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unified method for typical gear failure modeling and stiffness calculation based on the matrix equation

Frontiers of Mechanical Engineering 2024年第3期19卷 93-114页

作者： Fanshan MENG Xin ZHANG Heng XIA Jiaxu WANG School of Mechanical Engineering Southwest Jiaotong UniversityChengdu 610031China State Key Laboratory of Mechanical Transmissions for Advanced Equipment Chongqing UniversityChongqing 400044China

The failure types in gear systems vary,with typical ones mainly including pitting,cracking,wear,and broken *** modeling and stiffness calculation methods have been developed for various gear failure types.A unified method for typical gear failure modeling and stiffness calculation is introduced in this study by considering the deviations in the time-varying meshing stiffness(TVMS)of faulty gears resulting from the use of different ***,a gear tooth is discretized into a large number of microelements expressed with a matrix,and unified models of typical gear failures are built by adjusting the values of the matrix *** values and positions of the microelements in the tooth failure model matrix have the same physical meaning as the parameter variables in the potential energy method(PEM),so the matrix-based failure model can be perfectly matched with ***,a unified method for TVMS is *** of healthy and faulty gears with pitting,wear,crack,and broken tooth is performed with the matrix equation,and the corresponding TVMS values are calculated by incorporating the matrix models with *** the basis of the results,the mechanism of typical fault types that affect TVMS is analyzed,and the conclusions are verified through the finite element *** developed unified method is a promising technique for studying the dynamic response characteristics of gear systems with different failure types because of its superiority in eliminating stiffness deviations.

关键词： gears matrix equation failure modeling TVMS calculation unified method

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Analyzing the general biased data by additive risk model

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Science China Mathematics 2017年第4期60卷 685-700页

作者： LI YanFeng MA HuiJuan WANG DeHui ZHOU Yong College of Mathematics Jilin University Department of Biostatistics and Bioinformatics Emory University School of Statistics and Management Shanghai University of Finance and Economics Academy of Mathematics and Systems Science Chinese Academy of Sciences

This paper proposes a unified semiparametric method for the additive risk model under general biased sampling. By using the estimating equation approach, we propose both estimators of the regression parameters and nonparametric function. An advantage is that our approach is still suitable for the lengthbiased data even without the information of the truncation variable. Meanwhile, large sample properties of the proposed estimators are established, including consistency and asymptotic normality. In addition, the finite sample behavior of the proposed methods and the analysis of three groups of real data are given.

关键词： additive risk model unified method length-biased data case-cohort design

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Field and reverse field solitons in waveoperator nonlinear Schrödinger equation with space-time reverse: Modulation instability

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Communications in Theoretical Physics 2023年第6期75卷 39-50页

作者： H I Abdel-Gawad Mathematics Department Faculty of Science Cairo University GizaEgypt

The wave-operator nonlinear Schrödinger equation was introduced in the ***,nonlocal space-time reverse complex field equations were also recently *** in this area were focused on employing the inverse scattering method and Darboux ***,we present an approach to find the solutions of the wave-operator nonlinear Schrödinger equation with space and time reverse(W-O-NLSE-STR).It is based on implementing the unified method together with introducing a conventional formulation of the ***,a field and a reverse field may be ***,for deriving the solutions of W-O-NLSE-STR,it is evident to distinguish two cases(when the field and its reverse are interactive or not-interactive).In the non-interactive and interactive cases,exact and approximate solutions are *** both cases,the solutions are evaluated numerically and they are displayed *** is observed that the field exhibits solitons propagating essentially(or mainly)on the negative space variable,while those of the reverse field propagate on the other side(or vice versa).These results are completely novel,and we think that it is an essential behavior that characterizes a complex field system with *** the other hand,they may exhibit right and left cable patterns(or vice versa).It is found that the solutions of the field and its reverse exhibit self-phase modulation by solitary *** the interactive case,the pulses of the field and its reverse propagate in the whole *** analysis of modulation stability shows that,when the field is stable,its reverse is unstable or both are *** holds whenever the polarization of the medium is selfdefocusing.

关键词： wave-operator nonlinear Schrödinger equation space-time reverse unified method

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On the Refined Esitmates of All Homogeneous Expansions for a Subclass of Biholomorphic Starlike Mappings in Several Complex Variables

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Chinese Annals of Mathematics,Series B 2021年第6期42卷 909-920页

作者： Xiaosong LIU Taishun LIU School of Mathematics and Statistics Lingnan Normal UniversityZhanjiang 524048GuangdongChina Department of Mathematics Huzhou UniversityHuzhou 313000ZhejiangChina

The refined estimates of all homogeneous expansions for a subclass of biholomorphic starlike mappings are mainly established on the unit ball in complex Banach spaces or the unit polydisk in C^(n) with a unified *** the results are sharp if the above mappings are further k-fold symmetric starlike mappings or k-fold symmetric starlike mappings of orderα.The obtained results unify and generalize the corresponding results in some prior literatures.

关键词： Refined estimates of all homogeneous expansions Starlike mapping Starlike mapping of orderα k-fold symmetric unified method

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