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.

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.

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.

Natural Frequency Clusters in Planetary Gear Vibration

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Tristan M. Ericson ◽  
Robert G. Parker
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Planetary Gear ◽  
The Other ◽  
Or Groups ◽  
Mass Moment ◽  
Mass Moment Of Inertia ◽  
Bearing Stiffness ◽  
Planet Gear ◽  
Central Member

This paper investigates how the natural frequencies of planetary gears tend to gather into clusters (or groups). This behavior is observed experimentally and analyzed in further detail by numerical analysis. There are three natural frequency clusters at relatively high frequencies. The modes at these natural frequencies are marked by planet gear motion and contain strain energy in the tooth meshes and planet bearings. Each cluster contains one rotational, one translational, and one planet mode type discussed in previous research. The clustering phenomenon is robust, continuing through parameter variations of several orders of magnitude. The natural frequency clusters move together as a group when planet parameters change. They never intersect, but when the natural frequencies clusters approach each other, they exchange modal properties and veer away. When central member parameters are varied, the clusters remain nearly constant except for regions in which natural frequencies simultaneously shift to different cluster groups. There are two conditions that disrupt the clustering effect or diminish its prominence. One is when the planet parameters are similar to those of the other components, and the other is when there are large differences in mass, moment of inertia, bearing stiffness, or mesh stiffness among the planet gears. The clusters remain grouped together with arbitrary planet spacing.

The Research on Natural Characteristic and Eigensensitivity of Ravingneaux Compound Planetary Gear Sets

2013 ◽  
Vol 446-447 ◽  
pp. 590-596
Author(s):  
Bo Qian ◽  
Shi Jing Wu
Keyword(s):  
Natural Frequency ◽  
Planetary Gear ◽  
Torsional Stiffness ◽  
Ring Gear ◽  
Vibration Model ◽  
Planetary Gear Sets ◽  
Planet Gear ◽  
Natural Characteristic ◽  
Gear Ring ◽  
The Moment

The dynamic model of Ravingneaux compound planetary gear sets has been built. Then the Natural frequency and vibration model have been solved in the Ravingneaux compound planetary gear sets. The eigensensitivity to parameters have been researched based on the dynamical model. The varying trend of natural frequency according to the varying of parameters have been researched, which include gear mass (sun gear, ring gear , or planet gear), the moment of inertia of gears, the support stiffness , the torsional stiffness.

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 Natural Frequencies and Vibrating Modes for a Magnetic Planetary Gear Drive

2012 ◽  
Vol 19 (6) ◽  
pp. 1385-1401 ◽  
Author(s):  
Lizhong Xu ◽  
Xuejun Zhu
Keyword(s):  
Natural Frequencies ◽  
Planetary Gear ◽  
Drive System ◽  
Dynamic Equations ◽  
The Sun ◽  
System Parameters ◽  
Meshing Stiffness ◽  
Torsion Mode ◽  
Gear Drive ◽  
Pair Number

In this paper, a dynamic model for a magnetic planetary gear drive is proposed. Based on the model, the dynamic equations for the magnetic planetary gear drive are given. From the magnetic meshing forces and torques between the elements for the drive system, the tangent and radial magnetic meshing stiffness is obtained. Using these equations, the natural frequencies and the modes of the magnetic planetary gear drive are investigated. The sensitivity of the natural frequencies to the system parameters is discussed. Results show that the pole pair number and the air gap have obvious effects on the natural frequencies. For the planetary gear number larger than two, the vibrations of the drive system include the torsion mode of the center elements, the translation mode of the center elements, and the planet modes. For the planetary gear number equal to two, the planet mode does not occur, the crown mode and the sun gear mode occur.

Membrane and Bending Strain in Cylindrical Shell Vibrations

2009 ◽  
Author(s):  
Basem Alzahabi ◽  
Henry Kowalski
Keyword(s):  
Natural Frequency ◽  
Strain Energy ◽  
Natural Frequencies ◽  
Cylindrical Shells ◽  
Operating Conditions ◽  
Total Strain ◽  
Design Stage ◽  
Total Strain Energy ◽  
Scaled Model ◽  
Membrane Strain

Cylindrical Shells are widely used in many structural designs, such as offshore structures, liquid storage tanks, submarine hulls, and airplane hulls. Most of these structures are required to operate in a dynamic environment. Therefore, investigating the dynamic characteristics of cylindrical shells is very critical in developing a strategy for modal vibration control for specific operating conditions. Reduction of vibration amplitudes and in sound radiation is most efficiently achieved at the design stage, and the acoustic signatures may be determined by considering operational scenarios, and modal characteristics. In cylindrical shells, mode shapes associated with each natural frequency are combination of Radial, Longitudinal, and Circumferential modes, and unlike those of beam structure, the lowest natural frequency does not necessarily correspond to the lowest wave index. In fact, the natural frequencies do not fall in ascending order of the wave index in cylindrical shells. The ratio of membrane strain energy to total strain energy is high for modes with simple modal patterns and decrease toward zero as the number of nodal (n) lines increase, while the ratio of bending energy to total strain energy is small for simple nodal patterns and increase with increase in complexity of it. Modes associated with membrane deformation require a lot of strain energy while modes associated with bending deformation require less strain energy. The lowest natural frequency occurs where the sum of the two energies are at minimum. Moreover, the natural frequencies that are controlled by membrane strain energy are approximately independent of the shell thickness change. In this paper, a scaled model of submarine hull segment under shear diaphragm boundary conditions is analyzed analytically and numerically. Then the experimental modal analysis of the scaled model utilizing strain gauges was performed to decouple the strain components. Designing a boundary condition that simulate a shear diaphragm is very challenging task by itself. The experimental data were correlated with those results obtained analytically and numerically using the finite element methods using MSC.NASTRAN software. The results were found to be in excellent agreement.

Building Block Based Topology Synthesis Algorithm to Optimize the Natural Frequency in Large Stroke Flexure Mechanisms

2020 ◽  
Author(s):  
Mathijs E. Fix ◽  
Dannis M. Brouwer ◽  
Ronald G. K. M. Aarts
Keyword(s):  
Natural Frequency ◽  
Building Block ◽  
Strain Energy ◽  
Natural Frequencies ◽  
Compliant Mechanisms ◽  
Large Range ◽  
Building Blocks ◽  
Synthesis Algorithm ◽  
Block Based ◽  
High Support

Abstract Flexure based compliant mechanisms suited for a large range of motion can be designed by handling the challenges arising from combining low compliance in the desired directions, high support stiffness, low stresses and high unwanted natural frequencies. Current topology optimization tools typically can’t model large deflections of flexures, are too conceptual or are case specific. In this research, a new spatial topological synthesis algorithm based on building blocks is proposed to optimize the performance of an initial design. The algorithm consists of successive shape optimizations and layout syntheses. In each shape optimization the dimensions for some layout are optimized. The layout synthesis strategically replaces the most “critical” building block with a better option. To maximize the first unwanted natural frequency the replacement strategy depends the strain energy distribution of the accompanying mode shape. The algorithm is tested for the design of a 1-DOF flexure hinge. The obtained final layout agrees with results known from literature.

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.

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