scholarly journals Rattle dynamics of noncircular face gear under multifrequency parametric excitation

2021 ◽  
Vol 12 (1) ◽  
pp. 361-373
Author(s):  
Dawei Liu ◽  
Zhenzhen Lv ◽  
Guohao Zhao
Keyword(s):  
Dynamic Model ◽  
Parametric Excitation ◽  
Nonlinear Dynamic ◽  
Velocity Ratio ◽  
Harmonic Balance Method ◽  
Transmission Error ◽  
Dynamic Responses ◽  
Discrete Fourier Transformation ◽  
Nonlinear Dynamic Model ◽  
Face Gear

Abstract. A noncircular face gear (NFG) conjugated with a pinion is a new type of face gear which can transmit variable velocity ratio and in which two time-varying excitations exist, namely the meshing stiffness excitation and instantaneous center excitation. Considering the tooth backlash, static transmission error and multifrequency parametric excitation, a nonlinear dynamic model of the NFG pair is presented. Based on the harmonic balance method and discrete Fourier transformation, a semi-analytic approach for the nonlinear dynamic model is given to analyze the dynamic behaviors of the NFG. Results demonstrate that, with increase in the eccentric ratio, input velocity and error amplitude, the NFG will undergo a non-rattle, unilateral rattle and bilateral rattle state in succession, and a jump phenomenon will appear in the dynamic responses when the rattle state of the gears is transformed from unilateral rattle to bilateral rattle.

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.

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.

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

Dynamics of the Gear Train Set in Wind Turbine

2011 ◽  
Vol 697-698 ◽  
pp. 701-705
Author(s):  
D.D. Ji ◽  
Y.M. Song ◽  
J. Zhang
Keyword(s):  
Wind Turbine ◽  
Dynamic Model ◽  
Harmonic Balance Method ◽  
Planetary Gear ◽  
Gear Train ◽  
Dynamic Responses ◽  
Multi Stage ◽  
Lumped Parameter ◽  
Cartesian Coordinate ◽  
The Impact

A lumped-parameter dynamic model for gear train set in wind turbine is proposed to investigate the dynamics of the speed-increasing gear box. The proposed model is developed in a universal Cartesian coordinate, which includes transversal and torsional deflections of each component, time-varying mesh stiffness, gear profile errors and external excitations. By solving the dynamic model, a modal analysis is performed. The results indicate that the modal properties of the multi-stage gear train in wind turbine are similar to those of a single-stage planetary gear set. A harmonic balance method (HBM) is used to obtain the dynamic responses of the gearing system. The responses give insight into the impact of excitations on the vibrations.

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