Survey of nonlinear vibration of gear transmission systems

2003 ◽  
Vol 56 (3) ◽  
pp. 309-329 ◽  
Author(s):  
Jianjun Wang ◽  
Runfang Li and ◽  
Xianghe Peng
Keyword(s):  
Nonlinear Vibration ◽  
Review Article ◽  
Gear Transmission ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Transmission Systems ◽  
Driven Systems ◽  
The Past ◽  
Critical Issues ◽  
Basic Concepts

In this paper, the progress in nonlinear dynamics of gear driven systems in the past twenty years is reviewed, especially the gear dynamic behavior, by considering the backlash and time-varying mesh stiffness of teeth. The basic concepts, the mathematical models and the solving methods for the non-linear dynamics of geared systems are then reviewed. The critical issues for further research on the nonlinear vibration in gear transmission systems are also discussed. There are 204 references cited in this review article.

Analysis of tooth stiffness of nutation face gear

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Guangxin Wang ◽  
Lili Zhu ◽  
Peng Wang
Keyword(s):  
Gear Transmission ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Face Gear ◽  
Content Type ◽  
Gear Teeth ◽  
Meshing Stiffness ◽  
Single Tooth ◽  
Tooth Stiffness ◽  
External Face

Purpose The purpose of this paper is to obtain the single-tooth stiffness, single-tooth time-varying meshing stiffness and comprehensive meshing stiffness of the internal and external face gears and to analyze the influence of the modulus, pressure angle and tooth width of each face gear on the single-tooth stiffness of the gear in nutation face gear transmission. Design/methodology/approach From the point of view of material mechanics, the gear teeth of nutation face gear are simplified as spacial variable cross-section beams. The shear deformation of gear teeth, the bending deformation of tooth root and the additional elastic deformation caused by the base deformation are gotten by simplified trapezoidal section method, thus the stiffness of nutation face gear teeth can be obtained. The comparison with finite element method results verifies the rationality of simplified trapezoidal section method for calculating the tooth stiffness of nutation face gear. Findings The variation of stiffness of internal and external face gears along the meshing line and tooth height in nutation face gear transmission is studied, and the variation laws of single tooth stiffness, single-tooth-pair mesh stiffness and single tooth time-varying meshing stiffness of nutation face gear teeth are obtained. Originality/value Nutation face gear transmission is a new type of transmission. The stiffness of face gear teeth is analyzed, and the variation rules of single tooth stiffness, single-tooth-pair mesh stiffness and single tooth time-varying meshing stiffness of nutation face gear teeth are obtained, which not only enriches the research of nutation face gear transmission but also has important guiding significance for the application of nutation face gear in engineering practice.

Periodic and Chaotic Dynamic Responses of Face Gear Transmission System

2013 ◽  
Vol 834-836 ◽  
pp. 1273-1280
Author(s):  
Ze Hua Hu ◽  
Jin Yuan Tang ◽  
Si Yu Chen
Keyword(s):  
Periodic Motion ◽  
Chaotic Dynamic ◽  
Rotational Frequency ◽  
Transmission System ◽  
Gear Transmission ◽  
Dynamic Responses ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Face Gear ◽  
Gear Transmission System

The periodic and chaotic dynamic responses of face gear transmission system considering time-varying mesh stiffness and backlash nonlinearity are studied. Firstly, a nonlinear time-varying dynamic model of face gear pair is developed and the motion equations are presented, the real accurate mesh stiffness is obtained by applying Finite element approach. Then, the dynamic equations are solved using Runge-Kutta numerical integral method and bifurcation diagrams are presented and analyzed. The stability properties of steady state responses are illustrated with Floquet multipliers and Lyapunov exponents. The results show that a process of periodic-chaotic-periodic motion exists with the dimensionless pinion rotational frequency as control parameters. The analysis can be a reference to avoid the chaotic motion and unstable periodic motion through choosing suitable rotational frequency.

scholarly journals Influence of the Eccentric Error of Star Gear on the Bifurcation Properties of Herringbone Star Gear Transmission with Floating Sun Gear

2018 ◽  
Vol 2018 ◽  
pp. 1-32
Author(s):  
Fang Guo ◽  
Zongde Fang ◽  
Xijin Zhang ◽  
Yanmei Cui
Keyword(s):  
Load Balancing ◽  
Numerical Method ◽  
Dynamic Model ◽  
Phase Plane ◽  
Natural Frequencies ◽  
Rotation Frequency ◽  
Gear Transmission ◽  
Time Varying ◽  
Bifurcation Diagrams ◽  
Mesh Stiffness

Taking a herringbone star gear transmission (HSGT) with floating sun gear as an example, the system bifurcation characteristics with the changing of the eccentric error of star gear and the working frequencies are analyzed. For this analysis, a generalized dynamic model of HSGT considering the manufacturing eccentric errors, time-varying mesh stiffness, and load balancing mechanism is established and solved by numerical method. The floating process of sun gear is explained. In this paper, there are seven cases about the eccentric errors of star gears which are calculated, respectively. To study the effect of the working frequencies (including meshing frequency and rotation frequency), the calculation is done at three kinds of input speed in which the working frequencies are close to the system natural frequencies. The results are demonstrated in detail by the bifurcation diagrams, phase plane plots, and Poincare maps. The system bifurcation characteristics are particularly analyzed and compared in every case. This work provides important guidance to the engineering of HSGT.

Periodic Motions With Impacting Chatter and Stick in a Gear Transmission System

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
Albert C. J. Luo ◽  
Dennis O’Connor
Keyword(s):  
Transmission System ◽  
Gear Transmission ◽  
Time Varying ◽  
Impact Model ◽  
Periodic Motions ◽  
Transmission Systems ◽  
New Model ◽  
Gear Transmission System ◽  
Mapping Structures ◽  
First Time

In this paper, an impact model with possible stick between the two gears is proposed for gear transmission systems, which includes the piecewise backlash model and the traditional impact model for the first time. The new model presented in this paper possesses a time-varying boundary for two dynamical systems either to switch or to impact. Such a model can catch impacting chatter and stick phenomena in gear transmission systems. Based on the new model, periodic impacting chatter and stick in a gear transmission system can be investigated. For doing so, switching sets on the time-varying boundaries are introduced to define basic mappings. Mapping structures based on basic mappings are developed for characterizing motions in gear transmission systems, and from such mapping structures, periodic motions with impacting chatter and stick in such a gear transmission system are predicted analytically. Numerical simulations are performed for illustration of periodic motions with impacting chatter and stick phenomena.

Effect of Mesh Stiffness on the Dynamic Response of Face Gear Transmission System

2013 ◽  
Vol 135 (7) ◽  
Author(s):  
Zehua Hu ◽  
Jinyuan Tang ◽  
Siyu Chen ◽  
Duncai Lei
Keyword(s):  
Dynamic Response ◽  
Transmission System ◽  
Gear Transmission ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Face Gear ◽  
Gear Transmission System ◽  
The Face ◽  
Time Invariant ◽  
Backlash Nonlinearity

The effect of mesh stiffness on the dynamic response of face gear transmission system combining with backlash nonlinearity is studied. First, a nonlinear time-varying (NLTV) and a nonlinear time-invariant (NLTI) dynamic models of face gear transmission system with backlash nonlinearity are formulated. The 6DOF motion equations of the face gear pair considering the mesh stiffness, backlash, contact damping and supporting stiffness are proposed. Second, the effect of mesh stiffness on the dynamic response of the face gear drive system is analyzed with the numerical method, where the mesh stiffness is expressed in two patterns as time-varying form and time-invariant form. According to the comparative study, some significant phenomena as bifurcation, chaos, tooth separation and occurrence of multijump are detected. The results show that different forms of mesh stiffness generate an obvious change on the dynamic mesh force.

Literacy and Education: Fifth Release From the 1961 Census of Pakistan (Review Article)

1963 ◽  
Vol 3 (3) ◽  
pp. 424-442
Author(s):  
Jamila Akhtar
Keyword(s):  
Population Growth ◽  
Urban Areas ◽  
Review Article ◽  
Interim Report ◽  
Educational Levels ◽  
Rural And Urban Areas ◽  
The Past ◽  
Review Articles ◽  
Rural And Urban ◽  
Age And Sex

This review of the Literacy and Education Bklletin1 of the 1961 Census is fourth in the series of review articles published in this journal2. The Bulletin under review forms a part of the interim report on the characteristics of the population of Pakistan. It gives information on the number of illiterate and literate persons by age and sex for rural and urban areas on division and district basis; illiterate and literate.population in selected cities and towns; and the educational levels attained by the literate population by age and sex for divisions and districts. Relevant statistical notes and statements precede the tables in the Bulletin. The objective of this review is to describe the meaningfulness and significance of literacy statistics. To this end, a distinction is made between formal and functional levels of literacy. Comparisons of the 1951 and 1961 census figures are undertaken to indicate the progress of literacy and education during the past decade with reference to the effect of intercensal rate of population growth on such progress. Certain questions regarding the reliability of data are raised, which emphasize the need for caution in the interpretation of literacy statistics.

Nucleosides and Nucleoside Analogues as Emerging Antiviral Drugs

2020 ◽  
Vol 17 ◽  
Author(s):  
Mohamed Ibrahim Elzagheid
Keyword(s):  
Significant Role ◽  
Mode Of Action ◽  
Crucial Role ◽  
Viral Infections ◽  
Antiviral Drugs ◽  
Review Article ◽  
Nucleoside Analogues ◽  
The Past ◽  
Nucleoside Drugs

: Nucleosides and their analogues have been in use for many years and have become essential for treating patients with viral infections. Many additional nucleoside drugs have been approved over the past decades. This strongly demonstrates how important these compounds are and the crucial role they play. Given that a significant amount of research and literature has been documented regarding nucleoside analogues, this review article mainly focuses the discussion on nucleosides and nucleoside analogous that have proven to play significant role or be emerging in the treatment of known viral infections. This covers the names, structures, applications, toxicity, and mode of action of relevant nucleoside analogues.

Formation of Carbon-Oxygen Bond Mediated by Hypervalent Iodine Reagents Under Metal-free Conditions

2020 ◽  
Vol 17 ◽  
Author(s):  
Ayesha Jalil ◽  
Yaxin O Yang ◽  
Zhendong Chen ◽  
Rongxuan Jia ◽  
Tianhao Bi ◽  
...  
Keyword(s):  
Natural Products ◽  
Bond Formation ◽  
Building Blocks ◽  
Review Article ◽  
Hypervalent Iodine ◽  
Metal Free ◽  
Bioactive Natural Products ◽  
The Past ◽  
Oxygen Bond ◽  
Privileged Scaffolds

: Hypervalent iodine reagents are a class of non-metallic oxidants have been widely used in the construction of several sorts of bond formations. This surging interest in hypervalent iodine reagents is essentially due to their very useful oxidizing properties, combined with their benign environmental character and commercial availability from the past few decades ago. Furthermore, these hypervalent iodine reagents have been used in the construction of many significant building blocks and privileged scaffolds of bioactive natural products. The purpose of writing this review article is to explore all the transformations in which carbon-oxygen bond formation occurred by using hypervalent iodine reagents under metal-free conditions

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