Structured Vibration Modes of General Compound Planetary Gear Systems

2006 ◽  
Vol 129 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Daniel R. Kiracofe ◽  
Robert G. Parker
Keyword(s):  
Vibration Mode ◽  
Planetary Gear ◽  
Single Stage ◽  
Analytical Models ◽  
Vibration Modes ◽  
General Description ◽  
Planetary Gears ◽  
Multi Stage ◽  
Stage System ◽  
Frequency Properties

This paper extends previous analytical models of simple, single-stage planetary gears to compound, multi-stage planetary gears. This model is then used to investigate the structured vibration mode and natural frequency properties of compound planetary gears of general description, including those with equally spaced planets and diametrically opposed planet pairs. The well-defined cyclic structure of simple, single-stage planetary gears is shown to be preserved in compound, multi-stage planetary gears. The vibration modes are classified into rotational, translational, and planet modes and the unique properties of each type are examined and proved for general compound planetary gears. All vibration modes fall into one of these three categories. For most cases, both the properties of the modes and the modes themselves are shown to be insensitive to relative planet positions between stages of a multi-stage system.

Structured Vibration Modes of General Compound Planetary Gear Systems

2007 ◽  
Author(s):  
Daniel R. Kiracofe ◽  
Robert C. Parker
Keyword(s):  
Vibration Mode ◽  
Planetary Gear ◽  
Single Stage ◽  
Analytical Models ◽  
Vibration Modes ◽  
General Description ◽  
Planetary Gears ◽  
Multi Stage ◽  
Stage System ◽  
Frequency Properties

This paper extends previous analytical models of simple, single-stage planetary gears to compound, multi-stage planetary gears. This model is then used to investigate the structured vibration mode and natural frequency properties of compound planetary gears of general description, including those with equally-spaced planets and diametrically opposed planet pairs. The well-defined cyclic structure of simple, single-stage planetary gears is shown to be preserved in compound, multi-stage planetary gears. The vibration modes are classified into rotational, translational, and planet modes and the unique properties of each type are examined and proved for general compound planetary gears. All vibration modes fall into one of these three categories. For most cases, both the properties of the modes and the modes themselves are shown to be insensitive to relative planet positions between stages of a multi-stage system.

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.

Eigensensitivity of Planetary Gear Free Vibration Properties

1999 ◽  
Author(s):  
Jian Lin ◽  
Robert G. Parker
Keyword(s):  
Kinetic Energy ◽  
Free Vibration ◽  
Natural Frequency ◽  
Vibration Mode ◽  
Planetary Gear ◽  
Planetary Gears ◽  
System Parameters ◽  
Frequency Sensitivity ◽  
Vibration Properties ◽  
Inertia Parameters

Abstract The natural frequency and vibration mode sensitivities to system parameters are rigorously investigated for both tuned and mistimed 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 (cyclically symmetric) planetary gears [1], the eigensensitivities 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. While the terminology of planetary gears is used throughout, the results apply for general epicyclic gears.

Mean Sojourn Time in Multi Stage Fork-Join Network

2015 ◽  
Vol 6 (3) ◽  
pp. 80-99 ◽  
Author(s):  
Yonit Barron
Keyword(s):  
Supply Chains ◽  
Sojourn Time ◽  
Computer Processing ◽  
Single Stage ◽  
Assembly Systems ◽  
Parallel Tasks ◽  
Multi Stage ◽  
Stage System ◽  
Major Factors ◽  
Performance Behavior

Fork-Join queue networks (F-J) have received increasing attention during the last Decade, due to their ability to model parallel and distributed computer processing, supply chains and assembly systems. However, most research is focused on a single stage processing, and only scant work exists on F-J with two or more stages. In this paper, the author investigates (through simulation) the performance behavior of a multi-stage system; in particular, the performance of a synchronized system is compared to an unsynchronized system regarding three major factors: (1) the number of parallel tasks; (2) the number of serial stages and (3) the utilization.

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.

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.

Dynamic Modeling of Multi-Stage Planetary Gears Coupled with Bearings in Housing

2011 ◽  
Vol 86 ◽  
pp. 30-34
Author(s):  
Zheng Ming Xiao ◽  
Da Tong Qin
Keyword(s):  
Planetary Gear ◽  
Degree Of Freedom ◽  
Design Parameters ◽  
Parameter Method ◽  
Rotational Degree ◽  
Planetary Gears ◽  
Multi Stage ◽  
Lumped Parameter ◽  
Shield Tunnelling ◽  
Gyroscopic Effects

This work develops an analytical model of multi-stages planetary gear transmission (PGT) coupled with bearings in housing based on analyzing the displacement relationships of gearing system. The model adopts three planar degree-of-freedom for each of the central components, and the rotational degree-of-freedom for the planets of each stage. Considering the gyroscopic effects, the modified transverse-torsional model is established in the rotating Cartesian coordinates by lumped-parameter method, which is more accurate and may match with the physical model better than the purely torsional model. According to the design parameters of the 3-stage planetary gears of main reducer of shield tunnelling machine, the natural frequencies and vibration modes are investigated by using this transverse-torsional model.

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.

Vibration Properties of High-Speed Planetary Gears With Gyroscopic Effects

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Christopher G. Cooley ◽  
Robert G. Parker
Keyword(s):  
High Speed ◽  
Eigenvalue Problems ◽  
Planetary Gear ◽  
Vibration Modes ◽  
Planetary Gears ◽  
High Speeds ◽  
Wide Range ◽  
Modal Property ◽  
Gyroscopic Effects ◽  
Complex Valued

This study investigates the modal property structure of high-speed planetary gears with gyroscopic effects. The vibration modes of these systems are complex-valued and speed-dependent. Equally-spaced and diametrically-opposed planet spacing are considered. Three mode types exist, and these are classified as planet, rotational, and translational modes. The properties of each mode type and that these three types are the only possible types are mathematically proven. Reduced eigenvalue problems are determined for each mode type. The eigenvalues for an example high-speed planetary gear are determined over a wide range of carrier speeds. Divergence and flutter instabilities are observed at extremely high speeds.

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.

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