Perturbation Analysis and Parametric Study of Planetary Gear Vibration

2012 ◽  
Author(s):  
Cheon-Jae Bahk ◽  
Robert G. Parker
Keyword(s):  
Dynamic Response ◽  
Perturbation Analysis ◽  
Parametric Instability ◽  
Planetary Gear ◽  
Vibration Modes ◽  
Contact Ratio ◽  
System Parameters ◽  
Analysis System ◽  
The Impact ◽  
Perturbation Solutions

This study analytically investigates the impact of system parameters on planetary gear vibration by using perturbation solutions. Closed-form expressions, which explicitly includes the system parameters such as contact ratio, mesh stiffness, damping, and number of planets, of the peak resonant response amplitude and parametric instability width of subharmonic resonance are obtained from perturbation analysis. System parameters related with sun-planet and ring-planet meshes show different influence on dynamic response. The effects of the system parameters are found to be sensitive to vibration modes. With use of the well-defined planetary gear modal properties, mathematical expressions of the weighting factors are derived to quantify the different sensitivity of dynamic response to the sun-planet and ring-planet meshes and to the vibration modes. The perturbation solutions are effective to examine the dependence of dynamic response on the system parameters and help one seek optimal parameters to reduce planetary gear vibration.

Influence of the backlash generated by tooth accumulated wear on dynamic behavior of compound planetary gear set

2016 ◽  
Vol 231 (11) ◽  
pp. 2025-2041 ◽  
Author(s):  
Shijing Wu ◽  
Haibo Zhang ◽  
Xiaosun Wang ◽  
Zeming Peng ◽  
Kangkang Yang ◽  
...  
Keyword(s):  
Dynamic Response ◽  
Dynamic Model ◽  
Dynamic Behavior ◽  
Planetary Gear ◽  
Tooth Wear ◽  
Transmission Error ◽  
Gear Transmission ◽  
Tooth Surface ◽  
Contact Ratio ◽  
The Impact

Backlash is a key internal excitation on the dynamic response of planetary gear transmission. After the gear transmission running for a long time under load torque, due to tooth wear accumulation, the backlash between the tooth surface of two mating gears increases, which results in a larger and irregular backlash. However, the increasing backlash generated by tooth accumulated wear is generally neglected in lots of dynamics analysis for epicyclic gear trains. In order to investigate the impact of backlash generated by tooth accumulated wear on dynamic behavior of compound planetary gear set, in this work, first a static tooth surface wear prediction model is incorporated with a dynamic iteration methodology to get the increasing backlash generated by tooth accumulated wear for one pair of mating teeth under the condition that contact ratio equals to one. Then in order to introduce the tooth accumulated wear into dynamic model of compound planetary gear set, the backlash excitation generated by tooth accumulated wear for each meshing pair in compound planetary gear set is given under the condition that contact ratio equals to one and does not equal to one. Last, in order to investigate the impact of the increasing backlash generated by tooth accumulated wear on dynamic response of compound planetary gear set, a nonlinear lumped-parameter dynamic model of compound planetary gear set is employed to describe the dynamic relationships of gear transmission under the internal excitations generated by worn profile, meshing stiffness, transmission error, and backlash. The results indicate that the introduction of the increasing backlash generated by tooth accumulated wear makes a significant influence on the bifurcation and chaotic characteristics, dynamic response in time domain, and load sharing behavior of compound planetary gear set.

Effect of Ring-Planet Mesh Phasing and Contact Ratio on the Parametric Instabilities of a Planetary Gear Ring

2007 ◽  
Vol 130 (1) ◽  
Author(s):  
Sripathi Vangipuram Canchi ◽  
Robert G. Parker
Keyword(s):  
Parametric Excitation ◽  
Planetary Gear ◽  
Time Varying ◽  
Ring Gear ◽  
Contact Ratio ◽  
System Parameters ◽  
Gear Ring ◽  
Parametric Instabilities ◽  
Planetary Gear System ◽  
Mesh Phasing

Parametric excitation of a rotating ring subject to moving time-varying stiffnesses has previously been investigated and given as closed-form expressions in the system parameters. These conditions are applied to identify ring gear parametric instabilities in a planetary gear system. Certain mesh phasing and contact ratio conditions suppress parametric instabilities, and these conditions are presented with examples.

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.

Assessment of Workspace Attributes Under Simulated Index Finger Proximal Interphalangeal Arthrodesis

2016 ◽  
Vol 138 (5) ◽  
Author(s):  
Paul G. Arauz ◽  
Sue A. Sisto ◽  
Imin Kao
Keyword(s):  
Index Finger ◽  
Model Parameters ◽  
System Parameters ◽  
System A ◽  
Flexion Extension ◽  
Pip Joint ◽  
Interphalangeal Arthrodesis ◽  
Analysis System ◽  
The Impact ◽  
Proximal Interphalangeal Arthrodesis

This article presented an assessment of quantitative measures of workspace (WS) attributes under simulated proximal interphalangeal (PIP) joint arthrodesis of the index finger. Seven healthy subjects were tested with the PIP joint unconstrained (UC) and constrained to selected angles using a motion analysis system. A model of the constrained finger was developed in order to address the impact of the inclusion of prescribed joint arthrodesis angles on WS attributes. Model parameters were obtained from system identification experiments involving flexion–extension (FE) movements of the UC and constrained finger. The data of experimental FE movements of the constrained finger were used to generate the two-dimensional (2D) WS boundaries and to validate the model. A weighted criterion was formulated to define an optimal constraint angle among several system parameters. Results indicated that a PIP joint immobilization angle of 40–50 deg of flexion maximized the 2D WS. The analysis of the aspect ratio of the 2D WS indicated that the WS was more evenly distributed as the imposed PIP joint constraint angle increased. With the imposed PIP joint constraint angles of 30 deg, 40 deg, 50 deg, and 60 deg of flexion, the normalized maximum distance of fingertip reach was reduced by approximately 3%, 4%, 7%, and 9%, respectively.

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.

An Experimental Study of the Influence of Manufacturing Errors on the Planetary Gear Stresses and Planet Load Sharing

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
H. Ligata ◽  
A. Kahraman ◽  
A. Singh
Keyword(s):  
Experimental Study ◽  
Planetary Gear ◽  
Load Sharing ◽  
Position Errors ◽  
Manufacturing Errors ◽  
Time Histories ◽  
Analysis System ◽  
The Individual ◽  
Torque Values ◽  
The Impact

In this paper, results of an experimental study are presented to describe the impact of certain types of manufacturing errors on gear stresses and the individual planet loads of an n-planet planetary gear set (n=3–6). The experimental setup includes a specialized test apparatus to operate a planetary gear set under typical speed and load conditions and gear sets having tightly controlled intentional manufacturing errors. The instrumentation system consists of multiple strain gauges mounted on the ring gear and a multichannel data collection and analysis system. A method for computing the planet load-sharing factors from root strain-time histories is proposed. Influence of carrier pinhole position errors on gear root stresses is quantified for various error and torque values applied to gear sets having three to six planets. The results clearly indicate that manufacturing errors influence gear stresses and planet load sharing significantly. Gear sets having larger number of planets are more sensitive to manufacturing errors in terms of planet load-sharing behavior.

A Study on Planetary Gear Dynamics With Tooth Profile Modification

2011 ◽  
Author(s):  
Cheon-Jae Bahk ◽  
Robert G. Parker
Keyword(s):  
Dynamic Response ◽  
Gear Tooth ◽  
Planetary Gear ◽  
Transmission Error ◽  
Tooth Profile ◽  
Peak Amplitude ◽  
Profile Modification ◽  
Tooth Profile Modification ◽  
Static Transmission Error ◽  
The Impact

This study investigates the impact of tooth profile modification on planetary gear dynamic response. Micro-scale geometric deviations from an involute gear tooth profile add an additional excitation source, potentially reducing gear vibration. In order to take account of the excitation, tooth profile modification is included in an analytical planetary gear model. Nonlinearity due to tooth contact loss is considered. Time-varying mesh stiffness and both rotational and translational gear motions are modeled. The accuracy of the proposed model for dynamic analysis is correlated against a benchmark finite element analysis. Perturbation analysis is employed to obtain a closed-form approximation of planetary gear dynamic response with tooth profile modification. Mathematical expressions from the perturbation solution allow one to easily estimate the peak amplitude of resonant response using known parameters. Variation of the peak amplitude with the amount and the length of profile modification illustrates the effect of tooth profile modification on planetary gear dynamic response. For a given external load, the tooth profile modification parameters for minimal response are readily obtained. Static transmission error and dynamic response are minimized at different amounts of profile modification, which contradicts common practical thinking regarding strong correlation between static transmission error and dynamic response. Contrary to the expectation of further reduced vibration, the combination of the optimum sun-planet and ring-planet mesh tooth profile modifications that minimizes response when applied individually increases dynamic response.

The Homotopy Analysis for the Nonlinear Dynamics of Planetary Gear Trains

2018 ◽  
Author(s):  
Chao Xun ◽  
Sujuan Jiao ◽  
Yong Chen ◽  
Xinhua Long
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Response ◽  
Nonlinear Problems ◽  
Planetary Gear ◽  
Displacement Function ◽  
Strongly Nonlinear ◽  
Planetary Gear Trains ◽  
Homotopy Analysis ◽  
Gear Trains ◽  
The Impact

In this paper, the homotopy analysis method (HAM) is proposed to study the nonlinear oscillators of planetary gear trains, in which the periodically time-varying mesh stiffness and gear backlash are included through a nonlinear displacement function. In contrast to the traditional perturbation methods, the HAM does not require a small parameter in the equation under study, and then can be applied to both of the weakly and strongly nonlinear problems. In this article, firstly the closed-form approximations for the dynamic response of planetary gear trains are obtained by HAM. The analytical solutions give insight into the nonlinear dynamics and the impact of system parameters on dynamic response. The accuracy of HAM solutions is evaluated by numerical integration simulations. Results indicate that with large tooth separation times, the amplitude-frequency curves obtained by HAM agree better with the results obtained by NI than those obtained by the MMS.

Vibration Resonances in a Planetary Gear Ring: Effects of Mesh Phasing and Contact Ratio

2007 ◽  
Author(s):  
Sripathi Vangipuram Canchi ◽  
Robert G. Parker
Keyword(s):  
Parametric Excitation ◽  
Planetary Gear ◽  
Time Varying ◽  
Ring Gear ◽  
Contact Ratio ◽  
System Parameters ◽  
Gear Ring ◽  
Parametric Instabilities ◽  
Planetary Gear System ◽  
Mesh Phasing

Parametric excitation of a rotating ring subject to moving time-varying stiffnesses have previously been investigated and given as closed form expressions in the system parameters. These conditions are applied to identify ring gear parametric instabilities in a planetary gear system. Certain mesh phasing and contact ratio conditions suppress parametric instabilities, and these conditions are presented with examples.

An Experimental Investigation of the Influence of Manufacturing Errors on the Planetary Gear Stresses and Load Sharing

2007 ◽  
Author(s):  
Haris Ligata ◽  
Ahmet Kahraman ◽  
Avinash Singh
Keyword(s):  
Planetary Gear ◽  
Load Sharing ◽  
Position Errors ◽  
Manufacturing Errors ◽  
Time Histories ◽  
Analysis System ◽  
Set Up ◽  
The Individual ◽  
Torque Values ◽  
The Impact

In this paper, results of an experimental study are presented to describe the impact of certain types of manufacturing errors on gear stresses and the individual planet loads of an n-planet planetary gear set (n = 3 to 6). The experimental set-up includes a specialized test apparatus to operate a planetary gear set under typical speed and load conditions and gear sets having tightly controlled intentional manufacturing errors. The instrumentation system consists of multiple strain gauges mounted on the ring gear and a multi-channel data collection and analysis system. A method for computing the planet load sharing factors from root strain time histories is proposed. Influence of carrier pinhole position errors on gear root stresses are quantified for various error and torque values applied to gear sets having 3 to 6 planets. The results clearly indicate that manufacturing errors influence gear stresses and planet load sharing significantly. Gear sets having larger number of planets are more sensitive to manufacturing errors in terms of planet load sharing behavior.

Sign in / Sign up

Export Citation Format

Share Document