scholarly journals VIBRATION ANALYSIS OF PLANETARY GEAR SYSTEM

2013 ◽  
pp. 30-34
Author(s):  
MAJID MEHRABI ◽  
DRV.P. SINGH
Keyword(s):  
Vibration Analysis ◽  
Natural Frequencies ◽  
Linear Time ◽  
Planetary Gear ◽  
Vibration Modes ◽  
System Parameters ◽  
Linear Time Invariant ◽  
Inertia Parameters ◽  
Planetary Gear System ◽  
Time Invariant

In this work a dynamic model of a planetary gear transmission is developed to study the sensitivity of the natural frequencies and vibration modes to system parameters in perturbed situation. Parameters under consideration include component masses ,moment of inertia , mesh and support stiff nesses .The model admits three planar degree of freedom for planets ,sun, ring, and carrier. Vibration modes are classified into translational, rotational and planet modes .Well-defined modal properties of tuned (cyclically symmetric) planetary gears for linear ,time-invariant case are used to calculate eigensensitivities and express them in simple formulae .These formulae provide efficient mean to determine the sensitivity to stiffness ,mass and inertia parameters in perturbed situation.

Analytical Characterization of the Unique Properties of Planetary Gear Free Vibration

1999 ◽  
Vol 121 (3) ◽  
pp. 316-321 ◽  
Author(s):  
Jian Lin ◽  
R. G. Parker
Keyword(s):  
Degrees Of Freedom ◽  
Eigenvalue Problems ◽  
Linear Time ◽  
Planetary Gear ◽  
Vibration Modes ◽  
Planetary Gears ◽  
Factors Affecting ◽  
Linear Time Invariant ◽  
Gyroscopic Effects ◽  
Time Invariant

This work develops an analytical model of planetary gears and uses it to investigate their natural frequencies and vibration modes. The model admits three planar degrees of freedom for each of the sun, ring, carrier and planets. It includes key factors affecting planetary gear vibration such as gyroscopic effects and time-varying stiffness. For the linear, time-invariant case, examination of the associated eigenvalue problem reveals the well-defined structure of the vibration modes, where the special structure results from the cyclic symmetry of planetary gears. Vibration modes are classified into rotational, translational and planet modes. The unique characteristics of each type of mode are analytically investigated in detail. For each class of mode, reduced-order eigenvalue problems are derived.

Sensitivity of General Compound Planetary Gear Natural Frequencies and Vibration Modes to Model Parameters

2006 ◽  
Author(s):  
Yichao Guo ◽  
Robert G. Parker
Keyword(s):  
Natural Frequencies ◽  
Planetary Gear ◽  
Lumped Parameter Model ◽  
Model Parameters ◽  
Vibration Modes ◽  
Planetary Gears ◽  
System Parameters ◽  
Modal Properties ◽  
Mass Moment ◽  
Inertia Parameters

This paper studies sensitivity of compound planetary gear natural frequencies and vibration modes to system parameters. Based on a lumped parameter model of general compound planetary gears and their distinctive modal properties [1], the eigensensitivities to inertias and stiffnesses are calculated and expressed in compact formulae. Analysis reveals that eigenvalue sensitivities to stiffness parameters are directly proportional to modal strain energies, and eigenvalue sensitivities to inertia parameters are proportional to modal kinetic energies. Furthermore, the eigenvalue sensitivities to model parameters are determined by inspection of the modal strain and kinetic energy distributions. This provides an effective way to identify those parameters with the greatest impact on tuning certain natural frequencies. The present results, combined with the modal properties of general compound planetary gears, show that rotational modes are independent of translational bearing/shaft stiffnesses and masses of carriers/central gears, translational modes are independent of torsional bearing/shaft stiffnesses and moment of inertias of carriers/central gears, and planet modes are independent of all system parameters of other planet sets, the shaft/bearing stiffness parameters of carriers/rings, and the mass/moment of inertia parameters of carriers/central gears.

scholarly journals ANALYTICAL MODELING OF PLANETARY GEAR AND SENSITIVITY OF NATURAL FREQUENCIES

2013 ◽  
pp. 35-40
Author(s):  
MAJID MEHRABI ◽  
DR. V.P. SINGH
Keyword(s):  
Natural Frequency ◽  
Degrees Of Freedom ◽  
Analytical Modeling ◽  
Natural Frequencies ◽  
Vibration Mode ◽  
Planetary Gear ◽  
Vibration Modes ◽  
Planetary Gears ◽  
System Parameters ◽  
Inertia Parameters

This work develops an analytical model of planetary gears and uses it to investigate their natural frequencies and vibration modes. The model admits three planar degrees of freedom for each of the sun, ring, carrier and planets. Vibration modes are classified into rotational, translational and planet modes. The natural frequency sensitivities to system parameters are investigated for tuned (cyclically symmetric) planetary gears. Parameters under consideration include support and mesh stiffnesses, component masses, and moments of inertia. Using the well-defined vibration mode properties of tuned planetary gears, the eigen sensitivities are calculated and expressed in simple exact formulae. These formulae connect natural frequency sensitivity with the modal strain or kinetic energy and provide efficient means to determine the sensitivity to all stiffness and inertia parameters by inspection of the modal energy distribution.

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.

Nonlinear Analysis of Vibro-Impacts for Unloaded Gear Pairs With Various Excitations and System Parameters

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Jong-yun Yoon ◽  
Iljae Lee
Keyword(s):  
Degrees Of Freedom ◽  
Linear Time ◽  
System Model ◽  
System Parameters ◽  
Linear Time Invariant ◽  
Gear Mesh ◽  
The Stability ◽  
Linear Time Invariant System ◽  
Time Invariant ◽  
Gear Rattle

Torsional systems with clearance-type nonlinearities have inherent vibratory problems such as gear rattle. Such vibro-impacts generally occur on the unloaded gear pairs of a vehicle correlated with the firing excitation of an engine. This study investigates the gear rattle phenomena on unloaded gear pairs with different excitation conditions and various system parameters. First, a linear time-invariant system model with six degrees of freedom is constructed and then a numerical analysis is applied to the gear rattle motion. Smoothening factors for clutch stiffness and hysteresis are employed for the stability of numerical simulations. Second, the dynamic characteristics of vibro-impacts are studied by examining the fast Fourier transform (FFT) components of the gear mesh force in a high frequency range. The effects of various system parameters on the vibro-impacts are examined using a nonlinear system model. Finally, the vibro-impacts, in terms of “single-sided” and “double-sided” impacts, are identified in phase planes.

Sensitivity of General Compound Planetary Gear Natural Frequencies and Vibration Modes to Model Parameters

2007 ◽  
Author(s):  
Yichao Guo ◽  
Robert G. Parker
Keyword(s):  
Kinetic Energy ◽  
Natural Frequencies ◽  
Planetary Gear ◽  
Model Parameters ◽  
Vibration Modes ◽  
Energy Distributions ◽  
Planetary Gears ◽  
Inertia Parameters ◽  
Kinetic Energy Distributions

This paper studies sensitivity of general compound planetary gear natural frequencies and vibration modes to all inertia and stiffness parameters. The results are expressed in compact formulae for tuned and mistuned compound planetary gears. Analysis reveals that for tuned (i.e., cyclically symmetric) compound planetary gears, eigenvalue sensitivities to stiffness parameters are directly proportional to modal strain energies, and eigenvalue sensitivities to inertia parameters are proportional to modal kinetic energies. Furthermore, the eigenvalue sensitivities to all model parameters are determined by inspection of the modal strain and kinetic energy distributions for a given mode. For mistuned systems, the results differ for the cases of tuned one mistuned parameter, two or more independent mistuned parameters, and two or more dependent mistuned parameters. For cases of one mistuned parameter, and two or more independent mistuned parameters, compact formulae of eigensensitivities are derived, and they are proportional to modal strain/kinetic energies. For the case of two or more dependent mistuned parameters, however, only general expressions of eigensensitivities are derived. These eigensensitivities depend not only on modal energies, but also on how the dependent mistuned parameters are related. Hence inspection of modal energies alone may fail to locate the parameter that is most effective in tuning natural frequencies.

Sign in / Sign up

Export Citation Format

Share Document