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

2010 ◽  
Vol 132 (1) ◽  
Author(s):  
Yichao Guo ◽  
Robert G. Parker
Keyword(s):  
Natural Frequencies ◽  
Planetary Gear ◽  
Unperturbed System ◽  
Model Parameters ◽  
Vibration Modes ◽  
Planetary Gears ◽  
Modal Properties ◽  
Frequency Changes ◽  
Eigenvector Derivatives ◽  
Eigenvalue And Eigenvector

This paper studies the sensitivity of general compound planetary gear natural frequencies and vibration modes to inertia and stiffness parameters. The model admits planetary gears having any combination of stepped-planet, meshed-planet, and multiple stage arrangements. Eigensensitivities in terms of eigenvalue and eigenvector derivatives are analytically derived for both tuned (i.e., cyclically symmetric) and mistuned systems. The results are expressed in compact closed-form formulas. The well-defined modal properties of general compound planetary gears simplify the expressions of eigenvalue sensitivities to ones that are proportional to modal strain/kinetic energies. Inspection of the modal strain/kinetic energy distribution plots provides an effective way to quantitatively and qualitatively determine the parameters that have the largest impact on a certain mode. For parameter perturbations that preserve the system symmetry, the structured modal properties imply that the modes of the same type are independent of the same group of system parameters. Parameter mistuning, with a few exceptions, splits a degenerate natural frequency of the unperturbed system into two frequencies; one frequency keeps its original value and retains its well-defined modal properties, while the other frequency changes and its associated mode lose its structured modal properties.

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.

Structured Eigensolution Properties of Planetary Gears With Elastically Deformable Ring Gears

2009 ◽  
Author(s):  
Robert G. Parker ◽  
Xionghua Wu
Keyword(s):  
Planetary Gear ◽  
Unperturbed System ◽  
Vibration Modes ◽  
Elastic Ring ◽  
Small Perturbations ◽  
Planetary Gears ◽  
Modal Properties ◽  
Mode Method ◽  
Perturbation Parameters ◽  
Method Analysis

The distinctive modal properties of equally spaced planetary gears with elastic ring gears are studied through perturbation and a candidate mode method. All eigenfunctions fall into one of four mode types whose structured properties are derived analytically. Two perturbations are used to obtain closed-form expressions of all the eigenfunctions. In the Discrete Planetary Perturbation (DPP), the unperturbed system is a discrete planetary gear with a rigid ring. The stiffness of the ring is perturbed from infinite to a finite number. In the Elastic Ring Perturbation (ERP), the unperturbed system is an elastic ring supported by the ring-planet mesh springs; the sun, planet and carrier motions are treated as small perturbations. A subsequent candidate mode method analysis proves the perturbation results and removes any reliance on perturbation parameters being small. All vibration modes are classified into rotational, translational, planet and purely ring modes. The well defined properties of each type of mode are analytically determined. All modal properties are verified numerically.

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.

Analysis of Modal Properties of Spur Planetary Gears

2013 ◽  
Vol 300-301 ◽  
pp. 978-981
Author(s):  
Jun Gang Wang ◽  
Yong Wang ◽  
Zhi Pu Huo
Keyword(s):  
Radial Direction ◽  
Natural Frequencies ◽  
Planetary Gear ◽  
Vibration Modes ◽  
Rotational Mode ◽  
Planetary Gears ◽  
Translational Mode ◽  
Coupling Dynamic ◽  
Rotational Coupling ◽  
Coupling Dynamic Model

A translational-rotational-coupling dynamic model has been built in the carrier-attached coordinate system.Differential equations of the system have been derived, and the natural frequencies and vibration modes of the planetary gear set have been obtained through solution of the associated eigenvalue problem. Based on the properties of the transmission system, the vibration modes of 2K-H spur planetary gear set can be classified into three categories, i.e., translational mode along radial direction, rotational mode, and planet mode.

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.

Modal Properties of Planetary Gears With an Elastic Continuum Ring Gear

2008 ◽  
Vol 75 (3) ◽  
Author(s):  
Xionghua Wu ◽  
Robert G. Parker
Keyword(s):  
Planetary Gear ◽  
Unperturbed System ◽  
Elastic Ring ◽  
Elastic Continuum ◽  
Small Perturbations ◽  
Planetary Gears ◽  
Modal Properties ◽  
Mode Method ◽  
Perturbation Parameters ◽  
Method Analysis

The distinctive modal properties of equally spaced planetary gears with elastic ring gears are studied through perturbation and a candidate mode method. All eigenfunctions fall into one of four mode types whose structured properties are derived analytically. Two perturbations are used to obtain closed-form expressions of all the eigenfunctions. In the discrete planetary perturbation, the unperturbed system is a discrete planetary gear with a rigid ring. The stiffness of the ring is perturbed from infinite to a finite number. In the elastic ring perturbation, the unperturbed system is an elastic ring supported by the ring-planet mesh springs; the sun, planet and carrier motions are treated as small perturbations. A subsequent candidate mode method analysis proves the perturbation results and removes any reliance on perturbation parameters being small. All vibration modes are classified into rotational, translational, planet, and purely ring modes. The well defined properties of each type of mode are analytically determined. All modal properties are verified numerically.

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.

Comprehensive Dynamic Model and Vibration Characteristics of Step-Type Compound Planetary Gear Sets

2011 ◽  
Vol 308-310 ◽  
pp. 1923-1928
Author(s):  
Fu Chun Yang ◽  
Xiao Jun Zhou ◽  
Ming Xiang Xie
Keyword(s):  
Dynamic Model ◽  
Natural Vibration ◽  
Natural Frequencies ◽  
Planetary Gear ◽  
Vibration Characteristics ◽  
Vibration Modes ◽  
Shape Distribution ◽  
Type Compound ◽  
Planetary Gear Sets ◽  
Step Type

Step-type compound planetary gear sets are widely applied in vehicle systems. Comprehensive dynamic model of step-type compound planetary gear sets, which includes translational, rotational vibrations and static transmission errors, was established. Natural vibration characteristics of the system, such as natural frequencies and vibration modes, were analyzed. Belt shape distribution characteristics of its natural frequencies was researched. According to vibration characteristics of both central components and planets, natural vibration modes of the system are classified into three types: central components translational vibration and planets random vibration, central components rotational vibration and planets identical vibration, central components static and adjacent planets reverse vibration mode.

Grouping of Planetary Gear Modes With Significant Tooth Mesh Deflection

2012 ◽  
Author(s):  
Tristan M. Ericson ◽  
Robert G. Parker
Keyword(s):  
Natural Frequency ◽  
Strain Energy ◽  
Natural Frequencies ◽  
Planetary Gear ◽  
Planetary Gears ◽  
System Parameters ◽  
Planet Gear ◽  
Parameter Values ◽  
Grouping Behavior

High natural frequencies of planetary gears tend collect into groups. The modes at these natural frequencies are characterized by motion of the planet gears with strain energy in the tooth meshes and planet bearings. Each group has one rotational, one translational, and one planet mode. The groups change in natural frequency together when system parameters are varied. The grouping behavior is disrupted with significant differences in planet-to-planet gear parameter values.

Sign in / Sign up

Export Citation Format

Share Document