CN104462836A - Full-period segmented step-stress strategy based small sample acceleration failure evolution test method - Google Patents

Abstract

The invention discloses a minimum sample rolling component acceleration failure evolution test method and relates to a full-period segmented step-stress strategy based small sample acceleration failure evolution test method. The method includes: firstly, analyzing failure criteria of a function failure mode and a component damage and fracture failure mode as well as fault criteria and fault counting criteria, determining acceleration test truncation, selecting an acceleration model and acceleration stress, and determining a full-period segmented step-stress test scheme; simulating a service environment of rolling components, after the test is ended, respectively sampling each sub-segment and detecting precision and surface integrity off-line to determine whether failure and failure types exist nor not; acquiring total service time Ti at normal stress level on the basis of length of each sub-segment, equivalent loading force, equivalent running-in speed and running-in times. Online and offline state monitoring data of the rolling components under different time courses in the full-period service process can be acquired conveniently and efficiently only with one test, and bases are provided for deep exploration of various failure evolution processes and rules and lifetime prediction in the service process.

Description

The System in Small Sample Situation adding strategy based on complete period segmentation step accelerates the differentiation experimental technique that lost efficacy

Technical field

The invention belongs to acceleration inefficacy differentiation experimental technique, particularly a kind of extreme small sample Rolling Components acceleration inefficacy differentiation experimental technique adding strategy based on complete period segmentation step.

Background technology

The various inefficacies of Rolling Components in its military service process all will affect its military service performance (precision stability, reliability and life-span), serious may cause equipment stuck, shut down and other unpredictable fault.To the analysis and research of the inefficacy Evolution Mechanism in its military service process and affecting laws thereof, contribute to the care and maintenance of Rolling Components, promote its holocyclic military service performance, strengthen reliability and serviceable life, realize manufacturing again of product.Therefore to the research of the inefficacy Evolution Mechanism of Rolling Components, especially experimental study is most important.

The object spininess of traditional reliability and life experiment research is short to the military service cycle, and the electronic component products that cost is low, needs larger sample size.And Rolling Components is on active service, and the cycle is long, cost is high, and the input of experiment table is huge, available experiment table quantity is very limited, more crucially, be difficult to detect data by testing on a small quantity to obtain at short notice based on the multiple online of time history and off-line state, this experimental study developed to Rolling Components inefficacy brings very large difficulty.

Patented claim " huge revolving based on small sample supports remaining life Forecasting Methodology (CN103617364A) " is by an accelerated life test of applying 100% ultimate design load, revolving support raceway after inefficacy is divided into 4n section by the symmetry according to magnitude of load and distribution, and then measure the volume wear of every section of revolving support, its remaining life is predicted.But Rolling Components is from structure or functionally all have very big difference with bearing part, the method cannot be directly applied to the predicting residual useful life of Rolling Components; More crucially, due to surface integrity (unrelieved stress, microstructure, surfaceness) measurement be difficult to realize on-line checkingi, and need exemplar be destroyed during sampling, only can provide the volume wear information of having tested rear every section of revolving support in this way, and the various states information that cannot obtain based on time history in product military service process by an accelerated life test, be difficult to carry out experimental study to the inefficacy development law of product.

Summary of the invention

The object of the present invention is to provide a kind of extreme small sample Rolling Components acceleration inefficacy differentiation experimental technique adding strategy based on complete period segmentation step, only with once testing, online and the off-line state Monitoring Data in Rolling Components complete period military service process under different time course can being obtained easily and efficiently, providing foundation for furtheing investigate various inefficacy evolution process, rule and life prediction in its military service process.

The technical solution realizing the object of the invention is: a kind of extreme small sample Rolling Components accelerates to lose efficacy and develops experimental technique, and step is as follows:

Step 1: the failure criteria of analytic function failure mode and component damage and damage inactivation pattern, and failure criterion and failure count criterion, determine Acceleration study truncation, select acceleration model and accelerated stress, finally determine that all j walks the equivalent loading force F added in military service process _j, equivalent running-in speed v _jwith running-in number of times z _j, 1≤j≤n;

Step 2: determine that complete period segmentation step adds experimental program, be divided into n+1 subsegment in the axial direction by workpiece, subsegment number is 0,1 ..., i ..., n; Each subsegment length is respectively L ₀, L ₁... L _i..., L _n, subsegment 0 is not carried out military service experiment, to retain initial precision and the surface integrity information of workpiece; Come into effect complete period segmentation step from subsegment 1 and add experiment, namely at equivalent loading force F ₁with velocity equivalent v under effect ₁from the reciprocal running-in z of subsegment 1 to subsegment n ₁secondary, the 1st step adds military service process and terminates, now subsegment 1 running-in 2z ₁+ 1 time or 2z ₁-1 time, subsegment 2 to subsegment n running-in 2z ₁secondary; Then continue at equivalent loading force F ₂with velocity equivalent v under effect ₂from the reciprocal running-in z of subsegment 2 to subsegment n ₂secondary, the rest may be inferred, terminates, or occur unrepairable fault and stop until the n-th step adds military service process; When having tested, i-th subsegment experienced by i step altogether and adds military service process, wherein adds in military service process in a jth step, will at equivalent loading force F _junder with equivalent running-in speed v _jrunning-in 2z _jsecondary, 1≤j < i≤n; And add in military service process i-th step, will at equivalent loading force F _iunder with equivalent running-in speed v _irunning-in 2z _i+ 1 or 2z _i-1 time;

Step 3: simulation Rolling Components Service Environment, adds experimental program according to the complete period segmentation step determined in step 2 and starts experiment, and in experimentation, the status data that online acquisition workpiece is on active service, collects failure message;

Step 4: after the experiment of step 3 terminates, samples and offline inspection precision and surface integrity respectively to each subsegment, determines whether there is inefficacy and failure type;

Step 5: convert out active time T total under normal stress level in i-th subsegment unit length based on the length of each subsegment, equivalent loading force, equivalent running-in speed and running-in number of times _i, then presence data, failure message and the offline inspection data surveyed in step 3 and step 4, be converted active time T _itime every data.

The present invention compared with prior art, its remarkable advantage: (1) is due to surface integrity leading indicator (unrelieved stress, microstructure, surfaceness) for damaging detection, exemplar cannot carry out secondary experiment, the various surface integrity information that therefore will obtain under condition of small sample under different time course are especially difficult, and this experimental technique can under the restriction of System in Small Sample Situation, experiment is added by a complete period segmentation step, online and the off-line state that can obtain under the time history information and each time point that Rolling Components is on active service under normal stress level detects data.These data can be used for analyzing its inefficacy Evolution Mechanism and rule, carry out precision stability, reliability and life prediction.By System in Small Sample Situation Acceleration study, effectively reduce the required sample size of experiment, reduce experimental period, reduce experimental cost.(2) for simple segmentation running-in, namely the 1st section at loading force F ₁with speed v under effect ₁running-in z ₁secondary, then the 2nd section again with loading force F ₂, speed v ₂running-in z ₂secondary, this method also exists and often a bit ofly all needs frequent acceleration and deceleration, is difficult to the problem realized when length is shorter; Meanwhile, the problem that in runing condensation procedure, each section of wearing and tearing are uneven can also be increased the weight of.And the jth step that complete period of the present invention segmentation step adds experiment adds in military service process, will from jth subsegment to the n-th subsegment back and forth run continuously with, effectively prevent the problem of the frequent acceleration and deceleration that simple segmentation running-in causes, reduce each section of unevenness of wearing and tearing simultaneously.(3) the present invention also can be applicable to the acceleration inefficacy differentiation experimental study of other similar elongated workpiece or annular workpieces.

Below in conjunction with accompanying drawing, the present invention is described in further detail.

Accompanying drawing explanation

Fig. 1 is that complete period segmentation step adds experiment flow figure.

Fig. 2 is that complete period segmentation step adds experimental program one schematic diagram.

Fig. 3 is that complete period segmentation step adds experimental program two schematic diagram.

Embodiment

Composition graphs 1, the present invention is based on the System in Small Sample Situation Rolling Components acceleration inefficacy differentiation experimental technique that complete period segmentation step adds strategy, step is as follows:

Step 1: the failure criteria analyzing the component damage such as the disabler patterns such as workpiece accuracy forfeiture, performance regression and fatigue equivalent, material gummed, deformation damage and fracture and damage inactivation pattern, and failure criterion and failure count criterion, determine rational Acceleration study truncation, select suitable acceleration model and accelerated stress, finally determine that all j walks the equivalent loading force F added in military service process _j, equivalent running-in speed v _jwith running-in number of times z _j, 1≤j≤n.Wherein about failure mode and criterion, accelerating experiment technology scheduling theory research comparatively perfect, can consult domestic and international pertinent literature, as [1] Xu Lingling, the failure analysis of ball screw assembly, and performance test research [D] under high overload operating mode, Nanjing science and engineering, 2014.[2] Chen Xun etc., the research of accelerating experiment technology, application & development [J], mechanical engineering journal, 2009,45 (8): 130-136.

Truncation mode described in step 1, mainly contains Censoring and Based on Censored Data, because the appearance of Rolling Components fault in its military service process and inefficacy have contingency and uncontrollability, adds up failure message for convenience, adopts Censoring mode more convenient; Described acceleration model is inverse power rate model or Coffin-Mansion model; Described accelerated stress is at equivalent loading force F _j, equivalent running-in speed v _jthe vibration mean value of the lower generation of effect or maximal value, recommend to adopt vibration mean value.

Step 2: determine that complete period segmentation step adds experimental program, namely as shown in Figure 2 and Figure 3, workpiece is divided in the axial direction n+1 subsegment, subsegment number is 0,1 ..., i ..., n; Each subsegment length is respectively L ₀, L ₁... L _i..., L _n, subsegment 0 is not carried out military service experiment, to retain initial precision and the surface integrity information of workpiece; Come into effect complete period segmentation step from subsegment 1 and add experiment, namely at equivalent loading force F ₁with velocity equivalent v under effect ₁from the reciprocal running-in z of subsegment 1 to subsegment n ₁secondary, the 1st step adds military service process and terminates, now subsegment 1 running-in 2z ₁+ 1 time (with reference to figure 2) or 2z ₁-1 time (with reference to figure 3), subsegment 2 to subsegment n running-in 2z ₁secondary; Then continue at equivalent loading force F ₂with velocity equivalent v under effect ₂from the reciprocal running-in z of subsegment 2 to subsegment n ₂secondary, the rest may be inferred, until occur unrepairable fault and stop, or the n-th step adds military service process and terminates; When having tested, i-th subsegment experienced by i step altogether and adds military service process, and wherein a jth step adds military service process is at equivalent loading force F _junder with equivalent running-in speed v _jrunning-in 2z _jsecondary, 1≤j≤i; And i-th step adds military service process at equivalent loading force F _iunder with equivalent running-in speed v _jrunning-in 2z _j+ 1 or 2z _j-1 time.

Specifically, in step 1, parameter can have following selection, and described segments n+1, gets n>=3, the length L of described each subsegment i _imeet L ₀≤ L ₁≤ ... ≤ L _n, and ensure that the length of at every turn running and Shi Junyou is enough completes acceleration and deceleration motion; The inefficacy investigating the later stage of attaching most importance to develops, and described all steps add in military service process, running-in number of times z _jz should be met ₁>=z ₂>=...>=z _n>=Z/n, Z are theoretical running-in number of times total under normal stress level; Described all steps add the equivalent loading force F in military service process _jcan be constant force, also can be cyclic force, jth adds in military service process with cyclic force F step by step _j(t) CYCLIC LOADING, this cyclic force F _jt () can convert as equivalent force and respectively walk the equivalent loading force F added in military service process _jmeet F ₁≤ F ₂≤ ... ≤ F _n, and F _e≤ F _j≤ F _max, wherein F _efor rated load, F _maxfor the ultimate load that workpiece can bear; Described equivalent running-in speed v _jcan be constant speed, also can be cycle running-in speed, jth adds in military service process with cycle running-in speed v step by step _j(t) circulation running-in, this cycle running-in speed v _jt () can convert as equivalent running-in speed and each equivalent running-in speed added in military service process meets v step by step ₁≤ v ₂≤ ... ≤ v _n, and v _e≤ v _j≤ v _max, wherein v _efor specified running-in speed, v _maxfor limit running-in speed.

Wherein described in step 2 i-th (1≤i≤n) individual step adds military service process, specifically can be one of two schemes:

The first scheme: as shown in Figure 2, from subsegment j to subsegment n at equivalent loading force F _jwith velocity equivalent v under effect _jcarry out reciprocal running-in z _jsecondary, and continue in the running-in of jth subsegment one way once, now jth walks and adds military service process and terminate; In military service process, it is 2z that subsegment j adds corresponding running-in number of times in labour process at this hyposynchronization _jthe running-in number of times of+1, subsegment j+1 to subsegment n is 2z _j;

First scheme: as shown in Figure 3, from subsegment j to subsegment n at equivalent loading force F _jwith velocity equivalent v under effect _jcarry out reciprocal running-in z _jsecondary, and at 2z _jsecondary one way running-in terminates jth up to subsegment j and subsegment j+1 point of intersection and walks and add military service process; In military service process, it is 2z that subsegment j adds corresponding running-in number of times in labour process at this hyposynchronization _jthe running-in number of times of-1, subsegment j+1 to subsegment n is 2z _j.

Step 3: simulation Rolling Components Service Environment (as temperature, cleanliness factor, pretightning force, mounting means etc.).Add experimental program according to the complete period segmentation step determined in step 2 and start experiment.In experimentation, the status data that online acquisition workpiece is on active service, collects failure message.The status data (being also presence data) of online acquisition, is specially the vibration, noise, temperature, pretightning force etc. when online acquisition workpiece is on active service, and collects simultaneously and records as the failure messages such as raceway crackle, spot corrosion and corresponding generation time.

When there is recoverability fault in experimentation, as cracked in rolling body, block, lubricant passage way blocks, and end cover breaks, and pretightning force is lost, and must shut down in time, record trouble type and generation time, continues experiment after reparation.

Step 4: based on step 3, after experiment terminates, also offline inspection precision and surface integrity are sampled respectively to each subsegment and obtains offline inspection data, specifically comprise geometric accuracy, roughness, surface microscopic tissue, unrelieved stress, wear extent etc., and determine whether there is inefficacy and failure type (as wearing and tearing).

Step 5: convert out active time T total under normal stress level in i-th subsegment unit length based on the length of each subsegment, equivalent loading force, equivalent running-in speed and running-in number of times _i, then presence data, failure message and the offline inspection data surveyed in step 3 and step 4, be converted active time T _itime every data.

Described T _itranslation method, specifically comprises the following steps:

First suppose that the Rolling Components life-span all obeys Weibull distribution under normal stress and accelerated stress; The failure mechanism of Rolling Components is only relevant with the current disabling portion accumulated with current stress level, has nothing to do with accumulation mode.

The first step, converts i-th subsegment and adds the military service process corresponding seating time in a jth step, and i-th subsegment adds military service process in a jth step and be:

(1) as i > j, subsegment i adds in military service process in a jth step, loads F in equivalence _jeffect under with speed v _jexperienced by 2z _jsecondary running-in, now subsegment i is t in a jth step active time added in military service process _ij:

$t_{\mathrm{ij}}=\frac{{2z}_j\&CenterDot;L_i}{v_j},1\&le;i<j\&le;n---\left(1\right)$

(2) as i=j, subsegment i adds in military service process in a jth step, loads F in equivalence _jeffect under with speed v _jexperienced by 2z _j± 1 running-in, now subsegment i in a jth step active time added in military service procedure is:

$t_{\mathrm{ij}}=\frac{L_i}{v_j}\&CenterDot;({2z}_j\&PlusMinus;1),1\&le;i=j\&le;n---\left(2\right)$

Second step, convert i-th subsegment and to add in military service process the seating time under normal stress level in jth step:

(1) under Weibull distribution, the probability density function of product failure is

$f\left(t\right)=\frac{m}{\mathrm{\&eta;}}{\left(\frac{t}{\mathrm{\&eta;}}\right)}^{m-1}{e}^{{-\left(\frac{t}{\mathrm{\&eta;}}\right)}^m},t>0---\left(3\right)$

Failure distribution function is

$F\left(t\right)={1-e}^{{-\left(\frac{t}{\mathrm{\&eta;}}\right)}^m},t>0---\left(4\right)$

In formula, m is form parameter, and η is scale parameter;

(2) add up failure model according to Nelson, the j of certain subsegment i adds in military service process, at stress level S step by step _qlower working time t _ijaccumulated invalid probability F _q(t _ij) and in normal stress level the lower working time accumulated invalid probability F _q( ) equal, namely

$F_q\left(t_{\mathrm{ij}}\right)=F_{q^{\&prime;}}\left(t_{{\mathrm{ij}}^{\&prime;}}\right)---\left(5\right)$

(3) according to reliability distribution models, the failure distribution function of Weibull distribution is substituted into formula (5), can obtain

$1-\exp [-{(t_{\mathrm{ij}}/{\mathrm{\&eta;}}_{\mathrm{ij}})}^{m_{\mathrm{ij}}}]=1-\exp [-{(t_{{\mathrm{ij}}^{\&prime;}}/{\mathrm{\&eta;}}_{{\mathrm{ij}}^{\&prime;}})}^{m_{{\mathrm{ij}}^{\&prime;}}}]$

$t_{{\mathrm{ij}}^{\&prime;}}={\mathrm{\&eta;}}_{{\mathrm{ij}}^{\&prime;}}\exp \left[\frac{m_{\mathrm{ij}}}{m_{{\mathrm{ij}}^{\&prime;}}}\ln \left(\frac{t_{\mathrm{ij}}}{{\mathrm{\&eta;}}_{\mathrm{ij}}}\right)\right]---\left(6\right)$

Utilize formula (6) that i-th subsegment is walked in jth the active time t added in experiment _ijbe converted to the active time t ' under normal stress level _ij, wherein 1≤j≤i≤n;

3rd step, total active time on conversion subsegment i

For subsegment i, after experiment terminates, i-th subsegment experienced by successively and adds military service process to the i-th step from the 1st step and add military service process, and obtaining active time total on subsegment i according to the conversion time of second step is:

$T_i=\frac{\underset{j=1}{\overset{i}{\mathrm{\&Sigma;}}}{t}_{\mathrm{ij}}^{\&prime;}}{L_i}=\frac{t_{i1}^{\&prime;}+t_{i2}^{\&prime;}+...+t_{\mathrm{ii}}^{\&prime;}}{L_i},1\&le;j\&le;i\&le;n.---\left(7\right)$

Claims (8)

1. add a System in Small Sample Situation acceleration inefficacy differentiation experimental technique for strategy based on complete period segmentation step, it is characterized in that step is as follows:

Step 1: the failure criteria of analytic function failure mode and component damage and damage inactivation pattern, and failure criterion and failure count criterion, determine Acceleration study truncation, select acceleration model and accelerated stress, finally determine that all j walks the equivalent loading force F added in military service process _j, equivalent running-in speed v _jwith running-in number of times z _j, 1≤j≤n;

Step 2: determine that complete period segmentation step adds experimental program, be divided into n+1 subsegment in the axial direction by workpiece, subsegment number is 0,1 ..., i ..., n; Each subsegment length is respectively L ₀, L ₁... L _i..., L _n, subsegment 0 is not carried out military service experiment, to retain initial precision and the surface integrity information of workpiece; Come into effect complete period segmentation step from subsegment 1 and add experiment, namely at equivalent loading force F ₁with velocity equivalent v under effect ₁from the reciprocal running-in z of subsegment 1 to subsegment n ₁secondary, the 1st step adds military service process and terminates, now subsegment 1 running-in 2z ₁+ 1 time or 2z ₁-1 time, subsegment 2 to subsegment n running-in 2z ₁secondary; Then continue at equivalent loading force F ₂with velocity equivalent v under effect ₂from the reciprocal running-in z of subsegment 2 to subsegment n ₂secondary, the rest may be inferred, terminates, or occur unrepairable fault and stop until the n-th step adds military service process; When having tested, i-th subsegment experienced by i step altogether and adds military service process, wherein adds in military service process in a jth step, will at equivalent loading force F _junder with equivalent running-in speed v _jrunning-in 2z _jsecondary, 1≤j < i≤n; And add in military service process i-th step, will at equivalent loading force f _iunder with equivalent running-in speed v _irunning-in 2z _i+ 1 or 2z _i-1 time;

Step 3: simulation Rolling Components Service Environment, adds experimental program according to the complete period segmentation step determined in step 2 and starts experiment, and in experimentation, the status data that online acquisition workpiece is on active service, collects failure message;

Step 4: after the experiment of step 3 terminates, samples and offline inspection precision and surface integrity respectively to each subsegment, determines whether there is inefficacy and failure type;

Step 5: convert out active time T total under normal stress level in i-th subsegment unit length based on the length of each subsegment, equivalent loading force, equivalent running-in speed and running-in number of times _i, then presence data, failure message and the offline inspection data surveyed in step 3 and step 4, be converted active time T _itime every data.

2. the System in Small Sample Situation acceleration inefficacy differentiation experimental technique adding strategy based on complete period segmentation step according to claim 1, it is characterized in that in step 1, described truncation mode is Censoring or Based on Censored Data; Described acceleration model is inverse power rate model or Coffin-Mansion model; Described accelerated stress is the vibration mean value or maximal value that produce under equivalent loading force, equivalent running-in speed effect.

3. the System in Small Sample Situation acceleration inefficacy differentiation experimental technique adding strategy based on complete period segmentation step according to claim 1, it is characterized in that in step 2, described segments n+1, gets n>=3, the length L of described each subsegment i _imeet L ₀≤ L ₁≤ ...≤L _n; The inefficacy investigating the later stage of attaching most importance to develops, and described all steps add in military service process, and running-in number of times should meet z ₁>=z ₂>=...>=z _n>=Z/n, z are theoretical running-in number of times total under normal stress level.

4. the System in Small Sample Situation acceleration inefficacy differentiation experimental technique adding strategy based on complete period segmentation step according to claim 1, is characterized in that all steps described in step 2 add the equivalent loading force F in military service process _jfor constant force or be cyclic force, and respectively walk the equivalent loading force F added in military service process _jmeet F ₁≤ F ₂≤ ...≤F _n, and F _e≤ F _j≤ F _max, wherein F _efor rated load, F _maxfor the ultimate load that workpiece can bear; Described equivalent running-in speed v _jfor constant speed or be cycle running-in speed, and each equivalent running-in speed step by step added in military service process meets v ₁≤ v ₂≤ ...≤v _n, and v _e≤ v _j≤ v _maa, wherein v _efor specified running-in speed, v _maxfor limit running-in speed.

5. the System in Small Sample Situation acceleration inefficacy differentiation experimental technique adding strategy based on complete period segmentation step according to claim 4, is characterized in that cyclic force is: jth adds in military service process step by step, with cyclic force F _jt () CYCLIC LOADING, described cyclic force can be converted as equivalent force jth adds in military service process step by step, with cycle running-in speed v _jt () circulation running-in, described cycle running-in speed conversion is equivalent running-in speed $v_i=\frac{1}{T}{\&Integral;}_0^T{v}_j\left(t\right)\mathrm{dt}.$

6. the System in Small Sample Situation acceleration inefficacy differentiation experimental technique adding strategy based on complete period segmentation step according to claim 1, it is characterized in that in step 2, a jth step adds military service process, is specifically divided into one of two schemes:

The first scheme: from subsegment j to subsegment n at equivalent loading force F _jwith velocity equivalent v under effect _jcarry out reciprocal running-in z _jsecondary, and continue in the running-in of jth subsegment one way once, now jth walks and adds military service process and terminate; In military service process, it is 2z that subsegment j adds corresponding running-in number of times in labour process at this hyposynchronization _jthe running-in number of times of+1, subsegment j+1 to subsegment n is 2z _j;

First scheme: from subsegment j to subsegment n at equivalent loading force F _jwith velocity equivalent v under effect _jcarry out reciprocal running-in z _jsecondary, and at 2z _jsecondary one way running-in terminates jth up to subsegment j and subsegment j+1 point of intersection and walks and add military service process; In military service process, it is 2z that subsegment j adds corresponding running-in number of times in labour process at this hyposynchronization _jthe running-in number of times of-1, subsegment j+1 to subsegment n is 2z _j.

7. the System in Small Sample Situation acceleration inefficacy differentiation experimental technique adding strategy based on complete period segmentation step according to claim 1; it is characterized in that in the experimentation of step 3; shut down in time when there is recoverability fault, record trouble type and generation time, after reparation, continue experiment.

8. the System in Small Sample Situation acceleration inefficacy differentiation experimental technique adding strategy based on complete period segmentation step according to claim 1, is characterized in that in steps of 5, active time T total under normal stress level in described subsegment i unit length _iconversion step is:

The first step, converts i-th subsegment and adds the military service process corresponding seating time in a jth step, and i-th subsegment adds military service process in a jth step and be:

(1) as i > j, subsegment i adds in military service process in a jth step, loads F in equivalence _jeffect under with speed v _jexperienced by 2z _jsecondary running-in, now subsegment i is t in a jth step active time added in military service process _ij:

$t_{\mathrm{ij}}=\frac{{2z}_j\&CenterDot;L_i}{v_j},1\&le;i<j\&le;n---\left(1\right)$

(2) as i=j, subsegment i adds in military service process in a jth step, loads F in equivalence _jeffect under with speed v _jexperienced by 2z _j± 1 running-in, now subsegment i in a jth step active time added in military service procedure is:

$t_{\mathrm{ij}}=\frac{L_i}{v_j}\&CenterDot;({2z}_j\&PlusMinus;1),1\&le;i=j\&le;n---\left(2\right)$

Second step, convert i-th subsegment and to add in military service process the seating time under normal stress level in jth step:

(1) under Weibull distribution, the probability density function of product failure is

$f\left(t\right)=\frac{m}{\mathrm{\&eta;}}{\left(\frac{t}{\mathrm{\&eta;}}\right)}^{m-1}{e}^{{-\left(\frac{t}{\mathrm{\&eta;}}\right)}^m},t>0---\left(3\right)$

Failure distribution function is

$F\left(t\right)=1-e^{{-\left(\frac{t}{\mathrm{\&eta;}}\right)}^m},t>0---\left(4\right)$

In formula, m is form parameter, and η is scale parameter;

(2) add up failure model according to Nelson, the j of certain subsegment i adds in military service process, at stress level S step by step _qlower working time t _ijaccumulated invalid probability F _q(t _ij) and at the horizontal S of normal stress _{q '}lower working time t _{ij '}accumulated invalid probability F _q(t _{ij '}) equal, namely

F _q(t _ij)＝F _q′(t _ij′) (5)

(3) according to reliability distribution models, the failure distribution function of Weibull distribution is substituted into formula (5), can obtain

$1-\mathrm{eap}[-{(t_{\mathrm{ij}}/{\mathrm{\&eta;}}_{\mathrm{ij}})}^{m_{\mathrm{ij}}}]=1-\exp \left[{(t_{{\mathrm{ij}}^{\&prime;}}/{\mathrm{\&eta;}}_{{\mathrm{ij}}^{\&prime;}})}^{m_{{\mathrm{ij}}^{\&prime;}}}\right]$

$t_{{\mathrm{ij}}^{\&prime;}}={\mathrm{\&eta;}}_{{\mathrm{ij}}^{\&prime;}}\exp \left[\frac{m_{\mathrm{ij}}}{m_{{\mathrm{ij}}^{\&prime;}}}\ln \left(\frac{t_{\mathrm{ij}}}{{\mathrm{\&eta;}}_{\mathrm{ij}}}\right)\right]---\left(6\right)$

Utilize formula (6) that i-th subsegment is walked in jth the active time t added in experiment _ijbe converted to the active time t ' under normal stress level _ij, wherein 1≤j≤i≤n;

3rd step, total active time on conversion subsegment i

For subsegment i, after experiment terminates, i-th subsegment experienced by successively and adds military service process to the i-th step from the 1st step and add military service process, and obtaining active time total on subsegment i according to the conversion time of second step is:

$T_i=\frac{\underset{j=1}{\overset{i}{\mathrm{\&Sigma;}}}{t}_{\mathrm{ij}}^{\&prime;}}{L_i}=\frac{t_{i1}^{\&prime;}+t_{i2}^{\&prime;}+...+t_{\mathrm{ii}}^{\&prime;}}{L_i},1\&le;j\&le;i\&le;n.---\left(7\right)$