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.

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.

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.

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.

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.

VIBRATION PROPERTIES OF TRADITIONAL MASONRY WALLS OF CORTES CHURCH

2016 ◽  
Vol 3 (2) ◽  
Author(s):  
Noriko Takiyama ◽  
Akari Yamaguchi ◽  
Kohei Hara ◽  
Verdejo Juan Ramon Jimenez
Keyword(s):  
Natural Frequency ◽  
Structural Property ◽  
Vibration Mode ◽  
Vibration Characteristics ◽  
Masonry Walls ◽  
Material Thickness ◽  
Vibration Properties ◽  
Microtremor Measurement ◽  
The Church ◽  
Microtremor Measurements

The Santo Niño Church in Bohol Island was partially damaged in the Bohol Earthquake in October 2013. In this study, we investigated the structural property of the Santo Niño Church to understand the vibration characteristics of Philippine masonry constructions by checking the main damage and conducting measurement surveys and microtremor measurement on the structure and ground. The major findings of this study can be summarized as follows: (a) Collapsed walls, peeling wall stone, corner deformation, and collapsed ceiling were the main damages that were observed. The collapsed wall was measured, and the make-up and material thickness of the wall was verified. (b) By performing microtremor measurements on the walls, the vibration property of the church, such as the natural frequency and vibration mode of the longest wall A was clarified. The 1st natural frequency of the longest wall A is the lowest.

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.

Finite Element Modes Analysis of Involute Planetary Gear in RV Reducer

2010 ◽  
Vol 44-47 ◽  
pp. 1018-1021 ◽  
Author(s):  
Wei Dong He ◽  
Ying Hui Zhang
Keyword(s):  
Finite Element ◽  
Natural Frequency ◽  
Vibration Mode ◽  
Three Dimensional ◽  
Planetary Gear ◽  
Three Dimensional Modeling ◽  
Dimensional Modeling ◽  
Involute Gear ◽  
Modeling Software ◽  
Rv Reducer

Paper built the solid model of RV involute planetary gear with three dimensional modeling software Pro/E, dumped this model into ANSYS with IGES middle exchange file, define the three crankshaft solid connect with the three involute gear, carried on the modal analysis with finite element method, obtained the natural frequency and the vibration mode,. Results put out the danger frequency focus on 3645Hz, 8610Hz ,16729etc., then paper examined the different natural frequency and contrast them with the natural frequency of whole RV reducer, results shows that when the input speed of reducer turning at 1500r/min, for the three involute gear it’s not easy to cause resonance, but being the incentive frequency is 525Hz, it should to pay attention to avoid 451.63Hz, which was a key natural frequency of RV reducer, finally paper laid the system's dynamic response calculation and analysis of RV reducer.

Vibration analysis of rectangular plates resting on four rigid supports

2018 ◽  
Vol 15 (1) ◽  
pp. 110-118 ◽  
Author(s):  
Mohammad Gharaibeh
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Mode Shape ◽  
Geometric Parameters ◽  
Rectangular Plates ◽  
Fe Method ◽  
Empirical Formulas ◽  
Content Type ◽  
Vibration Properties ◽  
Rigid Supports

Purpose This paper aims to thoroughly investigate the free vibration characteristics of rectangular plates resting on symmetrically distributed four rigid supports by using a finite element (FE) method. Design/methodology/approach ANSYS parametric design language was used to generate the FE models and to run the analysis. The FE models were initially validated and were then used to solve for the plate first natural frequency and mode shape. The effect of the plate aspect ratio and support location on the free vibration properties of the plate was thoroughly studied by conducting several FE runs. Finally, simple empirical formulas were developed to conveniently calculate the plate first natural frequency based on the geometric parameters and support type, as well as support locations. Those well-formulated equations were in a great match with the FE data. Findings The results showed that the plate first natural frequency and mode shape are highly affected by the plate size and support locations. Specifically, the natural frequency deceases as the plates becomes larger. Also, the bending behavior of the first mode is highly affected by the support location, which results in a significant change in the natural frequency of the plate structure. In addition, the presently formulated empirical formulas are faithfully able to predict the natural frequency of the plate based on the geometric parameters and support location. Originality/value This paper provides numerous new data on the vibration properties of the rectangular plate resting on rigid supports. Also, it provides a simple way to easily calculate the natural frequency of this plate problem, unlike the very limited and complicated analytical solutions available in literature.

Free Torsional Vibration Characteristics of a Closed-Form Planetary Gear Set

2013 ◽  
Vol 300-301 ◽  
pp. 1042-1047 ◽  
Author(s):  
Qi Lin Huang ◽  
Yong Wang ◽  
Zhi Pu Huo ◽  
Jun Gang Wang ◽  
Ruo Yu Sheng
Keyword(s):  
Free Vibration ◽  
Closed Form ◽  
Dynamic Model ◽  
Natural Frequency ◽  
Torsional Vibration ◽  
High Speed ◽  
Planetary Gear ◽  
Vibration Modes ◽  
Ring Gear ◽  
Natural Modes

A purely torsional dynamic model of closed-form planetary gear set is developed to investigate its natural frequency and free vibration modes. The closed-form planetary gear set considered consists of two-stage planetary gear connected by high-speed carrier and ring gear. Three identical planet gears are equally spaced in each stage. Based on the precondition, the natural modes are classified into three types of vibration modes: overall modes，high-speed planet mode and low-speed planet mode

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.

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