CN105912842A - Testing method of incipient failure removal for machining center - Google Patents

Abstract

The invention discloses a testing method of incipient failure removal for a machining center with the view of solving problems of a current machining center such as long testing time for incipient failure removal and high economic cost. The method comprises following steps: 1, reliability modeling of a reference machining center:(1) selecting the reference machining center to track failure interval time recorded by a test, drawing a frequency histogram, primarily determining a hypothetical distribution model-Weibull distribution; (2) employing a maximum likelihood method to estimate unknown parameters Beta and Alfa in Weibull distribution;(3) carrying out Kolmogorov-Smirnov test to the hypothetical distribution model; 2, solving test time of incipient failure removal for a target machining center: (1) calculating a distribution range of quantile tpi; (2) establishing a prior distribution; (3) establishing a posteriori distribution; (4) optimizing test time; (5) distributing test time; 3. incipient failure removal test: (1) carrying out a incipient failure removal test of an overall machine; (2) carrying out an incipient failure removal test on a critical subsystem.

Description

A kind of machining center initial failure gets rid of test method

Technical field

The present invention relates to a kind of for machining center initial failure eliminating test method, more cut and really say, the present invention relates to A kind of initial failure being applied to vertical machining centre, horizontal Machining centers complete machine and key subsystem thereof gets rid of test method.

Background technology

Now, in the machinery manufacturing industry of China, machining center has been widely used in different mechanic factory workers.It There is the advantages such as production efficiency is high, processing element precision is high, precision stability is good, be conventional process tools incomparable. But increasing the raising with performance along with machining center function, its initial failure the most gradually increases.In general, machining center makes Can only achieve about the 60% of its stationary operational phase by the reliability at initial stage, the most substantial amounts of inside it manufacture and design Defect and potential faults, immature etc. as of poor quality, the design of error of supporting component or manufacturing process, these problems Must solve before dispatching from the factory.So the work in-process heart carries out initial failure eliminating work before dispatching from the factory, for mechanic factory workers The machining center providing reliability high just becomes most important.

China starts late, at present about the research of the initial failure eliminating test of machining center complete machine and key subsystem Although there being some methods eliminated about Digit Control Machine Tool initial failure, but lack perfect, can allow machining center manufacturing enterprise The scheme accepted with user.Current test method mainly assumes that fault of numerical control machine tool rate curve is tub curve, then looks for Go out the flex point of tub curve early fault period and random failure period, get rid of test using this flex point as Digit Control Machine Tool initial failure Deadline.But time corresponding to this flex point is long, and in actual applications, either machining center manufacturing enterprise still adds Work central user enterprise all cannot accept the highest Financial cost and time cost.Therefore one must be found the most excellent Change method, shortens initial failure and gets rid of the test period of test.

Summary of the invention

The technical problem to be solved is to overcome the machining center initial failure eliminating examination that prior art exists Test the problem that time length, Financial cost and time cost are high, it is provided that a kind of machining center initial failure gets rid of test method.

For solving above-mentioned technical problem, the present invention adopts the following technical scheme that realization: described a kind of machining center Initial failure is got rid of test method and is comprised the following steps that

1) with reference to machining center Reliability modeling:

(1) choose the time between failures with reference to machining center Field tracing test record, draw frequency histogram, tentatively Determine that machining center time between failures assumes distributed model-Weibull distribution；

(2) Maximum Likelihood Estimation Method is used to estimate to assume distributed model-Weibull distribution unknown parameter β and α；

(3) to assuming that distributed model carries out Kolmogorov-Smirnov inspection；

2) target machining center initial failure eliminating test period solves:

(1) quantile t is calculated_piDistributed area；

(2) prior distribution is set up；

(3) Posterior distrbutionp is calculated；

(4) test period optimization；

(5) test period distribution；

3) initial failure eliminating test:

(1) complete machine initial failure gets rid of test；

(2) key subsystem initial failure gets rid of test.

The time between failures choosing reference machining center Field tracing test record described in technical scheme, draws frequency Rate rectangular histogram, primarily determines that machining center time between failures assumes that distributed model-Weibull distribution refers to: assume machining center Time between failures obeys Weibull distribution, by drawing the method preliminary judgement of frequency histogram；Assume t₁,t₂,…,t_nIt is With reference to n time between failures sample observations of machining center Field tracing test record, then draw the step of frequency histogram Rapid as follows:

(1) t is found out₁,t₂,…,t_nIn minima and maximum, be denoted as t respectively₍₁₎And t_(n), choose and be less than or equal to t₍₁₎Several a, more than or equal to t_(n)Several b；

(2) empirically formula (1) determine group number k:

K=[1+3.32lgn] (1)

In formula: n is the total number of machining center time between failures, [] expression rounds；

(3) interval, (a b) is divided into k subinterval (x_j-1,x_j], x_jPlace's fight continuity, it is assumed that the length in each subinterval is equal, Its group is away from Δ x and branch x_jIt is respectively as follows:

$\mathrm{\Δ}x=\frac{b-a}{k}---\left(2\right)$

x_j=a+j Δ x (j=0,1,2 ..., k) (3)

(4) machining center time between failures t is counted₁,t₂,…,t_nFall the frequency in each subinterval i.e. number n_j, Calculate frequency f again_j

$f_j=\frac{n_j}{n},(j=1,2,\mathrm{...},k)---\left(4\right)$

(5) the estimated value f (x often organizing empirical probability density is calculated_j):

$f\left(x_j\right)=\frac{f_j}{\mathrm{\Δ}x}=\frac{n_j}{n\mathrm{\Δ}x},(j=1,2,\mathrm{...},k)---\left(5\right)$

(6) on transverse axis, each branch x is drawn_j, with each subinterval (x_j-1,x_j] it is the end, with f (x_j) it is that height makees little rectangle, Machining center frequency histogram can be drawn out；

There is machining center frequency histogram, drawn the probability density curve of time between failures；When form parameter β≤1 Time, the probability density function curve of Weibull distribution is monotonic decreasing type；During β > 1, in single peak type.If probability density curve with The probability density function Similar Broken Line of Weibull distribution, i.e. primarily determines that machining center time between failures is obeyed Weibull and divided Cloth；Formula (6), (7), (8), (9) be respectively Weibull distribution probability density function, cumulative distribution function, Reliability Function and Failure rate function

$f(\mathrm{\β},\mathrm{\α};t)=\frac{\mathrm{\β}}{\mathrm{\α}}{\left(\frac{t}{\mathrm{\α}}\right)}^{\mathrm{\β}-1}{e}^{\[-{\left(\frac{t}{\mathrm{\α}}\right)}^{\mathrm{\β}}\]}---\left(6\right)$

$F(\mathrm{\β},\mathrm{\α};t)=1-e^{-{(t/\mathrm{\α})}^{\mathrm{\β}}}---\left(7\right)$

$R(\mathrm{\β},\mathrm{\α};t)=e^{-{(t/\mathrm{\α})}^{\mathrm{\β}}}---\left(8\right)$

$\mathrm{\λ}(\mathrm{\β},\mathrm{\α};t)=\frac{\mathrm{\β}}{\mathrm{\α}}{\left(\frac{t}{\mathrm{\α}}\right)}^{\mathrm{\β}-1}---\left(9\right)$

In formula (6)-(9): α is scale parameter；β is form parameter；T is stochastic variable.

Utilization Maximum Likelihood Estimation Method described in technical scheme is estimated to assume distributed model-Weibull distribution unknown parameter β and α refers to: assume t₁,t₂,…,t_nIt is n the time between failures sample sight with reference to machining center Field tracing test record Measured value, separate and obedience Weibull distribution；

According to formulaUtilize multiplication formula, likelihood function can be obtained as follows；

$L(\mathrm{\β},\mathrm{\α};t_i)=\underset{i=1}{\overset{n}{\mathrm{\Π}}}f(\mathrm{\β},\mathrm{\α};t_i)$

$={\left(\frac{\mathrm{\β}}{\mathrm{\α}}\right)}^n{\left(\frac{\underset{i=1}{\overset{n}{\mathrm{\Π}}}{t}_i}{{\mathrm{\α}}^n}\right)}^{\mathrm{\β}-1}{e}^{-\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{(t_i/\mathrm{\α})}^{\mathrm{\β}}}---\left(10\right)$

Formula (10) both sides are taken natural logrithm simultaneously, then has

$\begin{array}{c}l(\mathrm{\β},\mathrm{\α};t_i)=\ln \left(L\right(\mathrm{\β},\mathrm{\α};t_i\left)\right)\\ =n\ln \left(\frac{\mathrm{\β}}{\mathrm{\α}}\right)+(\mathrm{\β}-1)\left(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\ln \right(t_i)-n\ln (\mathrm{\α}\left)\right)-\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{(t_i/\mathrm{\α})}^{\mathrm{\β}}\end{array}---\left(11\right)$

l(β,α；t_i) difference β, α local derviation, its estimated value can be tried to achieveWith

$\frac{\∂l(\mathrm{\β},\mathrm{\α};t_i)}{\∂\mathrm{\β}}=0---\left(12\right)$

$\frac{\∂l(\mathrm{\β},\mathrm{\α};t_i)}{\∂\mathrm{\α}}=0---\left(13\right)$

In formula: α, β are scale parameter and the form parameter of Weibull distribution respectively, t_iFor i-th time between failures.

Described in technical scheme to assume distributed model carry out Kolmogorov-Smirnov inspection refer to:

1) by β, the estimated value that α is the most correspondingWithBring formula intoIn added Work central fault assumes distributed model interval timeExpression formula

$\widehat{F\left(t_i\right)}=1-e^{{(t_i/\widehat{\mathrm{\α}})}^{\widehat{\mathrm{\β}}}}---\left(14\right)$

2) by n machining center time between failures t₁,t₂,…,t_nAscending arrangement, brings formula (14) into and calculates every Individual data are correspondingAnd by itself and empirical distribution function F (t_i) i.e. formula

$F\left(t_i\right)=\frac{i-1}{n},(i=1,2,\mathrm{...},n)---\left(15\right)$

$D_i=|F\left(t_i\right)-\widehat{F\left(t_i\right)}|,(i=1,2,\mathrm{...},n)---\left(16\right)$

Compare, wherein the maximum value of the difference i.e. observed value of statistic of test D；

3) by D and marginal value D_n,KS-αCompare, meet formula (17), then machining center time between failures obeys prestige cloth You are distributed；

D=max (D₁,D₂,...,D_n)≤D_n,KS-α (17)

KS-α is the significant level of Kolmogorov-Smirnov inspection, according to practical situation from 0.2,0.10,0.05, 0.01 these four significance level is appointed and takes one；D_n,KS-αAccording to sample size n sample range and significance level KS-α, from table 1- Kolmogorov-Smirnov one-sample test is looked in the tables of critical values of D and takes；

The tables of critical values of D in table 1 Kolmogorov-Smirnov one-sample test

Calculating quantile t described in technical scheme_piThe step of distributed area as follows:

1) calculating with reference to machining center probability of malfunction is p_iTime corresponding machining center time between failures t_pi,

$\begin{array}{c}{t}_{pi}=F^{-1}\left(p_i\right)\\ =\mathrm{\α}{\[\ln \left(\frac{1}{1-p_i}\right)\]}^{\frac{1}{\mathrm{\β}}},(i=1,2)\end{array}---\left(18\right)$

Wherein: F^-1It it is the inverse function of Weibull distribution cumulative distribution function；

p_iSpan be (0,1)；

2) expert contrasts seven kinds of reliability level influence factors of two class machining centers to provide target machining center and ginseng Pass the examination the reliability level of the heart:

(1) expert combines calculating quantile t_piDistributed area step in quantile t_piDistributed area, add according to seven kinds Work center reliability level influence factor, provides target machining center and the reliability level with reference to machining center, and by result Insert table 2-machining center reliability level grade form:

Table 2 machining center reliability level grade form

3) quantile integrating each expert is interval

If step 2) in target machining center and suitable with reference to the reliability level of machining center, the most each expert gives respectively Go out quantile t_piThe upper bound and lower bound, and give each expert's accuracy weight according to factors such as the experience of each expert, popularity Ej%, determines quantile t according to formula (20)_piDistributed area [t_{pi_L},t_{pi_U}], and result is inserted table 3-quantile t_piDistrict Between expert judgments integrate table；

$\underset{j=1}{\overset{n}{\mathrm{\Σ}}}Ej\%=1,(j=1,2,\mathrm{...},n)---\left(19\right)$

$t_{pi\_L}=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}(Ej\%\×t_{pij\_L}),t_{pi\_U}=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}(Ej\%\×t_{pij\_U}),(i=1,2;j=1,2,\mathrm{...},n)---\left(20\right)$

Table 3 quantile t_piInterval expert judgments integrates table

In formula: Ej% is expert's accuracy weight, t_{pi_L}、t_{pi_U}It is quantile t respectively_piLower bound and the upper bound.

Prior distribution of setting up described in technical scheme refers to: by quantile t_piInterval [t_{pi_L},t_{pi_U}] be converted to reference Interval [the θ of parameter vector θ=[α, β] in machining center time between failures distribution model_L,θ_U], at p_iOn the premise of Gei Ding, In conjunction with monte carlo method, from [t_{pi_L},t_{pi_U}] appoint take a t_pi, then θ_i=F (β, α | t_pi), thus realize quantile t_piInterval To the conversion that vector θ is interval；

Concrete calculation procedure is:

(1) from [t_{pi_L},t_{pi_U}] randomly draw a t_pi；

(2) θ is calculated_iValue；

(3) repeat (1) step and (2) step N-1 time, and record each θ_iValue；

(4) θ is found out respectively_iCorresponding maximum and minima；

(5)[θ_L,θ_U]=[min (θ_i),max(θ_i)]；

Machining center time between failures distribution model is Weibull distribution, it is assumed that the scale parameter α of Weibull distribution and Form parameter β is separate and obedience is uniformly distributed, then the probability density function of target machining center prior distribution is:

$\mathrm{\π}\left(\mathrm{\θ}\right)=\underset{i=1}{\overset{2}{\mathrm{\Π}}}\frac{1}{{\mathrm{\θ}}_U-{\mathrm{\θ}}_L}=\frac{1}{{\mathrm{\α}}_U-{\mathrm{\α}}_L}\×\frac{1}{{\mathrm{\β}}_U-{\mathrm{\β}}_L}---\left(21\right)$

In formula: θ=[α, β]；α, β are scale parameter and the form parameter of Weibull distribution respectively；θ_L、θ_UIt is vector θ respectively Lower bound and the upper bound；α_L、α_UIt is lower bound and the upper bound of α respectively；β_L、β_UIt is lower bound and the upper bound of β respectively.

Calculating Posterior distrbutionp described in technical scheme refers to:

(1) stochastic variable T is made to represent the time between failures that machining center is complete；Make t_rRepresent a certain observation of T, its Middle r=1,2 ... n, make the Posterior distrbutionp that π (θ | t) represents θ, according to Bayes theorem:

$\mathrm{\π}\left(\mathrm{\θ}\right|t)=\frac{\mathrm{\π}\left(\mathrm{\θ}\right)p\left(t\right|\mathrm{\θ})}{p\left(t\right)}---\left(22\right)$

Likelihood function is

$p\left(t\right|\mathrm{\θ})=\underset{r=1}{\overset{n}{\mathrm{\Π}}}p\left(t_r\right|\mathrm{\θ})=\underset{r=1}{\overset{n}{\mathrm{\Π}}}\{\frac{\mathrm{\β}}{\mathrm{\α}}{\left(\frac{t_r}{\mathrm{\α}}\right)}^{\mathrm{\β}-1}\exp \[-{\left(\frac{t_r}{\mathrm{\α}}\right)}^{\mathrm{\β}}\]\}---\left(23\right)$

Sample edge is distributed as

P (t)=∫ π (θ) p (t | θ) d θ (24)

In formula (22)-(24): θ=[α, β], α, β are scale parameter and the form parameter of Weibull distribution respectively；

(2) marginal distribution substitution formula (22) of prior distribution, likelihood function and sample being obtained Posterior distrbutionp expression formula is:

In formula: α, β are scale parameter and the form parameter of Weibull distribution respectively；

(3) excessively complicated due to formula (25), cause unknown parameter α, β, without analytic solutions, uses Markov Monte Carlo Method solves α, β；

(4) obeying Weibull distribution with reference to machining center time between failures, time between failures corresponding during β=1 is Target machining center flex point t from early fault period to random failure period_pri。

Test period optimization described in technical scheme refers to: carries out initial failure before dispatching from the factory with machining center and gets rid of examination The maintenance cost sum minimum that the experimentation cost tested and machining center cause in user enterprise generation initial failure is as optimization Target, the Optimized model thus setting up machining center initial failure eliminating test period is

MinZ=Y_m+Y_c

$s.t.\left\{\begin{array}{c}{Y}_m=(k_1+k_2+,\mathrm{...},+k_n)t\\ Y_c=k_c{\∫}_t^{t_{pri}}\mathrm{\λ}(\mathrm{\β},\mathrm{\α};t)dt=k_c{\∫}_t^{t_{pri}}\frac{f(\mathrm{\β},\mathrm{\α};t)}{R(\mathrm{\β},\mathrm{\α};t)}dt\\ t\≤t_{pri}\end{array}\right.---\left(26\right)$

In formula:

Z is that target machining center carries out the experimentation cost of initial failure eliminating test before dispatching from the factory and occurs in user enterprise Initial failure and the maintenance cost sum that causes, i.e. object function；

Y_mBe machining center carried out before dispatching from the factory initial failure get rid of test experimentation cost；

Y_cThe maintenance cost that to be machining center occur initial failure in user enterprise and causes；

k₁, k₂..., k_nThe electricity charge in representation unit test period, water rate, the consume of material take the wage with workman；

k_cMaintenance cost for average fault every time；

λ (t) is the failure rate function of machining center；

F (t) is the fault probability function of machining center；

R (t) is the Reliability Function of machining center；

In mathematical analysis software, work out corresponding calculation procedure can object function Z be solved, and then obtain mesh Mark machining center initial failure gets rid of the optimization time t of test_opt。

Test period distribution described in technical scheme refers to:

1) the failure-frequency f of each subsystem is calculated_k

$f_k=\frac{N_k}{N},(k=1,2,\mathrm{...},p)---\left(27\right)$

In formula: f_kIt it is the failure-frequency of machining center kth subsystem；

N_kIt it is the fault frequency of machining center kth subsystem；

N is the number of faults that machining center is total；

P is the number of machining center subsystem；

2) machining center key subsystem is determined

The failure-frequency of each for machining center subsystem is sorted from high to low, forward subsystem fault frequency is added, The failure-frequency sum subsystem more than 60% is referred to as key subsystem；

3) time distribution

Key subsystem test period t_j:

t_j=t_opt×f_j(j=1,2 ..., q) (28)

Then overall test time t_cm:

$t_{cm}=t_{opt}-\underset{j=1}{\overset{q}{\mathrm{\Σ}}}{t}_j,(j=1,2,...q)---\left(29\right)$

In formula (28)-(29):

f_jIt it is the failure-frequency of jth key subsystem；

t_jIt is that jth key subsystem initial failure gets rid of test period；

t_optThe optimization time of test is got rid of for target machining center initial failure；

Q is the number of key subsystem.

Initial failure described in technical scheme is got rid of test and is referred to:

1) complete machine initial failure eliminating test:

(1) manual function test；

(2) complete machine continuous dry run accelerated test；

(3) axis system torque power load test；

(4) typical case's test specimen cutting test；

2) key subsystem initial failure gets rid of test.

Compared with prior art the invention has the beneficial effects as follows:

A kind of machining center initial failure the most of the present invention gets rid of test method, by bent to machining center fault rate Line is analysed in depth, and using seven kinds of influence factors of machining center reliability level as prior information, utilizes Bayes theorem to set up and adds Work center Posterior distrbutionp also estimates parameter beta, flex point t corresponding when making β=1_priIt is more accurate to be worth.

A kind of machining center initial failure the most of the present invention gets rid of test method, is dispatching from the factory to advance with machining center Row initial failure gets rid of the maintenance cost that the experimentation cost tested and machining center cause in user enterprise generation initial failure And minimum as optimization aim, shorten initial failure and get rid of test period, save experimentation cost, economic benefit is obvious.

A kind of machining center initial failure the most of the present invention gets rid of test method, devises complete machine and key subsystem Initial failure gets rid of test specific embodiments, effectively excites machining center latent defect, reduces during using after dispatching from the factory Fault rate.

Accompanying drawing explanation

The present invention is further illustrated below in conjunction with the accompanying drawings:

Fig. 1 is the FB(flow block) that a kind of machining center initial failure of the present invention gets rid of test method；

Fig. 2 is the machining center system subdivision that a kind of machining center initial failure of the present invention gets rid of test method Block diagram；

Fig. 3 is that a kind of machining center initial failure of the present invention gets rid of in test method prestige under difformity parameter Boolean's distribution probability densogram；

Fig. 4 is the axonometric view that a kind of machining center initial failure of the present invention gets rid of the typical part of test method Figure；

Fig. 5 is the main shaft output torque characteristics song that a kind of machining center initial failure of the present invention gets rid of test method Line chart；

Fig. 6 is the main shaft characteristics of output power song that a kind of machining center initial failure of the present invention gets rid of test method Line chart.

Detailed description of the invention

Below in conjunction with the accompanying drawings the present invention is explained in detail:

Refering to Fig. 1, a kind of machining center initial failure of the present invention is got rid of test method and is included with reference to machining center Reliability modeling, target machining center initial failure are got rid of test period and are solved and initial failure eliminating test three steps.Target Machining center initial failure eliminating test period solves and includes calculating quantile t_piDistributed area, set up prior distribution, calculating Posterior distrbutionp, test period optimization, test period five steps of distribution.

A kind of machining center initial failure of the present invention gets rid of specifically comprising the following steps that of test method

1. with reference to machining center Reliability modeling

Described reference machining center Reliability modeling refers to choose the event with reference to machining center Field tracing test record Hinder interval time, draw frequency histogram, primarily determine that the hypothesis distributed model-Weibull distribution of time between failures, then Estimate to assume unknown parameter β and α in distributed model-Weibull distribution, finally to assuming that distributed model carries out Kolmogorov- Smirnov checks, and sets up with reference to machining center time between failures distribution model.

Can be vertical machining centre or the horizontal Machining centers being applied to all trades and professions with reference to machining center, it is also possible to be It is applied to production line or the manufacturing cell of the system of manufacture.Should be with the function of target machining center, technology water with reference to machining center Flat, structure complexity, Maturity and actual condition are close.Such as, target machining center is vertical machining centre, with reference to processing Center also should be vertical machining centre；Target machining center is horizontal Machining centers, also should be horizontal processing with reference to machining center Center；Target machining center is heavy machining center, also should be heavy machining center with reference to machining center；Target machining center should For the processing of auto parts and components, also should be the processing being applied to auto parts and components with reference to machining center.With reference to machining center Time between failures derives from early fault period and random failure period.

It is divided into relevant fault and non-relevant fault with reference to machining center fault.Relevant fault is owing to the quality of product own lacks Fall into and cause, explaining test or calculating the fault that reliability value must be charged to.Non-relevant fault is due to misuse or dimension Repair caused by improper and extraneous factor, the fault should got rid of when explaining test or calculating reliability value.Therefore, During with reference to machining center Reliability modeling, only choose relevant fault, and using time between failures as the sample of Reliability modeling Point.

Need the construction features according to self with reference to machining center, and lathe manufacturing enterprise is to the type machining center Definition, according to sanctified by usage, structural integrity, the principle of functional independence, and combines practical situation division subsystems.Refering to figure 2, machining center can divide 11 subsystems: axis system, feed system, automatic tool changer, digital control system, electrical system, Cooling system, lubricating system, pneumatic system, guard system, chip removal system, basic components.Machining center system subdivision completes After, add up the fault frequency of each subsystem.

1) choose the time between failures with reference to machining center Field tracing test record, draw frequency histogram, tentatively Determine the hypothesis distributed model-Weibull distribution of time between failures

In general, machining center time between failures obeys Weibull distribution, can be by drawing frequency histogram Method preliminary judgement.Assume t₁,t₂,…,t_nIt is n the time between failures sample with reference to machining center Field tracing test record This observation, then the step drawing frequency histogram is as follows:

(1) t is found out₁,t₂,…,t_nIn minima and maximum, be denoted as t respectively₍₁₎And t_(n), choose and be slightly less than or be equal to t₍₁₎Several a, slightly larger than or equal to t_(n)Several b.

(2) empirically formula (1) determine group number k:

K=[1+3.32lgn] (1)

In formula: n is the total number of machining center time between failures, [] expression rounds；

(3) interval, (a b) is divided into k subinterval (x_j-1,x_j], x_jPlace's fight continuity, it is assumed that the length in each subinterval is equal, Its group is away from Δ x and branch x_jIt is respectively as follows:

$\mathrm{\Δ}x=\frac{b-a}{k}---\left(2\right)$

x_j=a+j Δ x (j=0,1,2 ..., k) (3)

(4) machining center time between failures t is counted₁,t₂,…,t_nFall at each subinterval (x_j-1,x_jFrequency in] is i.e. Number n_j, then calculate frequency f_j:

$f_j=\frac{n_j}{n},(j=1,2,\mathrm{...},k)---\left(4\right)$

(5) the estimated value f (x often organizing empirical probability density is calculated_j):

$f\left(x_j\right)=\frac{f_j}{\mathrm{\Δ}x}=\frac{n_j}{n\mathrm{\Δ}x},(j=1,2,\mathrm{...},k)---\left(5\right)$

(6) on transverse axis, each branch x is drawn_j, with each subinterval (x_j-1,x_j] it is the end, with f (x_j) it is that height makees little rectangle, Machining center frequency histogram can be drawn out.

Refering to Fig. 3, there is machining center frequency histogram, it is possible to the probability density substantially drawing time between failures is bent Line.When form parameter β≤1, the probability density function curve of Weibull distribution is monotonic decreasing type；During β > 1, in single peak type. If probability density curve and the probability density function Similar Broken Line of Weibull distribution, can primarily determine that between machining center fault Interval obeys Weibull distribution.Formula (6), (7), (8), (9) are respectively Weibull distribution probability density function, cumulative distribution letter Number, Reliability Function and failure rate function.

$f(\mathrm{\β},\mathrm{\α};t)=\frac{\mathrm{\β}}{\mathrm{\α}}{\left(\frac{t}{\mathrm{\α}}\right)}^{\mathrm{\β}-1}{e}^{\[-{\left(\frac{t}{\mathrm{\α}}\right)}^{\mathrm{\β}}\]}---\left(6\right)$

$F(\mathrm{\β},\mathrm{\α};t)=1-e^{-{(t/\mathrm{\α})}^{\mathrm{\β}}}---\left(7\right)$

$R(\mathrm{\β},\mathrm{\α};t)=e^{-{(t/\mathrm{\α})}^{\mathrm{\β}}}---\left(8\right)$

$\mathrm{\λ}(\mathrm{\β},\mathrm{\α};t)=\frac{\mathrm{\β}}{\mathrm{\α}}{\left(\frac{t}{\mathrm{\α}}\right)}^{\mathrm{\β}-1}---\left(9\right)$

In formula (6)-(9): α is scale parameter；β is form parameter；T is stochastic variable.

2) Maximum Likelihood Estimation Method is used to estimate to assume unknown parameter β and α in distributed model-Weibull distribution

Assume t₁,t₂,…,t_nIt is n the time between failures sample observation with reference to machining center Field tracing test record Value, separate and obedience Weibull distribution.According to formula (6), utilize multiplication formula, likelihood function can be obtained as follows

$\begin{array}{c}L(\mathrm{\β},\mathrm{\α};t_i)=\underset{i=1}{\overset{n}{\mathrm{\Π}}}f(\mathrm{\β},\mathrm{\α};t_i)\\ ={\left(\frac{\mathrm{\β}}{\mathrm{\α}}\right)}^n{\left(\frac{\underset{i=1}{\overset{n}{\mathrm{\Π}}}{t}_i}{{\mathrm{\α}}^n}\right)}^{\mathrm{\β}-1}{e}^{-\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{(t_i/\mathrm{\α})}^{\mathrm{\β}}}\end{array}---\left(10\right)$

Formula (10) both sides are taken natural logrithm simultaneously, then has

$\begin{array}{c}l(\mathrm{\β},\mathrm{\α};t_i)=\ln \left(L\right(\mathrm{\β},\mathrm{\α};t_i\left)\right)\\ =n\ln \left(\frac{\mathrm{\β}}{\mathrm{\α}}\right)+(\mathrm{\β}-1)\left(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\ln \right(t_i)-n\ln (\mathrm{\α}\left)\right)-\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{(t_i/\mathrm{\α})}^{\mathrm{\β}}\end{array}---\left(11\right)$

l(β,α；t_i) difference β, α local derviation, its estimated value can be tried to achieveWith

$\frac{\∂l(\mathrm{\β},\mathrm{\α};t_i)}{\∂\mathrm{\β}}=0---\left(12\right)$

$\frac{\∂l(\mathrm{\β},\mathrm{\α};t_i)}{\∂\mathrm{\α}}=0---\left(13\right)$

In formula (10)-(13): α, β are scale parameter and the form parameter of Weibull distribution respectively, t_iFor between i-th fault Interval.

3) to assuming that distributed model carries out Kolmogorov-Smirnov (K-S) inspection

To assuming that distributed model carries out Kolmogorov-Smirnov inspection and is to ensure that assumed Weibull distribution mould The type appropriateness to machining center time between failures.By step 2) in obtainWithBring into during formula (7) processed Heart time between failures assumes distributed modelExpression formula (14).Then, by n machining center time between failures t₁, t₂,…,t_nAscending arrangement, bringing formula (14) into, to calculate each time between failures correspondingAnd it is divided with experience Cloth function F (t_i) i.e. formula (15) compares, the wherein maximum value of the difference i.e. observed value of statistic of test D.By D with face Dividing value D_n,KS-αCompare, meet formula (17), then machining center time between failures obeys Weibull distribution.

$\widehat{F\left(t_i\right)}=1-e^{{(t_i/\widehat{\mathrm{\α}})}^{\widehat{\mathrm{\β}}}}---\left(14\right)$

$F\left(t_i\right)=\frac{i-1}{n}---\left(15\right)$

$D_i=|F\left(t_i\right)-\widehat{F\left(t_i\right)}|---\left(16\right)$

D=max (D₁,D₂,...,D_n)≤D_n,KS-α (17)

In formula (14)-(17):

WithIt is the maximum likelihood estimation of Weibull distribution unknown parameter β and α respectively；

I=1,2 ..., n；

KS-α is the significant level of Kolmogorov-Smirnov inspection, according to practical situation from 0.2,0.10,0.05, 0.01 these four significance level is appointed and takes one；D_n,KS-αAccording to sample size n sample range and significance level KS-α, from table 1- Kolmogorov-Smirnov one-sample test is looked in the tables of critical values of D and takes；

The tables of critical values of D in table 1 Kolmogorov-Smirnov one-sample test

2. target machining center initial failure eliminating test period solves

Assume that distributed model-Weibull distribution model has passed through Kolmogorov-with reference to machining center time between failures Smirnov checks, then can also obey Weibull distribution by assertive goal machining center time between failures.Refering to Fig. 1, target is processed Center initial failure eliminating test period solves and includes calculating quantile t_piDistributed area, set up prior distribution, calculate posteriority Distribution, test period optimization, test period five steps of distribution:

1) quantile t is calculated_piDistributed area

(1) calculating with reference to machining center probability of malfunction is p_iTime corresponding machining center time between failures t_pi

$\begin{array}{c}{t}_{pi}=F^{-1}\left(p_i\right)\\ =\mathrm{\α}{\[\ln \left(\frac{1}{1-p_i}\right)\]}^{\frac{1}{\mathrm{\β}}},(i=1,2)\end{array}---\left(18\right)$

Wherein: F^-1It it is the inverse function of Weibull distribution cumulative distribution function；

p_iSpan be (0,1).

(2) expert contrasts seven kinds of reliability level influence factors of two class machining centers and provides target machining center and reference The reliability level at center

Expert combines 1) quantile t in step_piValue of calculation, according to seven kinds of reliability level influence factors of machining center, Provide target machining center and the reliability level with reference to machining center, and result is inserted table 2-machining center reliability level Grade form；

Table 2 machining center reliability level grade form

Wherein:

A. seven kinds of machining center reliability level influence factors are respectively machining center functional diversity, manufacturer's technology water Flat, complete machine cost, structure complexity, technology maturity, user satisfaction, operation performance；

B. expert is according to the significance level of every kind of reliability level influence factor, gives corresponding weight w1%, w2%, W3% ..., w7%, and must be fulfilled for

C. expert (does not consider the impact on reliability level of the other influences factor) with jth influence factor as standard, recognizes Make the reliability level of target machining center higher than with reference to machining center for this influence factor, then give target machining center S_ojCompose Value 1, gives with reference to machining center S_RjAssignment 0；Less than with reference to machining center, to target machining center S_ojAssignment 0, gives with reference to processing Center S_RjAssignment 1；Equal to reference to machining center, to target machining center S_ojAssignment 1, gives with reference to machining center S_RjAssignment 1；

D. the reliability level weighted scoring computing formula of target machining center jth influence factor is

S_Owj=S_Oj× wj%；

E. the reliability level weighted scoring computing formula with reference to machining center jth influence factor is S_Rwj=S_Rj× Wj%；

If f.Then target process reliability level and reference machining center reliability level phase When；Then target machining center reliability level is higher than with reference to machining center reliability level；Otherwise, Target machining center reliability level is less than with reference to machining center reliability level.

(3) quantile t that each expert is given is integrated_piInterval

If the reliability level of target machining center and reference machining center is suitable in (2), the most each expert is given respectively Quantile t_piLower bound and the upper bound, and give each expert's accuracy weight according to factors such as the experience of each expert, popularity Ej%, determines quantile t according to formula (20)_piDistributed area [t_{pi_L},t_{pi_U}], and result is inserted table 3-quantile t_piInterval Expert judgments integrates table.

Wherein:

$\underset{j=1}{\overset{n}{\mathrm{\Σ}}}Ej\%=1,(j=1,2,\mathrm{...},n)---\left(19\right)$

$t_{pi\_L}=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}(Ej\%\×t_{pij\_L}),t_{pi\_U}=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}(Ej\%\×t_{pij\_U}),(i=1,2;j=1,2,\mathrm{...},n)---\left(20\right)$

Table 3-quantile t_piInterval expert judgments integrates table

2) prior distribution is set up

By 1) quantile t required in (3) step of step_piInterval [t_{pi_L},t_{pi_U}] be converted to reference to machining center event Interval [the θ of parameter vector θ=[α, β] in barrier distributed model interval time_L,θ_U].At p_iOn the premise of Gei Ding, in conjunction with Meng Teka Lip river method, from [t_{pi_L},t_{pi_U}] appoint take a t_pi, then θ_i=F (β, α | t_pi.Thus realize quantile t_piInterval interval to vector θ Conversion.

Concrete calculation procedure is:

(1) from [t_{pi_L},t_{pi_U}] randomly draw a t_pi；

(2) θ is calculated_iValue；

(3) repeat (1) step and (2) step N-1 time, and record each θ_iValue；

(4) θ is found out respectively_iCorresponding maximum and minima；

(5)[θ_L,θ_U]=[min (θ_i),max(θ_i)]。

Machining center time between failures distribution model is Weibull distribution.Assume Weibull distribution scale parameter α and Form parameter β is separate and obedience is uniformly distributed, then the probability density function of target machining center prior distribution is:

$\mathrm{\π}\left(\mathrm{\θ}\right)=\underset{i=1}{\overset{2}{\mathrm{\Π}}}\frac{1}{{\mathrm{\θ}}_U-{\mathrm{\θ}}_L}=\frac{1}{{\mathrm{\α}}_U-{\mathrm{\α}}_L}\×\frac{1}{{\mathrm{\β}}_U-{\mathrm{\β}}_L}---\left(21\right)$

In formula: θ=[α, β]；α, β are scale parameter and the form parameter of Weibull distribution respectively；θ_L、θ_UIt is vector θ respectively Lower bound and the upper bound；α_L、α_UIt is lower bound and the upper bound of α respectively；β_L、β_UIt is lower bound and the upper bound of β respectively.

3) Posterior distrbutionp is calculated

(1) stochastic variable T is made to represent the time between failures that machining center is complete；Make t_rRepresent a certain observation of T, its Middle r=1,2 ... n.Make the Posterior distrbutionp that π (θ | t) represents θ, according to Bayes theorem:

$\mathrm{\π}\left(\mathrm{\θ}\right|t)=\frac{\mathrm{\π}\left(\mathrm{\θ}\right)p\left(t\right|\mathrm{\θ})}{p\left(t\right)}---\left(22\right)$

Likelihood function is

$p\left(t\right|\mathrm{\θ})=\underset{r=1}{\overset{n}{\mathrm{\Π}}}p\left(t_r\right|\mathrm{\θ})=\underset{r=1}{\overset{n}{\mathrm{\Π}}}\{\frac{\mathrm{\β}}{\mathrm{\α}}{\left(\frac{t_r}{\mathrm{\α}}\right)}^{\mathrm{\β}-1}\exp \[-{\left(\frac{t_r}{\mathrm{\α}}\right)}^{\mathrm{\β}}\]\}---\left(23\right)$

Sample edge is distributed as

P (t)=∫ π (θ) p (t | θ) d θ (24)

In formula: in (22)-(24): θ=[α, β], α, β are scale parameter and the form parameter of Weibull distribution respectively.

(2) marginal distribution substitution formula (22) of prior distribution, likelihood function and sample being obtained Posterior distrbutionp expression formula is:

In formula: α, β are scale parameter and the form parameter of Weibull distribution respectively.

(3) excessively complicated due to formula (25), cause unknown parameter α, β, without analytic solutions, uses Markov Monte Carlo side Method solves；

(4) obeying Weibull distribution with reference to machining center time between failures, time between failures corresponding during β=1 is Target machining center flex point t from early fault period to random failure period_pri。

4) test period optimization

Machining center early fault period is the longest.If with t_priWhen getting rid of test cut-off as machining center initial failure Between, either machining center manufacturing enterprise or user enterprise are all difficult to accept.Therefore, the test period Optimized model set up Machining center manufacturing enterprise and the interests of user enterprise should be taken into account.According to practical situation, carried out before dispatching from the factory with machining center Initial failure get rid of the experimentation cost of test and machining center user enterprise there is initial failure and the maintenance cost that causes it With minimum as optimization aim.The machining center initial failure set up gets rid of the Optimized model of test period

MinZ=Y_m+Y_c

$s.t.\left\{\begin{array}{c}{Y}_m=(k_1+k_2+,\mathrm{...},+k_n)t\\ Y_c=k_c{\∫}_t^{t_{pri}}\mathrm{\λ}(\mathrm{\β},\mathrm{\α};t)dt=k_c{\∫}_t^{t_{pri}}\frac{f(\mathrm{\β},\mathrm{\α};t)}{R(\mathrm{\β},\mathrm{\α};t)}dt\\ t\≤t_{pri}\end{array}\right.---\left(26\right)$

In formula:

Z is that target machining center carries out the experimentation cost of initial failure eliminating test before dispatching from the factory and occurs in user enterprise Initial failure and the maintenance cost sum that causes, i.e. object function；

Y_mBe machining center carried out before dispatching from the factory initial failure get rid of test experimentation cost；

Y_cThe maintenance cost that to be machining center occur initial failure in user enterprise and causes；

k₁, k₂..., k_nThe respectively electricity charge in representation unit test period, water rate, the consume of material take, the wage of workman Deng；

k_cMaintenance cost for average fault every time；

λ (t) is the failure rate function of machining center, i.e. formula (9)；

F (t) is the fault probability function of machining center, i.e. formula (6)；

R (t) is the Reliability Function of machining center, i.e. formula (8)；

In mathematical analysis software, work out corresponding calculation procedure can object function Z be solved, and then obtain mesh Mark machining center initial failure gets rid of the optimization time t of test_opt。

5) test period distribution

In machining center running, the failure-frequency of each subsystem differs greatly.Generally, axis system, feed system The 60% more than of machine failure rate is accounted for the fault rate sum of automatic tool changer.Therefore, based on each subsystem of machining center Total initial failure is got rid of test period t by fault rate_optIt is allocated tallying with the actual situation.By subsystem higher for fault rate It is classified as key subsystem, distributes more test period during failture evacuation test in early days, in order to eliminate in test more Initial failure.Other each subsystems are relatively low due to fault rate ratio, the most individually distribute test period, carrying out overall test or key During subsystems test, the initial failure synchronously completing these subsystems gets rid of test.Concrete test period allocation flow is as follows:

(1) the failure-frequency f of each subsystem is calculated_k

In formula:

f_kIt it is the failure-frequency of machining center kth subsystem；

N_kIt it is the fault frequency of machining center kth subsystem；

N is the number of faults that machining center is total；

P is the number of machining center subsystem.

(2) machining center key subsystem is determined

The failure-frequency of each for machining center subsystem is sorted from high to low, forward subsystem fault frequency is added, The failure-frequency sum subsystem more than 60% is referred to as key subsystem.

(3) time distribution

Key subsystem test period t_j:

t_j=t_opt×f_j(j=1,2 ..., q) (28)

Then overall test time t_cm:

$t_{cm}=t_{opt}-\underset{j=1}{\overset{q}{\mathrm{\Σ}}}{t}_j,(j=1,2,...q)---\left(29\right)$

In formula (28)-(29):

f_jIt it is the failure-frequency of jth key subsystem；

t_jIt is that jth key subsystem initial failure gets rid of test period；

t_optThe optimization time of test is got rid of for target machining center initial failure；

Q is the number of key subsystem.

3. initial failure gets rid of test

Complete machine initial failure is got rid of test and is included manual function test, complete machine continuous dry run accelerated test, main shaft system System torque power load test and typical case's test specimen cutting test, each test cycle number of times is no less than 1 time, can increase according to practical situation Add the cycle-index of typical case's test specimen cutting test.

1) complete machine initial failure gets rid of test

(1) manual function test

Test table according to table 4-manual function, machining center complete machine is carried out manual function test.

Table 4 manual function test table

(2) complete machine continuous dry run accelerated test

Refering to Fig. 4, machining center continuous dry run accelerated test is that the simulation of numerical programming program can body under repertoire The typical part course of processing of existing actual production feature, does and does not cuts continuous dry run accelerated test.Examination is accelerated in dry run continuously Test and should meet following requirement:

A. main shaft uses middling speed and runs up；

B. increase each feed shaft and quickly move the time with high-speed cruising；

C. full flow injection at coolant simulation cutting to be directed at；

D. the numerical control program of typical part should comprise linear interpolation, circular interpolation, linear interpolation circulation, and circular arc cutting follows Ring；

E. chip cleaner must not terminate operating in the circulating cycle；

Stop time between the most each circulation must not exceed 1min；

The most whole operation process should not break down, such as natural faults such as power failures, it is allowed to carry out after restarting, run Time can add up.Breaking down and shut down in all centres, then must re-start continuous dry run accelerated test after fixing a breakdown.

Dry run accelerated test continuously, uses normal orthogonal table, loads.Wherein having five factors is that main shaft turns respectively Speed A, X-axis feed speed B, Y-axis feed speed C, Z axis feed speed D and interpolation type E, these five factors respectively take 4 levels, The dry run each factor of accelerated test as continuous in table 5-and water-glass.By orthogonal test analysis, the continuous dry run of table 6-can be obtained and add Speed test load table.

The continuous each factor of dry run accelerated test of table 5 and water-glass

In table 5:

n_{S_Max}、F_{X_Max}、F_{Y_Max}And F_{Z_Max}Be respectively maximum speed of spindle, the highest feed speed of X feed shaft, Y feed shaft Roughing feed speed and Z feed shaft maximum feed speed.Δn_S、ΔF_X、ΔF_YWith Δ F_ZRepresent speed of mainshaft horizontal increment, X respectively Feed shaft feed speed horizontal increment, Y feed shaft feed speed horizontal increment and Z feed shaft feed speed horizontal increment.Calculate Formula is as follows:

${\mathrm{\Δn}}_S=\frac{n_{S\_Max}}{6}---\left(30\right)$

${\mathrm{\ΔF}}_X=\frac{F_{X\_Max}}{6}---\left(31\right)$

${\mathrm{\ΔF}}_Y=\frac{F_{Y\_Max}}{6}---\left(32\right)$

${\mathrm{\ΔF}}_Z=\frac{F_{Z\_Max}}{6}---\left(33\right)$

The continuous dry run accelerated test load table of table 6

(3) axis system torque power load test

Axis system torque power load test comprises main-shaft torque load test and spindle power load test.

A. axis system moment of torsion load test

Refering to Fig. 5, work in-process heart main shaft low [0, n_{T_Max}In the range of], select 5 grades of speeds of mainshaft n_i, change feeding step by step Amount or cutting depth, make machining center main shaft maximum output torque T_Max.In figure, n_{T_Max}Represent main shaft maximum output torque T_MaxTime Corresponding maximum speed；n_MaxRepresent the maximum speed of main shaft output；T_{n_Max}Represent main shaft output maximum speed n_MaxTime corresponding Moment of torsion.With the power of power meter measures main shaft output, tachoscope is measured the speed of mainshaft, is calculated by formula (34) in loading every time, main Peak torque T of the actual output of axle_{Max_i}, and result of the test is inserted form 7-axis system moment of torsion load test table.

$T_{Max\_i}=\frac{9550(P_i-P_{0i})}{n_i},(i=1,2,\mathrm{...},5)---\left(34\right)$

$n_i=\frac{n_{T\_Max}}{5}\×i,(i=1,2,\mathrm{...},5)---\left(35\right)$

In formula: P_iI & lt loads, main shaft peak power output, unit: kW；

P_0iI & lt loads, main shaft no-load power, unit: kW；

n_iI & lt loads, main shaft actual speed, unit: r/min.

Table 7 axis system moment of torsion load test table

B. axis system power load test

Refering to Fig. 6, the rotating speed [n that work in-process heart main axis constant power is corresponding_{T_Max},n_{P_Max}In the range of], 4 grades of main shafts are selected to turn Speed n_i, change the amount of feeding or cutting depth step by step, make machining center main shaft Maximum Power Output P_Max.In figure, n_{T_Max}Represent main shaft Maximum Power Output P_MaxTime corresponding minimum speed, the moment of torsion of now main shaft output is maximum；n_MaxShow that main shaft exports the highest turn Speed；n_{P_Max}Represent main shaft Maximum Power Output P_MaxTime corresponding maximum speed.With the power of power meter measures main shaft output, turn The speed of mainshaft measured by speed table, and result of the test is inserted form 8-axis system power load test table.

$n_i=n_{T\_Max}+\frac{n_{P\_Max}-n_{T\_Max}}{3}\×(i-1),(i=1,2,3,4)---\left(36\right)$

Table 8 axis system power load test table

(4) typical case's test specimen cutting test

Typical test specimen in typical case's test specimen cutting test both can be consulted with user enterprise, chooses and processes in actual applications Typical part, carry out cylinder cap processing as automobile engine manufacturing enterprise commonly uses machining center, carrying out typical case test specimen cutting examination When testing, cylinder cap can be chosen as typical case's test specimen, it is also possible to select the part in complete machine continuous dry run test as typical case's test specimen. After typical case's test specimen has cut, according to the accuracy standard of machining center and the tolerance of test specimen, test specimen should be carried out quality inspection.As Fruit cutting test specimen is overproof, again machining center should be carried out accuracy checking.

2) key subsystem initial failure gets rid of test

After machining center completes the eliminating of complete machine initial failure, for fully exposing machining center initial failure, need impact The key subsystem of complete machine carries out initial failure and gets rid of test.In general, the crucial son of machining center reliability level is affected System has axis system, feed system, automatic tool changer, digital control system, electrical system, pneumatic system etc..Wherein main shaft system System, feed system and automatic tool changer need by programming realization long run test.Digital control system and electrical system are being carried out Can realize when axis system, feed system simultaneously, therefore need not it is carried out routine tests.Pneumatic system can carried out automatically Realize during knife-changing system simultaneously.Therefore key subsystem is described as a example by axis system, feed system and automatic tool changer in early days Failture evacuation test loading scheme.

During test, the speed of mainshaft is loaded from high to low by rotating speed, and feed system loads from fast to slow with feed speed, automatically Knife-changing system is by the simulation descending loading of tool weight.Axis system rotating speed loaded value is from [0.5n_Max,n_Max] this scope In by be uniformly distributed extraction 24 groups, extraction result is sorted from small to large, n_MaxIt it is maximum speed of spindle.Feed system feeding speed Rate loaded value is from [0.5f_Max,f_Max] in the range of this by being uniformly distributed extraction 24 groups, extraction result is sorted from small to large, f_MaxIt it is maximum feed rate.The simulation cutter quality that ATC system loads is from [0, M_Max] this scope is random by being uniformly distributed Extract 24 groups, extraction result is sorted from big to small, M_MaxIt it is the maximum tool weight of tool magazine permission loading.After extraction, will Result inserts table 9-key subsystem load table, works out corresponding numerical control program and carries out load test.

Table 9 key subsystem load table

Cutter number	Simulation cutter quality (kg)	The speed of mainshaft (m/min)	Feed speed (mm/min)
				1
2
				…	…	…	…
24

Claims (10)

1. a machining center initial failure gets rid of test method, it is characterised in that described a kind of machining center initial failure Get rid of test method to comprise the following steps that

1) with reference to machining center Reliability modeling:

(1) choose the time between failures with reference to machining center Field tracing test record, draw frequency histogram, primarily determine that Machining center time between failures assumes distributed model-Weibull distribution；

(2) Maximum Likelihood Estimation Method is used to estimate to assume distributed model-Weibull distribution unknown parameter β and α；

(3) to assuming that distributed model carries out Kolmogorov-Smirnov inspection；

2) target machining center initial failure eliminating test period solves:

(1) quantile t is calculated_piDistributed area；

(2) prior distribution is set up；

(3) Posterior distrbutionp is calculated；

(4) test period optimization；

(5) test period distribution；

3) initial failure eliminating test:

(1) complete machine initial failure gets rid of test；

(2) key subsystem initial failure gets rid of test.

2. get rid of test method according to a kind of machining center initial failure described in claim 1, it is characterised in that described choosing Take the time between failures with reference to machining center Field tracing test record, draw frequency histogram, primarily determine that machining center Time between failures assumes that distributed model-Weibull distribution refers to:

Assume that machining center time between failures obeys Weibull distribution, by drawing the method preliminary judgement of frequency histogram； Assume t₁,t₂,…,t_nIt is n the time between failures sample observations with reference to machining center Field tracing test record, then paints The step of frequency histogram processed is as follows:

(1) t is found out₁,t₂,…,t_nIn minima and maximum, be denoted as t respectively₍₁₎And t_(n), choose less than or equal to t₍₁₎'s Number a, more than or equal to t_(n)Several b；

(2) empirically formula (1) determine group number k:

K=[1+3.32lgn] (1)

In formula: n is the total number of machining center time between failures, [] expression rounds；

(3) interval, (a b) is divided into k subinterval (x_j-1,x_j|, x_jPlace's fight continuity, it is assumed that the length in each subinterval is equal, its group Away from Δ x and branch x_jIt is respectively as follows:

$\mathrm{\Δ}x=\frac{b-a}{k}---\left(2\right)$

x_j=a+j Δ x (j=0,1,2 ..., k) (3)

(4) machining center time between failures t is counted₁,t₂,…,t_nFall at each subinterval (x_j-1,x_jFrequency in] i.e. number n_j, then calculate frequency f_j:

$f_j=\frac{n_j}{n},(j=1,2,...,k)---\left(4\right)$

(5) the estimated value f (x often organizing empirical probability density is calculated_j):

$f\left(x_j\right)=\frac{f_j}{\mathrm{\Δ}x}=\frac{n_j}{n\mathrm{\Δ}x},(j=1,2,...,k)---\left(5\right)$

(6) on transverse axis, each branch x is drawn_j, with each subinterval (x_j-1,x_j] it is the end, with f (x_j) it is that height makees little rectangle, Draw out machining center frequency histogram.

There is machining center frequency histogram, drawn the probability density curve of time between failures；When form parameter β≤1, The probability density function curve of Weibull distribution is monotonic decreasing type；During β > 1, in single peak type.If time between failures is general Rate density curve and the probability density function Similar Broken Line of Weibull distribution, i.e. primarily determine that machining center time between failures takes From Weibull distribution；Formula (6), (7), (8), (9) be respectively Weibull distribution probability density function, cumulative distribution function, can By degree function and failure rate function

$f(\mathrm{\β},\mathrm{\α};t)=\frac{\mathrm{\β}}{\mathrm{\α}}{\left(\frac{t}{\mathrm{\α}}\right)}^{\mathrm{\β}-1}{e}^{\[-{\left(\frac{t}{\mathrm{\α}}\right)}^{\mathrm{\β}}\]}---\left(6\right)$

$F(\mathrm{\β},\mathrm{\α};t)=1-e^{-{(t/\mathrm{\α})}^{\mathrm{\β}}}---\left(7\right)$

$R(\mathrm{\β},\mathrm{\α};t)=e^{-{(t/\mathrm{\α})}^{\mathrm{\β}}}---\left(8\right)$

$\mathrm{\λ}(\mathrm{\β},\mathrm{\α};t)=\frac{\mathrm{\β}}{\mathrm{\α}}{\left(\frac{t}{\mathrm{\α}}\right)}^{\mathrm{\β}-1}---\left(9\right)$

In formula (6)-(9): α is scale parameter；β is form parameter；T is stochastic variable.

3. get rid of test method according to a kind of machining center initial failure described in claim 1, it is characterised in that described fortune Estimate to assume that distributed model-Weibull distribution unknown parameter β and α refers to Maximum Likelihood Estimation Method:

Assume t₁,t₂,…,t_nIt is n the time between failures sample observations with reference to machining center Field tracing test record, Separate and obey Weibull distribution；

According to formulaUtilize multiplication formula, likelihood function can be obtained as follows；

$\begin{array}{c}L(\mathrm{\β},\mathrm{\α};t_i)=\underset{i=1}{\overset{n}{\Π}}f(\mathrm{\β},\mathrm{\α};t_i)\\ ={\left(\frac{\mathrm{\β}}{\mathrm{\α}}\right)}^n{\left(\frac{\underset{i=1}{\overset{n}{\Π}}{t}_i}{{\mathrm{\α}}^n}\right)}^{\mathrm{\β}-1}{e}^{-\underset{i=1}{\overset{n}{\Σ}}{(t_i/\mathrm{\α})}^{\mathrm{\β}}}\end{array}---\left(10\right)$

Formula (10) both sides are taken natural logrithm simultaneously, then has

$\begin{array}{c}l(\mathrm{\β},\mathrm{\α};t_i)=ln\left(L\right(\mathrm{\β},\mathrm{\α};t_i\left)\right)\\ =n\ln \left(\frac{\mathrm{\β}}{\mathrm{\α}}\right)+(\mathrm{\β}-1)\left(\underset{i=1}{\overset{n}{\Σ}}\ln \right(t_i)-n\ln (\mathrm{\α}\left)\right)-\underset{i=1}{\overset{n}{\Σ}}{(t_i/\mathrm{\α})}^{\mathrm{\β}}\end{array}---\left(11\right)$

l(β,α；t_i) respectively β, α are sought local derviation, its estimated value can be tried to achieveWith

$\frac{\∂l(\mathrm{\β},\mathrm{\α};t_i)}{\∂\mathrm{\β}}=0---\left(12\right)$

$\frac{\∂l(\mathrm{\β},\mathrm{\α};t_i)}{\∂\mathrm{\α}}=0---\left(13\right)$

In formula (10)-(13): α, β are scale parameter and the form parameter of Weibull distribution respectively, t_iDuring for i-th between-failures Between.

4. get rid of test method according to a kind of machining center initial failure described in claim 1, it is characterised in that described is right Assume that distributed model carries out Kolmogorov-Smirnov inspection and refers to:

1) by β, the estimated value that α is the most correspondingWithBring formula intoIn obtain machining center therefore Barrier assumes distributed model interval timeExpression formula

$\widehat{F\left(t_i\right)}=1-e^{{(t_i/\widehat{\mathrm{\α}})}^{\widehat{\mathrm{\β}}}}---\left(14\right)$

2) by n machining center time between failures t₁,t₂,…,t_nAscending arrangement, brings formula (14) into and calculates each event Barrier is corresponding for interval timeAnd by itself and empirical distribution function F (t_i) i.e. formula

$F\left(t_i\right)=\frac{i-1}{n},(i=1,2,\mathrm{...},n)---\left(15\right)$

$D_i=|F\left(t_i\right)-\widehat{F\left(t_i\right)}|,(i=1,2,\mathrm{...},n)---\left(16\right)$

Compare, wherein the maximum value of the difference i.e. observed value of statistic of test D；

3) by D and marginal value D_n,KS-αCompare, meet formula (17), then machining center time between failures distribution model is obeyed Weibull distribution；

D=max (D₁,D₂,...,D_n)≤D_n,KS-α (17)

KS-α be Kolmogorov-Smirnov inspection significant level, according to practical situation from 0.2,0.10,0.05,0.01 this Four kinds of significance levels are appointed and takes one；D_n,KS-αAccording to sample size n sample range and significance level KS-α, from table 1-Kolmogorov- Smirnov one-sample test is looked in the tables of critical values of D and takes；

The tables of critical values of D in table 1 Kolmogorov-Smirnov one-sample test

5. get rid of test method according to a kind of machining center initial failure described in claim 1, it is characterised in that described meter Point counting figure place t_piThe step of distributed area as follows:

1) calculating with reference to machining center probability of malfunction is p_iTime corresponding machining center time between failures t_pi,

$t_{pi}=F^{-1}\left(p_i\right)$

$=\mathrm{\α}{\[ln\left(\frac{1}{1-p_i}\right)\]}^{\frac{1}{\mathrm{\β}}},(i=1,2)---\left(18\right)$

Wherein: F^-1It it is the inverse function of Weibull distribution cumulative distribution function；

p_iSpan be (0,1)；

2) expert contrasts seven kinds of reliability level influence factors of two class machining centers to provide in target machining center and reference The reliability level of the heart:

(1) expert combines calculating quantile t_piDistributed area step in quantile t_piDistributed area, according to seven kinds processing in Heart reliability level influence factor, provides target machining center and the reliability level with reference to machining center, and result is inserted Table 2-machining center reliability level grade form:

Table 2 machining center reliability level grade form

3) quantile integrating each expert is interval

If step 2) in target machining center and suitable with reference to the reliability level of machining center, the most each expert is given point respectively Figure place t_piThe upper bound and lower bound, and give each expert's accuracy weight Ej% according to the experience of each expert, popularity two factor, Quantile t is determined according to formula (20)_piDistributed area [t_{pi_L},t_{pi_U}], and result is inserted table 3-quantile t_piInterval special Family judges to integrate table；

$\underset{j=1}{\overset{n}{\Σ}}Ej\%=1,(j=1,2,...,n)---\left(19\right)$

$t_{pi\_L}=\underset{j=1}{\overset{n}{\Σ}}(Ej\%\×t_{pij\_L}),t_{pi\_U}=\underset{j=1}{\overset{n}{\Σ}}(Ej\%\×t_{pij\_U}),(i=1,2;j=1,2,\mathrm{...},n)---\left(20\right)$

Table 3 quantile t_piInterval expert judgments integrates table

In formula: Ej% is expert's accuracy weight, t_{pi_L}、t_{pi_U}It is quantile t respectively_piLower bound and the upper bound.

6. get rid of test method according to the machining center initial failure described in claim 1, it is characterised in that described foundation is first Test distribution to refer to:

By quantile t_piInterval [t_{pi_L},t_{pi_U}] be converted to reference to parameter vector θ in machining center time between failures distribution model Interval [the θ of=[α, β]_L,θ_U], at p_iOn the premise of Gei Ding, in conjunction with monte carlo method, from [t_{pi_L},t_{pi_U}] appoint take one t_pi, then θ_i=F (β, α | t_pi), thus realize quantile t_piThe interval conversion interval to vector θ；

Concrete calculation procedure is:

(1) from [t_{pi_L},t_{pi_U}] randomly draw a t_pi；

(2) θ is calculated_iValue；

(3) repeat (1) step and (2) step N-1 time, and record each θ_iValue；

(4) θ is found out respectively_iCorresponding maximum and minima；

(5)[θ_L,θ_U]=[min (θ_i),max(θ_i)]；

Machining center time between failures distribution model is Weibull distribution, it is assumed that the scale parameter α of Weibull distribution and shape Parameter beta is separate and obedience is uniformly distributed, then the probability density function of target machining center prior distribution is:

$\mathrm{\π}\left(\mathrm{\θ}\right)=\underset{i=1}{\overset{2}{\Π}}\frac{1}{{\mathrm{\θ}}_U-{\mathrm{\θ}}_L}=\frac{1}{{\mathrm{\α}}_U-{\mathrm{\α}}_L}\×\frac{1}{{\mathrm{\β}}_U-{\mathrm{\β}}_L}---\left(21\right)$

In formula: θ=[α, β]；α, β are scale parameter and the form parameter of Weibull distribution respectively；θ_L、θ_URespectively under vector θ Boundary and the upper bound；α_L、α_UIt is lower bound and the upper bound of α respectively；β_L、β_UIt is lower bound and the upper bound of β respectively.

7. get rid of test method according to a kind of machining center initial failure described in claim 1, it is characterised in that described meter Calculation Posterior distrbutionp refers to:

(1) stochastic variable T is made to represent the time between failures that machining center is complete；Make t_rRepresent a certain observation of T, wherein r= 1,2 ..., n, make the Posterior distrbutionp that π (θ | t) represents θ, according to Bayes theorem:

$\mathrm{\π}\left(\mathrm{\θ}\right|t)=\frac{\mathrm{\π}\left(\mathrm{\θ}\right)p\left(t\right|\mathrm{\θ})}{p\left(t\right)}---\left(22\right)$

Likelihood function is

$p\left(t\right|\mathrm{\θ})=\underset{r=1}{\overset{n}{\Π}}p\left(t_r\right|\mathrm{\θ})=\underset{r=1}{\overset{n}{\Π}}\{\frac{\mathrm{\β}}{\mathrm{\α}}{\left(\frac{t_r}{\mathrm{\α}}\right)}^{\mathrm{\β}-1}\exp \[-{\left(\frac{t_r}{\mathrm{\α}}\right)}^{\mathrm{\β}}\]\}---\left(23\right)$

Sample edge is distributed as

P (t)=∫ π (θ) p (t | θ) d θ (24)

In formula (22)-(24): θ=[α, β], α, β are scale parameter and the form parameter of Weibull distribution respectively；

(2) marginal distribution substitution formula (22) of prior distribution, likelihood function and sample being obtained Posterior distrbutionp expression formula is:

In formula: α, β are scale parameter and the form parameter of Weibull distribution respectively；

(3) excessively complicated due to formula (25), cause unknown parameter α, β, without analytic solutions, uses Markov monte carlo method Solve α, β；

(4) obeying Weibull distribution with reference to machining center time between failures, time between failures corresponding during β=1 is target Machining center flex point t from early fault period to random failure period_pri。

8. get rid of test method according to a kind of machining center initial failure described in claim 1, it is characterised in that described examination Test time-optimized referring to:

Before dispatching from the factory, carry out initial failure with machining center and get rid of the experimentation cost tested and machining center in the generation of user enterprise Initial failure and the maintenance cost sum that causes is minimum as optimization aim, thus set up machining center initial failure and get rid of test The Optimized model of time is

MinZ=Y_m+Y_c

$s.t.\left\{\begin{array}{c}{Y}_m=(k_1+k_2+,\mathrm{...},+k_n)t\\ Y_c=k_c{\∫}_t^{t_{pri}}\mathrm{\λ}(\mathrm{\β},\mathrm{\α};t)dt=k_c{\∫}_t^{t_{pri}}\frac{f(\mathrm{\β},\mathrm{\α};t)}{R(\mathrm{\β},\mathrm{\α};t)}dt\\ t\≤t_{pri}\end{array}\right.---\left(26\right)$

In formula:

Z is that target machining center carries out the experimentation cost of initial failure eliminating test before dispatching from the factory and occurs in early days in user enterprise Fault and the maintenance cost sum that causes, i.e. object function；

Y_mBe machining center carried out before dispatching from the factory initial failure get rid of test experimentation cost；

Y_cThe maintenance cost that to be machining center occur initial failure in user enterprise and causes；

k₁, k₂..., k_nThe electricity charge in representation unit test period, water rate, the consume of material take the wage with workman；

k_cMaintenance cost for average fault every time；

λ (t) is the failure rate function of machining center；

F (t) is the fault probability function of machining center；

R (t) is the Reliability Function of machining center；

In mathematical analysis software, work out corresponding calculation procedure can object function Z be solved, and then obtain target and add Work center initial failure gets rid of the optimization time t of test_opt。

9. get rid of test method according to a kind of machining center initial failure described in claim 1, it is characterised in that described examination Test time distribution to refer to:

1) the failure-frequency f of each subsystem is calculated_k

$f_k=\frac{N_k}{N},(k=1,2,...,p)---\left(27\right)$

In formula: f_kIt it is the failure-frequency of machining center kth subsystem；

N_kIt it is the fault frequency of machining center kth subsystem；

N is the number of faults that machining center is total；

P is the number of machining center subsystem；

2) machining center key subsystem is determined

The failure-frequency of each for machining center subsystem is sorted from high to low, forward subsystem fault frequency is added, fault The frequency sum subsystem more than 60% is referred to as key subsystem；

3) time distribution

Key subsystem test period t_j:

t_j=t_opt×f_j(j=1,2 ..., q) (28)

Then overall test time t_cm:

$t_{cm}=t_{opt}-\underset{j=1}{\overset{q}{\Σ}}{t}_j,(j=1,2,...q)---\left(29\right)$

In formula (28)-(29):

f_jIt it is the failure-frequency of jth key subsystem；

t_jIt is that jth key subsystem initial failure gets rid of test period；

t_optThe optimization time of test is got rid of for target machining center initial failure；

Q is the number of key subsystem.

10. get rid of test method according to the machining center initial failure described in claim 1, it is characterised in that described early stage Failture evacuation test refers to:

1) complete machine initial failure eliminating test:

(1) manual function test；

(2) complete machine continuous dry run accelerated test；

(3) axis system torque power load test；

(4) typical case's test specimen cutting test；

2) key subsystem initial failure gets rid of test.