CN107091785A - The Forecasting Methodology of coke drum crack initiation life and crack propagation life - Google Patents
The Forecasting Methodology of coke drum crack initiation life and crack propagation life Download PDFInfo
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Abstract
The invention discloses a kind of Forecasting Methodology of coke drum crack initiation life, it includes step：Set up the probability Distribution Model of coke drum walls strain amplitude；Based on the model, Monte Carlo random device sampling strain amplitude datacycle sample is carried out, and calculate each strain amplitude corresponding fatigue life and the fatigue damage of given cycle period；Carry out accumulation under given iterations and meet or exceed 1.0 thinking crack initiation to giving the fatigue damage under cycle period；The ratio of the crack initiation cumulative number and given iterations obtains crack initiation probability；For the given cycle period, the crack initiation probability and given confidence level calculate the relation between prediction coke drum walls crack initiation probability and residual life.The invention also discloses a kind of Forecasting Methodology of coke drum crack propagation life, set up the probability Distribution Model of stress amplitude to predict the crack propagation life of active service coke drum.Methods described cost is low, can assess the risk of coke drum military service.
Description
Technical field
The present invention relates to petrochemical industry, more particularly to a kind of coke drum crack initiation life and crack propagation life
Forecasting Methodology.
Background technology
Coke drum is also known as coking tower or thermal cracking reactor, is the key equipment of delayed coking in petroleum refining industry.It is valency
The low poor oil of value is converted into costly gasoline and intermediate distillates, produces huge economic benefit.
The characteristics of due to delay coking process, make coke drum experience circulation heating, cooling process, in 16 to 48 hours
Circulation change between room temperature and 495 DEG C, while the medium of container carrying is by gaseous state to liquid to solid-state, working environment is complicated, dislike
It is bad, coke drum generally existing cylinder bulging after the operation several years is caused, cylinder, weld seam and skirt etc. ftractures.Appoint with these changes
The development of shape and damage will eventually lead to stop production, and even occur serious security incident when serious.American Petroleum Institute (API) point
Not in 1968, large-scale coke drum investigation is carried out within 1979 and 1996, according to investigation result, numerous researchers thinks burnt
The problem of charcoal tower, is caused by many reasons.But due to the dispersiveness of data, even if many user companies are all strongly required API
The specification of design and the operation of a coke drum can be put into effect, API thinks still put into effect such specification.
Although delay coking process keeps constant, field measurement is shown, the strain/stress of tower wall becomes with circulation
Change.Reason is likely to be many, such as internal pressure, the temperature fluctuated.But topmost reason is：In water cooling stage, cold water
Tower wall may directly be cooled down by the passage in coke bed, cause serious thermal gradient.Generally, the passage position on coke bed
It is random when putting.Therefore the circulation of coke drum is not permanent width circulation.It is that coke drum exists that high temperature resistant foil gauge is installed in tower wall
The conventional measure of line monitoring, but long-term monitoring cost is very high.
The data display of field measurement, the peak stress of coke drum tower wall is higher than the yield limit of material.Coke drum is followed
The ring cycle is 24-36 hours, and total cycle life is 20-30.Therefore many researchers think that the failure mode of coke drum is
Low-cycle fatigue.Fatigue life prediction has two methods, and one kind is Stress-Life method, and another is strain Life method.And strain quilt
Confirmation is the splendid parameter for characterizing low-cycle fatigue.In view of current research purpose, is carried out using Strain Method to crack initiation herein
Prediction, and being predicted come On Crack Propagation unstability using stress method, help coke drum user to formulate and safeguard and examine in the future
The strategy repaiied, the prediction of crack initiation and Crack Extension unstability is extremely important for them.
Moreover, practical experience shows, due to Vibration Model of Coke Drum Structure and the complexity of operating procedure, want by theory analysis
As a result it is extremely difficult that STRENGTH ON COKE tower, which carries out fatigue damage prediction,.Therefore field measurement and gone on the basis of actual measurement understanding
The problem of coke drum, STRENGTH ON COKE tower low-cycle fatigue analysis and security evaluation are particularly important.
The content of the invention
One of task of the present invention provides a kind of Forecasting Methodology of coke drum crack initiation life, and this method is based on actual measurement should
Become the active service coke drum crack initiation life that data set up Forecasting Methodology model to predict, it is to avoid the high cost of long term monitoring.
The technical scheme of use is as follows：
Set up the probability Distribution Model of coke drum walls strain amplitude；
To under given cycle period N, according to the probability Distribution Model of strain amplitude, Meng Teka is carried out to the strain amplitude
Sieve random device is sampled, and produces strain amplitude data sample, and calculate each strain amplitude corresponding fatigue life and fatigue damage；
The fatigue damage is accumulated under given iterations, if fatigue damage meets or exceeds 1.0, is split
Line germinates；
It is general that the ratio of crack initiation cumulative number and given iterations obtains crack initiation under the given cycle period N
Rate；
According to the given cycle period N, the crack initiation probability and given confidence level calculate prediction coke drum walls and split
Line germinates the relation between probability and residual life.
Further improvement to above-mentioned technical proposal：
The probability Distribution Model for setting up coke drum walls strain amplitude specifically includes following steps：
The strain data of the cycle period sample size of coke drum walls dangerous spot is gathered by high temperature resistant foil gauge；
Calculate the strain amplitude of each cycle period；
The strain amplitude is taken the logarithm, the probability Distribution Model that strain amplitude obeys logarithm normal distribution is obtained.
In the strain amplitude step for calculating each cycle period,
The strain amplitude is calculated by formula (1) and obtained,
Wherein,Minimum and maximum Von Mises equivalent strains in respectively each circulation, equivalent strain
Calculation expression it is as follows：ε in formulaz, εθRespectively axial strain and ring should
The strain data become, μ is material Poisson's ratio.
It is described to calculate in each strain amplitude corresponding fatigue life and fatigue damage step, specifically using Manson-
The low circumferential strain fatigue formulas of Coffin or plastic strain energy density method calculate each strain amplitude pair in the sampling strain amplitude sample
The fatigue life answered and fatigue damage.
The fatigue damage is carried out under given iterations in accumulation step, specific to damage rule to institute using Miner
The fatigue damage that strain amplitude is produced under given cycle period N is stated to be accumulated.
The two of the task of the present invention provide a kind of Forecasting Methodology of coke drum crack initiation life, and this method is based on actual measurement should
Force data sets up Forecasting Methodology model to predict the crack propagation life of active service coke drum, it is to avoid the high cost of long term monitoring.
The technical scheme of use is as follows, the Forecasting Methodology of coke drum crack propagation life, comprises the following steps：
Set up the probability Distribution Model of coke drum walls stress amplitude；
To under given cycle period N, according to the probability Distribution Model of the stress amplitude, stress amplitude is carried out Monte Carlo with
Machine method is sampled, and produces stress amplitude data sample, and calculate stress of the corresponding crackle of each stress amplitude along depth/length direction
Intensity factor；
Judge whether each stress amplitude under given cycle period N is split using the threshold of stress intensity factor of mother metal
Line extends unstability, is accumulated to giving the Crack Extension unstability under iterations；
The ratio of Crack Extension unstability cumulative number and the given iterations obtains crackle under given cycle period N and expanded
Open up failure probability；
According to the given cycle period N, the Crack Extension failure probability and given confidence level calculate prediction coke drum
Relation between wall Crack Extension failure probability and residual life.
Further improvement of these options：
The probability Distribution Model for setting up coke drum walls stress amplitude comprises the following steps：
Obtain the stress data of the cycle period sample size of coke drum walls dangerous spot；
Calculate the stress amplitude of each circulation sample；
The stress amplitude is taken the logarithm, the probability Distribution Model that stress amplitude obeys logarithm normal distribution is obtained.
In the stress amplitude step of each circulation sample of calculating, the stress amplitude is calculated by formula (2) and obtained,
ΔσZ=σzmax-σzmin (2)
Wherein, σzmax, σzminAxial stress maximum, the minimum value respectively each circulated.
The threshold of stress intensity factor of the utilization mother metal judge to each stress amplitude under given cycle period N whether
Crack Extension unstability step, it is concretely comprised the following steps：
Given crack initiation size, gives crack propagation critical size；
When the stress intensity factor is less than threshold of stress intensity factor, then it is assumed that the Crack Extension under current stress amplitude reaches
To instability status；
Or, each corresponding crack size of stress amplitude under given cycle period N is calculated according to Paris laws, if institute
The crack size for stating stress amplitude is more than crack propagation critical size, then it is assumed that the Crack Extension under current stress amplitude reaches unstability shape
State.
Beneficial effect：
(1) Forecasting Methodology of coke drum crack initiation life of the present invention propose it is a kind of it is inexpensive, based on Monte Carlo
The crack initiation life Forecasting Methodology of stochastic simulation, the strain data of tower wall dangerous spot is gathered by field measurement, is then corresponded to
Become data logarithm and carry out statistical analysis, it is established that the probability Distribution Model of strain amplitude, and then Large Copacity is produced based on probabilistic model
Strain data, finally, crack initiation life probabilistic forecasting is implemented to in-service coke drum, predict the outcome for coke drum use
Strategy more reliable for family, repairing and detect from now on available for the risk and formulation for assessing coke drum military service from now on.
(2) Forecasting Methodology of coke drum crack propagation life of the present invention propose it is a kind of it is inexpensive, based on Monte Carlo
The crack expansion life span predication method of stochastic simulation, the stress data of tower wall dangerous spot is gathered by field measurement, then to power
Become data and carry out statistical analysis, it is established that the probability Distribution Model of stress amplitude, and then answering for Large Copacity is produced based on probabilistic model
Force data, finally, crack propagation life probabilistic forecasting is implemented to in-service coke drum, is predicted the outcome and is come for coke drum user
Say more reliable, to repair and detect from now on available for the risk and formulation for assessing coke drum military service from now on strategy.
(3) present invention is provided a kind of coke drum crack initiation life and the Forecasting Methodology of crack propagation life, it is not necessary to
Temperature thermocouple is installed in tower wall, entered to tower wall not damaged, and according to the statistical regularity STRENGTH ON COKE tower of pulsating stress/strain
Row fatigue damage predicts, the more science and effective with conventional Forecasting Methodology compared with.
Brief description of the drawings
Fig. 1 is the schematic flow sheet of the probability forecasting method for the coke drum crack initiation that the present invention provides embodiment 1；
Fig. 2 is the step S101 of the Forecasting Methodology for the coke drum crack initiation life that the present invention provides embodiment 2 flow
Schematic diagram；
Fig. 3 is the step S102-S105 of the Forecasting Methodology for the coke drum crack initiation life that the present invention provides embodiment 2
Schematic flow sheet；
Fig. 4 is the coke drum walls strain amplitude of the Forecasting Methodology for the coke drum crack initiation life that the present invention provides embodiment 3
The bar graph of logarithm；
Fig. 5 is that the coke drum walls crackle of the Forecasting Methodology for the coke drum crack initiation life that the present invention provides embodiment 3 is sprouted
Graph of a relation between raw probability and residual life；
Fig. 6 is the schematic flow sheet of the Forecasting Methodology for the coke drum crack propagation life that the present invention provides embodiment 4；
Fig. 7 is the specific of the step S401 of the Forecasting Methodology for the coke drum crack propagation life that the present invention provides embodiment 4
Schematic flow sheet；
Fig. 8 is the coke drum fatigue crack of the Forecasting Methodology for the coke drum crack propagation life that the present invention provides embodiment 5
Graph of a relation between failure probability and residual life；
Fig. 9 is the step S402-S405 of the Forecasting Methodology for the coke drum crack propagation life that the present invention provides embodiment 4
Idiographic flow schematic diagram.
Embodiment
Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, complete
Site preparation is described, it is clear that described embodiment is only a part of embodiment of the invention, rather than whole embodiments.It is based on
Embodiment in the present invention, it is every other that those of ordinary skill in the art are obtained under the premise of creative work is not made
Embodiment, belongs to the scope of protection of the invention.
Embodiment 1
It is the Forecasting Methodology for the coke drum crack initiation life that the present invention is provided referring to Fig. 1, including
Step S101：Set up the probability Distribution Model of coke drum walls strain amplitude.
Step S102：To under given cycle period N, according to the probability Distribution Model of the strain amplitude, being carried out to strain amplitude
Monte Carlo random device sampling, produces strain amplitude data sample Δ εi/ 2, and calculate each strain amplitude corresponding fatigue life
And fatigue damage.
In this step, using the low circumferential strain fatigue life formulas of Manson-Coffin：
Calculate each Δ ε/2 corresponding crack initiation fatigue life, ε 'fFatigue ductile coefficient is represented, c represents fatigue ductility
Index number, represents i-th of strain amplitude (i=1,2 ..., N) under given cycle period N, testing fatigue shows the fatigue of material
Ductility factor and fatigue ductility index remain essentially as constant.
According to formulaCalculate the corresponding fatigue damage of each strain amplitude under the given cycle period N.
Step S103：According to Miner rules, the fatigue damage is accumulated under given iterations, if tired
Damage meets or exceeds 1.0, then crack initiation occurs.
Specifically, in each cycle period, all accumulate and calculate by iterations given herein above, given iterations is more than etc.
In 20000 times, the present embodiment is to ensure the abundant big of statistical sample, using given iterations 20000 times.Iteration variable is initial
Value M=0, k=0, M are used for the number of times for marking iteration to complete, and k is used for the number of times for representing to occur crack initiation in iterative process.
Accumulation to fatigue damage, per iteration once, correspondingly, judges the accumulation of fatigue damage(its
Middle i represents i-th strain amplitude i=1,2 ..., N under given cycle period N)) whether it is equal to or more than 1, if it is, thinking
There is crack initiation, crack initiation cumulative number k adds 1；If not, adding 1 accumulation to the iterations M under the previous cycle cycle.
Further, the iterations M after Jia 1 described under the previous cycle cycle is judged, if less than given
Iterations threshold value 20000 times, if it is, jump procedure S102, carries out next strain amplitude data in previous cycle cycle
Calculate；If it is not, then jump procedure S104.
Step S104：Crack initiation cumulative number k and given iterations M ratio obtains crack initiation Probability p=k/
M, wherein determining iterations M=20000；
Step S105：According to the given cycle period N, the crack initiation Probability p and given confidence level 1- α are calculated
Predict the relation between coke drum walls crack initiation probability and residual life.
In this step, strain amplitude meets logarithm normal distribution under normal conditions, according to formula (1-1), crack initiation life
Also logarithm normal distribution is obeyed.
Correspondingly fixation reliability 1- α confidential interval is：
Wherein u1-α/2For the quantile of 1- α/2 being just distributed very much,For the given circulation
The sample standard deviation of cycle N Monte Carlo random data, NfMFor the corresponding average longevity of sample strain data in the M times iteration
Life, i.e.,
Embodiment 2
Referring to Fig. 2, the present embodiment is based on embodiment 1, and one of its difference is that step S101 sets up coke drum walls and answered
The probability Distribution Model of luffing, specifically includes following steps：
S1011：Obtain the strain data of the cycle period sample size of coke drum walls dangerous spot.
In this step, obtain coke drum outer wall strain data and use high temperature resistant foil gauge and dynamic strain indicator, each measuring point
A piece of high temperature resistant foil gauge is respectively installed in axial direction and ring, a Measurement channel of each foil gauge and the dynamic strain indicator connects
Connect.
S1012：According to the strain data, the strain amplitude of each cycle period is calculated, the strain amplitude passes through public affairs
Formula (2-1), which is calculated, to be obtained,
Wherein,Minimum and maximum Von Mises equivalent strains in respectively each circulation, equivalent strain
Calculation expression it is as follows：ε in formulaz, εθRespectively axial strain and ring should
The strain data become, μ is material Poisson's ratio.
S1013：Strain amplitude is taken the logarithm, the probability Distribution Model that strain amplitude obeys logarithm normal distribution is obtained, its
In, whereinFor the expectation of distribution, for the variance of distribution,And s2Computational methods it is as follows：
Wherein, xiThe strain amplitude circulated for ith, n is the cycle-index of collection, s*For standard deviation.
Referring to Fig. 3, the present embodiment is based on embodiment 1, and the two of its difference is step S105, jumps to step S102
Next given cycle period N calculating is carried out, the relation curve of crack initiation Probability p and circulating cycle issue N is drawn out.
Embodiment 3
The Forecasting Methodology of coke drum crack initiation life is described in detail by a specific embodiment for the present embodiment, should
Method comprises the following steps：
S301. STRENGTH ON COKE tower material 15CrMor carries out low-cycle fatigue experiment, so as to obtain 15CrMoR low-cycle fatigue system
Number；The fatigue data is as shown in table 1：
The low-cycle fatigue test data of table 1
The present embodiment carries out tired extension test using MTS-810 Material Testing Machine, the design of test specimen, the method for experiment and
Data analysis is all according to national standard GB/T15248-94 requirement.Experiment is divided into 6 groups, and every group of strain level is as follows：0.4%,
0.6%, 0.8%, 1.0%, 1.2% and 1.5%；Using the loading spectrum of triangular waveform, strain ratio is Rε=-1.
S302. the data to table 1 carry out least square fitting, obtain Manson-coffin relational expressions, that is, strain-tired
Labor life-span following relational expression：
For strain amplitude, NfIt is fatigue ductile coefficient for crack initiation life, 0.2690, -0.5278 refers to for fatigue ductility
Number.
S303. the strain amplitude data of the N=108 cycle period obtained to monitoring are taken the logarithm after processing, are obtained such as the institute of table 2
The data shown：
Table 2
Monitoring position is selected in coke drum bottom at the cylinder of weld seam.This is a typical dangerous spot, and it strains water
It is flat generally very high so as to cause crack initiation.The monitoring time continues 6 months, totally 108 circulations.Calculated according to formula (2-1)
Effect luffing.Strain amplitude is taken the logarithm and carried out after statistical analysis, bar chart as shown in Figure 4 is drawn out.Logarithm as seen from the figure
Strain amplitude, which is believed that, meets normal distribution, and its average is -2.42, and variance is 0.2052, i.e.,
S304. give circulating cycle issue N=1700,1750,1800,1850,1900,1950,2000,2050,2100,
2150,2200 }, to each circulating cycle issue, with Monte Carlo random device, produced according to the probability distribution of strain amplitude corresponding
Unstrained sample data, to each unstrained sample data, all calculate its fatigue life by formula (1-1)And then calculate its corresponding fatigue damageWherein, i is data number (i in sample
=1,2 ..., n).
S305. the fatigue damage under the cycle period is accumulated, if fatigue damage meets or exceeds 1.0, occurred
Crack initiation.
Specifically, each circulating cycle issue, is all iterated to calculate 20000 times, to ensure filling for statistical sample as stated above
Divide big.Iteration variable initial value M=0, M is used for the number of times for marking iteration to complete, for representing that occurring crackle in iterative process sprouts
Raw number of times.
Accumulation to fatigue damage, per iteration once, correspondingly, judges the accumulation of fatigue damage(wherein i generations
Table i-th strain amplitude i=1,2 ..., N under given cycle period N) whether it is equal to or more than 1, if it is, thinking to split
Line germinates, and crack initiation cumulative number k adds 1；If not, adding 1 accumulation to the iterations M under the previous cycle cycle.
Further, the iterations M after Jia 1 described under the previous cycle cycle is judged, if less than given
Iterations 20000 times, if it is, jumping to step S304, carry out next strain amplitude data sample in previous cycle cycle
Calculating；If it is not, then jump procedure S306.
S306. for currently given circulating cycle issue N, its crack initiation Probability p is calculated accumulative secondary for crack initiation
The ratio of number and given iterations, gives confidence level, calculates its two-sided confidence interval：
WhereinNfMFor the corresponding average longevity of sample strain data in the M times iteration
Life, i.e.,
S307. the calculating of next given cycle period is carried out, the pass of crack initiation Probability p and circulating cycle issue N is drawn out
It is that curve is as shown in Figure 5.
Wherein sample size is 20000, and confidence level is 95%.As seen from the figure, when cycle period is more than 1900 (about 8 years)
When, the probability of crack initiation is more than 0.5.In fact, being found to have crackle in detection of the dangerous spot before 6 months, at that time
Active time is 8.5 years (about 2040 cycle periods).As can be seen here, predicting the outcome, it is suitable to be coincide with actually detected discovery
It is good.
Embodiment 4
Referring to Fig. 6 and Fig. 9, the present embodiment provides a kind of Forecasting Methodology of coke drum crack propagation life, including following step
Suddenly：
S401, the probability Distribution Model for setting up coke drum walls stress amplitude.With reference to Fig. 7, it specifically comprises the following steps：
S4011 obtains the stress data of the cycle period sample size of coke drum walls dangerous spot.
In this step, obtain coke drum outer wall strain data and use high temperature resistant foil gauge and dynamic strain indicator, each measuring point
A piece of high temperature resistant foil gauge is respectively installed in axial direction and ring, a Measurement channel of each foil gauge and the dynamic strain indicator connects
Connect.Formula is utilized according to strain dataCalculate stress data σz, wherein, εzFor axial strain number
According to εθFor hoop strain data, E is the modulus of elasticity of material, and μ is Poisson's ratio.
S4012 calculates the stress amplitude of each circulation sample according to the stress data；The stress amplitude leads to Δ σiCross
Formula (4-1), which is calculated, to be obtained,
Δσi=σzmax-σzmin (4-1)
Wherein, σzmax, σzminThe axial stress that respectively each circulates is maximum, the stress data of minimum value, and i is represented
Should have before under cycle period in sample stress amplitude data numbering.
S4013 takes the logarithm to the stress amplitude, obtains the probability Distribution Model that stress amplitude obeys logarithm normal distribution,
Wherein, whereinFor the expectation of distribution, for the variance of distribution,And s2Computational methods it is as follows：
Wherein, xiThe stress amplitude circulated for ith, n is the cycle-index of collection, s*For standard deviation.
S402, under given cycle period N, according to the probability Distribution Model of the stress amplitude, stress amplitude is carried out to cover special
Caro random device is sampled, and produces stress amplitude data sample, and calculate the corresponding crackle of each stress amplitude along depth/length direction
Stress intensity factor.
In this step, crackle is calculated along depth/length direction stress intensity factor：Formula
In
In formulaThe axial stress width of respectively inside and outside wall,
S403, the threshold of stress intensity factor K using mother metalthJudge to each stress amplitude under given cycle period N
Whether Crack Extension unstability, to give iterations under the Crack Extension unstability accumulate.
Under the current stress amplitude for judging previous cycle periodic samples whether Crack Extension unstability, specifically comprising step
For：
Given crack initiation size, gives crack propagation critical size.
Given iteration variable initial value M=0；M represents the number of times that current iteration is completed, and represents Crack Extension in current iteration
The number of times of unstability.
Calculate stress amplitude Δ σiCorresponding stress intensity factor Δ Ki,
Calculating stress strength factor threshold value
Wherein, RσFor stress ratio,
Stable Crack Growth judges：
If 1. Kth＜ Δs Ki＜ 0.6KIC, Crack Extension is stable, then current crack extension Δ a=A (Δ K)m；
If 2. Δ Ki＜ Kth, it is believed that crackle does not extend, and the crack extension of previous cycle is 0；
If 3. Δ Ki＞ 0.6KIC, Crack Extension is unstable.
If 1) under current Stable Crack Growth, i.e. stress intensity factor Δ KiIt is fixed according to Paris when under the conditions of 1. 3.
Rule calculates current crack size, and Paris laws are as follows：
Wherein, da represents the increment of crack size, and dN represents the increment of cycle period, and Δ K is stress intensive factor range, A
It is material parameter with m.
If the crack size under current stress amplitude is less than crack propagation critical size, then it is assumed that the crackle of current stress amplitude is steady
Fixed extension, continuation is calculated next stress amplitude in sample.
If the crack size under current stress amplitude is more than crack propagation critical size, then it is assumed that Crack Extension reaches that unstability is faced
Boundary's state, i.e. Crack Extension unstability, it is believed that Crack Extension is completed.
2) stress intensity factor Δ KiWhen under the conditions of 2., Crack Extension unstability, then it is assumed that Crack Extension is completed.
In the case of above-mentioned bursting, Crack Extension unstability cumulative number, if current iteration number of times M is less than what is given
Iterations threshold value 20000, carries out next sample iteration of this cycle period, otherwise jump procedure S404.Wherein, iterations
Threshold value is more than or equal to 20000 times, iterations threshold value is used in the present embodiment 20000 times.
The ratio of S404, Crack Extension unstability cumulative number and the given iterations is obtained under given cycle period N
Crack Extension failure probability, wherein, the given iterations is sufficiently large.
S405, according to the given cycle period N, the Crack Extension failure probability and given confidence level 1- α, calculate pre-
The relation surveyed between coke drum walls Crack Extension failure probability p and residual life.
In this step, stress amplitude meets logarithm normal distribution after statistical analysis, then the coke drum walls life-span also obey pair
Number normal distribution.
Correspondingly fixation reliability 1- α confidential interval is：
Wherein u1-α/2For the quantile of 1- α/2 being just distributed very much,For the given circulation
The sample standard deviation of cycle N Monte Carlo random data, NfMFor the corresponding average longevity of sample stress data in the M times iteration
Life, i.e.,
Wherein, it is the quantile that is just being distributed very much, the sample standard deviation for the Monte Carlo random data for being cycle period N.
After step S405, next given cycle period N calculating is carried out, and jumps to step S402.
Embodiment 5
The Forecasting Methodology of coke drum crack propagation life is described in detail by a specific embodiment 5 for the present embodiment, should
Method comprises the following steps：
S501, STRENGTH ON COKE tower material 15CrMor carry out low-cycle fatigue experiment, obtain data as shown in table 3：
Table 3
The axial stress amplitude data of 108 circulations that S502, monitoring obtain coke outer wall measuring point are as shown in table 4.
Table 4
S503, to the data of table 3 carry out statistical analysis, obtain the logarithm of outer wall axial stress width
According to distributed constant, to given circulating cycle issue (i.e. crackle residual life)
N, N number of outer wall axial stress width sample data is produced with Monte Carlo random device, and and then extrapolates inwall axial stress
Width data.
S504, crackle is judged by the following method to each stress amplitude in N number of stress amplitude sample data for randomly generating
Whether stablize extension and calculate crack extension.
1. through-thickness stress intensity factor is calculated：
In formula
In formulaThe axial stress width of respectively inside and outside wall,
2. calculating stress strength factor threshold value
Wherein, RσFor stress ratio,
Judge：If Kth＜ Δ K ＜ 0-6KIC, Crack Extension is stable, then current crack extension Δ a=A (Δ K)m；
If Δ K ＜ Kth, it is believed that crackle does not extend, and the crack extension of previous cycle is 0；
If Δ K ＞ 0.6KIC, Crack Extension is unstable.
S505, to each cycle period (i.e. crackle residual life) N, all iterated to calculate 20000 times by the method for accompanying drawing 7,
To ensure the abundant big of statistical sample.
S506, cycle period (i.e. crackle residual life) N for giving, are calculated after its instable growth of crack p, are given
Confidence level 1-a=95%, calculates its two-sided confidence interval：
WhereinNfMFor the corresponding average residual of sample stress data of the M times iteration
Life-span, i.e.,
S507, the calculating for carrying out next given cycle period, draw out Crack Extension failure probability p and residual life N's
Relation curve is as shown in Figure 8.
Described above is the preferred embodiment of the present invention, it is noted that for those skilled in the art
For, under the premise without departing from the principles of the invention, some improvements and modifications can also be made, these improvements and modifications are also considered as
Protection scope of the present invention.
Claims (9)
1. the Forecasting Methodology of coke drum crack initiation life, it is characterised in that comprise the following steps：
Set up the probability Distribution Model of coke drum walls strain amplitude；
To under given cycle period N, according to the probability Distribution Model of strain amplitude, the strain amplitude is carried out Monte Carlo with
Machine method is sampled, and produces strain amplitude data sample, and calculate each strain amplitude corresponding fatigue life and fatigue damage；
The fatigue damage is accumulated under given iterations, if fatigue damage meets or exceeds 1.0, crackle is occurred and is sprouted
It is raw；
The ratio of crack initiation cumulative number and given iterations obtains crack initiation probability under the given cycle period N；
According to the given cycle period N, the crack initiation probability and given confidence level calculate prediction coke drum walls crackle and sprouted
Relation between raw probability and residual life.
2. the Forecasting Methodology of coke drum crack initiation life as claimed in claim 1, it is characterised in that described to set up coke drum
The probability Distribution Model of wall strain amplitude specifically includes following steps：
The strain data of the cycle period sample size of coke drum walls dangerous spot is gathered by high temperature resistant foil gauge；
Calculate the strain amplitude of each cycle period；
The strain amplitude is taken the logarithm, the probability Distribution Model that strain amplitude obeys logarithm normal distribution is obtained.
3. the Forecasting Methodology of coke drum crack initiation life as claimed in claim 2, it is characterised in that the calculating is each followed
In the strain amplitude step in ring cycle,
The strain amplitude is calculated by formula (1) and obtained,
<mrow>
<mfrac>
<mrow>
<mi>&Delta;</mi>
<mi>&epsiv;</mi>
</mrow>
<mn>2</mn>
</mfrac>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mrow>
<mo>(</mo>
<msub>
<mover>
<mi>&epsiv;</mi>
<mo>&OverBar;</mo>
</mover>
<mi>max</mi>
</msub>
<mo>-</mo>
<msub>
<mover>
<mi>&epsiv;</mi>
<mo>&OverBar;</mo>
</mover>
<mi>min</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein,Minimum and maximum Von Mises equivalent strains in respectively each circulation, the calculating of equivalent strain
Expression formula is as follows：
ε in formulaz, εθRespectively axial strain and hoop strain, μ is material Poisson
Than.
4. the Forecasting Methodology of coke drum crack initiation life as claimed in claim 1, it is characterised in that the calculating each should
It is specific to use the low circumferential strain fatigue formulas of Manson-Coffin or modeling in luffing corresponding fatigue life and fatigue damage step
Property strain energy density method calculate each strain amplitude corresponding fatigue life and fatigue damage in the sampling strain amplitude sample.
5. the Forecasting Methodology of coke drum crack initiation life as claimed in claim 1, it is characterised in that the fatigue damage exists
Carried out under given iterations in accumulation step,
The specific fatigue damage produced using Miner damage rules to strain amplitude under the given cycle period N is accumulated.
6. the Forecasting Methodology of coke drum crack propagation life, it is characterised in that comprise the following steps：
Set up the probability Distribution Model of coke drum walls stress amplitude；
To under given cycle period N, according to the probability Distribution Model of the stress amplitude, Monte Carlo side at random is carried out to stress amplitude
Method is sampled, and produces stress amplitude data sample, and calculate stress intensity of the corresponding crackle of each stress amplitude along depth/length direction
The factor；
Using the threshold of stress intensity factor of mother metal judge to each stress amplitude under given cycle period N whether Crack Extension
Unstability, accumulates to giving the Crack Extension unstability under iterations；
The ratio of Crack Extension unstability cumulative number and the given iterations obtains Crack Extension under given cycle period N and lost
Steady probability；
According to the given cycle period N, the Crack Extension failure probability and given confidence level calculate prediction coke drum walls and split
Line extends the relation between failure probability and residual life.
7. the Forecasting Methodology of coke drum crack propagation life as claimed in claim 6, it is characterised in that described to set up coke drum
The probability Distribution Model of wall stress width comprises the following steps：
Obtain the stress data of the cycle period sample size of coke drum walls dangerous spot；
Calculate the stress amplitude of each circulation sample；
The stress amplitude is taken the logarithm, the probability Distribution Model that stress amplitude obeys logarithm normal distribution is obtained.
8. the Forecasting Methodology of coke drum crack propagation life as claimed in claim 7, it is characterised in that the calculating is each followed
In the stress amplitude step of ring sample,
The stress amplitude is calculated by formula (2) and obtained,
ΔσZ=σzmax-σzmin (2)
Wherein, σzmax, σzminAxial stress maximum, the minimum value respectively each circulated.
9. the Forecasting Methodology of coke drum crack propagation life as claimed in claim 6, it is characterised in that the utilization mother metal
The threshold of stress intensity factor judge to each stress amplitude under given cycle period N whether Crack Extension unstability step, it has
Body step is：
Given crack initiation size, gives crack propagation critical size；
When the stress intensity factor is less than threshold of stress intensity factor, then it is assumed that the Crack Extension under current stress amplitude reaches mistake
Steady state；
Or, each corresponding crack size of stress amplitude under given cycle period N is calculated according to Paris laws, if described should
The crack size of power width is more than crack propagation critical size, then it is assumed that the Crack Extension under current stress amplitude reaches instability status.
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| CN109165407A (en) * | 2018-07-18 | 2019-01-08 | 上海工程技术大学 | A kind of predictor method for the mechanical component fatigue crack service life |
| CN109781611A (en) * | 2018-12-10 | 2019-05-21 | 苏州热工研究院有限公司 | Method for quantitatively evaluating for long service PWR of Nuclear Power Station main pipeline stress corrosion cracking |
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| CN109165407A (en) * | 2018-07-18 | 2019-01-08 | 上海工程技术大学 | A kind of predictor method for the mechanical component fatigue crack service life |
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| CN110738753A (en) * | 2019-09-23 | 2020-01-31 | 中国船舶重工集团公司第七一九研究所 | ship power pipeline fatigue damage prediction system and prediction method |
| CN110738753B (en) * | 2019-09-23 | 2022-01-18 | 中国船舶重工集团公司第七一九研究所 | System and method for predicting fatigue damage of ship power pipeline |
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