CN107122521A - A kind of two-dimensional random load acts on the computational methods of lower fatigue life - Google Patents
A kind of two-dimensional random load acts on the computational methods of lower fatigue life Download PDFInfo
- Publication number
- CN107122521A CN107122521A CN201710191129.9A CN201710191129A CN107122521A CN 107122521 A CN107122521 A CN 107122521A CN 201710191129 A CN201710191129 A CN 201710191129A CN 107122521 A CN107122521 A CN 107122521A
- Authority
- CN
- China
- Prior art keywords
- mrow
- msub
- load
- msup
- fatigue life
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
- 238000000205 computational method Methods 0.000 title claims abstract description 14
- 239000013077 target material Substances 0.000 claims abstract description 52
- 230000000694 effects Effects 0.000 claims abstract description 30
- 238000009825 accumulation Methods 0.000 claims abstract description 21
- 238000009826 distribution Methods 0.000 claims abstract description 21
- 238000004364 calculation method Methods 0.000 claims abstract description 15
- 238000002474 experimental method Methods 0.000 claims abstract description 4
- 238000007619 statistical method Methods 0.000 claims abstract description 4
- 125000004122 cyclic group Chemical group 0.000 claims description 7
- 239000000463 material Substances 0.000 claims description 7
- 240000002853 Nelumbo nucifera Species 0.000 claims description 6
- 235000006508 Nelumbo nucifera Nutrition 0.000 claims description 6
- 235000006510 Nelumbo pentapetala Nutrition 0.000 claims description 6
- 230000010354 integration Effects 0.000 claims description 3
- 238000013461 design Methods 0.000 abstract description 6
- 238000010276 construction Methods 0.000 abstract description 3
- 230000009467 reduction Effects 0.000 abstract description 3
- 238000000034 method Methods 0.000 description 7
- 238000004458 analytical method Methods 0.000 description 4
- 238000011160 research Methods 0.000 description 4
- 230000008859 change Effects 0.000 description 3
- 230000009471 action Effects 0.000 description 2
- 238000005516 engineering process Methods 0.000 description 2
- 238000012986 modification Methods 0.000 description 2
- 230000004048 modification Effects 0.000 description 2
- 230000008569 process Effects 0.000 description 2
- 238000001228 spectrum Methods 0.000 description 2
- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 description 1
- 244000131316 Panax pseudoginseng Species 0.000 description 1
- 235000005035 Panax pseudoginseng ssp. pseudoginseng Nutrition 0.000 description 1
- 235000003140 Panax quinquefolius Nutrition 0.000 description 1
- 238000007630 basic procedure Methods 0.000 description 1
- 230000008901 benefit Effects 0.000 description 1
- 230000015572 biosynthetic process Effects 0.000 description 1
- 238000012938 design process Methods 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 235000008434 ginseng Nutrition 0.000 description 1
- 238000011835 investigation Methods 0.000 description 1
- 238000003672 processing method Methods 0.000 description 1
- 238000004904 shortening Methods 0.000 description 1
- 238000010183 spectrum analysis Methods 0.000 description 1
- 238000012360 testing method Methods 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2111/00—Details relating to CAD techniques
- G06F2111/08—Probabilistic or stochastic CAD
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/04—Ageing analysis or optimisation against ageing
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- Geometry (AREA)
- General Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Pharmaceuticals Containing Other Organic And Inorganic Compounds (AREA)
- Investigating Strength Of Materials By Application Of Mechanical Stress (AREA)
Abstract
The invention discloses the computational methods that a kind of two-dimensional random load acts on lower fatigue life, implementation steps include：Both amplitude, average by obtaining load modal data through statistical analysis to target material progress experiment collection load modal data respective distribution character and probability density function；Extrapolate the probability density function of the equivalent load of load modal data；The accumulation of fatigue damage computation model under the effect of two-dimensional random load is drawn using the Miner rules under random loading and three parameter empirical equations；Calculation of Fatigue Life model during according to accumulation of fatigue damage computation model reverse accumulation of fatigue damage equal to 1；Fatigue life of the target material under the effect of two-dimensional random load is tried to achieve according to Calculation of Fatigue Life model.The present invention can rapidly, be more accurately predicted in the early stage of Element Design to fatigue life, and early stage reference, the failure risk of reduction parts on stream, so as to shorten the construction cycle of parts are provided for the durability Design of part.
Description
Technical field
The present invention relates to load spectral analysis technology, and in particular to a kind of two-dimensional random load (considers load amplitude and load
Average is stochastic variable) effect lower fatigue life computational methods.
Background technology
Load analysis of spectrum is a key content in motor live time prediction and fatigue endurance design process.Carrying out fatigue
During durable research, the application of load typically has two kinds of processing methods, and one is to apply cyclic loading, and two be to apply random load.Adopt
The statistical property due to considering load is loaded with random load, therefore than more meeting the reality of automobile using cyclic loading loading
Border use condition.Random load is typically obeying certain successional probability distribution, such as normal distribution, exponential distribution, logarithm just
State distribution, the extreme value distribution and three-parameter Weibull distribution etc..The analysis of fatigue of random loading lower member should integrate fortune
The problem of in being analyzed and designed come relieving fatigue with Probability Statistics Theory and mechanical analyzing method.Automobile is under random loading
During work, the average and amplitude of its load all change at random, and average should be regarded as binary in loading spectrum with amplitude and become at random
Amount.In most cases, load amplitude X obeys Weibull distribution, average Y Normal Distributions.Due to load amplitude and load
The change of lotus average equally can all be affected greatly to the fatigue life of part, in order that result of study more meets the reality of part
Border working condition, so as to be more accurately predicted to the fatigue life of part, to being random based on load amplitude and average
Fatigue life under the two-dimensional random load effect of variable carries out further investigation and is necessary.Two-dimensional random load is acted on
The calculating of lower fatigue life, has become a crucial technical problem urgently to be resolved hurrily.
The content of the invention
The technical problem to be solved in the present invention：For the above mentioned problem of prior art, solved there is provided one kind need to be while examine
Consider load amplitude and the computational problem of the fatigue life under the respective statistical property of load average, can Element Design early stage
Rapidly, more accurately fatigue life is predicted, provides early stage reference for the durability Design of part, reduction parts exist
Failure risk in development process, so that the two-dimensional random load for shortening the construction cycle of parts acts on the meter of lower fatigue life
Calculation method.
In order to solve the above-mentioned technical problem, the technical solution adopted by the present invention is：
A kind of two-dimensional random load acts on the computational methods of lower fatigue life, and implementation steps include：
1) by carrying out experiment collection load modal data to target material, the load modal data is obtained through statistical analysis
Amplitude, both averages respective distribution character and probability density function；
2) the equivalent load S of the load modal data is extrapolatedeqProbability density function f (Seq)；
3) it is shown in whole, long life range using the Miner rules and formula (2) under random loading shown in formula (1)
Between three parameter empirical equations between fatigue life and load draw the lower accumulation of fatigue damage calculating of two-dimensional random load effect
Model；
Nf(S-S0)β=α (2)
In formula (1) and formula (2), D represents the accumulation of fatigue damage of target material, and N represents that the circulation that target material is subject to is carried
Lotus total quantity, f (S) represents the probability density function of random load, NfRepresent tired longevity of the target material under load S effects
Life, S represents the load that target material is subject to, S0The loading coefficient of constant is expressed as, α, β are constant coefficient；
4) Calculation of Fatigue Life mould during according to the accumulation of fatigue damage computation model reverse accumulation of fatigue damage equal to 1
Type；
5) fatigue life of the target material under the effect of two-dimensional random load is tried to achieve according to the Calculation of Fatigue Life model.
Preferably, step 2) detailed step include：
2.1) the equivalent load S according to Goodman formula Chinese style (3)eqExpression formula in load amplitude SaProbability it is close
Degree function tries to achieve Y=SaProbability density function fY(y), and according to load average SmProbability density function obtain the drawing of material
Stretch intensity σbWith load average SmDifference divided by tensile strength σbBusiness X probability density function fX(x)；
In formula (3), σbRepresent the tensile strength of target material, SaRepresent load amplitude, SmRepresent load average；
2.2) solved according to formula (4) and obtain equivalent load SeqProbability density function f (Seq)；
In formula (4), fZ(Y/X) equivalent load S is representedeqProbability density function, variable Z is equal to Y divided by X, Y and represents target
The load amplitude S of materiala, X represents the tensile strength σ of target materialbWith load average SmDifference divided by tensile strength σbIt
Business.
Preferably, step 2.2) solve obtain equivalent load SeqProbability density function f (Seq) as shown in formula (5)；
In formula (5), f (Seq) represent equivalent load SeqProbability density function, the load of target material is load amplitude Sa
With load average SmAll meet normal distribution, and load amplitude SaWith load average SmSeparate two-dimensional random load, wherein
Load amplitude SaObey N (μa,σa 2), load average SmObey N (μm,σm 2), μaRepresent load amplitude SaAverage, σa 2Represent to carry
Lotus amplitude SaVariance, μmRepresent load average SmAverage, σm 2Represent load average SmVariance, a, b, c, σ1、σ2、μ1、μ2
It is intermediate parameters, intermediate parameters μ2Value and load amplitude SaMean μaIt is identical, σ2 2Value and load amplitude SaSide
Poor σa 2It is identical, intermediate parameters μ1Value be μ1=-μm/σb+ 1, σbThe tensile strength of target material is represented, variable Z is removed equal to Y
With X, Y represents the load amplitude S of target materiala, X represents the tensile strength σ of target materialbWith load average SmDifference divided by
Tensile strength σbBusiness, q is integration variable.
Preferably, step 3) in the effect of two-dimensional random load it is lower accumulation of fatigue damage computation model such as formula (6) it is shown；
In formula (6), D represents the accumulation of fatigue damage of target material, and N represents the cyclic loading sum that target material is subject to
Amount, f (Seq) represent equivalent load SeqProbability density function, S0The loading coefficient of constant is expressed as, α, β are constant coefficient.
Preferably, step 4) in Calculation of Fatigue Life model such as formula (7) shown in；
In formula (7), NfFatigue life is represented, α, β are constant coefficient, f (Seq) represent equivalent load SeqProbability density letter
Number, S0It is expressed as the loading coefficient of constant.
Preferably, step 5) detailed step include：The Calculation of Fatigue Life model is passed through into Gauss-Legendre
Quadrature formula is integrated computing, so as to calculate fatigue life of the target material under the effect of two-dimensional random load.
Preferably, step 5) detailed step include：Fatigue life corresponding equivalent load S is calculated according to formula (8)D, root
According to equivalent load SDTry to achieve fatigue life of the corresponding fatigue life as target material under the effect of two-dimensional random load；
In formula (8), SDRepresent fatigue life corresponding equivalent load, S0It is expressed as the loading coefficient of constant, NfRepresent fatigue
Life-span, α, β are constant coefficient
The computational methods tool of two-dimensional random load effect lower fatigue life of the present invention has the advantage that：The calculating side of the present invention
Method is due to having taken into full account load amplitude and the respective statistical property of load average so that the loading of load more meets the reality of part
Border working condition, so as to more accurately calculate fatigue life.Using this method can Element Design early stage it is fast
Fastly, more accurately fatigue life is predicted, provides early stage reference for the durability Design of part, reduction parts are being opened
Failure risk during hair, so as to shorten the construction cycle of parts.
Brief description of the drawings
Fig. 1 is the basic procedure schematic diagram of the method for the embodiment of the present invention one.
Fig. 2 is parameter μ in the embodiment of the present invention one1Probability density function curve comparison figure under different distributions.
Fig. 3 is parameter σ in the embodiment of the present invention one1Probability density function curve comparison figure under different distributions.
Fig. 4 is parameter μ in the embodiment of the present invention one2Probability density function curve comparison figure under different distributions.
Fig. 5 is parameter σ in the embodiment of the present invention one2Probability density function curve comparison figure under different distributions.
Embodiment
Embodiment one：
As shown in figure 1, the implementation steps of the computational methods of the present embodiment two-dimensional random load effect lower fatigue life include：
1) by carrying out experiment collection load modal data to target material, the load modal data is obtained through statistical analysis
Amplitude, both averages respective distribution character and probability density function；
2) the equivalent load S of the load modal data is extrapolatedeqProbability density function f (Seq)；
3) it is shown in whole, long life range using the Miner rules and formula (2) under random loading shown in formula (1)
Between three parameter empirical equations between fatigue life and load draw the lower accumulation of fatigue damage calculating of two-dimensional random load effect
Model；
Nf(S-S0)β=α (2)
In formula (1) and formula (2), D represents the accumulation of fatigue damage of target material, and N represents that the circulation that target material is subject to is carried
Lotus total quantity, f (S) represents the probability density function of random load, NfRepresent tired longevity of the target material under load S effects
Life, S represents the load that target material is subject to, S0The loading coefficient of constant is expressed as, α, β are constant coefficient；
4) Calculation of Fatigue Life mould during according to the accumulation of fatigue damage computation model reverse accumulation of fatigue damage equal to 1
Type；
5) fatigue life of the target material under the effect of two-dimensional random load is tried to achieve according to the Calculation of Fatigue Life model.
In the present embodiment, step 2) detailed step include：
2.1) the equivalent load S according to Goodman formula Chinese style (3)eqExpression formula in load amplitude SaProbability it is close
Function is spent, Y=S is obtainedaProbability density function fY(y), and according to load average SmProbability density function obtain the drawing of material
Stretch intensity σbWith load average SmDifference divided by tensile strength σbBusiness X probability density function fX(x)；
In formula (3), σbRepresent the tensile strength of target material, SaRepresent load amplitude, SmRepresent load average；
2.2) solved according to formula (4) and obtain equivalent load SeqProbability density function f (Seq)；
In formula (4), fZ(Y/X) equivalent load S is representedeqProbability density function, variable Z is equal to Y divided by X, Y and represents target
The load amplitude S of materiala, X represents the tensile strength σ of target materialbWith load average SmDifference divided by tensile strength σbIt
Business.
In order to calculate the fatigue life under the effect of two-dimensional random load, load amplitude and load average are present embodiments provided
All meet the equivalent load S of the two-dimensional random load of normal distributioneqProbability density function f (Seq).In the present embodiment, step
2.2) solve and obtain equivalent load SeqProbability density function f (Seq) as shown in formula (5)；
In formula (5), f (Seq) represent equivalent load SeqProbability density function, the load of target material is load amplitude Sa
With load average SmAll meet normal distribution, and load amplitude SaWith load average SmSeparate two-dimensional random load, wherein
Load amplitude SaObey N (μa,σa 2), load average SmObey N (μm,σm 2), μaRepresent load amplitude SaAverage, σa 2Represent to carry
Lotus amplitude SaVariance, μmRepresent load average SmAverage, σm 2Represent load average SmVariance, a, b, c, σ1、σ2、μ1、μ2
It is intermediate parameters, intermediate parameters μ2Value and load amplitude SaMean μaIt is identical, σ2 2Value and load amplitude SaSide
Poor σa 2It is identical, intermediate parameters μ1Value be μ1=-μm/σb+ 1, σbThe tensile strength of target material is represented, variable Z is removed equal to Y
With X, Y represents the load amplitude S of target materiala, X represents the tensile strength σ of target materialbWith load average SmDifference divided by
Tensile strength σbBusiness, q is integration variable.
In the present embodiment, step 3) in accumulation of fatigue damage computation model such as formula (6) institute under the effect of two-dimensional random load
Show；
In formula (6), D represents the accumulation of fatigue damage of target material, and N represents the cyclic loading sum that target material is subject to
Amount, f (Seq) represent equivalent load SeqProbability density function, S0The loading coefficient of constant is expressed as, α, β are constant coefficient.
In the present embodiment, step 4) in Calculation of Fatigue Life model such as formula (7) shown in；
In formula (7), NfFatigue life is represented, α, β are constant coefficient, f (Seq) represent equivalent load SeqProbability density letter
Number, S0It is expressed as the loading coefficient of constant.
In the present embodiment, step 5) detailed step include：The Calculation of Fatigue Life model is passed through into Gauss-
Legendre quadrature formulas are integrated computing, so as to calculate tired longevity of the target material under the effect of two-dimensional random load
Life.
In the present embodiment, respectively for intermediate parameters σ1、σ2、μ1、μ2Different values are carried out, and respectively will different middle ginsengs
Equivalent load S under number value conditioneqProbability density function f (Seq) (f is expressed as in figureZ(Z)) formation curve, is respectively obtained
Fig. 2, Fig. 3, Fig. 4, Fig. 5.Fig. 2 describes σ1Value 0.08, σ2Value 30, μ2In the case of value 190, μ1Value is respectively
0.5th, 0.75,1,1.25,1.5 when probability density function f (Seq) correlation curve.Fig. 3 describes σ2Value 30, μ1Value
0.75、μ2In the case of value 190, σ1Probability density function f when value is 0.05,0.06,0.07,0.08,0.09,0.1 respectively
(Seq) correlation curve.Fig. 4 describes σ1Value 0.08, σ2Value 30, μ1In the case of value 0.75, μ2Value is respectively
150th, 170,190,210,230,250 when probability density function f (Seq) correlation curve.Fig. 5 describes σ1Value 0.08, μ1Take
Value 0.75, μ2In the case of value 190, σ2Probability density function f (S when value is 5,10,20,30,40,50 respectivelyeq) pair
Compare curve.Carrying out analysis to Fig. 2~Fig. 5 can draw：1)fZ(z) function graft shape and normal distyribution function shape phase
Seemingly, predominantly following three points：A) functional value has peak point, and z is more remote from peak point, and functional value is smaller；B) function is in peak value
There is flex point point both sides；C) curve is using trunnion axis as asymptote.2) in the case of other three parameter constants, μ1Reduction,
σ1、μ2、σ2Increase reduce peak of function, while function curve shape becomes gentle.3)μ2Increase peak point is moved right
It is dynamic, μ1And σ1Increase be moved to the left peak point, σ2Change do not change peak point position.
Embodiment two：
Essentially identical with embodiment one in the present embodiment, its main distinction point is：Step 5) according to the fatigue life gage
Calculate the method difference that model tries to achieve fatigue life of the target material under the effect of two-dimensional random load.
In the present embodiment, the research to fatigue life is converted into the research of equivalent load.Define equivalent load as follows：From
From the point of view of total action effect, the final result under random load and the effect of the class load of cyclic loading two will all cause the damage of component
Hinder state to reach critical value and fail, it is believed that corresponding to certain random load process, certainly exist one it is equivalent with it
Constant amplitude loading so that component is damaged simultaneously under identical original state by identical action time.Define the perseverance
Width load is the equivalent load of random load, uses SDRepresent.The corresponding relation formula of equivalent load and fatigue life are shown in that three parameters are passed through
Test formula.
In the present embodiment, step 5) detailed step include：Fatigue life corresponding equivalent load is calculated according to formula (8)
SD, according to equivalent load SDTry to achieve fatigue life of the corresponding fatigue life as target material under the effect of two-dimensional random load；
In formula (8), SDRepresent fatigue life corresponding equivalent load, S0The theory fatigue that expression is represented with equivalent stress width
The limit, NfFatigue life is represented, α, β are constant coefficient.By taking 16Mn materials as an example, according to existing research, α=3.95 × 108, S0
=261MPa, β=2.According to formula (7) and formula (8), equivalent load of the 16Mn materials under the effect of two-dimensional random load is：
In formula (10), SDRepresent fatigue life corresponding equivalent load, SeqRepresent equivalent load.
It is still public using Gauss-Legendre quadratures under the statistical distribution parameter of different loads amplitude and load average
Formula is integrated computing to function, calculates part equivalent load data and is shown in Table 1~table 5, while in order to be compared, calculating
The equivalent load of one-dimensional random load is shown in Table 6.After equivalent load is drawn, it can be drawn fatigue life according to counter push away of formula (8).
Table 1：Different μ1、σ1Equivalent load (MPa) (μ2=210, σ2=40).
| μ1\σ1 | 0.05 | 0.06 | 0.07 | 0.08 | 0.09 | 0.1 |
| 0.5 | >600 | >600 | >600 | >600 | >600 | >600 |
| 0.75 | 314 | 316 | 344 | 417 | 526 | >600 |
| 1 | 270 | 271 | 272 | 273 | 274 | 275 |
| 1.25 | 262 | 262 | 262 | 262 | 263 | 263 |
| 1.5 | 261 | 261 | 261 | 261 | 261 | 261 |
Table 2：Different μ2、σ2Equivalent load (MPa) (μ1=0.75, σ1=0.05).
| σ2\μ2 | 150 | 170 | 190 | 210 | 230 | 250 |
| 10 | 262 | 265 | 274 | 291 | 314 | 340 |
| 20 | 264 | 270 | 281 | 298 | 319 | 343 |
| 30 | 269 | 277 | 289 | 306 | 325 | 348 |
| 40 | 276 | 285 | 298 | 314 | 333 | 354 |
| 50 | 283 | 294 | 307 | 323 | 341 | 362 |
Table 3：Different μ2、σ2Equivalent load (MPa) (μ1=1, σ1=0.05).
| σ2\μ2 | 150 | 170 | 190 | 210 | 230 | 250 |
| 10 | 261 | 261 | 261 | 261 | 263 | 268 |
| 20 | 261 | 261 | 261 | 263 | 266 | 273 |
| 30 | 261 | 262 | 263 | 266 | 271 | 279 |
| 40 | 262 | 264 | 266 | 270 | 277 | 286 |
| 50 | 264 | 267 | 271 | 276 | 283 | 292 |
Table 4：Different μ2、σ2Equivalent load (MPa) (μ1=1, σ1=0.1).
Table 5：Different μ2、σ2Equivalent load (MPa) (μ1=1.25, σ1=0.1).
| σ2\μ2 | 150 | 170 | 190 | 210 | 230 | 250 |
| 10 | 261 | 261 | 261 | 261 | 261 | 262 |
| 20 | 261 | 261 | 261 | 261 | 262 | 263 |
| 30 | 261 | 261 | 261 | 262 | 263 | 264 |
| 40 | 261 | 261 | 262 | 263 | 264 | 267 |
| 50 | 262 | 262 | 263 | 265 | 267 | 270 |
Table 6：The equivalent load (MPa) of one-dimensional random load.
| σ\μ | 150 | 170 | 190 | 210 | 230 | 250 |
| 10 | 261 | 261 | 261 | 261 | 261 | 264 |
| 20 | 261 | 261 | 261 | 262 | 264 | 270 |
| 30 | 261 | 261 | 262 | 265 | 269 | 277 |
| 40 | 262 | 263 | 265 | 269 | 275 | 284 |
| 50 | 264 | 266 | 269 | 274 | 281 | 291 |
According to analysis result, load average has large effect to the equivalent load of two-dimentional normal state random load, in load
Average SmMean μmDuring less than 0, equivalent load reduces rapidly the equivalent load for being even below one-dimensional random load；Work as μmEqual to 0
When, it is considered to the equivalent load of load average is more slightly higher than the equivalent load for not considering load average；Work as μmDuring more than 0, with μ2、σ2
Increase, the equivalent load of two-dimensional random load increases sharply, until much larger than the equivalent load of one-dimensional random load.
Described above is only the preferred embodiment of the present invention, and protection scope of the present invention is not limited merely to above-mentioned implementation
Example, all technical schemes belonged under thinking of the present invention belong to protection scope of the present invention.It should be pointed out that for the art
Those of ordinary skill for, some improvements and modifications without departing from the principles of the present invention, these improvements and modifications
It should be regarded as protection scope of the present invention.
Claims (7)
1. a kind of two-dimensional random load acts on the computational methods of lower fatigue life, it is characterised in that implementation steps include：
1) by carrying out experiment collection load modal data to target material, the width of the load modal data is obtained through statistical analysis
Both value, average respective distribution character and probability density function；
2) the equivalent load S of the load modal data is extrapolatedeqProbability density function f (Seq)；
3) utilize tired in whole, between long life range shown in the Miner rules and formula (2) under random loading shown in formula (1)
Three parameter empirical equations between labor life-span and load draw the accumulation of fatigue damage computation model under the effect of two-dimensional random load；
<mrow>
<mi>D</mi>
<mo>=</mo>
<msubsup>
<mo>&Integral;</mo>
<mrow>
<mo>-</mo>
<mi>&infin;</mi>
</mrow>
<mrow>
<mo>=</mo>
<mi>&infin;</mi>
</mrow>
</msubsup>
<mfrac>
<mrow>
<mi>N</mi>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>S</mi>
<mo>)</mo>
</mrow>
</mrow>
<msub>
<mi>N</mi>
<mi>f</mi>
</msub>
</mfrac>
<mi>d</mi>
<mi>S</mi>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
Nf(S-S0)β=α (2)
In formula (1) and formula (2), D represents the accumulation of fatigue damage of target material, and N represents that the cyclic loading that target material is subject to is total
Quantity, f (S) represents the probability density function of random load, NfRepresent fatigue life of the target material under load S effects, S tables
Show the load that target material is subject to, S0The loading coefficient of constant is expressed as, α, β are constant coefficient；
4) Calculation of Fatigue Life model during according to the accumulation of fatigue damage computation model reverse accumulation of fatigue damage equal to 1；
5) fatigue life of the target material under the effect of two-dimensional random load is tried to achieve according to the Calculation of Fatigue Life model.
2. two-dimensional random load according to claim 1 acts on the computational methods of lower fatigue life, it is characterised in that step
2) detailed step includes：
2.1) the equivalent load S according to Goodman formula Chinese style (3)eqExpression formula in load amplitude SaProbability density letter
Number tries to achieve Y=SaProbability density function fY(y), and according to load average SmProbability density function obtain material stretching it is strong
Spend σbWith load average SmDifference divided by tensile strength σbBusiness X probability density function fX(x)；
<mrow>
<msub>
<mi>S</mi>
<mrow>
<mi>e</mi>
<mi>q</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>&sigma;</mi>
<mi>b</mi>
</msub>
<msub>
<mi>S</mi>
<mi>a</mi>
</msub>
</mrow>
<mrow>
<msub>
<mi>&sigma;</mi>
<mi>b</mi>
</msub>
<mo>-</mo>
<msub>
<mi>S</mi>
<mi>m</mi>
</msub>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>3</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula (3), σbRepresent the tensile strength of target material, SaRepresent load amplitude, SmRepresent load average；
2.2) equivalent load S is obtained according to formula (4) solutioneqProbability density function f (Seq)；
<mrow>
<msub>
<mi>f</mi>
<mi>Z</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>Y</mi>
<mo>/</mo>
<mi>X</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msubsup>
<mo>&Integral;</mo>
<mrow>
<mo>-</mo>
<mi>&infin;</mi>
</mrow>
<mrow>
<mi>=</mi>
<mi>&infin;</mi>
</mrow>
</msubsup>
<mo>|</mo>
<mi>x</mi>
<mo>|</mo>
<msub>
<mi>f</mi>
<mi>X</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<msub>
<mi>f</mi>
<mi>Y</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>Z</mi>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mi>d</mi>
<mi>x</mi>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula (4), fZ(Y/X) equivalent load S is representedeqProbability density function, variable Z is equal to Y divided by X, Y and represents target material
Load amplitude Sa, X represents the tensile strength σ of target materialbWith load average SmDifference divided by tensile strength σbBusiness.
3. two-dimensional random load according to claim 2 acts on the computational methods of lower fatigue life, it is characterised in that step
2.2) solve and obtain equivalent load SeqProbability density function f (Seq) as shown in formula (5)；
<mrow>
<mo>{</mo>
<mtable>
<mtr>
<mtd>
<mrow>
<mi>f</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>S</mi>
<mrow>
<mi>e</mi>
<mi>q</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<msup>
<mi>e</mi>
<mrow>
<mo>-</mo>
<mi>c</mi>
</mrow>
</msup>
<mrow>
<mn>2</mn>
<msub>
<mi>&pi;a&sigma;</mi>
<mn>1</mn>
</msub>
<msub>
<mi>&sigma;</mi>
<mn>2</mn>
</msub>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<mrow>
<msup>
<mi>be</mi>
<mrow>
<mo>(</mo>
<msup>
<mi>b</mi>
<mn>2</mn>
</msup>
<mo>/</mo>
<mn>4</mn>
<mi>a</mi>
<mo>-</mo>
<mi>c</mi>
<mo>)</mo>
</mrow>
</msup>
</mrow>
<mrow>
<mn>4</mn>
<msub>
<mi>&pi;a&sigma;</mi>
<mn>1</mn>
</msub>
<msub>
<mi>&sigma;</mi>
<mn>2</mn>
</msub>
<msqrt>
<mrow>
<mn>2</mn>
<mi>a</mi>
</mrow>
</msqrt>
</mrow>
</mfrac>
<msubsup>
<mo>&Integral;</mo>
<mrow>
<mo>-</mo>
<mi>b</mi>
<mo>/</mo>
<msqrt>
<mrow>
<mn>2</mn>
<mi>a</mi>
</mrow>
</msqrt>
</mrow>
<mrow>
<mi>b</mi>
<mo>/</mo>
<msqrt>
<mrow>
<mn>2</mn>
<mi>a</mi>
</mrow>
</msqrt>
</mrow>
</msubsup>
<msup>
<mi>e</mi>
<mrow>
<mo>-</mo>
<msup>
<mi>q</mi>
<mn>2</mn>
</msup>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msup>
<mi>d</mi>
<mi>q</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>a</mi>
<mo>=</mo>
<mfrac>
<mrow>
<msup>
<msub>
<mi>&sigma;</mi>
<mn>2</mn>
</msub>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mi>Z</mi>
<mn>2</mn>
</msup>
<msup>
<msub>
<mi>&sigma;</mi>
<mn>1</mn>
</msub>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<mn>2</mn>
<msup>
<msub>
<mi>&sigma;</mi>
<mn>1</mn>
</msub>
<mn>2</mn>
</msup>
<msup>
<msub>
<mi>&sigma;</mi>
<mn>2</mn>
</msub>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>b</mi>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>&mu;</mi>
<mn>1</mn>
</msub>
<msup>
<msub>
<mi>&sigma;</mi>
<mn>2</mn>
</msub>
<mn>2</mn>
</msup>
<mo>+</mo>
<msub>
<mi>Z&mu;</mi>
<mn>2</mn>
</msub>
<msup>
<msub>
<mi>&sigma;</mi>
<mn>1</mn>
</msub>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<msup>
<msub>
<mi>&sigma;</mi>
<mn>1</mn>
</msub>
<mn>2</mn>
</msup>
<msup>
<msub>
<mi>&sigma;</mi>
<mn>2</mn>
</msub>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>c</mi>
<mo>=</mo>
<mfrac>
<mrow>
<msup>
<msub>
<mi>&mu;</mi>
<mn>1</mn>
</msub>
<mn>2</mn>
</msup>
<msup>
<msub>
<mi>&sigma;</mi>
<mn>2</mn>
</msub>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<msub>
<mi>&mu;</mi>
<mn>2</mn>
</msub>
<mn>2</mn>
</msup>
<msup>
<msub>
<mi>&sigma;</mi>
<mn>1</mn>
</msub>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<mn>2</mn>
<msup>
<msub>
<mi>&sigma;</mi>
<mn>1</mn>
</msub>
<mn>2</mn>
</msup>
<msup>
<msub>
<mi>&sigma;</mi>
<mn>2</mn>
</msub>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&sigma;</mi>
<mn>1</mn>
</msub>
<mo>=</mo>
<mfrac>
<msub>
<mi>&sigma;</mi>
<mi>m</mi>
</msub>
<msub>
<mi>&sigma;</mi>
<mi>b</mi>
</msub>
</mfrac>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>5</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula (5), f (Seq) represent equivalent load SeqProbability density function, the load of target material is load amplitude SaAnd load
Lotus average SmAll meet normal distribution, and load amplitude SaWith load average SmSeparate two-dimensional random load, wherein load
Amplitude SaObey N (μa,σa 2), load average SmObey N (μm,σm 2), μaRepresent load amplitude SaAverage, σa 2Represent load width
Value SaVariance, μmRepresent load average SmAverage, σm 2Represent load average SmVariance, a, b, c, σ1、σ2、μ1、μ2It is
Intermediate parameters, intermediate parameters μ2Value and load amplitude SaMean μaIt is identical, σ2 2Value and load amplitude SaVariances sigmaa 2
It is identical, intermediate parameters μ1Value be μ1=-μm/σb+ 1, σbThe tensile strength of target material is represented, variable Z is equal to Y divided by X, Y
Represent the load amplitude S of target materiala, X represents the tensile strength σ of target materialbWith load average SmDifference divided by stretching it is strong
Spend σbBusiness, q is integration variable.
4. two-dimensional random load according to claim 1 acts on the computational methods of lower fatigue life, it is characterised in that step
3) shown in the accumulation of fatigue damage computation model such as formula (6) under the effect of two-dimensional random load；
<mrow>
<mi>D</mi>
<mo>=</mo>
<msubsup>
<mo>&Integral;</mo>
<mrow>
<mo>-</mo>
<mi>&infin;</mi>
</mrow>
<mrow>
<mo>=</mo>
<mi>&infin;</mi>
</mrow>
</msubsup>
<mfrac>
<mrow>
<mi>N</mi>
<mi>f</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>S</mi>
<mrow>
<mi>e</mi>
<mi>q</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mi>&alpha;</mi>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>S</mi>
<mrow>
<mi>e</mi>
<mi>q</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>S</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
<mrow>
<mo>-</mo>
<mi>&beta;</mi>
</mrow>
</msup>
</mrow>
</mfrac>
<mi>d</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>S</mi>
<mrow>
<mi>e</mi>
<mi>q</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>6</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula (6), D represents the accumulation of fatigue damage of target material, and N represents the cyclic loading total quantity that target material is subject to, f
(Seq) represent equivalent load SeqProbability density function, S0The loading coefficient of constant is expressed as, α, β are constant coefficient.
5. two-dimensional random load according to claim 4 acts on the computational methods of lower fatigue life, it is characterised in that step
4) shown in the Calculation of Fatigue Life model such as formula (7) in；
<mrow>
<msub>
<mi>N</mi>
<mi>f</mi>
</msub>
<mo>=</mo>
<mfrac>
<mi>&alpha;</mi>
<mrow>
<msubsup>
<mo>&Integral;</mo>
<mrow>
<mo>-</mo>
<mi>&infin;</mi>
</mrow>
<mrow>
<mi>=</mi>
<mi>&infin;</mi>
</mrow>
</msubsup>
<mi>f</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>S</mi>
<mrow>
<mi>e</mi>
<mi>q</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>S</mi>
<mrow>
<mi>e</mi>
<mi>q</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>S</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
<mi>&beta;</mi>
</msup>
<mi>d</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>S</mi>
<mrow>
<mi>e</mi>
<mi>q</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>7</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula (7), NfFatigue life is represented, α, β are constant coefficient, f (Seq) represent equivalent load SeqProbability density function, S0
It is expressed as the loading coefficient of constant.
6. the two-dimensional random load according to any one in Claims 1 to 5 acts on the computational methods of lower fatigue life, its
Be characterised by, step 5) detailed step include：The Calculation of Fatigue Life model is public by Gauss-Legendre quadratures
Formula is integrated computing, so as to calculate fatigue life of the target material under the effect of two-dimensional random load.
7. the two-dimensional random load according to any one in Claims 1 to 5 acts on the computational methods of lower fatigue life, its
Be characterised by, step 5) detailed step include：Fatigue life corresponding equivalent load S is calculated according to formula (8)D, according to equivalent
Load SDTry to achieve fatigue life of the corresponding fatigue life as target material under the effect of two-dimensional random load；
<mrow>
<msub>
<mi>S</mi>
<mi>D</mi>
</msub>
<mo>=</mo>
<msub>
<mi>S</mi>
<mn>0</mn>
</msub>
<mo>+</mo>
<mroot>
<mfrac>
<mi>&alpha;</mi>
<msub>
<mi>N</mi>
<mi>f</mi>
</msub>
</mfrac>
<mi>&beta;</mi>
</mroot>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>8</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula (8), SDRepresent fatigue life corresponding equivalent load, S0It is expressed as the loading coefficient of constant, NfRepresent the tired longevity
Life, α, β are constant coefficient.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710191129.9A CN107122521B (en) | 2017-03-28 | 2017-03-28 | A kind of two-dimensional random load acts on the calculation method of lower fatigue life |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710191129.9A CN107122521B (en) | 2017-03-28 | 2017-03-28 | A kind of two-dimensional random load acts on the calculation method of lower fatigue life |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN107122521A true CN107122521A (en) | 2017-09-01 |
| CN107122521B CN107122521B (en) | 2019-11-05 |
Family
ID=59718036
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201710191129.9A Expired - Fee Related CN107122521B (en) | 2017-03-28 | 2017-03-28 | A kind of two-dimensional random load acts on the calculation method of lower fatigue life |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN107122521B (en) |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108984866A (en) * | 2018-06-28 | 2018-12-11 | 中国铁道科学研究院集团有限公司金属及化学研究所 | A kind of preparation method of test load spectrum |
| CN111855383A (en) * | 2020-07-29 | 2020-10-30 | 石河子大学 | Method for predicting fatigue life of wind turbine blade under icing load |
| CN112906164A (en) * | 2021-03-29 | 2021-06-04 | 河南科技大学 | Rolling bearing reliability design method based on stress-intensity interference model |
| CN116011195A (en) * | 2022-12-19 | 2023-04-25 | 广东水电二局股份有限公司 | Fan foundation fatigue load spectrum modeling method based on data driving |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104020062A (en) * | 2014-05-20 | 2014-09-03 | 北京航空航天大学 | Method for compiling fatigue accelerated testing load spectrum |
| CN104978490A (en) * | 2015-07-06 | 2015-10-14 | 北京航空航天大学 | Novel method for forecasting calendar life of metal structure of aging aircraft |
| CN105808865A (en) * | 2016-03-15 | 2016-07-27 | 北京航空航天大学 | Low-temperature fatigue property characterization and life estimation method |
-
2017
- 2017-03-28 CN CN201710191129.9A patent/CN107122521B/en not_active Expired - Fee Related
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104020062A (en) * | 2014-05-20 | 2014-09-03 | 北京航空航天大学 | Method for compiling fatigue accelerated testing load spectrum |
| CN104978490A (en) * | 2015-07-06 | 2015-10-14 | 北京航空航天大学 | Novel method for forecasting calendar life of metal structure of aging aircraft |
| CN105808865A (en) * | 2016-03-15 | 2016-07-27 | 北京航空航天大学 | Low-temperature fatigue property characterization and life estimation method |
Non-Patent Citations (2)
| Title |
|---|
| 武滢 等: "随机载荷作用下疲劳寿命分布预测模型", 《工程设计学报》 * |
| 郭虎 等: "汽车试验场可靠性试验强化系数的研究", 《机械工程学报》 * |
Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108984866A (en) * | 2018-06-28 | 2018-12-11 | 中国铁道科学研究院集团有限公司金属及化学研究所 | A kind of preparation method of test load spectrum |
| CN108984866B (en) * | 2018-06-28 | 2022-09-30 | 中国铁道科学研究院集团有限公司金属及化学研究所 | Compilation method of test load spectrum |
| CN111855383A (en) * | 2020-07-29 | 2020-10-30 | 石河子大学 | Method for predicting fatigue life of wind turbine blade under icing load |
| CN111855383B (en) * | 2020-07-29 | 2023-09-05 | 石河子大学 | Fatigue life prediction method for wind turbine blade under icing load |
| CN112906164A (en) * | 2021-03-29 | 2021-06-04 | 河南科技大学 | Rolling bearing reliability design method based on stress-intensity interference model |
| CN116011195A (en) * | 2022-12-19 | 2023-04-25 | 广东水电二局股份有限公司 | Fan foundation fatigue load spectrum modeling method based on data driving |
| CN116011195B (en) * | 2022-12-19 | 2024-03-15 | 广东水电二局股份有限公司 | Fan foundation fatigue load spectrum modeling method based on data driving |
Also Published As
| Publication number | Publication date |
|---|---|
| CN107122521B (en) | 2019-11-05 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN107122521A (en) | A kind of two-dimensional random load acts on the computational methods of lower fatigue life | |
| Detommaso et al. | A Stein variational Newton method | |
| Gorham et al. | Measuring sample quality with diffusions | |
| Parchami et al. | Process capability indices as fuzzy numbers | |
| Le Gratiet et al. | A Bayesian approach for global sensitivity analysis of (multifidelity) computer codes | |
| Nunes et al. | abctools: an R package for tuning approximate Bayesian computation analyses | |
| Osiewalski et al. | Numerical tools for the Bayesian analysis of stochastic frontier models | |
| Arnold et al. | Existence of nontrivial steady states for populations structured with respect to space and a continuous trait | |
| Habiger | Multiple test functions and adjusted p-values for test statistics with discrete distributions | |
| CN107909282A (en) | A kind of e _-Government Service efficiency evaluation system and method | |
| CN104573277A (en) | Vehicle suspension system performance analysis method | |
| Gouvêa et al. | Global optimization using q-gradients | |
| Yamaguchi | Attribute dependency functions considering data efficiency | |
| Lye et al. | A review of stochastic sampling methods for Bayesian inference problems | |
| JP4299508B2 (en) | Operation and quality related analysis device in manufacturing process, related analysis method, and computer-readable storage medium | |
| Del Moral et al. | Interacting Markov chain Monte Carlo methods for solving nonlinear measure-valued equations | |
| CN112330112A (en) | User energy evaluation method of new energy combined cooling heating and power system based on cloud model | |
| CN113128676A (en) | Pruning method and device based on target detection model and storage medium | |
| CN107526710A (en) | A kind of place suitability Hierarchy Analysis Method based on Monte Carlo EGS4 method | |
| Owada et al. | Limit theorems for process-level Betti numbers for sparse, critical, and Poisson regimes | |
| Hernández-Orallo | C-tests revisited: Back and forth with complexity | |
| Klar | A class of tests for exponentiality against HNBUE alternatives | |
| Devroye et al. | The double CFTP method | |
| CN103984810B (en) | Part curve and surface small echo method for fairing based on multiresolution analysis | |
| Maratea et al. | Solving disjunctive temporal problems with preferences using maximum satisfiability |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant | ||
| CF01 | Termination of patent right due to non-payment of annual fee | ||
| CF01 | Termination of patent right due to non-payment of annual fee |
Granted publication date: 20191105 |