Graph-Based Models of Compound Planetary Gear Boxes

2013 ◽  
Vol 199 ◽  
pp. 143-148 ◽  
Author(s):  
Józef Drewniak ◽  
Stanisław Zawiślak
Keyword(s):  
Planetary Gear ◽  
Planetary Gears ◽  
Graph Transformations

In the paper, graph-based models of planetary gears are presented. Especially, compound planetary gear boxes are analyzed. The rules of assignment of particular graphs are shortly described. Based upon these models, ratios for consecutive drives are calculated. Graph transformations are introduced aiming for presentation of every single drive separately. Kinematic equations are generated in algorithmic way based on the adequate subgraphs as well as their codes. Compatibility of results - obtained by means of different methods - was achieved. The presented method is simple and effective, moreover it can be used for other design tasks as e.g. optimization and further analyzes i.e. evaluation of effectiveness.

scholarly journals Simulative investigation of ring creep on a planetary bearing of a wind turbine gearbox

2021 ◽  
Author(s):  
Jonas Gnauert ◽  
Felix Schlüter ◽  
Georg Jacobs ◽  
Dennis Bosse ◽  
Stefan Witter
Keyword(s):  
Experimental Data ◽  
Finite Element Method ◽  
Sensitivity Analysis ◽  
Planetary Gear ◽  
The Finite Element Method ◽  
Relative Movement ◽  
Wind Turbine Gearbox ◽  
Interference Fit ◽  
Planetary Gears ◽  
Module Coefficient

AbstractWind turbines (WT) must be further optimized concerning availability and reliability. One of the major reasons of WT downtime is the failure of gearbox bearings. Some of these failures occur, due to the ring creep phenomenon, which is mostly detected in the planetary bearings. The ring creep phenomenon describes a relative movement of the outer ring to the planetary gear. In order to improve the understanding of ring creep, the finite element method (FEM) is used to simulate ring creep in planetary gears. First, a sensitivity analysis is carried out on a small bearing size (NU205), to characterize relevant influence parameters for ring creep—considered parameters are teeth module, coefficient of friction, interference fit and normal tooth forces. Secondly, a full-scale planetary bearing (SL185030) of a 1MW WT is simulated and verified with experimental data.

Dynamic Analysis of Planetary Gear Reducer

2018 ◽  
Vol 880 ◽  
pp. 87-92
Author(s):  
Daniela Vintilă ◽  
Laura Diana Grigorie ◽  
Alina Elena Romanescu
Keyword(s):  
Finite Elements ◽  
Differential Equations ◽  
Dynamic Analysis ◽  
Frequency Response ◽  
Planetary Gear ◽  
Resonance Phenomenon ◽  
Superposition Method ◽  
Planetary Gears ◽  
Tower Crane ◽  
Systems Of Differential Equations

This paper presents dynamic analysis of a three stage planetary gear reducer for operate a tower crane. Ordinary and planetary gears have been designed respecting the coaxial, neighboring and mounting conditions. Harmonic analysis has been processed to identify frequency response for displacements, strains and deformations. The aim of the study was to determine critical frequencies to avoid mechanical resonance phenomenon. The obtained results are based on the superposition method for solving the systems of differential equations resulting from the analysis with finite elements.

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.

Synthesis of Planetary Gears by Means of Artificial Intelligence Approach ‒ Graph-Theoretical Modeling

2010 ◽  
Vol 164 ◽  
pp. 243-248 ◽  
Author(s):  
Józef Drewniak ◽  
Stanisław Zawiślak
Keyword(s):  
Research Work ◽  
Planetary Gear ◽  
Systems Of Equations ◽  
Modes Of Operation ◽  
Planetary Gears ◽  
Intelligence Approach ◽  
Artificial Intelligence Approach ◽  
Selection Of ◽  
Structure Layout

Graph-based modeling of planetary gears was applied in the presented research work for their synthesis. The tailored Hsu and contour graphs were used. Graphs encode the structure (layout) of a planetary gear and upon them - the systems of equations can be generated. These systems enable determination of rotational velocities of planetary gear elements. The method is algorithmic and simple. It allows for an easy comparison of different design solutions and selection of the most appropriate one. The list of the possible modes of operation for an exemplary planetary gear is also provided in the paper.

The Balanced Two-Satellite Planetary Gear with the Equal Distribution of Loading on Satellites

2014 ◽  
Vol 1040 ◽  
pp. 708-713
Author(s):  
Ya.A. Andreeva
Keyword(s):  
Planetary Gear ◽  
Structural Synthesis ◽  
Equal Distribution ◽  
Program Complex ◽  
Planetary Gears

Aspects of the structural synthesis of planetary gears without excess communications are analyzed. The possibility of creation of self-established multisatellite planetary reducers, by addition in the structure of gear of the group of links with zero mobility is proved. The solution of the problem of an equal distribution of loading on satellites is given. Computing experiments in the program complex «T-Flex Dynamics» are carried out. The new scheme of the planetary gear is shown.

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.

scholarly journals Modeling, Testing, and Characteristic Analysis of a Planetary Flywheel Inerter

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Zheng Ge ◽  
Weirui Wang
Keyword(s):  
Theoretical Analysis ◽  
Planetary Gear ◽  
Gear Ratio ◽  
Ball Screw ◽  
Ring Gear ◽  
Characteristic Analysis ◽  
Planetary Gears ◽  
Nonlinear Dynamical ◽  
Output Force ◽  
New Type

We propose the planetary flywheel inerter, which is a new type of ball screw inerter. A planetary flywheel consists of several planetary gears mounted on a flywheel bracket. When the flywheel bracket is driven by a screw and rotating, each planetary gear meshing with an outer ring gear generates a compound motion composed of revolution and rotation. Theoretical analysis shows that the output force of the planetary flywheel inerter is proportional to the relative acceleration of one terminal of the inerter to the other. Optimizing the gear ratio of the planetary gears to the ring gear allows the planetary flywheel to be lighter than its traditional counterpart, without any loss on the inertance. According to the structure of the planetary flywheel inerter, nonlinear factors of the inerter are analyzed, and a nonlinear dynamical model of the inerter is established. Then the parameters in the model are identified and the accuracy of the model is validated by experiment. Theoretical analysis and experimental data show that the dynamical characteristics of a planetary flywheel inerter and those of a traditional flywheel inerter are basically the same. It is concluded that a planetary flywheel can completely replace a traditional flywheel, making the inerter lighter.

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.

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