Nonlinear Dynamics of Planetary Gears Using Analytical and Finite Element Models

2007 ◽  
Author(s):  
Robert G. Parker ◽  
Vijaya Kumar Ambarisha
Keyword(s):  
Finite Element ◽  
Period Doubling ◽  
Element Model ◽  
Lumped Parameter Model ◽  
Finite Element Models ◽  
Two Dimensional ◽  
Tooth Contact ◽  
Planetary Gears ◽  
Lumped Parameter ◽  
Mesh Phasing

Vibration induced gear noise and dynamic loads remain key concerns in many transmission applications that use planetary gears. Tooth separations at large vibrations introduce nonlinearity in geared systems. The present work examines the complex, nonlinear dynamic behavior of spur planetary gears using two models: (i) a lumped-parameter model, and (ii) a finite element model. The two-dimensional lumped-parameter model represents the gears as lumped inertias, the gear meshes as nonlinear springs with tooth contact loss and periodically varying stiffness due to changing tooth contact conditions, and the supports as linear springs. The two-dimensional finite element model is developed from a unique finite elementcontact analysis solver specialized for gear dynamics. Mesh stiffness variation excitation, corner contact, and gear tooth contact loss are all intrinsically considered in the finite element analysis. The dynamics of planetary gears show a rich spectrum of nonlinear phenomena. Nonlinear jumps, chaotic motions, and period-doubling bifurcations occur when the mesh frequency or any of its higher harmonics are near a natural frequency of the system. Responses from the dynamic analysis using analytical and finite element models are successfully compared qualitatively and quantitatively. These comparisons validate the effectiveness of the lumped-parameter model to simulate the dynamics of planetary gears. Mesh phasing rules to suppress rotational and translational vibrations in planetary gears are valid even when nonlinearity from tooth contact loss occurs. These mesh phasing conclusions, however, are not valid in the chaotic and period-doubling regions.

scholarly journals Analysis of Fly Fishing Rod Casting Dynamics

2011 ◽  
Vol 18 (6) ◽  
pp. 839-855
Author(s):  
Gang Wang ◽  
Norman Wereley
Keyword(s):  
Finite Element ◽  
Initial Boundary ◽  
Element Model ◽  
Nonlinear Finite Element ◽  
Lumped Parameter Model ◽  
Parameter Method ◽  
Line System ◽  
Fly Fishing ◽  
Lumped Parameter ◽  
Rigid Rod

An analysis of fly fishing rod casting dynamics was developed comprising of a nonlinear finite element representation of the composite fly rod and a lumped parameter model for the fly line. A nonlinear finite element model was used to analyze the transient response of the fly rod, in which fly rod responses were simulated for a forward casting stroke. The lumped parameter method was used to discretize the fly line system. Fly line motions were simulated during a cast based on fly rod tip response, which was used as the initial boundary condition for the fly line. Fly line loop generation, propagation, and line turn-over were simulated numerically. Flexible rod results were compared to the rigid rod case, in which the fly tip path was prescribed by a given fly rod butt input. Our numerical results strongly suggest that nonlinear flexibility effects on the fly rod must be included in order to accurately simulate casting dynamics and associated fly line motion.

Influence of assembly error and bearing elasticity on the dynamics of spur gear pair

2015 ◽  
Vol 230 (11) ◽  
pp. 1805-1818 ◽  
Author(s):  
Jianhong Wang ◽  
Jian Wang ◽  
Teik C Lim
Keyword(s):  
Finite Element ◽  
Dynamic Behavior ◽  
Transmission Error ◽  
Spur Gear ◽  
Lumped Parameter Model ◽  
Gear Pair ◽  
Tooth Contact ◽  
Lumped Parameter ◽  
Bearing Stiffness ◽  
Assembly Error

The elasticity and geometrical errors of precision elements are one of the major factors affecting vibration responses in geared transmission systems. In this study, the influences of assembly error and bearing elasticity on the spur gear dynamic behavior are analyzed. A lumped parameter model for spur gear pair is formulated by representing the bearing elasticity with infinitesimal spring elements and tooth stiffness time function as rectangular waveform. The nonuniform tooth contact load is also considered. The severity of assembly error is assumed to be sufficiently small such that no partial loss of tooth contact occurs. A harmonic balance method is applied to the resultant second-order partial differential equation governing the gear pair dynamic behavior. The variations of dynamic transmission error and tooth contact load with respect to mesh frequency for a set of bearing stiffness are analyzed. The influences of bearing stiffness on the dynamic transmission error are also evaluated. The variation of actual cross angle, an indicator on the tooth meshing state, is examined with respect to nominal cross angle and bearing stiffness. The analysis shows that the presence of bearing elasticity and assembly error can degenerate tooth contact significantly, and hence the appropriate specifications of bearing and mesh stiffness are critical at gearbox design stage. The analysis demonstrates that the proposed lumped parameter model can provide detailed contact information like finite element model, but it avoids finite element model’s prohibitive computation burden and can be completed easily and be computed quickly.

scholarly journals Estimation of Optimal Values for Lumped Elements in a Finite Element — Lumped Parameter Model of a Loudspeaker

2020 ◽  
Vol 28 (02) ◽  
pp. 2050012
Author(s):  
Daniel Gert Nielsen ◽  
Peter Risby Andersen ◽  
Jakob Søndergaard Jensen ◽  
Finn Thomas Agerkvist
Keyword(s):  
Finite Element ◽  
Element Model ◽  
Lumped Parameter Model ◽  
Model Complexity ◽  
Fe Model ◽  
High Frequencies ◽  
Lumped Parameter ◽  
Lumped Elements ◽  
Optimal Values ◽  
Very High Frequencies

Finite element methods are progressively being utilized to assist in the continuous development of loudspeakers. The core of this paper is the method of lumping certain parts of the finite element model, creating a significant reduction in the model complexity that allows for e.g. faster structural optimization. This is illustrated in the paper with a loudspeaker example where the electromagnetic parts are lumped as well as the spider. It is shown that the simplified model still matches the complex response of the full FE model at very high frequencies.

scholarly journals Influence of the Preformed Coil Design on the Thermal Behavior of Electric Traction Machines

Energies ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 959
Author(s):  
Benedikt Groschup ◽  
Florian Pauli ◽  
Kay Hameyer
Keyword(s):  
Finite Element ◽  
Fill Factor ◽  
Test Bench ◽  
Simulation Models ◽  
Lumped Parameter Model ◽  
Finite Element Models ◽  
Lumped Parameter ◽  
Detailed Simulation ◽  
Electric Traction ◽  
Heat Transition

Preformed coils are used in electrical machines to improve the copper slot fill factor. A higher utilization of the machine can be realized. The improvement is a result of both, low copper losses due to the increased slot fill factor and an improved heat transition out of the slot. In this study, the influence of these two aspects on the operational improvement of the machine is studied. Detailed simulation models allow a separation of the two effects. A preform wound winding in comparison to a round wire winding is studied. Full machine prototypes as well as motorettes of the two designs are built up. Thermal finite element models of the stator slot are developed and parameterized with the help of motorette microsections. The resulting thermal lumped parameter model is enlarged to represent the entire electric machine. Electromagnetic finite element models for loss calculation and the thermal lumped parameter models are parameterized using test bench measurements. The developed models show very good agreement in comparison to the test bench evaluation. The study indicates that both, the improvements in the heat transition path and the advantages of the reduced losses in the slot contribute to the improved operational range in dependency of the studied operational point.

Hybrid Dynamic Modeling and Analysis of High-speed Thin-rimmed Gears

2021 ◽  
pp. 1-23
Author(s):  
Changzhao Liu ◽  
Yu Zhao ◽  
Yong Wang ◽  
Tie Zhang ◽  
Hanjie Jia
Keyword(s):  
Finite Element ◽  
Dynamic Model ◽  
High Speed ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Lumped Parameter Model ◽  
Modeling And Analysis ◽  
Lumped Parameter ◽  
Proposed Model ◽  
Angular Displacements

Abstract In this study, a hybrid dynamic model of high-speed thin-rimmed gears is developed. In this model, the translational and angular displacements (including the rigid and vibration displacements) with a total of six degrees of freedom (DOFs) are selected as the generalized coordinates for each gear, and the meshing force distributions along the contact line and between the teeth are considered. Thus, the model can be implemented under stationary and non-stationary conditions. The condensed finite element models are developed with the centrifugal and inertia forces for gear bodies. This paper proposes a novel method to couple the lumped parameter model and condensed finite element model for the hybrid dynamic model system, which considers the variation of the meshing tooth during the gear operation, namely, the variations of the acting point of meshing force. Based on the model, the dynamic analysis of high-speed thin-rimmed gears is conducted under stationary speed and acceleration processes. The effects of the flexible gear body, high speed, and tooth errors on the system dynamics and tooth load distribution are investigated. The analysis results are also compared with the current reference and pure finite element method to validate the proposed model.

An Assessed Model for the Vibro-Acoustic Analysis of Gear Pumps

2013 ◽  
Author(s):  
Emiliano Mucchi ◽  
Giorgio Dalpiaz
Keyword(s):  
Finite Element ◽  
Boundary Element ◽  
Acoustic Analysis ◽  
Simulated Data ◽  
Element Model ◽  
Lumped Parameter Model ◽  
Fe Model ◽  
Gear Pump ◽  
Operational Conditions ◽  
Lumped Parameter

In this work a combined model for the vibro-acoustic analysis of an external gear pump for automotive applications is presented and experimentally assessed. The model includes a lumped-parameter model, a finite-element model and a boundary-element model. The lumped-parameter (LP) model regards the interior parts of the pump (bearing blocks and gears), the finite element (FE) model regards the external parts of the pump (casing and end plates), while the boundary element (BE) model estimates the noise generation in operational conditions. Attention has been devoted to the inclusion of the oil effect inside the pump casing: the fluid-structure interaction between oil and pump casing was taken into account. The model has been assessed using experiments: the experimental accelerations and acoustic pressure measured in operational conditions have been compared with the simulated data coming from the combined LP/FE/BE model. Eventually, model results and limitations are presented.

Dynamic Analysis of Planetary Gears With Bearing Clearance

2012 ◽  
Vol 7 (4) ◽  
Author(s):  
Yi Guo ◽  
Robert G. Parker
Keyword(s):  
Harmonic Balance Method ◽  
Period Doubling ◽  
Nonlinear Behavior ◽  
Nonlinear Effects ◽  
Lumped Parameter Model ◽  
Solution Stability ◽  
Planetary Gears ◽  
Gear Mesh ◽  
Bearing Clearance ◽  
Lumped Parameter

This study investigates the dynamics of planetary gears where nonlinearity is induced by bearing clearance. Lumped-parameter and finite element models with bearing clearance, tooth separation, and gear mesh stiffness variation are developed. The harmonic balance method with arc length continuation is applied to the lumped-parameter model to obtain the dynamic response. Solution stability is analyzed using Floquet theory. Rich nonlinear behavior is exhibited, consisting of nonlinear jumps, a hardening effect induced by the transition from no bearing contact to contact, and softening induced by tooth separation. Bearings of the central members (sun, carrier, and ring) impact against the bearing races near resonances, which leads to coexisting solutions in wide speed ranges, grazing bifurcation, and chaos. Secondary Hopf and period-doubling bifurcations are the routes to chaos. Input torque can suppress some of the nonlinear effects caused by bearing clearance.

Contrastive Study on Finite Element Models of High-Strength Pipelines Crossing Active Faults

2016 ◽  
Vol 850 ◽  
pp. 957-964
Author(s):  
Wei Zheng ◽  
Hong Zhang ◽  
Xiao Ben Liu ◽  
Le Cai Liang ◽  
Yin Shan Han
Keyword(s):  
Finite Element ◽  
Design Method ◽  
Active Faults ◽  
Shell Element ◽  
High Strength ◽  
Element Model ◽  
Beam Element ◽  
Finite Element Models ◽  
Fixed Boundary ◽  
Equivalent Boundary

There is a potential for major damage to the pipelines crossing faults, therefore the strain-based design method is essential for the design of buried pipelines. Finite element models based on soil springs which are able to accurately predict pipelines’ responses to such faulting are recommended by some international guidelines. In this paper, a comparative analysis was carried out among four widely used models (beam element model; shell element model with fixed boundary; shell element model with beam coupled; shell element model with equivalent boundary) in two aspects: differences of results and the efficiency of calculation. The results show that the maximum and minimum strains of models coincided with each other under allowable strain and the calculation efficiency of beam element model was the highest. Besides, the shell element model with beam coupled or equivalent boundary provided the reasonable results and the calculation efficiency of them were higher than the one with fixed boundary. In addition, shell element model with beam coupled had a broader applicability.

Elasto-Plastic Coupled Temperature-Displacement Finite Element Analysis of Two-Dimensional Rolling-Sliding Contact With a Translating Heat Source

1991 ◽  
Vol 113 (1) ◽  
pp. 93-101 ◽  
Author(s):  
S. M. Kulkarni ◽  
C. A. Rubin ◽  
G. T. Hahn
Keyword(s):  
Finite Element ◽  
Half Space ◽  
Plastic Material ◽  
Element Model ◽  
Rolling Contact ◽  
Two Dimensional ◽  
Element Analysis ◽  
Element Mesh ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

The present paper, describes a transient translating elasto-plastic thermo-mechanical finite element model to study 2-D frictional rolling contact. Frictional two-dimensional contact is simulated by repeatedly translating a non-uniform thermo-mechanical distribution across the surface of an elasto-plastic half space. The half space is represented by a two dimensional finite element mesh with appropriate boundaries. Calculations are for an elastic-perfectly plastic material and the selected thermo-physical properties are assumed to be temperature independent. The paper presents temperature variations, stress and plastic strain distributions and deformations. Residual tensile stresses are observed. The magnitude and depth of these stresses depends on 1) the temperature gradients and 2) the magnitudes of the normal and tangential tractions.

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