An Analytical Approach to Tooth Friction Losses in Spur and Helical Gears—Influence of Profile Modifications

2009 ◽  
Vol 131 (10) ◽  
Author(s):  
P. Velex ◽  
F. Ville
Keyword(s):  
Numerical Simulations ◽  
Analytical Approach ◽  
Tooth Profile ◽  
Design Stage ◽  
Power Losses ◽  
Helical Gears ◽  
Friction Power ◽  
Wide Range ◽  
Analytical Formulas ◽  
Displacement Based

An original displacement-based formulation of tooth friction power losses in spur and helical gears is established, which can account for the influence of tooth profile modifications. Several analytical formulas are derived enabling friction losses to be easily estimated for a wide range of gears at the design stage. Numerous comparisons with both the classic formulas in the literature and the results of numerical simulations are presented, which confirm the accuracy of the proposed approach.

CAD and Optimization of Spur and Helical Gear Sets

1996 ◽  
Author(s):  
Sayed M. Metwalli ◽  
Ehab A. El Danaf
Keyword(s):  
Computer Aided Design ◽  
Full Range ◽  
Optimization Techniques ◽  
Design Stage ◽  
Helical Gears ◽  
Face Width ◽  
Optimum Parameters ◽  
Number Of Teeth ◽  
Wide Range ◽  
The Face

Abstract The present work is an application of Computer Aided Design and optimization techniques to solve the problem of designing a pair of gears. The CAD programs have the initial freedom to change the design variables: the module, the number of teeth, the face width, and the material through a data base display, and a full detailed design stage that applies the AGMA bending and contact number checking criteria, and the bending fatigue strength and the surface endurance strength criteria. Other programs are also linked to optimize spur gears under the objective of minimizing the volume. The design vector is taken to be the module, the number of teeth, and the face width, with the interaction between bending and contact stress constraints. These programs were utilized to study the behavior of the optimum parameters for a full range of cases. Charts of the optimum results are plotted. For optimizing helical gears, the design vector is taken as the module, the number of teeth, the face width, and the helix angle. A comparison is made between values of the objective function and optimum parameters for spur and helical gears for a wide range of cases. A comparison is also made of the results with other previous works of optimization and proved that the approach presented here gives better optimum results for the same loading case.

An approach of calculation on sliding friction power losses in involute helical gears with modification

2015 ◽  
Vol 230 (9) ◽  
pp. 1521-1531 ◽  
Author(s):  
Cheng Wang ◽  
Huan Yong Cui ◽  
Qing Ping Zhang ◽  
Wen Ming Wang
Keyword(s):  
Sliding Friction ◽  
Tooth Surface ◽  
Surface Load ◽  
Power Losses ◽  
Tooth Contact Analysis ◽  
Helical Gears ◽  
Friction Power ◽  
Transmission Errors ◽  
Normal Forces ◽  
Load Distributions

Sliding friction between the teeth is recognized as one of the main reasons of power losses in transmission as well as a potential reason of vibration and noise. A new approach is proposed to accurately calculate the sliding friction power losses in involute helical gears considered modification and geometric deviations resulting from the manufacturing processes, assembly errors, and deflections of support structures based on the simulation of gear mesh under light and significant load. Firstly, the paths of contact points on the pinion tooth surface are obtained from tooth contact analysis. Tooth surface load distributions and loaded transmission errors in one mesh period are obtained from loaded tooth contact analysis. Secondly, tooth surface load distributions are converted into the normal forces of tooth surface points of contact, loaded transmission errors are brought to the calculation formulas of sliding velocity, and the sliding friction coefficients of tooth surface points of contact are calculated by a non-Newtonian thermal elastohydrodynamic lubrication model. Substituting the sliding velocities, the normal forces, and the sliding friction coefficients into the power calculation formulas gives the sliding friction power losses of tooth surface points of contact. By the soft MATLAB, the values of the sliding friction power losses are integrated and the sliding friction power loss in helical gears from engagement to disengagement is obtained. Finally, an example of this approach is shown in the end. The results indicate that it is very necessary to consider the influence of loaded transmission errors for calculation of sliding friction power losses.

scholarly journals The Impact of Initial Conditions in N-Body Simulations of Debris Discs

2015 ◽  
Vol 32 ◽  
Author(s):  
E. Thilliez ◽  
S. T. Maddison
Keyword(s):  
Numerical Simulations ◽  
Initial Conditions ◽  
Parent Body ◽  
Dust Trapping ◽  
Physical Context ◽  
Disc Width ◽  
Wide Range ◽  
Belt Width ◽  
New Generation ◽  
The Impact

AbstractNumerical simulations are a crucial tool to understand the relationship between debris discs and planetary companions. As debris disc observations are now reaching unprecedented levels of precision over a wide range of wavelengths, an appropriate level of accuracy and consistency is required in numerical simulations to confidently interpret this new generation of observations. However, simulations throughout the literature have been conducted with various initial conditions often with little or no justification. In this paper, we aim to study the dependence on the initial conditions of N-body simulations modelling the interaction between a massive and eccentric planet on an exterior debris disc. To achieve this, we first classify three broad approaches used in the literature and provide some physical context for when each category should be used. We then run a series of N-body simulations, that include radiation forces acting on small grains, with varying initial conditions across the three categories. We test the influence of the initial parent body belt width, eccentricity, and alignment with the planet on the resulting debris disc structure and compare the final peak emission location, disc width and offset of synthetic disc images produced with a radiative transfer code. We also track the evolution of the forced eccentricity of the dust grains induced by the planet, as well as resonance dust trapping. We find that an initially broad parent body belt always results in a broader debris disc than an initially narrow parent body belt. While simulations with a parent body belt with low initial eccentricity (e ~ 0) and high initial eccentricity (0 < e < 0.3) resulted in similar broad discs, we find that purely secular forced initial conditions, where the initial disc eccentricity is set to the forced value and the disc is aligned with the planet, always result in a narrower disc. We conclude that broad debris discs can be modelled by using either a dynamically cold or dynamically warm parent belt, while in contrast eccentric narrow debris rings are reproduced using a secularly forced parent body belt.

scholarly journals A broadbanded pressure differential wave energy converter based on dielectric elastomer generators

2021 ◽  
Author(s):  
Michele Righi ◽  
Giacomo Moretti ◽  
David Forehand ◽  
Lorenzo Agostini ◽  
Rocco Vertechy ◽  
...  
Keyword(s):  
Wave Energy ◽  
Large Deformations ◽  
Dielectric Elastomer ◽  
Wave Energy Converter ◽  
Pressure Differential ◽  
Design Stage ◽  
Small Scale ◽  
Energy Converter ◽  
Wide Range ◽  
The Waves

AbstractDielectric elastomer generators (DEGs) are a promising option for the implementation of affordable and reliable sea wave energy converters (WECs), as they show considerable promise in replacing expensive and inefficient power take-off systems with cheap direct-drive generators. This paper introduces a concept of a pressure differential wave energy converter, equipped with a DEG power take-off operating in direct contact with sea water. The device consists of a closed submerged air chamber, with a fluid-directing duct and a deformable DEG power take-off mounted on its top surface. The DEG is cyclically deformed by wave-induced pressure, thus acting both as the power take-off and as a deformable interface with the waves. This layout allows the partial balancing of the stiffness due to the DEG’s elasticity with the negative hydrostatic stiffness contribution associated with the displacement of the water column on top of the DEG. This feature makes it possible to design devices in which the DEG exhibits large deformations over a wide range of excitation frequencies, potentially achieving large power capture in a wide range of sea states. We propose a modelling approach for the system that relies on potential-flow theory and electroelasticity theory. This model makes it possible to predict the system dynamic response in different operational conditions and it is computationally efficient to perform iterative and repeated simulations, which are required at the design stage of a new WEC. We performed tests on a small-scale prototype in a wave tank with the aim of investigating the fluid–structure interaction between the DEG membrane and the waves in dynamical conditions and validating the numerical model. The experimental results proved that the device exhibits large deformations of the DEG power take-off over a broad range of monochromatic and panchromatic sea states. The proposed model demonstrates good agreement with the experimental data, hence proving its suitability and effectiveness as a design and prediction tool.

Particle degradation in pneumatic conveyors: Use of data from a pilot-sized test facility to predict degradation in an industrial conveyor

2002 ◽  
Vol 216 (2) ◽  
pp. 65-71
Author(s):  
I Bridle ◽  
S R Woodhead
Keyword(s):  
Solid Material ◽  
Basmati Rice ◽  
Test Facility ◽  
Design Stage ◽  
Pneumatic Conveying ◽  
Process Industries ◽  
Industrial Practice ◽  
Use Of Data ◽  
Bulk Solid ◽  
Wide Range

Degradation of bulk solid product during pneumatic conveying is of concern in a range of process industries. However, prediction of product degradation levels at the conveyor design stage has proved challenging. This paper presents a proposed prediction technique, based on the use of a pilot-sized test facility to provide relevant empirical data. The results of experiments undertaken using malted barley, basmati rice, and granulated sugar are reported. For each bulk solid material, a wide range of conveying conditions have been examined, consistent with common industrial practice. Correlations between predictions and experimental data obtained in an industrial-scale conveyor are presented and discussed.

Large Eddy Simulations of Staggered Parallel-Plate Flows

2005 ◽  
Author(s):  
M. V. Pham ◽  
F. Plourde ◽  
S. K. Doan
Keyword(s):  
Heat Transfer ◽  
Numerical Simulations ◽  
Heat Transfer Enhancement ◽  
Parallel Plate ◽  
Large Scale ◽  
Primary Objective ◽  
Transfer Enhancement ◽  
Turbulent Structures ◽  
Wide Range ◽  
Large Eddy

Heat transfer enhancement is a subject of major concern in numerous fields of industry and research. Having received undivided attention over the years, it is still studied worldwide. Given the exponential growth of computing power, large-scale numerical simulations are growing steadily more realistic, and it is now possible to obtain accurate time-dependent solutions with far fewer preliminary assumptions about the problems. As a result, an increasingly wide range of physics is now open for exploration. More specifically, it is time to take full advantage of large eddy simulation technique so as to describe heat transfer in staggered parallel-plate flows. In fact, from simple theory through experimental results, it has been demonstrated that surface interruption enhances heat transfer. Staggered parallel-plate geometries are of great potential interest, and yet many numerical works dedicated to them have been tarnished by excessively simple assumptions. That is to say, numerical simulations have generally hypothesized lengthwise periodicity, even though flows are not periodic; moreover, the LES technique has not been employed with sufficient frequency. Actually, our primary objective is to analyze turbulent influence with regard to heat transfers in staggered parallel-plate fin geometries. In order to do so, we have developed a LES code, and numerical results are compared with regard to several grid mesh resolutions. We have focused mainly upon identification of turbulent structures and their role in heat transfer enhancement. Another key point involves the distinct roles of boundary restart and the vortex shedding mechanism on heat transfer and friction factor.

Site-bond percolation in two-dimensional kagome lattices: Analytical approach and numerical simulations

2021 ◽  
Vol 104 (1) ◽  
Author(s):  
M. I. González-Flores ◽  
A. A. Torres ◽  
W. Lebrecht ◽  
A. J. Ramirez-Pastor
Keyword(s):  
Numerical Simulations ◽  
Analytical Approach ◽  
Bond Percolation ◽  
Two Dimensional

Numerical simulations of wet snow avalanches: interplay between cohesion and friction

2021 ◽  
Author(s):  
Guillaume Chambon ◽  
Thierry Faug ◽  
Mohamed Naaim
Keyword(s):  
Numerical Simulations ◽  
Flow Regimes ◽  
Liquid Water Content ◽  
Snow Avalanches ◽  
Shallow Flow ◽  
Distinctive Features ◽  
Wide Range ◽  
Wet Snow ◽  
Sensitivity Studies ◽  
Avalanche Flow

&lt;p&gt;Wet snow avalanches present distinctive features such as unusual trajectories, peculiar deposit shapes, and a rheological behavior displaying a combination of granular and pasty features depending on the actual snow liquid water content. Complex transitions between dry (cold) and wet (hot) flow regimes can also occur during a single avalanche flow. In an attempt to account for this complexity, we report on numerical simulations of avalanches using a frictional-cohesive rheology implemented in a depth-averaged shallow-flow model. Through extensive sensitivity studies on synthetic and real topographies, we show that cohesion plays a key role to enrich the physics of the simulated flows, and to represent realistic avalanche behaviors. First, when coupled to a proper treatment of the yielding criterion, cohesion provides a way to define objective stopping criteria for the flow, independently of the issues incurred by artificial diffusion of the numerical scheme. Second, and more importantly, the interplay between cohesion and friction gives raise to a variety of nontrivial physical effects affecting the dynamics of the avalanches and the morphology of the deposits. The relative weights of frictional and cohesive contributions to the overall stress are investigated as a function of space and time during the propagation, and related to the formation of specific features such as lateral lev&amp;#233;es, hydraulic jumps, etc. This study represents a first step towards robust avalanches simulations, spanning the wide range of possible flow regimes, through shallow-flow approaches. Future improvements involving more refined cohesion parameterizations will be discussed.&lt;/p&gt;

Influence of Longitudinal Roughness on Friction in EHL Contacts

2004 ◽  
Vol 126 (3) ◽  
pp. 473-481 ◽  
Author(s):  
B. Jacod ◽  
C. H. Venner ◽  
P. M. Lugt
Keyword(s):  
Numerical Simulations ◽  
Operating Conditions ◽  
Simplified Approach ◽  
Curve Fit ◽  
Longitudinal Roughness ◽  
Wide Range ◽  
Equivalent Wave ◽  
Harmonic Components ◽  
Comparison Of The Results ◽  
Relative Friction

The effect of longitudinal roughness on the friction in EHL contacts is investigated by means of numerical simulations. In the theoretical model the Eyring equation is used to describe the rheological behavior of the lubricant. First the relative friction variation caused by a single harmonic roughness component is computed as a function of the amplitude and wavelength for a wide range of operating conditions. From the results a curve fit formula is derived for the relative friction variation as a function of the out-of-contact geometry of the waviness and a newly derived parameter characterizing the response of the lubricant to pressure variations. Subsequently, the case of a superposition of two harmonic components is considered. It is shown that for the effect on friction such a combined pattern can be represented by a single equivalent wave. The amplitude and the wavelength of the equivalent wave can be determined from a nonlinear relation in terms of the amplitudes and wavelengths of the individual harmonic components. Finally the approach is applied to the prediction of the effect of a real roughness profile (many components) on the friction. From a comparison of the results with full numerical simulations it appears that the simplified approach is quite accurate.

Comparison of Numerical Methods for Determining Torsion Stiffness of Automotive Chassis

2011 ◽  
Author(s):  
Steven Tebby ◽  
Ebrahim Esmailzadeh ◽  
Ahmad Barari
Keyword(s):  
Finite Element Analysis ◽  
Analytical Approach ◽  
Torsional Stiffness ◽  
Design Stage ◽  
Element Analysis ◽  
Detailed Design ◽  
Vertical Displacements ◽  
Comparison Of The Results ◽  
Torsion Stiffness

The torsion stiffness of an automotive chassis can be determined using an analytical approach based purely on geometry, using an experimental method, or alternatively by employing a Finite Element Analysis (FEA) process. These three methods are suitable at different design stages and combined together could prove to be practical methods of determining the torsion stiffness of a chassis. This paper describes and compares two distinct FEA processes to determine the torsion stiffness of an automotive chassis during the detailed design stage. The first process iteratively applies forces to the model and records displacements, while the second process gradually applies vertical displacements in place of force to determine the torsional stiffness threshold. Each method is explained and supported with a case study to provide a basis of comparison of the results.

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