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.

Effects of Bearing Radial Internal Clearance on Dynamic Behavior and Bifurcations in Planetary Gears

2011 ◽  
Author(s):  
Yi Guo ◽  
Robert G. Parker
Keyword(s):  
Dynamic Response ◽  
Harmonic Balance Method ◽  
Nonlinear Behavior ◽  
Nonlinear Effects ◽  
Lumped Parameter Model ◽  
Solution Stability ◽  
Planetary Gears ◽  
Gear Mesh ◽  
Bearing Clearance ◽  
Lumped Parameter

This study investigates the dynamics of planetary gears where nonlinearity is induced by bearing clearance. Lumped-parameter and finite element models of planetary gears with bearing clearance, tooth separation, and gear mesh stiffness variation are developed. The harmonic balance method with arc-length continuation is used to obtain the dynamic response of the lumped-parameter model. Solution stability is analyzed using Floquet theory. Rich nonlinear behavior is exhibited in the dynamic response, consisting of nonlinear jumps and a hardening effect induced by the transition from no bearing contact to contact. The bearings of the central members (sun, ring, and carrier) impact against the bearing races near resonance, which leads to coexisting solutions in wide speed ranges, grazing bifurcation, and chaos. Secondary Hopf bifurcation is the route to chaos. Input torque can significantly suppress the nonlinear effects caused by bearing clearance.

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.

Dynamic modeling and response of a spur planetary gear system with journal bearings under gravity effects

2017 ◽  
Vol 24 (16) ◽  
pp. 3569-3586 ◽  
Author(s):  
Zhenxing Liu ◽  
Zhansheng Liu ◽  
Xiangyu Yu
Keyword(s):  
Planetary Gear ◽  
Journal Bearings ◽  
Gear System ◽  
Lumped Parameter Model ◽  
Force Model ◽  
Back Side ◽  
Gravity Effect ◽  
Oil Film ◽  
Bearing Force ◽  
Planetary Gear System

This paper focuses on the modeling method and the gravity-induced dynamic response of a spur planetary gear system with journal bearings. The lumped-parameter model of a planetary gear system with journal bearings is established. Both contact on drive-side and back-side of the tooth are considered simultaneously. Linear and nonlinear bearing force models are introduced into the system model separately to take the planet bearing oil-film forces into account. A demonstration is given to show the adopted nonlinear oil-film force model is still valid for the lubrication of support for planet gears. Equilibrium positions of the planet gear are depicted under different input rotational speeds and input torques. Under gravity effect, system responses at different rotational speeds are calculated by employing Newmark integration; tooth wedging at ring-planet meshes is examined with different backlashes. The system responses are presented as vibration spectra, planet bearing forces, orbits of members, tooth forces, and the percentage of tooth wedging in one carrier cycle. The results show that the gravity effect dominates the response at low rotational speeds. The linear bearing force model is not valid in some cases. The fluctuation of the bearing force and the enlargement of the planet orbits are induced by gravity effect. Tooth wedging is the combined effect of gravity, centrifugal force, and planet bearing clearance.

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.

Impedance Analysis of Silicone Rubber Filled by Electrically Conductive Nanoparticles

2012 ◽  
Vol 729 ◽  
pp. 326-331 ◽  
Author(s):  
Attila Bojtos ◽  
Antal Huba
Keyword(s):  
Electron Microscopy ◽  
Scanning Electron Microscopy ◽  
Construction Material ◽  
Impedance Analysis ◽  
Tensile Tests ◽  
Lumped Parameter Model ◽  
Lumped Parameter ◽  
Wide Range ◽  
Mechanical Sensors ◽  
Scanning Electron

During the research, scanning electron microscopy, compression, tensile and frequency analysis were performed on silicone rubbers filled with conductive particles , in order to understand the electrical conduction mechanism. The distribution of the conductive nanoparticles and its relationship with the substrate was examined with scanning electron microscopy (SEM). During the SEM studies, the conductive elastomers were investigated in their deformed and original state too. The connection between the deformation and the resistivity was examined with compression and tensile tests. The impedance of the material was examined on a wide range of frequency. The correctness of the lumped parameter model that is mentioned in the literature , was examined and its parameters were determined. The dependence of the resistivity on the aspect ratio of the specimens was also investigated. The aim of this research is to make this construction material intelligent, and to use it to produce hyperelastic mechanical sensors (for strain, force, torque, ect. measuring).

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.

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