An approximate numerical method for solving Cauchy singular integral equations composed of multiple implicit parameter functions with unknown integral limits in contact mechanics

Qi, Wen; Du, Qiang

doi:10.1016/j.jmaa.2019.123530

Cited by 8 publications

(6 citation statements)

References 43 publications

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“…Given that the oscillatory function exhibits certain oscillations within the integration domain, its exact value is known to be 13.403 900. Results obtained using the artificial firefly algorithm from literature [15] yield a value of 13.404 865 83, while the artificial fish swarm algorithm from literature [13]…”

Section: mentioning

confidence: 99%

“…Given that the exact value of the double integral of this function is 5.100 170, results obtained using the artificial firefly algorithm from literature [15] yield a value of 5. 099 686 404 664 276, while the artificial fish swarm algorithm from literature [13]…”

Section: mentioning

confidence: 99%

“…The exact value of the integral is known to be 0.250. Results obtained using the artificial firefly algorithm from literature [15] yield a value of 0.287 700 299 795 69, while the artificial fish swarm algorithm from literature [13] yields a value of 0.251 735 783. In this study, a multi-strategy improved arithmetic optimization algorithm was employed to calculate the double integral of the function associated with this integral.…”

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confidence: 99%

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A Novel Arithmetic Ant Colony Hybrid Optimization Algorithm for Numerical Computing

Wang

2023

Preprint

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The problem of finding all extremal points of a multimodal function and integrating complex functions are among the challenging problems in the field of intelligent optimization. To solve these numerical computation problems, a hybrid optimization algorithm named AOA-ACO, which combines the arithmetic optimization algorithm (AOA) and the ant colony optimization (ACO), is proposed in this paper. AOA is a newly proposed meta-heuristic algorithm in recent years, which has strong global exploration ability and local exploitation ability, and its optimization process has excellent characteristics of randomness and dispersion. ACO, on the other hand, has the characteristics of distributed computing and uses a positive feedback mechanism, but it is difficult to escape local optimum. Based on the characteristics of these two algorithms, AOA-ACO retains the position updating strategy of AOA and incorporates AOA's multiplication and division strategy and addition and subtraction strategy into the ACO optimization process, to enhance the balance between the algorithm's global exploration ability and local exploitation ability while maintaining its diversity, thereby improving the algorithm's computational accuracy y and convergence speed. The numerical experimental results show that compared with other intelligent optimization algorithms, AOA-ACO can calculate extremal points and integrals more accurately and with faster convergence speed. AMS(2010)68W40

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confidence: 99%

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confidence: 99%

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A Novel Arithmetic Ant Colony Hybrid Optimization Algorithm for Numerical Computing

Wang

2023

Preprint

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“…For pinion: Moving from the CS O alp X alp Y alp Z alp into O awp X awp Y awp Z awp with transformation matrix M alp2awp and then moving into CS O o X o Y o Z o with transformation matrix M awp2o , which can be expressed as equation (10), the surface profile equation E op,i located in the mesh CS O o X o Y o Z o and parallel to the plane X awp O awp Y awp of actual local working CS of pinion can be obtained.…”

Section: The Surface Profile Equation Of Slice Modelmentioning

confidence: 99%

“…2,3 However, the Ishikawa theory simplifies the surface profile of the tooth, which also leads to some calculation errors. In contrast, the surface profile of the tooth is described accurately in the Weber theory, 4–10 which is another commonly used analytical method. Based on the Weber theory, the influences of tooth parameters 11 (helix angle, normal modulus), friction, 12 surface morphology, 13 roller radii, 14 crack, 15–21 modified, 22 tooth profile errors, 23 lead crown relief 24 and dedendum circle fillet 25 on the TVMS are analysed.…”

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confidence: 99%

Time-varying mesh stiffness calculation for gear pairs with misalignment errors in multiple degrees of freedom based on an analytical method

Chen

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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Misalignment errors (MEs) in multiple degrees of freedom (multi-DOFs) at the mesh position will lead to a change in the time-varying mesh stiffness (TVMS) and then affect the dynamic behaviour of gear pairs. Therefore, a new, more rapid, three-dimensional analytical model for TVMS calculation for gear pairs with three rotational and three translational MEs is established in this paper, and a new solution method based on potential energy theory is presented. In addition, the correctness of the new model is verified by the finite element method (FEM). Moreover, the effective contact line, uneven distribution of mesh force on the contact line, and mesh position change are taken into account. Finally, the TVMS under different ME conditions is calculated with the new analytical model. The results showed that the different MEs have dissimilar effects on the TVMS, and the relationship between the ME and TVMS is nonlinear. In addition, the region of single-pair and double-pair teeth in contact would also change with ME.

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Analytical calculation of the tooth surface contact stress of spur gear pairs with misalignment errors in multiple degrees of freedom

Zhai

2020

Mechanism and Machine Theory

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An approximate numerical method for solving Cauchy singular integral equations composed of multiple implicit parameter functions with unknown integral limits in contact mechanics

Cited by 8 publications

References 43 publications

A Novel Arithmetic Ant Colony Hybrid Optimization Algorithm for Numerical Computing

A Novel Arithmetic Ant Colony Hybrid Optimization Algorithm for Numerical Computing

Time-varying mesh stiffness calculation for gear pairs with misalignment errors in multiple degrees of freedom based on an analytical method

Analytical calculation of the tooth surface contact stress of spur gear pairs with misalignment errors in multiple degrees of freedom

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