A hybrid model to study the effect of tooth lead modifications on the dynamic behavior of double helical planetary gears

2019 ◽  
Vol 233 (21-22) ◽  
pp. 7224-7235
Author(s):  
Stéphane Portron ◽  
Philippe Velex ◽  
Vincent Abousleiman
Keyword(s):  
Dynamic Behavior ◽  
Hybrid Model ◽  
Load Distribution ◽  
Element Model ◽  
Ring Gear ◽  
Planetary Gears ◽  
Lumped Parameter ◽  
Lumped Parameter Models ◽  
Lumped Parameters ◽  
Planet Carrier

In this paper, a hybrid model is used to investigate the dynamic behavior of planetary gears. Sun-gear, planets, and ring-gear are modeled using lumped parameters elements, while planet carrier is integrated via a condensed finite element model. This approach intends to be more precise than the traditional lumped parameter models while keeping acceptable computational times. In some aeronautical applications, tooth lead modifications can be necessary to counterbalance the effect of planet carrier deflections on tooth load distribution. This study focuses on the influence of various lead modifications on the dynamic behavior of double helical planetary gears over a broad range of loads.

The Dynamic Behavior Research of Coupling Shafts in Tufted Carpet Looms

2013 ◽  
Vol 427-429 ◽  
pp. 142-145
Author(s):  
Zhi Jun Sun ◽  
Yang Xu ◽  
Shuang Huang ◽  
Yi Ze Sun
Keyword(s):  
Dynamic Behavior ◽  
Transfer Matrix ◽  
Natural Frequencies ◽  
Elastic Support ◽  
Behavior Model ◽  
Lumped Parameter ◽  
Lumped Parameter Models ◽  
Lumped Masses ◽  
Parts Transfer ◽  
The Relationship

Firstly, based on the structure of tufted carpet looms (DHGN801D-400), the lumped parameter models were built, in which included the massless shafts, lumped masses, disk and elastic support. Secondly, according to various parts of the relationship between force and deformation, the transfer matrix of right and left ends were established, thus the universal transfer matrix of shaft units was determined by solving the various parts transfer matrix simultaneously. Thirdly, the dynamic behavior model of coupling shafts in tufted carpet looms was given, and different natural frequencies were acquired by simulating the model in Matlab. Lastly, the dynamic behavior model using transfer matrix was verified to be effective and feasible by experiment.

Reliability of parameter estimates from models applied to respiratory impedance data

1987 ◽  
Vol 62 (2) ◽  
pp. 403-413 ◽  
Author(s):  
K. R. Lutchen ◽  
A. C. Jackson
Keyword(s):  
Random Noise ◽  
Element Model ◽  
Parameter Estimates ◽  
Frequency Range ◽  
High Frequencies ◽  
Estimated Parameters ◽  
Impedance Data ◽  
Lumped Parameter ◽  
Lumped Parameter Models ◽  
Very High Frequencies

Many previous studies have fit lumped parameter models to respiratory input (Zin) and transfer (Ztr) impedance data. For frequency ranges higher than 4–32 Hz, a six-element model may be required in which an airway branch (with a resistance and inertance) is separated from a tissue branch (with a resistance, inertance, and compliance) by a shunt compliance. A sensitivity analysis is applied to predict the effects of frequency range on the accuracy of parameter estimates in this model obtained from Zin or Ztr data. Using a parameter set estimated from experimental data between 4 and 64 Hz in dogs, both Zin and Ztr were simulated from 4 to 200 Hz. Impedance sensitivity to each parameter was also calculated over this frequency range. The simulation predicted that for Zin a second resonance occurs near 80 Hz and that the impedance is considerably more sensitive to several of the parameters at frequencies surrounding this resonance than at any other frequencies. Also, unless data is obtained at very high frequencies (where the model is suspect), Zin data provides more accurate estimates than Ztr data. After adding random noise to the simulated Zin data, we attempted to extract the original parameters by using a nonlinear regression applied to three frequency ranges: 4–32, 4–64, and 4–110 Hz. Estimated parameters were substantially incorrect when using only 4- to 32-Hz or 4- to 64-Hz data, but nearly correct when fitting 4- to 110-Hz data. These results indicate that respiratory system parameters can be more accurately extracted from Zin than Ztr, and to make physiological inferences from parameter estimates based on Zin impedance data in dogs, the data must include frequencies surrounding the second resonance.

Research on Stress and Load with the Effect of Number of Teeth Planetary Gears Matching

2014 ◽  
Vol 1014 ◽  
pp. 120-123
Author(s):  
Zhi Qiang Xu ◽  
Jian Huang
Keyword(s):  
Load Distribution ◽  
Planetary Gear ◽  
Element Model ◽  
Strength Analysis ◽  
Planetary Gears ◽  
Planetary Gear Trains ◽  
Number Of Teeth ◽  
Capacity Calculation ◽  
Gear Trains ◽  
Planetary Transmission

Impact of number of tooth matching to load distribution of planetary gears is mainly investigated in this paper. The entire finite element model of planetary gear trains is established so as to analyze and calculate gear stress and number of tooth matching have an impact on load distribution homogeneity of planetary gears on the rated load working conditions. A new method of number of teeth design of planetary gear trains is put forward that number of teeth of sun wheel and number of teeth of gear ring are multiples as great as numbers of planetary gears. Load uneven coefficient of the example is proposed and solved, which provides theoretical basis on carrying capacity calculation, strength analysis and calculation of fatigue life of planetary transmission.

A Lumped Parameter Approach for Analysing a Metamaterial Beam Based Piezoelectric Energy Harvester Around Fundamental Resonance

2020 ◽  
Author(s):  
Guobiao Hu ◽  
Lihua Tang ◽  
Yaowen Yang
Keyword(s):  
Mode Shape ◽  
Fundamental Mode ◽  
Reaction Force ◽  
Element Model ◽  
Static Deflection ◽  
Lumped Parameter ◽  
Lumped Parameters ◽  
Mass Spring ◽  
Parameter Approach

Abstract This paper proposes a lumped parameter approach to simplify the modelling of a metamaterial based PEH to predict its energy harvesting performance around the fundamental resonance. The metamaterial based PEH consists of a host beam with a piezoelectric patch bonded at the clamped end. A series of local resonators are attached onto the host beam. In the first case study, the local resonators are modelled as mass-spring systems. By applying Rayleigh’s method and approximating the fundamental mode shape by the static deflection, the host beam is represented by a SDOF system. The equivalent lumped parameters are assumed to concentrate at the tip of the host beam and their explicit expressions are presented. Though the local resonators are identical, they have different influences on the host beam when being attached at different positions. To reflect the interaction degree (i.e., reacting force) between the local resonator and the host beam, a scaling factor that is a function of the attaching position is derived. On the other hand, due to the action of the local resonators, the fundamental mode shape of the host beam is actually changed. Based on the linear superposition principle, the static deflection approximated fundamental mode shape is corrected and the electromechanical coupling coefficient that is sensitive to the slope of the mode shape is updated to improve the accuracy. Based on the derived equivalent lumped parameters and correction factors, a multiple-degree-of-freedom (MDOF) model is constructed to predict the dynamic behavior of the metamaterial based PEH with mass-spring resonators. A corresponding finite element model is built to verify the developed MDOF model. In the second case study, the local resonators are modelled as practical parasitic beams. The parasitic beams are converted into equivalent lumped systems as well. However, the lumped parameters are the effective parameters at the beam tip. For the force interaction at the root of a parasitic beam, a factor is derived to correct the reaction force when a parasitic beam is represented by a SDOF mass-spring system. Using the reaction force correction factor, a MDOF model for the metamaterial based PEH with beam-like resonators is also established and verified by the finite element model.

scholarly journals The Analysis and Modeling of the Synthetical Meshing Stiffness of Inner Gearing considering the Flexible Inner Ring Gear

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Shengyang Hu ◽  
Zongde Fang
Keyword(s):  
Planetary Gear ◽  
Element Model ◽  
Transmission System ◽  
Lumped Parameter Model ◽  
Ring Gear ◽  
Gear Teeth ◽  
Meshing Stiffness ◽  
Lumped Parameter ◽  
Sectional Shape ◽  
The Finite Element Model

As a key part of vibration generation and transmission of planetary gear transmissions, thin-walled inner ring gear deforms under the influence of meshing excitation and seriously affects the reliability and fatigue life of the transmission system. The effect of the flexibility of the inner ring gear on the transmission system is ignored in the calculation of making the inner ring gear as a rigid body in the lumped parameter model, while the calculation amount of the finite element model is too large. Therefore, it is very important to establish an accurate and reasonable model to solve the flexibility of the inner ring gear. In this paper, according to the supporting mode, supporting quantity, thickness, and sectional shape of the inner ring gear, the inner ring gear is reasonably separated into the form of multisection curved beam. The displacement of the gear teeth in the meshing line caused by the flexibility of the inner ring gear is obtained rapidly and accurately. It lays an important theoretical foundation for the dynamic analysis of planetary gear transmission.

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.

Dynamic Response of Beams With Lumped Parameters

1965 ◽  
Vol 32 (2) ◽  
pp. 453-454 ◽  
Author(s):  
Robert K. Wen
Keyword(s):  
Dynamic Response ◽  
Elastic Beam ◽  
Lumped Mass ◽  
Lumped Parameter ◽  
Lumped Parameter Models ◽  
Lumped Parameters

The dynamic response of two lumped-parameter models for an elastic beam is considered. It is shown that, as compared to the beam with continuous properties, the model of lumped flexibility yields response that is too high, and the model of lumped mass yields response that is too low.

Study of the Lumped Parameter Models and Parameters Identification of Hydraulic Bushing

2013 ◽  
Vol 321-324 ◽  
pp. 1805-1811
Author(s):  
Lin Li
Keyword(s):  
Dynamic Behavior ◽  
Parameters Identification ◽  
Computation Method ◽  
Digital Computation ◽  
System Parameters ◽  
Lumped Parameter ◽  
Development Cycle ◽  
Lumped Parameter Models ◽  
Lp Model

This article proposes two types of Lumped parameter models for the hydraulic bushing. Digital computation method is used to estimate the system parameters of LP model, provides a new way to reduce development cycle of hydro bushing. Two results of hydro-bushing dynamic behavior using two LP models are compared and analyzed. This article provides more channel to analyze the operation principle of the hydraulic bushing.

scholarly journals A computationally efficient hybrid 2D–3D subwoofer model

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Ahmad H. Bokhari ◽  
Martin Berggren ◽  
Daniel Noreland ◽  
Eddie Wadbro
Keyword(s):  
Hybrid Model ◽  
3D Model ◽  
Element Model ◽  
Acoustic Properties ◽  
Computational Time ◽  
Average Response ◽  
Frequency Range ◽  
Computationally Efficient ◽  
Lumped Element ◽  
Lumped Element Model

AbstractA subwoofer generates the lowest frequency range in loudspeaker systems. Subwoofers are used in audio systems for live concerts, movie theatres, home theatres, gaming consoles, cars, etc. During the last decades, numerical simulations have emerged as a cost- and time-efficient complement to traditional experiments in the design process of different products. The aim of this study is to reduce the computational time of simulating the average response for a given subwoofer design. To this end, we propose a hybrid 2D–3D model that reduces the computational time significantly compared to a full 3D model. The hybrid model describes the interaction between different subwoofer components as interacting modules whose acoustic properties can partly be pre-computed. This allows us to efficiently compute the performance of different subwoofer design layouts. The results of the hybrid model are validated against both a lumped element model and a full 3D model over a frequency band of interest. The hybrid model is found to be both accurate and computationally efficient.

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