Lumped Parameter Model of Planetary Gear Systems

1978 ◽  
Vol 192 (1) ◽  
pp. S61-S64 ◽  
Keyword(s):  
Planetary Gear ◽  
Lumped Parameter Model ◽  
Lumped Parameter ◽  
Gear Systems

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.

Planetary Gear Modal Properties and Dynamic Response: Experiments and Analytical Simulation

2011 ◽  
Author(s):  
Tristan M. Ericson ◽  
Robert G. Parker
Keyword(s):  
Natural Frequencies ◽  
Planetary Gear ◽  
Forced Response ◽  
Operating Conditions ◽  
Modal Testing ◽  
Lumped Parameter Model ◽  
Lumped Parameter ◽  
Analytical Simulation ◽  
Analytical Research ◽  
Independent Motion

Planetary gear vibration is a major source of noise and may lead to fatigue-induced failures in bearings or other drivetrain components. Gear designers use mathematical models to analyze potential designs, but these models remain unverified by experimental data. This paper presents experiments that completely characterize the dynamic behavior of a spur planetary gear by modal testing and spinning tests under representative operating conditions, focusing on the independent motion of planetary components. Accelerometers are mounted directly to individual gear bodies. Rotational and translational accelerations obtained from the experiments are compared to the predictions of a lumped parameter model. Natural frequencies, modes, and forced response agree well between experiments and the model. Rotational, translational, and planet mode types presented in published analytical research are observed experimentally.

A Discrete Lumped-Parameter Dynamic Model for a Planetary Gear Set with Flexible Ring Gear

2011 ◽  
Vol 86 ◽  
pp. 756-761 ◽  
Author(s):  
Jun Zhang ◽  
Yi Min Song ◽  
Jin You Xu
Keyword(s):  
Individual Component ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Planetary Gear ◽  
Lumped Parameter Model ◽  
Vibration Modes ◽  
Ring Gear ◽  
Lumped Parameter ◽  
Planetary Gear System ◽  
Flexible Ring

A discrete lumped-parameter model for a general planetary gear set is proposed, which models the continuous flexible ring gear as discrete rigid ring gear segments connected with each other through virtual springs. The ring-planet mesh is analyzed to derive equations of motion of ring segments and planet. By assembling equations of motion of each individual component, the governing equations of planetary gear system are obtained. The solution for eigenvalue problem yields to natural frequencies and corresponding vibration modes. The simulations of example system reveal that the ring gear flexibility decreases system lower natural frequencies and the vibration modes can be classified into rotational, translational, planet and ring modes.

Lumped Parameter Model of Planetary Gear Systems

1978 ◽  
Vol 192 (1) ◽  
pp. 251-258 ◽  
Author(s):  
J. W. Polder
Keyword(s):  
Degrees Of Freedom ◽  
Planetary Gear ◽  
Lumped Parameter Model ◽  
Damping Coefficients ◽  
Planetary Gear Trains ◽  
Lumped Parameter ◽  
Vibration Model ◽  
Close Relationship ◽  
Angular Velocities ◽  
Gear Trains

A model system is described by parameters for shafts, planetary gear trains and nodes. Moments of inertia, spring stiffnesses and damping coefficients are assigned to the shafts; gear ratios and efficiencies are assigned to planetary gear trains. The equivalence of angular velocities and torques is demonstrated for shafts (vibration model), as well as for planetary gear trains and nodes (configuration of the system). This brings about a new view on the concept of degrees of freedom. The close relationship between gear ratios and torque ratios yields identical functions for these ratios when applied to the input and output shafts of a system. The full use of this relationship requires strict conventions of signs and an extension of the interpretation of values. The introduction of a new concept, named responsivity, expresses the relationships between torques and between powers of arbitrary shafts. With suitable equations, it becomes possible to investigate torque and power distributions exhaustively.

scholarly journals Modal analysis of back-to-back planetary gear: experiments and correlation against lumped-parameter model

2015 ◽  
pp. 125 ◽  
Author(s):  
Ahmed Hammami ◽  
Alfonso Fernandez Del Rincon ◽  
Fernando Viadero Rueda ◽  
Fakher Chaari ◽  
Mohamed Haddar
Keyword(s):  
Modal Analysis ◽  
Planetary Gear ◽  
Lumped Parameter Model ◽  
Lumped Parameter

Random Vibration Analysis of Planetary Gear Trains

2013 ◽  
Vol 135 (2) ◽  
Author(s):  
Jianming Yang ◽  
Ping Yang
Keyword(s):  
Sample Path ◽  
Planetary Gear ◽  
Gear Train ◽  
Lumped Parameter Model ◽  
State Variables ◽  
Random Loads ◽  
Planetary Gear Trains ◽  
Lumped Parameter ◽  
Gear Trains ◽  
The Mean

This article investigates the vibration response of a planetary gear train under excitations of both deterministic and random loads. A lumped parameter model has been used in this investigation and the random excitations are represented by white noise. One version of the stochastic Newmark algorithms is employed to solve for both sample path response and the statistics of the response. The mean and the variance for all state variables are obtained through the same algorithm. The effects of three different levels of noise on the statistics are compared against each other.

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.

scholarly journals The Analysis and Modeling of the Synthetical Meshing Stiffness of Inner Gearing considering the Flexible Inner Ring Gear

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Shengyang Hu ◽  
Zongde Fang
Keyword(s):  
Planetary Gear ◽  
Element Model ◽  
Transmission System ◽  
Lumped Parameter Model ◽  
Ring Gear ◽  
Gear Teeth ◽  
Meshing Stiffness ◽  
Lumped Parameter ◽  
Sectional Shape ◽  
The Finite Element Model

As a key part of vibration generation and transmission of planetary gear transmissions, thin-walled inner ring gear deforms under the influence of meshing excitation and seriously affects the reliability and fatigue life of the transmission system. The effect of the flexibility of the inner ring gear on the transmission system is ignored in the calculation of making the inner ring gear as a rigid body in the lumped parameter model, while the calculation amount of the finite element model is too large. Therefore, it is very important to establish an accurate and reasonable model to solve the flexibility of the inner ring gear. In this paper, according to the supporting mode, supporting quantity, thickness, and sectional shape of the inner ring gear, the inner ring gear is reasonably separated into the form of multisection curved beam. The displacement of the gear teeth in the meshing line caused by the flexibility of the inner ring gear is obtained rapidly and accurately. It lays an important theoretical foundation for the dynamic analysis of planetary gear transmission.

Planetary Gear Modal Vibration Properties Torque Sensitivity

2013 ◽  
Author(s):  
Tristan M. Ericson ◽  
Robert G. Parker
Keyword(s):  
Natural Frequencies ◽  
Planetary Gear ◽  
Lumped Parameter Model ◽  
Mode Shapes ◽  
High Frequency Mode ◽  
Vibration Properties ◽  
Lumped Parameter ◽  
Planet Gear ◽  
Element Bearing ◽  
Modal Vibration

The effect of preload torque on planetary gear behavior is investigated with experiments and mathematical models. Natural frequencies, mode shapes, and damping are influenced by mean torque levels. Natural frequencies increase with greater torque. Damping increases in some modes and decreases in others. The mode shapes undergo various changes as torque increases as demonstrated in the trajectory of a planet gear in a high frequency mode. A finite element bearing model is used to obtain the load dependent stiffness of the planet bearings, and these values greatly increase the accuracy of a lumped parameter model in predicting the natural frequencies measured in experiments.

Suppression of Planet Mode Response in Planetary Gear Dynamics Through Mesh Phasing

2005 ◽  
Vol 128 (2) ◽  
pp. 133-142 ◽  
Author(s):  
Vijaya Kumar Ambarisha ◽  
Robert G. Parker
Keyword(s):  
Gear Tooth ◽  
Planetary Gear ◽  
Rotational Degree ◽  
Dynamic Simulations ◽  
Gear Dynamics ◽  
Lumped Parameter ◽  
Bearing Stiffness ◽  
Gear Systems ◽  
Mesh Phasing ◽  
Mode Response

This work analytically derives design rules to suppress certain harmonics of planet mode response in planetary gear dynamics through mesh phasing. Planet modes are one of three categories of planetary gear vibration modes. In these modes, only the plantes deflect while the carrier, ring, and sun gears have no motion (Lin, J., and Parker, R. G., 1999, ASME J. Vib. Acoust., 121, pp. 316–321;J. Sound Vib, 233(5), pp. 921–928). The dynamic mesh forces are not explicitly modeled for this study; instead, the symmetry of planetary gear systems and gear tooth mesh periodicity are sufficient to establish rules to suppress planet modes. Thus, the conclusions are independent of the mesh modeling details. Planetary gear systems with equally spaced planets and with diametrically opposed planet pairs are examined. Suppression of degenerate mode response in purely rotational degree-of-freedom models achieved in the limit of infinite bearing stiffness is also investigated. The mesh phasing conclusions are verified by dynamic simulations of various planetary gears using a lumped-parameter analytical model and by comparisons to others’ research.

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