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.

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.

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.

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.

Experimental Determination of the Mass Moment of Inertia of a Flywheel Using Dynamics and Statistical Methods

2015 ◽  
Author(s):  
Pezhman Hassanpour ◽  
Monica Weaser ◽  
Ray Colquhoun ◽  
Khaled Alghemlas ◽  
Abdullah Alrashdan
Keyword(s):  
Experimental Determination ◽  
Accurate Result ◽  
Moment Of Inertia ◽  
The Other ◽  
Experimental Measurements ◽  
Ball Bearings ◽  
Experiment Data ◽  
Mass Moment ◽  
Mass Moment Of Inertia

This paper presents the analysis of the mass moment of inertia (MMI) of a flywheel using experiment data. This analysis includes developing two models for determining the MMI of the flywheel. The first model considers the effect of mass moment of inertia only, while the second model takes the effect of friction in the ball bearings into consideration. The experiment results have been used along with both models to estimate the MMI of the flywheel. It has been demonstrated that while the model with no friction can be used for estimating the MMI to some extent, the model with friction produces the most accurate result. On the other hand, an effective application of the model with friction requires several experimental measurements using different standard masses. This translates into more expensive method in terms of experiment time and equipment cost.

The NAVMI Factor and Natural Frequency of a Circular Plate Exposed to Water in Flexural Vibration

2011 ◽  
Vol 199-200 ◽  
pp. 1445-1450
Author(s):  
Hui Juan Ren ◽  
Mei Ping Sheng
Keyword(s):  
Boundary Condition ◽  
Natural Frequency ◽  
Circular Plate ◽  
Natural Frequencies ◽  
Integration Method ◽  
Flexural Vibration ◽  
The Other ◽  
Additional Mass ◽  
Simply Supported ◽  
Higher Order Modes

The expression of NAVMI factor and the natural frequency of a circular plate, which is placed in a hole of an infinite grid wall with one side exposed to water, are derived from the viewpoint of the additional mass. 10 Nodes Gauss-Legender integration method and the iteration method are employed to obtain the numerical results of the NAVMI factors, AVMI factors and the natural frequencies. It can be found from the results that NAVMI factors of the first two order modes are far bigger than those of the other modes when the boundary condition of a circular plate is certain. The first two order modal NAVMI factors of the circular plate with clamped and simply supported boundary conditions are far bigger than those of the circular plate with free-edged boundary condition, and the NAVMI factors are almost the same for the three order or much higher order modes regardless of the boundary condition. It is also observed that the natural frequencies of the circular plate exposed to water are smaller than those exposed to air, and the natural frequencies of the circular plate exposed to water with both sides are smaller than those of the circular plate exposed to water with one side.

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.

Natural Frequencies of Nonuniform Beams on Multiple Elastic Supports

1958 ◽  
Vol 25 (1) ◽  
pp. 57-63
Author(s):  
R. A. Di Taranto
Keyword(s):  
Natural Frequencies ◽  
Forced Vibrations ◽  
Moment Of Inertia ◽  
Elastic Supports ◽  
Mass Moment ◽  
End Conditions ◽  
Mass Moment Of Inertia ◽  
Gyroscopic Effects

Abstract A method is presented for the determination of the natural frequencies of nonuniform beams on two or more torsionally and linearly elastic supports, including the effect of rotary mass moment of inertia. The method employed is an extension of the Myklestad method. The cases of two supports with varied end conditions and three supports with a torsional and linear restraint at each support are formulated. It is indicated how this method may be used for problems concerning forced vibrations of beams on multiple elastic supports and for the determination of critical rotor speeds including gyroscopic effects.

Vibration Frequencies for a Uniform Beam With One End Elastically Supported and Carrying a Mass at the Other End

1975 ◽  
Vol 42 (4) ◽  
pp. 878-880 ◽  
Author(s):  
D. A. Grant
Keyword(s):  
Normal Modes ◽  
Frequency Equation ◽  
The Other ◽  
Concentrated Mass ◽  
Mass Moment ◽  
Wide Range ◽  
Modes Of Vibration ◽  
Mass Moment Of Inertia ◽  
Elastically Supported ◽  
Range Of Values

In this paper the author obtains the frequency equation for the normal modes of vibration of uniform beams with linear translational and rotational springs at one end and having a concentrated mass at the other free end. The eigenfrequencies for the fundamental mode are given for a wide range of values of mass ratio, mass moment of inertia ratios, and stiffness ratios.

Diagnosing Coupled Lateral-Torsional Vibrations in Turbomachinery

2008 ◽  
Author(s):  
Vinayaka N. Rajagopalan ◽  
John M. Vance
Keyword(s):  
Mathematical Model ◽  
Natural Frequency ◽  
Real World ◽  
Diagnostic Method ◽  
Natural Frequencies ◽  
The Other ◽  
Torsional Vibrations ◽  
Test Rig ◽  
Objective Being ◽  
Heavy Damage

Rotordynamic instability, commonly observed as subsynchronous vibration, is a serious problem that can cause heavy damage to a turbomachine or make it incapable of operation due to high vibration levels. However, all subsynchronous vibrations are not necessarily unstable. A way to quickly diagnose them would be helpful. In an earlier paper, the authors presented data from experiments that simulated various causes of sub-synchronous vibrations, some causes being genuine rotordynamic instabilities and some others being benign (stable), and identified ways to diagnose and classify the subsynchronous motions. In a continuation of the same study, subsynchronous vibrations due to coupled lateral-torsional effects are experimentally simulated, the objective being to signal-analyze these vibrations to find unique signatures that identify this cause and also be able to recognize if they are a true rotordynamic instability or not. To this end, a test rig was built with parallel shafts coupled by gears, driven by a DC motor at one end and loaded at the other end, to closely simulate a real-world machine. A torsional mathematical model for the test rig is also presented to predict its torsional natural frequencies. Experiments were conducted wherein the first torsional natural frequency was externally excited, with the shaft spinning at a higher speed. The result was a false sub-synchronous “instability” signal in the lateral measurements. A method to distinguish these vibrations from a genuine lateral non-synchronous instability is presented. Also, a new diagnostic method to classify the subsynchronous vibration as benign is elucidated.

Connecting Rod Dynamics

2014 ◽  
Author(s):  
Samuel Doughty
Keyword(s):  
The Other ◽  
Connecting Rod ◽  
Complex Motion ◽  
Additional Mass ◽  
Mass Model ◽  
Usual Model ◽  
Automotive Engines ◽  
Correct Analysis ◽  
Mass Moment ◽  
Mass Moment Of Inertia

The complex motion of a slider-crank connecting rod has motivated analysts to work in terms of an “equivalent link,” comprised of two point masses at the ends of a massless link, where one end is located at the crank pin and the other end is at the wrist pin. It has long been known that this limited model is not fully equivalent in the dynamic sense, but the practice persists and errors are routinely introduced into torsional vibration and shaking force calculations. The purpose of this paper is to expose this error and show the nature of its effects. This is accomplished by means of a fully correct analysis, based on the two point mass model extended to include a massless additional mass moment of inertia, and then examining the terms that the usual model omits. Numerical results are given for several actual automotive engines.

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