure, so the probability occurring is larger, harmfulness is stronger.Along with the concern of Chinese scholars to dependent failure in recent years, relevant research deepens continuously, but the phase mutual interference fault type correlative study being prevalent between the subsystem on numerically-controlled machine has no report.

The degree of the mutual interference effect between subsystem is defined as related coefficient.The document of research of being absorbed in dependent interaction degree is less, and only document is also to carry out guestimate using it as parameter in order to realize other reliability index, has ignored its importance and preciseness in the middle of Calculation of Reliability.Although existing analytical approach and model have all been realized determining of related coefficient to a certain extent, all exist certain theory limit.Main analysis means has: 1. Statistics Method, utilize dependent failure incidence as related coefficient, so the quantity of sample collection number determined the variation of related coefficient, error is larger; 2. test method(s), utilizes research technique to obtain a large amount of test figures and determines related coefficient model.The method specific aim is stronger, and it is higher to realize cost, does not have general generalization; 3. subjective assignment method, experienced expert, to the degree of correlation marking between related system, calculates comprehensive grading value as related coefficient.The method is subjective, and assignment error is larger; 4.Copula function method, Copula function representation be the correlativity between variable, variable is combined to the function that cumulative distribution function couples together with variable edge cumulative distribution function, can utilize the dependent failure data of subsystem to calculate the related coefficient between subsystem, this related coefficient is common unique.The method is calculated comparatively complicated, and can not specify interaction relationship and the action direction between subsystem, and therefore model cannot be realized the analysis of complicated correlationship and the establishment of the model of multiple related coefficients between multisystem; 5. narrow boundary theory method, utilize the power function of the chife failure models of correlation subsystem to calculate related coefficient, the method is only suitable in the multimode of parts itself relevant, owing to cannot determining the correlationship of the power function of chife failure models between multisystem, be therefore difficult to realize the calculating of the related coefficient between multisystem; 6. failure rate method, sets up the relational expression of failure rate between correlation subsystem, derives related coefficient, determines the degree of correlation of subsystem.But the research of existing failure rate method ends at the calculating of two related coefficients between subsystem.

In analytical approach for the degree of correlation between all correlation subsystem, it is more accurate that failure rate method utilizes the variation relation of independent failure rate and dependent failure rate to embody degree of correlation, because method, except having quantification result, can specify the interaction direction between subsystem simultaneously.But existing analytic process but exists theory limit, this analytical approach only can be determined two dependent interaction degree between correlation subsystem, in the situation of the correlationship of multisystem complexity, the correlationship existing due to each subsystem is not limited to one, so for same subsystem fault data, may derive from different correlation subsystem, so caused the difficulty of further analysis.

Summary of the invention

The object of the invention is to overcome prior art can not determine in the fault chain of phase mutual interference fault (I.F), the problem that has the degree of correlation between the multisystem of complicated correlationship, provides a kind of fault of numerical control machine tool correlationship Dynamic Variation Analysis method.

For achieving the above object, technical scheme provided by the invention is that a kind of fault of numerical control machine tool correlationship Dynamic Variation Analysis method, comprises the following steps:

Step 1: utilize FMECA analytical technology to process fault data, the fault data of the each subsystem of lathe is carried out to statistical study, arrange the data between subsystems with dependent failure.

Step 2: analyze dependent failure data, conclude action mode, the kind of failure definition chain and the fault chain key element of summing up the phase mutual interference fault I.F fault type between correlation subsystem.

Step 3: for different dependent failure chains, utilize the dependence relation of independent failure rate, dependent failure rate and resultant fault rate, utilize the resultant fault rate model of dependent failure subsystem, derive respectively the Calculation of correlation factor model of all fault chains, the related coefficient model system of the related coefficient model composition dependent failure of all fault chains.

Step 4: consider the analysis of the maintenance policy of dependent failure.

The kind of the chain of fault described in technical scheme comprises five kinds:

The first: fault chain only has two subsystems, and for single effect, the bad motion state of subsystem i can have influence on subsystem j in lathe operational process, until subsystem j breaks down, and subsystem j does not exert an influence to subsystem i;

The second: fault chain only has two subsystems, and two sub-system interactions, the bad motion state of two subsystems influences each other, and forms vicious cycle, until one of them system is moved because of failure stopping;

The third: fault chain is made up of multiple subsystems, and the motion state of subsystem i has influence on multiple subsystems simultaneously, and itself is not subject to the impact of other correlation subsystem;

The 4th kind: fault chain is made up of multiple subsystems, subsystem j is subject to the impact of multiple subsystems, and it does not have dependent interaction to other any subsystem;

The 5th kind: fault chain is made up of more than three or three subsystem, it is the part or all of array configuration of aforementioned four kinds of basic fault chains, have at least a subsystem to be subject to the dependent interaction of more than two subsystem, and there is fault intermediate point subsystem, between correlation subsystem, form complicated correlationship, belonged to the type of complicated dependent failure chain.

The chain of failure definition described in technical scheme key element, refers to according to the position of fault subsystem in fault generating process in fault chain and effect fault subsystem is defined; Fault chain key element comprises:

(1) dependent failure starting point:

In the fault chain with correlationship, only affect other subsystem but the subsystem that not affected by other subsystem is called dependent failure starting point;

(2) dependent failure terminal:

In the fault chain with correlationship, be only subject to the impact of other subsystem, and the subsystem that does not affect other subsystem is called dependent failure terminal;

(3) fault intermediate point:

In the fault chain with correlationship, exist impact and the subsystem that is affected relation to be referred to as fault intermediate point simultaneously.

Described in technical scheme for different dependent failure chains, utilize the dependence relation of independent failure rate, dependent failure rate and resultant fault rate, utilize the resultant fault rate model of dependent failure subsystem, derive respectively the Calculation of correlation factor model of all fault chains, specifically according to resultant fault rate computation model:

Z _j(t): be the resultant fault rate of dependent failure subsystem j, calculate and obtain by the fault data in producing;

Z _ij(t): for the independent failure rate of subsystem j, determined by inherent reliability, obtain by test or production data before product export, in the situation that subsystem j is not subject to dependent failure and affects, z in theory _j(t)=z _ij(t);

for subsystem j is subject to the related coefficient of subsystem i effect, in the time of θ=0, without relevant, subsystem i breaks down and can not cause that j breaks down, in the time of θ=1, and complete dependence, subsystem i breaks down and must cause that j breaks down;

for subsystem j being produced to the dependent failure rate of the subsystem i of dependent interaction;

According to resultant fault rate model, according to formula (1), for the feature of fault chain, set up respectively the Calculation of correlation factor model of all fault chains, the related coefficient model system of the Calculation of correlation factor model composition dependent failure of all fault chains.

In technical scheme for the first of described fault chain and the third, the correlationship of fault chain is simple unidirectional relevant, dependent failure terminal subsystem j is only subject to the impact of a subsystem i, and the resultant fault rate of dependent failure subsystem j is obtained by formula (1):

$z_j\left(t\right)=z_{\mathrm{Ij}}\left(t\right)+{\mathrm{\θ}}_{i_j}\left(t\right)z_{i_j}{\left(t\right)}_g---\left(2\right)$

Have:

${\mathrm{\θ}}_{i_j}\left(t\right)=\frac{|z_j\left(t\right)-z_{\mathrm{Ij}}\left(t\right)|}{z_{i_j}{\left(t\right)}_g}---\left(3\right)$

Because correlation subsystem i is dependent failure starting point, be not subject to other subsystem dependent interaction, therefore wherein:

Z _ii(t): be the independent failure rate of subsystem i;

Z _j(t): be the resultant fault rate of dependent failure subsystem j;

for subsystem j is subject to the related coefficient of subsystem i effect.

In technical scheme for the 4th kind of described fault chain, the correlationship of fault chain is that multisystem is unidirectional relevant, dependent failure terminal j is subject to the dependent interaction of multiple subsystems simultaneously, and j is dependent failure terminal, and dependent failure terminal j running status does not affect other correlation subsystem; The resultant fault rate z of subsystem j _j(t) determined by k correlationship, for computing subsystem j is subject to the related coefficient of subsystem i effect value, do following hypothesis:

(1) subsystem j and k the related coefficient that subsystem is relevant between linear independence, i=1,2 ... K; Order time, there is formula (2) (3) to set up, derive formula (4) by formula (2):

$\left\{\begin{array}{c}{z}_{j1}\left(t_1\right)=z_{\mathrm{Ij}}\left(t\right)+{\mathrm{\θ}}_{1_j}\left(t\right)z_{1_j}{\left(t\right)}_g\\ z_{j2}\left(t_2\right)=z_{\mathrm{Ij}}\left(t\right)+{\mathrm{\θ}}_{2_j}\left(t\right)z_{2_j}{\left(t\right)}_g\\ .\\ .\\ .\\ z_{\mathrm{ji}}\left(t_i\right)=z_{\mathrm{Ij}}\left(t\right)+{\mathrm{\θ}}_{i_j}\left(t\right)z_{i_j}{\left(t\right)}_g\\ .\\ .\\ .\\ z_{\mathrm{jk}}\left(t_k\right)=z_{\mathrm{Ij}}\left(t\right)+{\mathrm{\θ}}_{k_j}\left(t\right)z_{k_j}\left(t\right)g\end{array}\right.i=\mathrm{1,2},...K---\left(4\right)$

Z _ji(t _i) be subject to point failure rate of i subsystem dependent interaction for subsystem j; Removed the dependent failure data of other subsystem beyond i by the fault data of subsystem j and carry out modeling.

(2) subsystem j is subject to point failure rate z of the dependent interaction of i subsystem _ji(t _i) and subsystem j resultant fault rate z _j(t) have functional relation:

z _j(t)＝φ _i(z _j1(t ₁),z _j2(t ₂),…z _jk(t _k),t) (5)

Subsystem i is all dependent failure starting point, the dependent failure rate of subsystem j is equaled to the independent failure rate of subsystem i; Formula

(4) in $z_{1_j}{\left(t\right)}_g=z_{I1}\left(t\right),z_{2_j}{\left(t\right)}_g=z_{I2}\left(t\right),...z_{k_j}{\left(t\right)}_g=z_{\mathrm{Ik}}\left(t\right),$ Thus can ask, according to formula (1), (4), formula (5) be derived as formula (6):

$\begin{array}{c}{z}_j\left(t\right)=z_{\mathrm{Ij}}\left(t\right)+\underset{i_j}{\mathrm{\Σ}}{\mathrm{\θ}}_{i_j}\left(t\right)z_{i_j}{\left(t\right)}_g\\ =z_{\mathrm{Ij}}\left(t\right)+\underset{i}{\mathrm{\Σ}}{\left(z\right)}_{\mathrm{ji}}\left(t_i\right)-z_{\mathrm{Ij}}\left(t\right)\end{array}i=\mathrm{1,2},...K---\left(6\right)$

for subsystem j is subject to the related coefficient of subsystem i effect.

In technical scheme for the second of described fault chain and the 5th kind, the correlationship of fault chain is that multisystem is complicated relevant, while calculating the resultant fault rate of each subsystem, need to obtain respectively dependent failure rate and the related coefficient of this subsystem and other correlation subsystem; If subsystem title is respectively: dependent failure starting point i, dependent failure terminal j, dependent failure intermediate point k, the resultant fault rate model of dependent failure terminal j is as follows:

$z_j\left(t\right)=z_{\mathrm{Ij}}\left(t\right)+{\mathrm{\θ}}_{i_j}\left(t\right)z_{i_j}{\left(t\right)}_g+{\mathrm{\θ}}_{k_j}{\left(t\right)z}_{k_j}{\left(t\right)}_g---\left(7\right)$

A point failure rate model that is obtained subsystem j by formula (4) is:

$\left\{\begin{array}{c}{z}_{\mathrm{ji}}\left(t_i\right)=z_{\mathrm{Ij}}\left(t\right)+{\mathrm{\θ}}_{i_j}\left(t\right)z_{i_j}{\left(t\right)}_g\\ z_{\mathrm{jk}}\left(t_k\right)=z_{\mathrm{Ij}}\left(t\right)+{\mathrm{\θ}}_{k_j}\left(t\right)z_{k_j{\left(t\right)}_g}\end{array}\right.---\left(8\right)$

Z _ji(t _i): for being subject to the dependent failure rate of the subsystem j that subsystem i affects;

Z _jk(t _k): for being subject to the dependent failure rate of the subsystem j that subsystem k affects;

for subsystem j being produced to the dependent failure rate of the subsystem i of dependent interaction;

for subsystem j being produced to the dependent failure rate of the subsystem k of dependent interaction;

for subsystem j is subject to the related coefficient of subsystem i effect;

for subsystem j is subject to the related coefficient of subsystem k effect;

Z _ji(t _i), z _jk(t _k) calculate as described in the calculating of point failure rate; I is dependent failure starting point, so ? can obtain.

Described in technical scheme, subsystem j is produced the dependent failure rate of the subsystem k of dependent interaction value analytic process as follows, taking subsystem k as research object, subsystem k is fault intermediate point, is also subject to the impact of subsystem i when subsystem j is affected, the resultant fault rate model of subsystem k is:

$z_k\left(t\right)=z_{\mathrm{Ik}}\left(t\right)+{\mathrm{\θ}}_{i_k}\left(t\right)z_{i_k}{\left(t\right)}_g---\left(9\right)$

Z _k(t): be the resultant fault rate of subsystem k;

Z _ik(t): be the independent failure rate of subsystem k;

for subsystem k is subject to the related coefficient of subsystem i effect;

for subsystem k being produced to the dependent failure rate of the subsystem i of dependent interaction;

Because i is dependent failure starting point, so z _k(t) tried to achieve z by the fault in production data of k _ik(t) for the independent failure rate of subsystem k is known, can be determined by formula (9); According to with whether be correlated with, for subsystem j is subject to the related coefficient of subsystem k effect, value in two kinds of situation,

The first: $z_{k_j}{\left(t\right)}_g=z_{\mathrm{Ik}}\left(t\right),{\mathrm{\θ}}_{k_j}\left(t\right)$ With irrelevant

The second: $z_{k_j}{\left(t\right)}_g=z_k\left(t\right),{\mathrm{\θ}}_{k_j}\left(t\right)$ With relevant

value is definite, can obtain according to formula (8).

Described in technical scheme, consider the analysis of the maintenance policy of dependent failure, specifically utilize the fiduciary level of the related coefficient model system revision subsystem between definite subsystem, calculate predictive maintenance node;

The maintenance policy of system, taking fiduciary level as according to formulating and optimizing, in the time that fiduciary level system or subsystem is less than the threshold value of plan regulation, needs system or subsystem to carry out preventive maintenance maintenance; If the fault of subsystem j is without dependent failure, its reliability is:

$R_j\left(t\right)=\exp (-\∫z_{\mathrm{Ij}}\left(t\right)\mathrm{dt}---\left(11\right)$

R _j(t): for subsystem j only has the reliability model in independent failure rate situation;

The reliability model of considering the subsystem j with dependent failure is:

$R_j^{\′}\left(t\right)=\exp (-\∫z_j\left(t\right)\mathrm{dt}=\exp (-\∫(z_{\mathrm{Ij}}\left(t\right)+\underset{i_j}{\mathrm{\Σ}}{\mathrm{\θ}}_{i_j}\left(t\right)z_{i_j}{\left(t\right)}_g)\mathrm{dt}---\left(12\right)$

So have: R _j(t)>=R ' _j(t) (13)

R ' _j(t): be the reliability model of the resultant fault rate foundation with subsystem j;

The described fiduciary level of calculating with independent failure rate has possibility bigger than normal, in the time that the reliability of subsystem j reaches the threshold value of regulation, the time point being calculated by the reliability model of subsystem j is during as maintenance node, because the timing node calculating with independent failure rate is greater than the timing node calculating with dependent failure rate, therefore by formula (11) calculate subsystem j servicing time node as maintenance schedule according to time, must cause preventive maintenance scheduling after prolong.

Compared with prior art beneficial effect of the present invention:

1. a kind of fault of numerical control machine tool correlationship Dynamic Variation Analysis method of the present invention is to investigate a large amount of fault datas as foundation, seek the rule of the data variation of I.F dependent failure, taking the correlationship form between subsystem as dividing according to I.F fault type being carried out to fault chain kind, for the analysis of dependent failure provides important analysis foundation.

2. a kind of fault of numerical control machine tool correlationship Dynamic Variation Analysis method of the present invention is taking failure rate method as analysis means, taking the dependence relation between independent failure rate, dependent failure rate and resultant fault rate as foundation, for the feature of different I.F dependent failure chains, determine the related coefficient model between subsystem, form related coefficient model system, set up correlationship between complicated multisystem and the analytical approach of degree of correlation..

3. a kind of fault of numerical control machine tool correlationship Dynamic Variation Analysis method of the present invention has broken through the theory limit of prior art, has expanded dependent failure theoretical system.Be optimized predictive maintenance maintenance project with analytical approach of the present invention, improved the accuracy of maintenance node, reduced the failure rate of equipment, thereby provide method and theoretical foundation to the reliability growth of equipment.

Brief description of the drawings

Fig. 1 is the FB(flow block) of a kind of fault of numerical control machine tool correlationship Dynamic Variation Analysis method of the present invention;

Fig. 2 is i.e. two the subsystem single effect schematic diagram of the first fault chain of five kinds of fault chains described in a kind of fault of numerical control machine tool correlationship Dynamic Variation Analysis method of the present invention;

Fig. 3 is i.e. two the sub-system interaction schematic diagram of the second fault chain of five kinds of fault chains described in a kind of fault of numerical control machine tool correlationship Dynamic Variation Analysis method of the present invention;

Fig. 4 is that the third fault chain of five kinds of fault chains described in a kind of fault of numerical control machine tool correlationship Dynamic Variation Analysis method of the present invention is that single subsystem acts on multiple subsystem schematic diagram simultaneously;

Fig. 5 is that the 4th kind of fault chain of five kinds of fault chains described in a kind of fault of numerical control machine tool correlationship Dynamic Variation Analysis method of the present invention is that single subsystem is subject to multiple subsystem effect schematic diagram simultaneously;

Fig. 6 is the 5th kind of a kind of schematic diagram that fault chain is complicated correlationship of five kinds of fault chains described in a kind of fault of numerical control machine tool correlationship Dynamic Variation Analysis method of the present invention;

Fig. 7 is the correlationship figure of servo-drive system, hydraulic system and tool holder system in a kind of fault of numerical control machine tool correlationship Dynamic Variation Analysis method.

Embodiment

Below in conjunction with accompanying drawing, a kind of fault of numerical control machine tool correlationship Dynamic Variation Analysis method is elaborated:

A kind of fault of numerical control machine tool correlationship Dynamic Variation Analysis method of the present invention is taking a large amount of investigation fault datas as foundation, seek the rule of the data variation of dependent failure, carry out the classification of fault chain for the interaction type between subsystem, find out independent failure rate according to different fault chains, dependence relation between dependent failure rate and resultant fault rate, determine the related coefficient model between subsystem, taking failure rate method as analyzing foundation, set up correlationship between complicated multisystem and the analytical approach of degree of correlation, break existing methodical theory limit, be optimized predictive maintenance maintenance project with this analytical approach.

A kind of fault of numerical control machine tool correlationship Dynamic Variation Analysis method comprises the following steps:

Step 1. utilizes FMECA analytical technology to process fault data, and the fault data of the each subsystem of lathe is carried out to statistical study, arranges the data between subsystems with dependent failure.

1) according to fault mode feature and fault happening part and fault occurrence cause, divide under fault, determine the fault occurrence frequency of subsystem and the severity of fault mode and harmfulness.

2) time between failures of calculating machine failure interval time and subsystems.

3) screening has the fault data of correlationship, determines the interaction type between subsystems.

Step 2. is analyzed dependent failure data, concludes phase mutual interference fault (I.F) interaction type of summing up between correlation subsystem, the kind of failure definition chain and fault chain key element:

1) kind of failure definition chain:

Consult Fig. 2, Fig. 3, Fig. 4, Fig. 5 and Fig. 6, complicated correlationship between the multiple subsystems of numerically-controlled machine is gone to numerous letter of depositing, open complicated surface phenomena, summarize five kinds of citation forms of phase mutual interference fault.Suppose that numerically-controlled machine is made up of K subsystem, be respectively 1,2 ... K, the dependent failure relation of any complexity all can be made up of these five kinds or several fault chains wherein.

Consult Fig. 2, the first: fault chain only has two subsystems, and for single effect, the bad motion state of subsystem i can have influence on subsystem j in lathe operational process, until j breaks down, and subsystem j does not exert an influence to subsystem i;

Consult Fig. 3, the second: fault chain only has two subsystems, and two sub-system interactions, the bad motion state of two subsystems influences each other, and forms vicious cycle, until one of them system is moved because of failure stopping;

Consult Fig. 4, the third: fault chain is made up of multiple subsystems, and the motion state of subsystem i has influence on multiple subsystems simultaneously, and itself is not subject to the impact of other correlation subsystem;

Consult Fig. 5, the 4th kind: fault chain is made up of multiple subsystems, subsystem j is subject to the impact of multiple subsystems, and it does not have dependent failure effect to other any system;

Consult Fig. 6, the 5th kind: fault chain is made up of more than three or three subsystem, is the simplest array configuration of aforementioned four kinds of basic fault chains, belong to the type of complicated correlationship fault chain.

2) failure definition chain key element:

According to the position of fault subsystem in fault generating process in fault chain and effect, it is defined.The present invention is defined as follows:

1. dependent failure starting point:

In the fault chain of correlationship, only affect the subsystem that other system is not subject to other systematic influence and be called dependent failure starting point, as Fig. 2,4,5 and Fig. 6 in i;

2. dependent failure terminal:

In the fault chain of correlationship, be only subject to the impact of other subsystem, and the subsystem that does not affect other subsystem is called dependent failure terminal, as the j in Fig. 2,4,5,6;

3. dependent failure intermediate point

In the fault chain of correlationship, exist impact and the subsystem that is affected relation to be referred to as dependent failure intermediate point simultaneously, as the k in Fig. 4, i, j in Fig. 3.

Step 3., for different dependent failure chain features, utilizes the dependence relation of independent failure rate, dependent failure rate and resultant fault rate to set up the model system of related coefficient:

1) described in, for different dependent failure chain features, utilize the dependence relation of independent failure rate, dependent failure rate and resultant fault rate, set up the model system of related coefficient.Specifically according to dependent failure rate computation model:

Z _j(t): be the resultant fault rate of dependent failure subsystem j, calculate and obtain by the fault data in producing;

Z _ij(t): for the independent failure rate of subsystem j, determined by inherent reliability, conventionally before product export, obtain by test or production data, in the situation that subsystem j is not subject to dependent failure and affects, z in theory _j(t)=z _ij(t);

for subsystem j is subject to the related coefficient of subsystem i effect, in the time of θ=0, without relevant, subsystem i breaks down and can not cause that j breaks down, in the time of θ=1, and complete dependence, subsystem i breaks down and must cause that j breaks down;

for subsystem j being produced to the dependent failure rate of the subsystem i of dependent interaction.

2) described in, for different dependent failure chain features, utilize the dependence relation of independent failure rate, dependent failure rate and resultant fault rate, set up the model system of related coefficient.Specifically, according to formula (1), for the feature of five kinds of fault chains, set up respectively the Calculation of correlation factor model of all fault chains, the related coefficient model system that forms dependent failure is as follows:

1. the correlationship of fault chain is simple unidirectional relevant, be the first and the third (the consulting Fig. 2, Fig. 4) of fault chain, dependent failure terminal subsystem j is only subject to the impact of a subsystem i, and the resultant fault rate of dependent failure terminal subsystem j is obtained by formula (1):

$z_j\left(t\right)=z_{\mathrm{Ij}}\left(t\right)+{\mathrm{\θ}}_{i_j}\left(t\right)z_{i_j}{\left(t\right)}_g---\left(2\right)$

Calculation of correlation factor model is:

${\mathrm{\θ}}_{i_j}\left(t\right)=\frac{|z_j\left(t\right)-z_{\mathrm{Ij}}\left(t\right)|}{z_{i_j}{\left(t\right)}_g}---\left(3\right)$

Because correlation subsystem i is dependent failure starting point, be not subject to other subsystem dependent interaction, therefore for the independent failure rate of subsystem i. for subsystem j is subject to the related coefficient of subsystem i effect;

2. the correlationship of fault chain is that multisystem is unidirectional relevant, be the 4th kind of fault chain, consult shown in Fig. 5, dependent failure terminal j is subject to the dependent interaction of multiple subsystems simultaneously, and j is dependent failure terminal, dependent failure terminal j running status does not affect other correlation subsystem.Resultant fault rate z _j(t) determined by k correlationship, as shown in formula (1).For computing subsystem j is subject to the related coefficient of subsystem i effect value meets following (1), (2) two hypothesis simultaneously:

(1) subsystem j and k the related coefficient that subsystem is relevant between linear independence, i=1,2 ... K.Even time have formula (2) (3) to set up, Fig. 4 correlationship figure can resolve into k relational expression as expressed in Fig. 1, derives formula (4) by formula (2).

$\left\{\begin{array}{c}{z}_{j1}\left(t_1\right)=z_{\mathrm{Ij}}\left(t\right)+{\mathrm{\θ}}_{1_j}\left(t\right)z_{1_j}{\left(t\right)}_g\\ z_{j2}\left(t_2\right)=z_{\mathrm{Ij}}\left(t\right)+{\mathrm{\θ}}_{2_j}\left(t\right)z_{2_j}{\left(t\right)}_g\\ .\\ .\\ .\\ z_{\mathrm{ji}}\left(t_i\right)=z_{\mathrm{Ij}}\left(t\right)+{\mathrm{\θ}}_{i_j}\left(t\right)z_{i_j}{\left(t\right)}_g\\ .\\ .\\ .\\ z_{\mathrm{jk}}\left(t_k\right)=z_{\mathrm{Ij}}\left(t\right)+{\mathrm{\θ}}_{k_j}\left(t\right)z_{k_j}\left(t\right)g\end{array}\right.i=\mathrm{1,2},...K---\left(4\right)$

Z _ji(t _i) for the failure rate that subsystem j is subject to i subsystem dependent interaction, on the basis of hypothesis (1), from the fault data of subsystem j, reject subsystem i other correlation subsystem in addition the dependent failure data modeling of subsystem j is tried to achieve.

(2) subsystem j is subject to point failure rate z of the dependent interaction of i subsystem _ji(t) with subsystem j resultant fault rate z _j(t) have functional relation.

z _j(t)＝φ _i(z _j1(t ₁),z _j2(t ₂),…z _jk(t _k),t) (5)

Taking the relation form of Fig. 4 as example, subsystem i is all dependent failure starting point, and the dependent failure rate of subsystem j is equaled to subsystem j independent failure rate.In formula (4) $z_{1_j}{\left(t\right)}_g=z_{I1}\left(t\right),z_{2_j}{\left(t\right)}_g=z_{I2}\left(t\right),...z_{k_j}{\left(t\right)}_g=z_{\mathrm{Ik}}\left(t\right),$ Thus can ask, according to formula (1), (4), formula (5) be derived as formula (6):

$\begin{array}{c}{z}_j\left(t\right)=z_{\mathrm{Ij}}\left(t\right)+\underset{i_j}{\mathrm{\Σ}}{\mathrm{\θ}}_{i_j}\left(t\right)z_{i_j}{\left(t\right)}_g\\ =z_{\mathrm{Ij}}\left(t\right)+\underset{i}{\mathrm{\Σ}}{\left(z\right)}_{\mathrm{ji}}\left(t_i\right)-z_{\mathrm{Ij}}\left(t\right)\end{array}i=\mathrm{1,2},...K---\left(6\right)$

3. the correlationship of fault chain is that multisystem is complicated relevant, i.e. the 5th kind and the second fault chain, and as Fig. 3,6 (Fig. 3 can be considered the special case of Fig. 6, and i and j are all considered as fault intermediate point), in figure, each subsystem all has more than two correlationship.While calculating the failure rate of each subsystem, need to obtain respectively dependent failure rate and the related coefficient of this subsystem and other correlation subsystem.Be calculated as example with the subsystem j failure rate in Fig. 6, establish subsystem title and be respectively: dependent failure starting point i, dependent failure terminal j, relevant intermediate point k, has according to formula (1)

$z_j\left(t\right)=z_{\mathrm{Ij}}\left(t\right)+{\mathrm{\θ}}_{i_j}\left(t\right)z_{i_j}{\left(t\right)}_g+{\mathrm{\θ}}_{k_j}{\left(t\right)z}_{k_j}{\left(t\right)}_g---\left(7\right)$

Obtained by formula (4)

$\left\{\begin{array}{c}{z}_{\mathrm{ji}}\left(t_i\right)=z_{\mathrm{Ij}}\left(t\right)+{\mathrm{\θ}}_{i_j}\left(t\right)z_{i_j}{\left(t\right)}_g\\ z_{\mathrm{jk}}\left(t_k\right)=z_{\mathrm{Ij}}\left(t\right)+{\mathrm{\θ}}_{k_j}\left(t\right)z_{k_j{\left(t\right)}_g}\end{array}\right.---\left(8\right)$

Z _ji(t _i): for being subject to the dependent failure rate of the subsystem j that subsystem i affects; for being subject to the dependent failure rate of the subsystem j that subsystem k affects; for subsystem j being produced to the dependent failure rate of the subsystem i of dependent interaction; for subsystem j being produced to the dependent failure rate of the subsystem k of dependent interaction; for subsystem j is subject to the related coefficient of subsystem i effect; for subsystem j is subject to the related coefficient of subsystem k effect.

calculate the calculating of point failure rate as described in formula (4); I in formula (8) is dependent failure starting point, so ? can obtain; definite relative complex because subsystem k is fault intermediate point, when j is affected, be also subject to the impact of i, its value analytic process is as follows, first taking k as research object, the resultant fault rate of subsystem k is:

$z_k\left(t\right)=z_{\mathrm{Ik}}\left(t\right)+{\mathrm{\θ}}_{i_k}\left(t\right)z_{i_k}{\left(t\right)}_g---\left(9\right)$

Z _k(t): the resultant fault rate of subsystem k; z _ik(t): the independent failure rate of subsystem k; for subsystem k is subject to the related coefficient of subsystem i effect: for subsystem k being produced to the dependent failure rate of the subsystem i of dependent interaction.

Because i is dependent failure starting point, so z _k(t) tried to achieve z by the fault in production data of k _ik(t) for the independent failure rate of subsystem k is known, can be determined by formula (9).According to with whether be correlated with, value in two kinds of situation

① $z_{k_j}{\left(t\right)}_g=z_{\mathrm{Ik}}\left(t\right),{\mathrm{\θ}}_{k_j}\left(t\right)$ With irrelevant

② $z_{k_j}{\left(t\right)}_g=z_k\left(t\right),{\mathrm{\θ}}_{k_j}\left(t\right)$ With relevant (10)

value is definite, can obtain according to formula (8).

So far, set up for the Calculation of correlation factor model system between multiple subsystems of the I.F fault type of complication system.Related coefficient is the function of time t, after dependent failure causes subsystem j to break down, interaction stops, fault is after maintenance, numerical control device remains in operation, and dependent interaction starts again, and this process is gone round and begun again, therefore correlationship survival is during each between-failures, and if only if t=MTBF (R _j(t)), related coefficient is definite value.Wherein, R ' _j(t): be the reliability model of the resultant fault rate foundation with subsystem j.

Step 4. is considered the analysis of the maintenance policy of dependent failure

1) analysis of the maintenance policy of described consideration dependent failure, specifically utilizes the fiduciary level of related coefficient between definite subsystem revision subsystem, calculates predictive maintenance node.

The maintenance policy of system, taking fiduciary level as according to formulating and optimizing, in the time that fiduciary level system or subsystem is less than the threshold value of plan regulation, needs system or subsystem to carry out preventive maintenance maintenance.If the fault of subsystem j is independent failure, its reliability model is:

$R_j\left(t\right)=\exp (-\∫z_{\mathrm{Ij}}\left(t\right)\mathrm{dt}---\left(11\right)$

R _j(t): be the reliability model in independent failure rate situation that only has of subsystem j;

The certainty that in actual production, dependent failure exists, cause the calculating of reliability to occur larger deviation, and this deviation is especially more obvious in the time calculating whole aircraft reliability, the I.F dependent failure of studying taking the present invention is as example, the fiduciary level of calculating with independent failure has trend bigger than normal, considers that the reliability model of the subsystem j of dependent failure is:

$R_j^{\′}\left(t\right)=\exp (-\∫z_j\left(t\right)\mathrm{dt}=\exp (-\∫(z_{\mathrm{Ij}}\left(t\right)+\underset{i_j}{\mathrm{\Σ}}{\mathrm{\θ}}_{i_j}\left(t\right)z_{i_j}{\left(t\right)}_g)\mathrm{dt}---\left(12\right)$

R ' _j(t): be the reliability model of the resultant fault rate foundation with subsystem j;

So have: R _j(t) >R ' _j(t)

Consider the fiduciary level value of dependent failure because the fiduciary level value of calculating with independent failure is greater than, therefore formula (11) caused preventive maintenance scheduling after prolong.

The inventive method is by the analysis of a large amount of fault of numerical control machine tool data, according to the action mode of dependent failure, summarize the fault chain kind of phase mutual interference fault model, according to independent failure rate in dependent failure, the dependence relation of dependent failure rate and resultant fault rate, set up dependent failure rate model, then for the feature of every kind of fault chain, set up the related coefficient solving model system between correlation subsystem, realize thus the definite analytical approach of dependent interaction degree between numerically-controlled machine correlation subsystem, for considering that the system of dependent failure or the predictive maintenance plan of subsystem provide foundation.

Embodiment:

The present invention is taking the complicated correlationship analysis between three subsystems of numerically-controlled machine as example.

Step 1: utilize FMECA analytical technology to process fault data, carry out the division of the trouble location of the each subsystem of lathe, arrange the data with dependent failure.

Data from 175 lathes of certain same model fault in production track record of 13 months.After fault data being processed by FMECA analytical technology, find out the subsystem with correlationship, the correlationship of consulting Fig. 7 is example.

After processing by FMECA method, obtain fault-time point and the dependent failure time point of subsystems, calculate time between failures value as fault data by putting fault-time, lathe day working system be double shift, the data processed result that table 1 is tool holder system.Its computing formula is as follows:

$T_j^d=\frac{(t_i^d-t_{i-1})*14.5*240}{365}---\left(13\right)$

$T_{j+1}=\frac{(t_{i+1}-t_i^d)*14.5*240}{365}---\left(14\right)$

j time between failures, classification is for relevant, and between-failures terminal is dependent failure time point, as 28.60 of table 1 intermediate slide system failure data ^*; i time of failure point, and this fault is dependent failure; t _i-1: with the same subsystem of a machine tool fault-time point next-door neighbour previous fault-time of point; T _j+1: with the same subsystem of a machine tool next-door neighbour's next time between failures; t _i+1with the same subsystem of a machine tool fault-time point next-door neighbour rear one fault-time point.

The fault data processing of table 1 tool holder system

The data processing of servo-drive system and hydraulic system is as the data handling procedure of tool holder system, and time between failures value after treatment is as table 2.

Table 2 subsystem fault interval time

In Fig. 7, servo-drive system is dependent failure starting point, is not subject to other system effect.In table 2, in hydraulic system fault data, this time between failures of band " * " data representation is caused by the dependent failure of servo-drive system; In tool holder system fault data, this time between failures of data representation of band " ※ " is caused by hydraulic system dependent failure; Band " # " data show that this time between failures is to be caused by servo-drive system dependent failure.

Step 2: according to the interaction type between subsystem, the kind of Judging fault chain:

The complicated correlationship of three subsystems that show according to Fig. 7, this fault chain belongs to the 5th kind of fault chain, is the simplest complicated correlation form, carries out modeling determine facies relationship numerical value according to formula (7)～(10).

Step 3: for the definite dependent failure chain kind of step 2, utilize corresponding related coefficient model to carry out analysis and solution.

1. by independent failure rate model, resultant fault rate model and the dependent failure rate model of three subsystems of fault in production data acquisition.

The subsystems of lathe is got rid of the interference of dependent failure factor, and under the production status of arm's length standard, failure rate is itself intrinsic independent failure rate.

Table 3 is above-mentioned three subsystem independent failure rate functions, and reliability function meets Weibull distribution.

Table 3 subsystem independent failure rate function

The fault data processing that the resultant fault rate of three subsystems is collected by production scene obtains, and Weibull distribution is hypothesis distributed model, adopts D method of inspection to carry out fitting of distribution inspection.As table 4 Chinese style (18)～(20).

Table 4 subsystem resultant fault rate function

Present case is taking the related coefficient Modeling Calculation deduction process of trying to achieve tool holder system and other two other subsystem in the correlationship of three subsystems in Fig. 7 as example.If z _ds(t) be by the dependent failure rate of the tool holder system of servo-drive system dependent interaction, calculate removed the fault data of hydraulic system cutter setting frame system dependent interaction by the fault data of tool holder system after, suc as formula (21); z _dy(t) be by the dependent failure rate of the tool holder system of hydraulic system dependent interaction, after the fault data by knife rest fault data removal servo-drive system cutter setting frame system dependent interaction, calculate, suc as formula (22).

Table 5 tool holder system dependent failure rate function

2. the correlation analysis of tool holder system:

Determine the correlation subsystem of tool holder system according to correlationship Fig. 7, as follows according to the resultant fault rate formula of formula (7) tool holder system:

$z_d\left(t\right)=z_{\mathrm{Id}}\left(t\right)+{\mathrm{\θ}}_{s_d}\left(t\right)z_{s_d}{\left(t\right)}_g+{\mathrm{\θ}}_{y_d}\left(t\right)z_{y_d}{\left(t\right)}_g---\left(23\right)$

Wherein for the dependent failure rate of servo-drive system cutter setting frame system; for the dependent failure rate of hydraulic system cutter setting frame system.According to formula (8), by formula (23) resolve into tool holder system respectively with the dependent failure rate model of servo-drive system and hydraulic system, suc as formula (24).

$\left\{\begin{array}{c}{z}_{\mathrm{ds}}\left(t\right)=z_{\mathrm{Id}}\left(t\right)+{\mathrm{\θ}}_{s_d}{\left(t\right)z}_{s_d}{\left(t\right)}_g\\ z_{\mathrm{dy}}\left(t\right)=z_{\mathrm{Id}}\left(t\right)+{\mathrm{\θ}}_{y_d}\left(t\right)z_{y_d}{\left(t\right)}_g\end{array}\right.---\left(24\right)$

The fault related coefficient of servo-drive system cutter setting frame system is:

${\mathrm{\θ}}_{s_d}\left(t\right)=\frac{|z_{\mathrm{ds}}\left(t\right)-z_{\mathrm{Id}}\left(t\right)|}{z_{s_d}{\left(t\right)}_g}---\left(25\right)$

Because servo-drive system is fault starting point, so

$z_{s_d}{\left(t\right)}_g=z_{\mathrm{Is}}\left(t\right)=z_s\left(t\right)---\left(26\right)$

By failure rate model (15), (17), (21) for people's equation (25), if right expression formula is for people R _ds(t) MTBF point estimate t _ds=407.2, there is θ _sd=0.1081,

The model of the dependent failure coefficient of hydraulic system cutter setting frame system is:

Obtained by formula (23)

${\mathrm{\θ}}_{y_d}\left(t\right)=\frac{|z_{\mathrm{dy}}\left(t\right)-z_{\mathrm{Id}}\left(t\right)|}{z_{y_d}{\left(t\right)}_g}---\left(27\right)$

Wherein z _dy(t), z _id(t) be known fault rate, to be determined.Further analyze, the dependent failure of hydraulic system cutter setting frame system is relevant to the fault chain of hydraulic system to servo-drive system, i.e. the related coefficient θ of servo-drive system to hydraulic system _sy(t) with relevant, hydraulic system is subject to the failure rate of servo-drive system dependent interaction can have influence on the variation of the failure rate of its cutter setting frame system, has according to formula (10):

$z_{y_d}{\left(t\right)}_g=z_y\left(t\right)---\left(28\right)$

By failure rate model (17), (19), (22) for people's equation (27), if substitution R _dy(t _i) MTBF point estimate t _dy=400.1, there is θ _yd=0.0833,

3. the related coefficient that basis is tried to achieve above, according to the resultant fault rate of formula (23) tool holder system is: $z_d\left(t\right)=z_{\mathrm{Id}}\left(t\right)+{0.1081z}_{s_d}{\left(t\right)}_g+{0.0833z}_{y_d}{\left(t\right)}_g$

Step 4: consider the analysis of the maintenance policy of dependent failure.

According to formula (11), the predictive maintenance of the tool holder system of being analyzed by independent failure is as follows: be R when giving fiduciary level threshold value _d(t)=0.9 o'clock, the predictive maintenance time was t=54 hour; The predictive maintenance time of the tool holder system of consideration dependent failure is as follows: be R when giving fiduciary level threshold value _d(t)=0.9 o'clock, the predictive maintenance time was t=48 hour; From the analysis of maintenance policy of considering dependent failure, ignore dependent failure and after node, prolong the servicing time taking independent fiduciary level as design considerations.Cause lathe subsystem or parts in the threshold range of fiduciary level decline, not to carry out on-call maintenance, thereby machine-spoiled rate rising, fiduciary level declines, and has also affected accessory simultaneously and has ordered batch and the formulation of ordering the date.

Claims (9)

1. a fault of numerical control machine tool correlationship Dynamic Variation Analysis method, is characterized in that, comprises the following steps:

Step 1: utilize FMECA analytical technology to process fault data, the fault data of the each subsystem of lathe is carried out to statistical study, arrange the data between subsystems with dependent failure;

Step 2: analyze dependent failure data, conclude the action mode of summing up the phase mutual interference fault I.F fault type between correlation subsystem, the kind of failure definition chain and fault chain key element;

Step 3: for different dependent failure chains, utilize the dependence relation of independent failure rate, dependent failure rate and resultant fault rate, utilize the resultant fault rate model of dependent failure subsystem, derive respectively the Calculation of correlation factor model of all fault chains, the related coefficient model system of the related coefficient model composition dependent failure of all fault chains;

Step 4: consider the analysis of the maintenance policy of dependent failure.

2. a kind of fault of numerical control machine tool correlationship Dynamic Variation Analysis method according to claim 1, is characterized in that:

The kind of described fault chain comprises five kinds:

The first: fault chain only has two subsystems, and for single effect, the bad motion state of subsystem i can have influence on subsystem j in lathe operational process, until subsystem j breaks down, and subsystem j does not exert an influence to subsystem i;

The second: fault chain only has two subsystems, and two sub-system interactions, the bad motion state of two subsystems influences each other, and forms vicious cycle, until one of them system is moved because of failure stopping;

The third: fault chain is made up of multiple subsystems, and the motion state of subsystem i has influence on multiple subsystems simultaneously, and itself is not subject to the impact of other correlation subsystem;

The 4th kind: fault chain is made up of multiple subsystems, subsystem j is subject to the impact of multiple subsystems, and it does not have dependent interaction to other any subsystem;

The 5th kind: fault chain is made up of more than three or three subsystem, it is the part or all of array configuration of aforementioned four kinds of basic fault chains, have at least a subsystem to be subject to the dependent interaction of more than two subsystem, and there is fault intermediate point subsystem, between correlation subsystem, form complicated correlationship, belonged to the type of complicated dependent failure chain.

3. a kind of fault of numerical control machine tool correlationship Dynamic Variation Analysis method according to claim 1, is characterized in that:

Described failure definition chain key element, refers to according to the position of fault subsystem in fault generating process in fault chain and effect fault subsystem is defined; Fault chain key element comprises:

(1) dependent failure starting point:

In the fault chain with correlationship, only affect other subsystem but the subsystem that not affected by other subsystem is called dependent failure starting point;

(2) dependent failure terminal:

In the fault chain with correlationship, be only subject to the impact of other subsystem, and the subsystem that does not affect other subsystem is called dependent failure terminal;

(3) fault intermediate point:

In the fault chain with correlationship, exist impact and the subsystem that is affected relation to be referred to as fault intermediate point simultaneously.

4. according to a kind of fault of numerical control machine tool correlationship Dynamic Variation Analysis method claimed in claim 1, it is characterized in that:

Described for different dependent failure chains, utilize the dependence relation of independent failure rate, dependent failure rate and resultant fault rate, utilize the resultant fault rate model of dependent failure subsystem, derive respectively the Calculation of correlation factor model of all fault chains, specifically according to resultant fault rate computation model:

Z _j(t): be the resultant fault rate of dependent failure subsystem j, calculate and obtain by the fault data in producing;

Z _ij(t): for the independent failure rate of subsystem j, determined by inherent reliability, obtain by test or production data before product export, in the situation that subsystem j is not subject to dependent failure and affects, z in theory _j(t)=z _ij(t);

for subsystem j is subject to the related coefficient of subsystem i effect, in the time of θ=0, without relevant, subsystem i breaks down and can not cause that j breaks down, in the time of θ=1, and complete dependence, subsystem i breaks down and must cause that j breaks down;

for subsystem j being produced to the dependent failure rate of the subsystem i of dependent interaction;

According to formula (1), for the feature of fault chain, set up respectively the Calculation of correlation factor model of all fault chains, the related coefficient model system of the Calculation of correlation factor model composition dependent failure of all fault chains.

5. a kind of fault of numerical control machine tool correlationship Dynamic Variation Analysis method according to claim 2, is characterized in that:

For the first of described fault chain and the third, the correlationship of fault chain is simple unidirectional relevant, and dependent failure terminal subsystem j is only subject to the impact of a subsystem i, and the resultant fault rate of dependent failure subsystem j is obtained by formula (1):

$z_j\left(t\right)=z_{\mathrm{Ij}}\left(t\right)+{\mathrm{\θ}}_{i_j}\left(t\right)z_{i_j}{\left(t\right)}_g---\left(2\right)$

Have:

${\mathrm{\θ}}_{i_j}\left(t\right)=\frac{|z_j\left(t\right)-z_{\mathrm{Ij}}\left(t\right)|}{z_{i_j}{\left(t\right)}_g}---\left(3\right)$

Because correlation subsystem i is dependent failure starting point, be not subject to other subsystem dependent interaction, therefore wherein:

Z _ii(t): be the independent failure rate of subsystem i;

Z _j(t): be the resultant fault rate of dependent failure subsystem j;

for subsystem j is subject to the related coefficient of subsystem i effect.

6. a kind of fault of numerical control machine tool correlationship Dynamic Variation Analysis method according to claim 2, is characterized in that:

For the 4th kind of described fault chain, the correlationship of fault chain is that multisystem is unidirectional relevant, and dependent failure terminal j is subject to the dependent interaction of multiple subsystems simultaneously, and j is dependent failure terminal, and dependent failure terminal j running status does not affect other correlation subsystem; The resultant fault rate zj (t) of subsystem j determines by k correlationship, for computing subsystem j is subject to the related coefficient of subsystem i effect value, do following hypothesis:

(1) subsystem j and k the related coefficient that subsystem is relevant between linear independence, i=1,2 ... K; Order time, there is formula (2) (3) to set up, derive formula (4) by formula (2):

$\left\{\begin{array}{c}{z}_{j1}\left(t_1\right)=z_{\mathrm{Ij}}\left(t\right)+{\mathrm{\θ}}_{1_j}\left(t\right)z_{1_j}{\left(t\right)}_g\\ z_{j2}\left(t_2\right)=z_{\mathrm{Ij}}\left(t\right)+{\mathrm{\θ}}_{2_j}\left(t\right)z_{2_j}{\left(t\right)}_g\\ .\\ .\\ .\\ z_{\mathrm{ji}}\left(t_i\right)=z_{\mathrm{Ij}}\left(t\right)+{\mathrm{\θ}}_{i_j}\left(t\right)z_{i_j}{\left(t\right)}_g\\ .\\ .\\ .\\ z_{\mathrm{jk}}\left(t_k\right)=z_{\mathrm{Ij}}\left(t\right)+{\mathrm{\θ}}_{k_j}\left(t\right)z_{k_j}\left(t\right)g\end{array}\right.i=\mathrm{1,2},...K---\left(4\right)$

Z _ji(t _i) be subject to point failure rate of i subsystem dependent interaction for subsystem j; Removed the dependent failure data of other subsystem beyond i by the fault data of subsystem j and carry out modeling;

(2) subsystem j is subject to point failure rate z of the dependent interaction of i subsystem _ji(t _i) and subsystem j resultant fault rate z _j(t) have functional relation:

z _j(t)＝φ _i(z _j1(t ₁),z _j2(t ₂),…z _jk(t _k),t) (5)

Subsystem i is all dependent failure starting point, the dependent failure rate of subsystem j is equaled to the independent failure rate of subsystem i; Formula

(4) in $z_{1_j}{\left(t\right)}_g=z_{I1}\left(t\right),z_{2_j}{\left(t\right)}_g=z_{I2}\left(t\right),...z_{k_j}{\left(t\right)}_g=z_{\mathrm{Ik}}\left(t\right),$ Thus can ask, according to formula (1), (4), formula (5) be derived as formula (6):

$\begin{array}{c}{z}_j\left(t\right)=z_{\mathrm{Ij}}\left(t\right)+\underset{i_j}{\mathrm{\Σ}}{\mathrm{\θ}}_{i_j}\left(t\right)z_{i_j}{\left(t\right)}_g\\ =z_{\mathrm{Ij}}\left(t\right)+\underset{i}{\mathrm{\Σ}}{\left(z\right)}_{\mathrm{ji}}\left(t_i\right)-z_{\mathrm{Ij}}\left(t\right)\end{array}i=\mathrm{1,2},...K---\left(6\right)$

for subsystem j is subject to the related coefficient of subsystem i effect.

7. a kind of fault of numerical control machine tool correlationship Dynamic Variation Analysis method according to claim 2, is characterized in that:

For the second of described fault chain and the 5th kind, the correlationship of fault chain is that multisystem is complicated relevant, while calculating the resultant fault rate of each subsystem, need to obtain respectively dependent failure rate and the related coefficient of this subsystem and other correlation subsystem; If subsystem title is respectively: dependent failure starting point i, dependent failure terminal j, dependent failure intermediate point k, the resultant fault rate model of dependent failure terminal j is as follows:

$z_j\left(t\right)=z_{\mathrm{Ij}}\left(t\right)+{\mathrm{\θ}}_{i_j}\left(t\right)z_{i_j}{\left(t\right)}_g+{\mathrm{\θ}}_{k_j}{\left(t\right)z}_{k_j}{\left(t\right)}_g---\left(7\right)$

A point failure rate model that is obtained subsystem j by formula (4) is:

$\left\{\begin{array}{c}{z}_{\mathrm{ji}}\left(t_i\right)=z_{\mathrm{Ij}}\left(t\right)+{\mathrm{\θ}}_{i_j}\left(t\right)z_{i_j}{\left(t\right)}_g\\ z_{\mathrm{jk}}\left(t_k\right)=z_{\mathrm{Ij}}\left(t\right)+{\mathrm{\θ}}_{k_j}\left(t\right)z_{k_j{\left(t\right)}_g}\end{array}\right.---\left(8\right)$

Z _ji(t _i): for being subject to the dependent failure rate of the subsystem j that subsystem i affects;

Z _jk(t _k): for being subject to the dependent failure rate of the subsystem j that subsystem k affects;

for subsystem j being produced to the dependent failure rate of the subsystem i of dependent interaction;

for subsystem j being produced to the dependent failure rate of the subsystem k of dependent interaction;

for subsystem j is subject to the related coefficient of subsystem i effect;

for subsystem j is subject to the related coefficient of subsystem k effect;

Z _ji(t _i), z _jk(t _k) calculating that divides failure rate of calculating as described in formula (4); I in formula (8) is dependent failure starting point, so ? can obtain.

8. a kind of fault of numerical control machine tool correlationship Dynamic Variation Analysis method according to claim 7, is characterized in that:

The described dependent failure rate that subsystem j is produced to the subsystem k of dependent interaction value analytic process as follows, taking subsystem k as research object, subsystem k is fault intermediate point, is also subject to the impact of subsystem i when subsystem j is affected:

$z_k\left(t\right)=z_{\mathrm{Ik}}\left(t\right)+{\mathrm{\θ}}_{i_k}\left(t\right)z_{i_k}{\left(t\right)}_g---\left(9\right)$

Z _k(t): be the resultant fault rate of subsystem k;

Z _ik(t): be the independent failure rate of subsystem k;

for subsystem k is subject to the related coefficient of subsystem i effect;

for subsystem k being produced to the dependent failure rate of the subsystem i of dependent interaction;

Because i is dependent failure starting point, so fault in production data by k are tried to achieve, z _ik(t) for the independent failure rate of subsystem k is known, can be determined by formula (9); According to whether be correlated with, for subsystem j is subject to the related coefficient of subsystem k effect, value in two kinds of situation,

The first: $z_{k_j}{\left(t\right)}_g=z_{\mathrm{Ik}}\left(t\right),{\mathrm{\θ}}_{k_j}\left(t\right)$ With irrelevant

The second: $z_{k_j}{\left(t\right)}_g=z_k\left(t\right),{\mathrm{\θ}}_{k_j}\left(t\right)$ With relevant (10)

value is definite, can obtain according to formula (8).

9. a kind of fault of numerical control machine tool correlationship Dynamic Variation Analysis method according to claim 1, is characterized in that:

The analysis of the maintenance policy of described consideration dependent failure, the fiduciary level of the related coefficient model system revision subsystem between the subsystem that specifically utilization is set up, calculates predictive maintenance node;

The maintenance policy of system, taking fiduciary level as according to formulating and optimizing, in the time that fiduciary level system or subsystem is less than the threshold value of plan regulation, needs system or subsystem to carry out preventive maintenance maintenance; If the fault of subsystem j is without dependent failure, its reliability is:

$R_j\left(t\right)=\exp (-\∫z_{\mathrm{Ij}}\left(t\right)\mathrm{dt}---\left(11\right)$

R _j(t): be the reliability model in independent failure rate situation that only has of subsystem j;

The reliability model of considering the subsystem j with dependent failure is:

$R_j^{\′}\left(t\right)=\exp (-\∫z_j\left(t\right)\mathrm{dt}=\exp (-\∫(z_{\mathrm{Ij}}\left(t\right)+\underset{i_j}{\mathrm{\Σ}}{\mathrm{\θ}}_{i_j}\left(t\right)z_{i_j}{\left(t\right)}_g)\mathrm{dt}---\left(12\right)$

Have:

R _j(t)≥R′ _j(t) (13)

R ' _j(t): be the reliability model of the resultant fault rate foundation with subsystem j;

The described fiduciary level of calculating with independent failure rate has possibility bigger than normal, in the time that the reliability of subsystem j reaches the threshold value of regulation, the time point being calculated by the reliability model of subsystem j is during as maintenance node, because the timing node calculating with independent failure rate is greater than the timing node calculating with dependent failure rate, therefore by formula (11) calculate subsystem j servicing time node as maintenance schedule according to time, must cause preventive maintenance scheduling after prolong.