An Inexact Probabilistic Reliability Evaluation Method for Gear Transmission

Abstract

The invention discloses an imprecise probability reliability evaluation method for a gear transmission device, and the method comprises the steps: describing uncertain factors in a reliability evaluation process of the gear transmission device through an evidence theory, and building a limit state function of the gear transmission device; in order to guarantee the calculation precision and the calculation efficiency in the reliability evaluation process of the gear transmission device, solving a midpoint through the intersection point of the maximum possible failure point and the limit state function with the edge of the uncertain region; then, carrying out first-order Taylor expansion on the limit state function at each midpoint, and carrying out joint focal element extreme value analysison each joint focal element on the first-order Taylor expansion function by applying a first-order approximate reliability analysis method, so as to obtain credibility and likelihood for measuring the reliability of the gear transmission device. According to the method, the calculation efficiency and the solving quality of the solving credibility and the similarity can be essentially improved, and the method has wide engineering application value in the field of reliability evaluation of gear transmission devices.

Description

technical field [0001] The invention relates to the field of reliability evaluation of gear transmission devices, in particular to an inaccurate probabilistic reliability evaluation method of gear transmission devices. Background technique [0002] Gear transmission is one of the most common forms of transmission in mechanical transmission systems. The reliability of the gear transmission will directly affect the transmission efficiency of the mechanical system, and during the design process of the gear transmission, the maximum stress borne by the gear must be less than its maximum allowable stress. [0003] For the reliability evaluation and design of gear transmission, the existing methods have the following problems: [0004] 1. Most of the existing design methods for gear transmissions are studied under the deterministic condition of the system parameter model. However, in the actual design process of gear transmissions, there are errors in boundary conditions, initial...

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Problems solved by technology

[0004] 1. Most of the existing design methods for gear transmissions are studied under the deterministic condition of the system parameter model. However, in the actual design process of gear transmissions, there are errors in boundary conditions, initial conditions, and measurement conditions. or uncertainty, if these factors are still treated as deterministic factors, it will lead to a large deviation between the system response and the actual response

[0005] 2. For the reliability evaluation method of gear transmission, some existing methods use probability models to describe uncertain design variables, such as the patent "A Method for Reliability Evaluation of Spur Gear Transmission System" with publication number CN105138794A and publication number It is the patent of CN107273609A "A method for evaluating the reliability of gear transmission based on the Kriging model". The uncertain variables in the above patents are all described by random variables, that is, the distribution type of random variables needs to be obtained through data collection and hypothesis testing, but the actual design process In many uncertain variables, the probability distribution density is unknown due to lack of sufficient sample data, which makes it difficult to accurately obtain the probability distribution of uncertain design variables

[0006] 3. For the reliability evaluation methods of gear transmissions, some existing methods use non-probability convex set models to describe uncertain design variables, such as the patent with publication number CN102446239A "Gear Transmission Considering Cognitive and Random Uncertainty Multidisciplinary Reliability Analysis Method”, this patent describes the uncertain design parameters through the probability model and the non-probability convex set model based on the completeness of the design parameter uncertainty data, although the non-probability convex set describing the uncertain design parameters The model does not require an accurate probability distribution, but because the non-probability convex set model emphasizes too much extreme conditions, it will result in a conservative design

[0007] 4. For the reliability evaluation methods of gear transmissions, some existing methods use evidence theory to describe uncertain design variables, and these methods only consider the maximum possible failure point of the limit state function in the reliability evaluation process, but In the reliability evaluation process, the boundary points where the limit state function intersects with the boundary of the uncertainty domain play an important role in the judgment of the reliability and plausibility. These methods do not consider these boundary points, which affects the gear transmission. The reliability assessment accuracy of

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