Nonlinear Dynamic Modelling of Gear-Shaft-Disk-Bearing Systems Using Finite Elements and Describing Functions

2003 ◽  
Author(s):  
Rafiq Maliha ◽  
Can U. Dog˘ruer ◽  
H. Nevzat O¨zgu¨ven
Keyword(s):  
Dynamic Model ◽  
Nonlinear Dynamic ◽  
Dynamic Modelling ◽  
Spur Gear ◽  
Discrete Models ◽  
Nonlinear Dynamic Model ◽  
Disk System ◽  
Describing Functions ◽  
Gear Mesh ◽  
System A

This study presents a new nonlinear dynamic model for a gear-shaft-disk-bearing system. A nonlinear dynamic model of a spur gear pair is coupled with linear finite element models of shafts carrying them, and with discrete models of bearings and disks. The nonlinear elasticity term resulting from backlash is expressed by a describing function, and a method developed in previous studies to determine the harmonic responses of nonlinear multi degree of freedom systems is employed for the solution. The code developed, Nonlinear Geared Rotor Dynamics (NLGRD), combines the versatility of modeling a shaft-bearing-disk system that can have any configuration, with the accuracy of an advanced nonlinear gear mesh interface model. Thus any single stage gear mesh configuration can be modeled easily and accurately. NLGRD is capable of calculating dynamic gear loads, dynamic bearing forces, bearing displacements and making modal analysis of the corresponding linear system. Theoretical results obtained by NLGRD are compared with the experimental data available in literature.

Nonlinear Dynamic Modeling of Gear-Shaft-Disk-Bearing Systems Using Finite Elements and Describing Functions

2003 ◽  
Vol 126 (3) ◽  
pp. 534-541 ◽  
Author(s):  
Rafiq Maliha ◽  
Can U. Dogˇruer ◽  
H. Nevzat O¨zgu¨ven
Keyword(s):  
Dynamic Model ◽  
Nonlinear Dynamic ◽  
Gear Tooth ◽  
Transmission Error ◽  
Spur Gear ◽  
Degree Of Freedom ◽  
Discrete Models ◽  
Nonlinear Dynamic Model ◽  
Disk System ◽  
Gear Mesh

This study presents a new nonlinear dynamic model for a gear-shaft-disk-bearing system. A nonlinear dynamic model of a spur gear pair is coupled with linear finite element models of shafts carrying them, and with discrete models of bearings and disks. The nonlinear elasticity term resulting from backlash is expressed by a describing function, and a method developed in previous studies to determine multi harmonic responses of nonlinear multi-degree-of-freedom systems is employed for the solution. The excitations considered in the model are external static torque and internal excitation caused by mesh stiffness variation, gear errors and gear tooth profile modifications. The model suggested and the solution method presented combine the versatility of modeling a shaft-bearing-disk system that can have any configuration without a limitation to the total degree of freedom, with the accuracy of a nonlinear gear mesh interface model that allows to predict jumps and double solutions in frequency response. Thus any single stage gear mesh configuration can be modeled easily and accurately. With the model developed it is possible to calculate dynamic gear loads, dynamic bearing forces, dynamic transmission error and bearing displacements. Theoretical results obtained by using the method suggested are compared with the experimental data available in literature, as well as with the theoretical values calculated by employing a previously developed nonlinear single degree of freedom model.

Bifurcation and Chaos of a Spur Gear Transmission System With Non-Uniform Wear

2020 ◽  
Vol 143 (3) ◽  
Author(s):  
Zhibo Geng ◽  
Ke Xiao ◽  
Junyang Li ◽  
Jiaxu Wang
Keyword(s):  
Dynamic Model ◽  
Dynamic Characteristics ◽  
Nonlinear Dynamic ◽  
Operating Time ◽  
Spur Gear ◽  
Gear Transmission ◽  
Nonlinear Dynamic Model ◽  
Gear Backlash ◽  
Gear Transmission System ◽  
Nonlinear Dynamic Characteristics

Abstract In this study, a nonlinear dynamic model of a spur gear transmission system with non-uniform wear is proposed to analyze the interaction between surface wear and nonlinear dynamic characteristics. A quasi-static non-uniform wear model is presented, with consideration of the effects of operating time on mesh stiffness and gear backlash. Furthermore, a nonlinear dynamic model with six degrees-of-freedom is established considering surface friction, time-varying gear backlash, time-varying mesh stiffness, and eccentricity, and the Runge–Kutta method applied to solve this model. The bifurcation and chaos in the proposed dynamic model with the change of the operating time and the excitation frequency are investigated by bifurcation and spectrum waterfall diagrams to analyze the bifurcation characteristics and the dimensionless mesh force. It is found that surface wear is generated with a change in operating time and affects the nonlinear dynamic characteristics of the spur gear system. This study provides a better understanding of nonlinear dynamic characteristics of gear transmission systems operating under actual conditions.

scholarly journals Research on nonlinear dynamic model of spur gear pair

2021 ◽  
Vol 1820 (1) ◽  
pp. 012038
Author(s):  
Chen Zhang ◽  
Xuew Liu ◽  
Xingl Shi ◽  
Xiaom Ling
Keyword(s):  
Dynamic Model ◽  
Nonlinear Dynamic ◽  
Spur Gear ◽  
Gear Pair ◽  
Nonlinear Dynamic Model

Frictional dynamic model predictions of FZG-A10 spur gear pairs considering profile errors

2020 ◽  
pp. 135065012096297
Author(s):  
Nabih Feki ◽  
Maroua Hammami ◽  
Olfa Ksentini ◽  
Mohamed Slim Abbes ◽  
Mohamed Haddar
Keyword(s):  
Dynamic Model ◽  
Coefficient Of Friction ◽  
Power Loss ◽  
Spur Gear ◽  
Operating Conditions ◽  
Time Dependent ◽  
Nonlinear Dynamic Model ◽  
Gear Mesh ◽  
Proposed Model ◽  
Profile Errors

In this work, a nonlinear dynamic model of an FZG-A10 spur gear was investigated by taking into account for the actual time-varying gear mesh stiffness and the frictional effects between meshing gear teeth to evaluate the influence of the dynamic effects on frictional gear power loss predictions. The equations of motion of the generalized translational-torsional coupled dynamic system derived from Lagrange principle was extended compared to authors’ previous work in order to account for time dependent coefficient of friction and profile errors. The dynamic response of spur gears, computed by an iterative implicit scheme of Newmark, is changed due to the presence of coefficient of friction and profile errors. A dynamic analysis was performed and the influence of frictional effect including tooth shape deviations, in particular, was scrutinized since a time-dependent coefficient of friction is deeply related to the gear surface roughness and all parameters dependent on gears error profiles are introduced in the proposed model. The predicted meshing gear power losses with constant and local friction coefficient were compared. The influence of constant and variable profile errors considered in the local coefficient of friction formulation was also studied and their corresponding root mean square (RMS) power loss was compared to the experimental results. The results using FZG A10 spur gear pairs running under several operating conditions (different loads and speeds) validate the superiority of the proposed model against previous similar models.

An Improved Nonlinear Dynamic Model of Gear Transmission

2007 ◽  
Author(s):  
Jinyuan Tang ◽  
Siyu Chen ◽  
Changjiang Zhou
Keyword(s):  
Frequency Response ◽  
Dynamic Model ◽  
Friction Force ◽  
Nonlinear Dynamic ◽  
Nonlinear Models ◽  
Harmonic Balance Method ◽  
Gear Transmission ◽  
Force Model ◽  
Nonlinear Dynamic Model ◽  
Gear Mesh

This paper develops a new nonlinear dynamic model of gear transmission on the basis of combining friction, gear mesh stiffness and backlash. In calculating friction force, the dynamic distribution of the load along the actual line of action is taken into consideration. A new period-enlargement method is proposed to set up a friction force model and a gear meshing stiffness model. The non-linear dynamic model is a non-autonomous system. Compared with the former models, the damping coefficient and stiff coefficient in this model developed by the period enlargement method is a periodic function with the same period. Thus it is easier to apply EM (energy method) or other methods for finding the approximate analytical solution of the gear transmission dynamic equations combining with time-varying damping and stiffness. Frequency response function of the nonlinear dynamic model is obtained by using harmonic balance method. Compared the analytic and numerical results of the improved nonlinear model with that of the nonlinear models in the published papers, it is shown that: (a) the former numerical simulation techniques may not work or may result in misleading answers; (b) the coexistence of several different periodic solutions and various impacts are the same with the results in formerly published papers when gear parameters are the same. Finally, the accurate solutions of all three regimes are combined to obtain the overall frequency response of the gear pair.

scholarly journals The Solitary Wave Solution for Quantum Plasma Nonlinear Dynamic Model

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Yihu Feng ◽  
Lei Hou
Keyword(s):  
Solitary Wave ◽  
Dynamic Model ◽  
Nonlinear Dynamic ◽  
Wave Solution ◽  
Solitary Wave Solution ◽  
Wave Transformation ◽  
Quantum Plasma ◽  
Nonlinear Dynamic Model ◽  
Plasma System ◽  
System A

In this paper, we discussed the quantum plasma system. A nonlinear dynamic disturbed model is studied. We used the undetermined coefficients method, dimensionless transformation and traveling wave transformation for the hyperbolic functions, and perturbation theory and method; then, the solitary wave solution for the quantum plasma nonlinear dynamic model is solved. Finally, the characteristics of the corresponding physical quantity are described.

scholarly journals RESEARCH OF DEFECTS IN SPUR GEAR

2010 ◽  
Vol 2 (4) ◽  
pp. 91-94
Author(s):  
Viktor Skrickij
Keyword(s):  
Dynamic Model ◽  
Nonlinear Dynamic ◽  
Spur Gear ◽  
Diagnostic Methods ◽  
Nonlinear Dynamic Model

This study presents a review of gear diagnostic methods. Also presented nonlinear dynamic model of spur gear. We modeled backlash, bearing flexibility and variable teeth stiffness.

scholarly journals Research on nonlinear dynamic model and characteristics of a spur gear pair considering the meshing state of multiple pairs of teeth

2021 ◽  
Vol 15 (6) ◽  
pp. JAMDSM0068-JAMDSM0068
Author(s):  
Rui XU ◽  
Jing ZHANG ◽  
Jiugen WANG ◽  
Renjun LI
Keyword(s):  
Dynamic Model ◽  
Nonlinear Dynamic ◽  
Spur Gear ◽  
Gear Pair ◽  
Nonlinear Dynamic Model

Analysis of Tourism Ecology Capacity Based on the Nonlinear Dynamic Model

2009 ◽  
Vol 11 (2) ◽  
pp. 163-168
Author(s):  
Long LV ◽  
Zhenfang HUANG ◽  
Jiang WU
Keyword(s):  
Dynamic Model ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Model
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