CN109977550B - Importance sampling method for shaft reliability design - Google Patents
Importance sampling method for shaft reliability design Download PDFInfo
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- CN109977550B CN109977550B CN201910239220.2A CN201910239220A CN109977550B CN 109977550 B CN109977550 B CN 109977550B CN 201910239220 A CN201910239220 A CN 201910239220A CN 109977550 B CN109977550 B CN 109977550B
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- 238000005070 sampling Methods 0.000 title claims abstract description 19
- 238000000034 method Methods 0.000 title claims abstract description 16
- 238000005452 bending Methods 0.000 claims abstract description 10
- 238000004364 calculation method Methods 0.000 claims abstract description 7
- 239000011159 matrix material Substances 0.000 claims description 2
- 238000000342 Monte Carlo simulation Methods 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 239000000463 material Substances 0.000 description 1
- 238000005065 mining Methods 0.000 description 1
- 239000003208 petroleum Substances 0.000 description 1
- 230000010349 pulsation Effects 0.000 description 1
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
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- G06F30/17—Mechanical parametric or variational design
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- 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
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- 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
- G06F2119/06—Power analysis or power optimisation
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
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Abstract
The invention provides an importance sampling method for shaft reliability design, which is used for carrying out the reliability design on the shaft, so that the weight of the shaft is reduced, the safety and the reliability are improved, and the product quality is improved. Considering the influence of random factors, M, T and d are seen as normal random variables, M is bending moment, T is torque (torque), and d is the diameter of the shaft; determining a probability density function, importance sampling the probability density function, and calculating the reliability of the shaft strength by applying an importance sampling method of reliability calculation.
Description
Technical Field
The invention relates to an importance sampling method for shaft reliability design, belonging to the fields of mechanical design, mechanical reliability design and mechanical modern design methods.
Background
The shaft is a common, important mechanical part. A shaft is a mechanical part that supports and rotates with a rotating part to transmit motion, torque, or bending moment. The shaft is widely applied to machine tools, engineering machinery, metallurgical machinery, mining machinery, petroleum machinery, agricultural machinery, vehicles and the like. The shaft is complex to manufacture, the working condition is complex, and the influence factors on the normal working of the shaft are more. The mechanical reliability design treats some variables in the conventional design, such as load, material strength, geometric dimensions of parts and the like, as random variables, and considers the influence of working condition changes and various random factors. The domestic scholars propose a stress-intensity interference model method for shaft reliability design, a Monte Carlo method for shaft reliability design, and the like.
Currently, no importance sampling method for shaft reliability design has emerged.
Disclosure of Invention
The invention provides an importance sampling method for shaft reliability design, which is used for carrying out the reliability design on the shaft, so that the weight of the shaft is reduced, the shaft is safer and more reliable, and the product quality is improved.
For this purpose, the technical scheme of the invention is as follows:
the importance sampling method for the shaft reliability design comprises the following specific steps:
considering the influence of random factors, M, T and d are seen as normal random variables, M is bending moment, T is torque (torque), and d is the diameter of a shaft;
the probability density function is:
the failure probability is:
the importance sampling probability density function is:
by the calculation, a convergent calculation result is obtained, the failure probability of the shaft strength is obtained, and the reliability of the shaft strength is obtained.
The beneficial effects of the invention are as follows: according to the method, the importance sampling method is used for calculating the shaft strength and the bending fatigue strength, so that the failure probability of the shaft strength is obtained, and the reliability of the shaft strength is obtained.
Drawings
FIG. 1 is a simplified diagram of an importance sampling method for an axis reliability design.
Detailed Description
The importance sampling method for the shaft reliability design comprises the following specific steps:
the stress formula of the dangerous section of the shaft is as follows:
wherein sigma e Stress of dangerous section of shaft, alpha is a coefficient of folding according to torque property (alpha is equal to 0.3 for invariable torque, alpha is equal to 0.6 when torque pulsation changes, alpha is equal to 1 for shaft with frequent positive and negative rotation), W is flexural section modulus of dangerous section of shaft, M e Is equivalent bending moment, M is bending moment, T is torque (torque), d is the diameter of the shaft;
the limit state equation is:
g 2 (x 3 )＝[σ e ]-σ e
wherein x is 3 Representing a plurality of normal random variables [ sigma ] e ]Representing allowable bending stresses;
considering the influence of random factors, M, T, d are looked at normal random variables;
the probability density function is:
wherein,,e () is the sign of the average value, C 11 Is a covariance matrix;
the failure probability is:
wherein I (g) 11 (x i ) Let.ltoreq.0) =1 is an indicator function if x i 0 in the failure domain; psi (x) i ) Is an importance sampling probability density function;
the importance sampling probability density function is:
by the calculation, a convergent calculation result is obtained, the failure probability of the shaft strength is obtained, and the reliability of the shaft strength is obtained.
As shown in fig. 1, is a flow chart of an importance sampling method of the reliability of the shaft strength.
Claims (1)
1. The importance sampling method for the shaft reliability design comprises the following specific steps:
the stress formula of the dangerous section of the shaft is as follows:
wherein sigma e For stress of dangerous section of shaft, alpha is a coefficient of folding according to torque property, W is flexural section modulus of dangerous section of shaft, M e Is equivalent bending moment, M is bending moment, T is torque (torque), d is the diameter of the shaft;
the limit state equation is:
g 2 (x 3 )＝[σ e ]-σ e
wherein x is 3 Representing a plurality of normal random variables [ sigma ] e ]Representing allowable bending stresses;
considering the influence of random factors, M, T, d are looked at normal random variables;
the probability density function is:
wherein,,e () is the sign of the average value, C 11 Is a covariance matrix;
the failure probability is:
wherein I (g) 11 (x i ) Let.ltoreq.0) =1 is an indicator function if x i 0 in the failure domain; psi (x) i ) Is an importance sampling probability density function;
the importance sampling probability density function is:
by the calculation, a convergent calculation result is obtained, the failure probability of the shaft strength is obtained, and the reliability of the shaft strength is obtained.
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| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910239220.2A CN109977550B (en) | 2019-03-27 | 2019-03-27 | Importance sampling method for shaft reliability design |
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| CN201910239220.2A CN109977550B (en) | 2019-03-27 | 2019-03-27 | Importance sampling method for shaft reliability design |
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| Publication Number | Publication Date |
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| CN109977550A CN109977550A (en) | 2019-07-05 |
| CN109977550B true CN109977550B (en) | 2023-07-18 |
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| CN110533796B (en) * | 2019-07-11 | 2020-08-18 | 肇庆学院 | Vehicle rollover prediction algorithm based on truncation importance sampling failure probability method |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| GB201506614D0 (en) * | 2014-05-12 | 2015-06-03 | Pattakos Manousos And Pattakos Emmanouel And Pattakos Efthimios | CVT v-belt over-clamping |
| CN106709104A (en) * | 2015-11-17 | 2017-05-24 | 黑龙江恒能自控科技有限公司 | Design method for fatigue reliability of gear shaft of speed reducer |
Family Cites Families (5)
| Publication number | Priority date | Publication date | Assignee | Title |
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| JP3430660B2 (en) * | 1994-09-19 | 2003-07-28 | 有限会社品川通信計装サービス | Strength reliability evaluation test equipment |
| CN105890884B (en) * | 2016-04-07 | 2018-05-22 | 东北大学 | A kind of analysis of main shaft of hoister reliability calculates appraisal procedure |
| CN107194063A (en) * | 2017-05-19 | 2017-09-22 | 厦门大学 | The extension line methods of sampling that a kind of efficient configuration liquefaction probability function is solved |
| CN107291989B (en) * | 2017-05-25 | 2018-09-14 | 中国矿业大学 | Km deep-well main shaft of hoister multi-invalidation mode reliability estimation method |
| CN109284545B (en) * | 2018-09-05 | 2022-11-04 | 西北工业大学 | Optimal condition important sampling method-based structural failure probability solving method |
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Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| GB201506614D0 (en) * | 2014-05-12 | 2015-06-03 | Pattakos Manousos And Pattakos Emmanouel And Pattakos Efthimios | CVT v-belt over-clamping |
| CN106709104A (en) * | 2015-11-17 | 2017-05-24 | 黑龙江恒能自控科技有限公司 | Design method for fatigue reliability of gear shaft of speed reducer |
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