scholarly journals Investigation of Parametric Instability of the Planetary Gear under Speed Fluctuations

2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
Xinghui Qiu ◽  
Qinkai Han ◽  
Fulei Chu
Keyword(s):  
Parametric Instability ◽  
Phase Speed ◽  
Planetary Gear ◽  
Lumped Parameter Model ◽  
Time Varying ◽  
Mesh Stiffness ◽  
New Thought ◽  
Lumped Parameter ◽  
Speed Fluctuation ◽  
Speed Fluctuations

Planetary gear is widely used in engineering and usually has symmetrical structure. As the number of teeth in contact changes during rotation, the time-varying mesh stiffness parametrically excites the planetary gear and may cause severe vibrations and instabilities. Taking speed fluctuations into account, the time-varying mesh stiffness is frequency modulated, and therefore sideband instabilities may arise and original instabilities are significantly affected. Considering two different speed fluctuations, original and sideband instabilities are numerically and analytically investigated. A rotational lumped-parameter model of the planetary gear is developed, in which the time-varying mesh stiffness, input speed fluctuations, and damping are considered. Closed-form approximations of instability boundaries for primary and combination instabilities are obtained by perturbation analysis and verified by numerical analysis. The effects of speed fluctuations and damping on parametric instability are systematically examined. Because of the frequency modulation, whether a parametric instability occurs cannot be simply predicted by the planet meshing phase which is applicable to constant speed. Besides adjusting the planet meshing phase, speed fluctuation supplies a new thought to minimize certain instability by adjusting the amplitude or frequency of the speed fluctuation. Both original and sideband instabilities are shrunken by damping, and speed fluctuation further shrinks the original instability.

Parametric Instability in Planetary Gears With Frequency-Modulated Time-Varying Mesh Stiffness

2014 ◽  
Author(s):  
Xinghui Qiu ◽  
Qinkai Han ◽  
Fulei Chu
Keyword(s):  
Parametric Instability ◽  
Operating Conditions ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Rotational Model ◽  
Planetary Gears ◽  
Gear Mesh ◽  
Stiffness Variation ◽  
Speed Fluctuations ◽  
Gear Mesh Stiffness

A rotational model of planetary gears is developed which incorporates mesh stiffness variation and input speed fluctuations. Gear mesh stiffness is approximated by rectangle wave and different harmonic orders are considered. Because of speed fluctuations, the mesh stiffness is frequency modulated. The parametric instability associated with frequency-modulated time-varying stiffness is numerically investigated. The operating conditions leading to parametric instability are identified using Floquet theory and numerical integration. Whether the general laws derived for steady speed to suppress particular instabilities are applicable for fluctuating speed is verified. The effects of speed fluctuations on parametric instability are examined.

Dynamic Response Analysis of Wind Turbine Planetary Gear System With Interval Stiffness Parameters

2014 ◽  
Author(s):  
Sha Wei ◽  
Qinkai Han ◽  
Zhipeng Feng ◽  
Yanhua Shen ◽  
Fulei Chu
Keyword(s):  
Wind Turbine ◽  
Planetary Gear ◽  
Transmission Error ◽  
Gear System ◽  
Dynamic Responses ◽  
Lumped Parameter Model ◽  
Response Analysis ◽  
Mesh Stiffness ◽  
Gear Trains ◽  
Planetary Gear System

Planetary gear transmission system is one of the primary parts of the wind turbine drive train. Due to the assembly state, lubrication conditions and wear, the mesh stiffness of the planetary gear system is an uncertain parameter. In this paper, taking the uncertainty of mesh stiffness into account, the dynamic responses of a wind turbine gear system subjected to wind loads and transmission error excitations are studied. Firstly, a lumped-parameter model is extended to include both the planetary and parallel gears. Then the fluctuation ranges of dynamic mesh forces are predicted quantitatively and intuitively based on the combined Chebyshev interval inclusion function and numerical integration method. Finally, examples of gear trains with different interval mesh stiffnesses are simulated and the results show that tooth separations are becoming more obvious at the resonant speed by considering the fluctuating mesh stiffness of the second parallel gear stage. The nonlinear tooth separations are degenerated obviously as the fluctuation error of the mesh stiffness of the second parallel gear set is increased.

Vibration isolation with clutch disk pre-damper mechanism for the idle rattle phenomenon

2016 ◽  
Vol 24 (8) ◽  
pp. 1518-1534 ◽  
Author(s):  
Alişan Yüceşan ◽  
Semih Sezer
Keyword(s):  
Engine Speed ◽  
Vibration Isolation ◽  
Test Bench ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Speed Measurement ◽  
Proposed Model ◽  
Speed Fluctuations ◽  
Gear Mesh Stiffness

In this paper, the influence of clutch disk pre-damper mechanism constituents on the idle rattle phenomenon was investigated with an analytical model containing a new time-varying gear mesh stiffness function. Comparing experimental results to simulation results for the same excitation input was the key implementation for the validation of proposed model. The engine speed fluctuations represented in the simulation was imported from a speed measurement of a diesel engine in the test bench.

Dynamic Modeling and Analysis of a Planetary Gear Involving Tooth Wedging and Bearing Clearance Nonlinearity

2009 ◽  
Author(s):  
Yi Guo ◽  
Robert G. Parker
Keyword(s):  
Gear Tooth ◽  
Planetary Gear ◽  
Lumped Parameter Model ◽  
Back Side ◽  
Modeling And Analysis ◽  
Bearing Clearance ◽  
Gravity Forces ◽  
Lumped Parameter ◽  
Bearing Failures ◽  
Wide Range

Tooth wedging occurs when a gear tooth comes into contact on the drive-side and back-side simultaneously. Tooth wedging risks bearing failures from elevated forces. This work studies the nonlinear tooth wedging behavior and its correlation with planet bearing forces by analyzing the dynamic response of an example planetary gear based on a real application of a wind turbine geartrain. The two-dimensional lumped-parameter model [1] is extended to include tooth separation, back-side contact, tooth wedging, and bearing clearances. The simulation results show significant impact of tooth wedging on planet bearing forces for a wide range of operating speeds. To develop a physical understanding of the tooth wedging mechanism, connections between planet bearing forces and tooth forces are studied by investigating physical forces and displacements acting throughout the planetary gear. A method to predict tooth wedging based on geometric interactions is developed and verified. The major causes of tooth wedging relate directly to translational vibrations caused by gravity forces and the presence of clearance-type nonlinearities in the form of backlash and bearing clearance.

A Static and Dynamic Model of Spiral Bevel Gears

2011 ◽  
Vol 86 ◽  
pp. 35-38
Author(s):  
Jing Wang ◽  
Joël Teixeira Alves ◽  
Michèle Guingand ◽  
Jean Pierre de Vaujany ◽  
Philippe Velex
Keyword(s):  
Dynamic Models ◽  
Three Dimensional ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Linear Distribution ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Lumped Parameter ◽  
Potential Contact ◽  
Spiral Bevel

Two three-dimensional lumped parameter dynamic models of spiral bevel gears are presented and compared. The first approach is classic and relies on a single averaged mesh stiffness element connecting the gears whereas a time-varying non-linear distribution of discrete stiffness elements over the potential contact area is used in the second model.

Effects of Temperature on the Time-Varying Mesh Stiffness, Vibration Response, and Support Force of a Multi-Stage Planetary Gear

2020 ◽  
Vol 142 (5) ◽  
Author(s):  
Hui Liu ◽  
Pengfei Yan ◽  
Pu Gao
Keyword(s):  
Temperature Change ◽  
Dynamic Characteristics ◽  
Nonlinear Dynamic ◽  
Thermal Deformation ◽  
Planetary Gear ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Vibration Displacement ◽  
Influence Of Temperature ◽  
Nonlinear Dynamic Characteristics

Abstract The thermal deformation of gears will affect the vibration of the planetary system; this research mainly studied the effect of thermal conditions on planetary systems nonlinear vibration under the thermal equilibrium state. To study the influence of gear temperature on the planetary gear system, a nonlinear dynamic model considering thermal deformation was established. The mathematical expression of the thermal time-varying mesh stiffness (TTVMS) varied with temperature, and the backlash caused by the temperature change was also computed. The influence of temperature on the TTVMS was investigated. The calculation results indicated that the methods used to determine the TTVMS and backlash of gear pairs were effective, and the trends of the change in the nonlinear dynamic characteristics with temperature were obtained. According to the fast Fourier transform (FFT) spectrums and root-mean-square (RMS) analysis, the influence of temperature change on the nonlinear dynamic characteristics of the system was analyzed. When the temperature was lower than 80 °C, the vibration displacement and the supporting shaft load remained unchanged or decreased. Once the temperature was higher than 80 °C, the vibration displacement and load of the system were strengthened.

scholarly journals An Improved Rigid Multibody Model for the Dynamic Analysis of the Planetary Gearbox in a Wind Turbine

2016 ◽  
Vol 2016 ◽  
pp. 1-18 ◽  
Author(s):  
Wenguang Yang ◽  
Dongxiang Jiang
Keyword(s):  
Dynamic Analysis ◽  
Transient Analysis ◽  
Planetary Gear ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Vibration Signals ◽  
Planetary Gearbox ◽  
Multibody Model ◽  
Improved Model ◽  
Rigid Multibody

This paper proposes an improved rigid multibody model for the dynamic analysis of the planetary gearbox in a wind turbine. The improvements mainly include choosing the inertia frame as the reference frame of the carrier, the ring, and the sun and adding a new degree of freedom for each planet. An element assembly method is introduced to build the model, and a time-varying mesh stiffness model is presented. A planetary gear study case is employed to verify the validity of the improved model. Comparisons between the improvement model and the traditional model show that the natural characteristics are very close; the improved model can obtain the right equivalent moment of inertia of the planetary gear in the transient simulation, and all the rotation speeds satisfy the transmission relationships well; harmonic resonance and resonance modulation phenomena can be found in their vibration signals. The improved model is applied in a multistage gearbox dynamics analysis to reveal the prospects of the model. Modal analysis and transient analysis with and without time-varying mesh stiffness considered are conducted. The rotation speeds from the transient analysis are consistent with the theory, and resonance modulation can be found in the vibration signals.

The influence of mesh misalignment on planetary gear set with time-varying mesh stiffness

2017 ◽  
pp. 219-230
Author(s):  
S. T. Ping ◽  
Y. M. Shao ◽  
L. M. Wang ◽  
H. W. Li ◽  
J. Xu ◽  
...  
Keyword(s):  
Planetary Gear ◽  
Time Varying ◽  
Mesh Stiffness

Time-varying mesh stiffness calculation of a planetary gear set with the spalling defect under sliding friction

Meccanica ◽  
2020 ◽  
Vol 55 (1) ◽  
pp. 245-260
Author(s):  
Wei Luo ◽  
Baijie Qiao ◽  
Zhixian Shen ◽  
Zhibo Yang ◽  
Xuefeng Chen
Keyword(s):  
Sliding Friction ◽  
Planetary Gear ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Spalling Defect
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