Improved method for analysing the dynamic response of gear transmission systems

Li, Xiaofeng; Liu, Xiaoxue; Li, Xiangwei; Wang, He; Guo, Hanfei

doi:10.1108/ec-08-2021-0500

Cited by 3 publications

(1 citation statement)

References 37 publications

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“…In the literature, the problem of determining a solution to several matrix equations has been widely studied (Hasanov and Ivanov, 2006; Ivanov and El-Sayed, 1998; Ivanov et al ., 2001; Ivanov, 2006; Erfanifar et al ., 2020, 2022a, b; Sayevand et al. , 2023; Hajarian, 2014, 2017; Li et al ., 2022).…”

Section: Introductionmentioning

confidence: 99%

Efficient iterative schemes based on Newton's method and fixed-point iteration for solving nonlinear matrix equation X^p = Q±A(X⁻¹+B)⁻¹A^T

Erfanifar,

Hajarian

2023

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PurposeIn this paper, the authors study the nonlinear matrix equation Xp=Q±A(X-1+B)-1AT, that occurs in many applications such as in filtering, network systems, optimal control and control theory.Design/methodology/approachThe authors present some theoretical results for the existence of the solution of this nonlinear matrix equation. Then the authors propose two iterative schemes without inversion to find the solution to the nonlinear matrix equation based on Newton's method and fixed-point iteration. Also the authors show that the proposed iterative schemes converge to the solution of the nonlinear matrix equation, under situations.Findings The efficiency indices of the proposed schemes are presented, and since the initial guesses of the proposed iterative schemes have a high cost, the authors reduce their cost by changing them. Therefore, compared to the previous scheme, the proposed schemes have superior efficiency indices.Originality/value Finally, the accuracy and effectiveness of the proposed schemes in comparison to an existing scheme are demonstrated by various numerical examples. Moreover, as an application, by using the proposed schemes, the authors can get the optimal controller state feedback of $x(t+1) = A x(t) + C v(t)$.

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Section: Introductionmentioning

confidence: 99%

Efficient iterative schemes based on Newton's method and fixed-point iteration for solving nonlinear matrix equation X^p = Q±A(X⁻¹+B)⁻¹A^T

Erfanifar,

Hajarian

2023

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Research Progress on Gear Transmission System Dynamics

Gao

Wang

Guo

2024

EEENG

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Background: The dynamics research of gear transmission systems mainly revolves around "excitation-model-response". The increasing number of dynamic incentive factors considered in the study has brought new problems to selecting modeling and solution methods and analyzing dynamic characteristics. Objective: This study aims to sort out the main research content of gear transmission system dynamics. Moepver, the commonly used analysis models, modeling, and solution methods are compared, and references for method selection and in-depth research are provided. Methods: This paper reviews the representative papers and patents related to the dynamic analysis of the gear system. The main contents of the dynamic excitation, dynamic model and dynamic characteristic analysis of the gear system are discussed, and suggestions for future development directions are given. Results: The dynamic excitations mainly considered in the current research are internal excitations and external excitations; random excitations are rarely considered. This paper analyzes and summarizes the commonly used modeling methods, model classification, solution methods, and dynamic characteristics research content. The advantages and disadvantages of several commonly used analysis models, modeling, and solution methods and their applicable occasions are summarized for the reference of researchers. Conclusion: The dynamics study of the gear system is a systematic work. It requires comprehensively considering the influence of dynamic excitations and selecting appropriate methods to establish and solve the model to obtain the dynamic characteristics that can better reflect the actual working conditions of the gear system. It is of great significance to improve the performance of the gear system.

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The influence of gear load distribution based on coupled systems on gearbox meshing noise

Zhang,

Wan,

Zhang

2024

Front. Mech. Eng.

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Introduction: With the rapid development of the gearbox manufacturing industry, the internal gear response has received attention, and the control of meshing noise during gear operation has been studied. Conventional noise reduction methods are usually based on gear order, and with the improvement of gearbox manufacturing technology, this method gradually becomes difficult to cope with a wide range of data.Methods: To expand the search domain of noise control systems, this study combines gear response and gear order, and adds the condition of gear uniform load. For common noise reduction problems in composite systems, this study improves the time-varying stiffness excitation mechanism and generates a coupled system.Results: Finally, this study conducts experiments on the Gmnoi dataset and compares it with three systems including quantum genetics to verify the superiority of the proposed system. The suppression effects of the four systems on gear meshing noise were 98.4%, 95.8%, 93.5%, and 92.7%, respectively. Their highest performance for different gear groups was 623, 514, 406, and 423, respectively.Discussion: The experimental results showed that the proposed coupling system has strong robustness and high accuracy in controlling gearbox meshing noise, and is of great significance in reducing noise pollution and improving the working environment of the gearbox.

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Improved method for analysing the dynamic response of gear transmission systems

Cited by 3 publications

References 37 publications

Efficient iterative schemes based on Newton's method and fixed-point iteration for solving nonlinear matrix equation X^p = Q±A(X⁻¹+B)⁻¹A^T

Efficient iterative schemes based on Newton's method and fixed-point iteration for solving nonlinear matrix equation X^p = Q±A(X⁻¹+B)⁻¹A^T

Research Progress on Gear Transmission System Dynamics

The influence of gear load distribution based on coupled systems on gearbox meshing noise

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Improved method for analysing the dynamic response of gear transmission systems

Cited by 3 publications

References 37 publications

Efficient iterative schemes based on Newton's method and fixed-point iteration for solving nonlinear matrix equation Xp = Q±A(X−1+B)−1AT

Efficient iterative schemes based on Newton's method and fixed-point iteration for solving nonlinear matrix equation Xp = Q±A(X−1+B)−1AT

Research Progress on Gear Transmission System Dynamics

The influence of gear load distribution based on coupled systems on gearbox meshing noise

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Product

Resources

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Efficient iterative schemes based on Newton's method and fixed-point iteration for solving nonlinear matrix equation X^p = Q±A(X⁻¹+B)⁻¹A^T

Efficient iterative schemes based on Newton's method and fixed-point iteration for solving nonlinear matrix equation X^p = Q±A(X⁻¹+B)⁻¹A^T