scholarly journals A Three-Dimensional Fractal Contact Model for a Rough Friction Surface With Multiple-Scale Asperities

2021 ◽  
Author(s):  
Ao Liang ◽  
Yongming Bian ◽  
Guangjun Liu
Keyword(s):  
Friction Surface ◽  
Three Dimensional ◽  
Multiple Scale ◽  
Fractal Model ◽  
Contact Model ◽  
Proposed Model ◽  
Area Distribution ◽  
Fractal Parameters ◽  
Scale Levels ◽  
Total Contact Area

Abstract This paper describes a new fractal contact model for a rough three-dimensional friction surface considering scale dependence. The model predicts the total contact area as a function of contact load. The microcontact fractal model for asperities at multiple-scale levels is derived. The truncated area distribution function of asperities at multiple-scale levels is revised. The effects of each scale level and fractal parameters on the proposed model are evaluated by numerical simulations. Results obtained from the complex fractal model with several scales are accurate as demonstrated by comparing them to experimental results and models taken from literature. Friction and wear of rough surfaces can be further studied using the proposed model.

scholarly journals Fractal grain distribution in snow avalanche deposits

2012 ◽  
Vol 58 (208) ◽  
pp. 340-346 ◽  
Author(s):  
Valerio De Biagi ◽  
Bernardino Chiaia ◽  
Barbara Frigo
Keyword(s):  
Size Distribution ◽  
Three Dimensional ◽  
Fractal Model ◽  
Snow Avalanche ◽  
Mathematical Tool ◽  
Distribution Law ◽  
Scale Invariant ◽  
Fractal Parameters ◽  
Avalanche Flow ◽  
Grain Distribution

AbstractScale-invariant phenomena are common in nature and fractals represent a suitable mathematical tool to describe them. Snow avalanche flow is made up of a mixture of grains and aggregates (granules) which can be broken or sintered together. The granular properties and interactions are important in understanding how avalanches flow. In this paper a fractal model for describing the grain-size distribution in the deposit of a snow avalanche is formulated by introducing the concept of aggregation probability. Although the model is two-dimensional, an extension to the three-dimensional case is proposed in the conclusions. The cumulative size distribution law is extrapolated from the model, and a physical discussion on fractal parameters is conducted. Finally, an experimental application to a real avalanche event is considered to confirm the predictions of the model and to present an extension to multifractality.

Fractal Model for Thermal Contact Conductance

2008 ◽  
Vol 130 (10) ◽  
Author(s):  
Mingqing Zou ◽  
Boming Yu ◽  
Jianchao Cai ◽  
Peng Xu
Keyword(s):  
Random Number ◽  
Rough Surfaces ◽  
Thermal Contact ◽  
Fractal Model ◽  
Thermal Contact Conductance ◽  
Bulk Resistance ◽  
Contact Conductance ◽  
Proposed Model ◽  
Fractal Parameters ◽  
Good Agreement

A random number model based on fractal geometry theory is developed to calculate the thermal contact conductance (TCC) of two rough surfaces in contact. This study is carried out by geometrical and mechanical investigations. The present study reveals that the fractal parameters D and G have important effects on TCC. The predictions by the proposed model are compared with existing experimental data, and good agreement is observed by fitting parameters D and G. The results show that the effect of the bulk resistance on TCC, which is often neglected in existing models, should not be neglected for the relatively larger G and D. The main advantage of this model is the randomization of roughness distributions on rough surfaces. The present results also show a better agreement with the practical situation than the results of other models. The proposed technique may have the potential in prediction of other phenomena such as friction, radiation, wear and lubrication on rough surfaces.

Study on the generalized k-Hilfer–Prabhakar fractional viscoelastic–plastic model

2021 ◽  
pp. 108128652110258
Author(s):  
Yi-Ying Feng ◽  
Xiao-Jun Yang ◽  
Jian-Gen Liu ◽  
Zhan-Qing Chen
Keyword(s):  
Constitutive Model ◽  
Three Dimensional ◽  
Sensitivity Analyses ◽  
Creep Process ◽  
Fractional Operator ◽  
Modified Model ◽  
Proposed Model ◽  
Accelerated Creep ◽  
The Laplace Transform ◽  
Classical Models

The general fractional operator shows its great predominance in the construction of constitutive model owing to its agility in choosing the embedded parameters. A generalized fractional viscoelastic–plastic constitutive model with the sense of the k-Hilfer–Prabhakar ( k-H-P) fractional operator, which has the character recovering the known classical models from the proposed model, is established in this article. In order to describe the damage in the creep process, a time-varying elastic element [Formula: see text] is used in the proposed model with better representation of accelerated creep stage. According to the theory of the kinematics of deformation and the Laplace transform, the creep constitutive equation and the strain of the modified model are established and obtained. The validity and rationality of the proposed model are identified by fitting with the experimental data. Finally, the influences of the fractional derivative order [Formula: see text] and parameter k on the creep process are investigated through the sensitivity analyses with two- and three-dimensional plots.

Effects of Wheel-Shaft-Fluid Coupling and Local Wheel Deformations on the Global Behavior of Shaft Lines

2002 ◽  
Vol 124 (4) ◽  
pp. 953-957 ◽  
Author(s):  
D. Lornage ◽  
E. Chatelet ◽  
G. Jacquet-Richardet
Keyword(s):  
Three Dimensional ◽  
Fluid Film ◽  
Global Behavior ◽  
Three Dimensional Model ◽  
Fluid Films ◽  
Strongly Coupled ◽  
Proposed Model ◽  
Structural Deformations ◽  
Time Marching ◽  
Fluid Coupling

Rotating parts of turbomachines are generally studied using different uncoupled approaches. For example, the dynamic behavior of shafts and wheels are considered independently and the influence of the surrounding fluid is often taken into account in an approximate way. These approaches, while often sufficiently accurate, are questionable when wheel-shaft coupling is observed or when fluid elements are strongly coupled with local structural deformations (leakage flow between wheel and casing, fluid bearings mounted on a thin-walled shaft, etc.). The approach proposed is a step toward a global model of shaft lines. The whole flexible wheel-shaft assembly and the influence of specific fluid film elements are considered in a fully three-dimensional model. In this paper, the proposed model is first presented and then applied to a simple disk-shaft assembly coupled with a fluid film clustered between the disk and a rigid casing. The finite element method is used together with a modal reduction for the structural analysis. As thin fluid films are considered, the Reynolds equation is solved using finite differences in order to obtain the pressure field. Data are transferred between structural and fluid meshes using a general method based on an interfacing grid concept. The equations governing the whole system are solved within a time-marching procedure. The results obtained show significant influence of specific three-dimensional features such as disk-shaft coupling and local disk deformations on global behavior.

A Greenwood-Williamson Model of Small-Scale Friction

2005 ◽  
Vol 74 (1) ◽  
pp. 31-40 ◽  
Author(s):  
Reese E. Jones
Keyword(s):  
Numerical Method ◽  
Recursion Formula ◽  
Three Dimensional ◽  
Interfacial Friction ◽  
Small Scale ◽  
Analytical Estimate ◽  
Normal Loading ◽  
Proposed Model ◽  
Loading Case ◽  
Transition Length

A Greenwood and Williamson based model for interfacial friction is presented that incorporates the presliding transition phenomenon that can significantly affect small devices. This work builds on previous similar models by developing: an analytical estimate of the transition length in terms of material and surface parameters, a general recursion formula for the case of slip in one direction with multiple reversals and constant normal loading, and a numerical method for the general three-dimensional loading case. In addition, the proposed model is developed within a plasticity-like framework and is shown to have qualitative similarities with published experimental observations. A number of model problems illustrate the response of the proposed model to various loading conditions.

An Equivalent 3-D Method for Analyzing Orthogonally Stiffened Plate Structures

1987 ◽  
Vol 31 (02) ◽  
pp. 101-106
Author(s):  
Kyu Nam Cho ◽  
William S. Vorus
Keyword(s):  
Bridge Decks ◽  
Three Dimensional ◽  
Stiffened Plate ◽  
Plate Structures ◽  
Work Related ◽  
Beam Elements ◽  
Proposed Model ◽  
The Relationship

A new three-dimensional method is proposed for analyzing orthogonally stiffened grillage structures. The method is based on earlier work related to bridge decks. The relationship between system displacement and loads is described mathematically, and matrices are developed to examine the shear compatibility between plate and beam elements. The paper concludes with a comparison between deflections obtained by several different procedures and the proposed model.

scholarly journals Numerical Simulation of Water Absorption and Swelling in Dehulled Barley Grains during Canned Porridge Cooking

Processes ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 230 ◽  
Author(s):  
Lei Wang ◽  
Mengting Wang ◽  
Mingming Guo ◽  
Xingqian Ye ◽  
Tian Ding ◽  
...  
Keyword(s):  
Moisture Absorption ◽  
Three Dimensional ◽  
Processing Conditions ◽  
Relative Deviation ◽  
Cooking Process ◽  
Proposed Model ◽  
Hygroscopic Swelling ◽  
3D Numerical Model ◽  
Barley Grains ◽  
Experimental Values

Understanding the hydration behavior of cereals during cooking is industrially important in order to optimize processing conditions. In this study, barley porridge was cooked in a sealed tin can at 100, 115, and 121 °C, respectively, and changes in water uptake and hygroscopic swelling in dehulled barley grains were measured during the cooking of canned porridge. In order to describe and better understand the hydration behaviors of barley grains during the cooking process, a three-dimensional (3D) numerical model was developed and validated. The proposed model was found to be adequate for representing the moisture absorption characteristics with a mean relative deviation modulus (P) ranging from 4.325% to 5.058%. The analysis of the 3D simulation of hygroscopic swelling was satisfactory for describing the expansion in the geometry of barley. Given that the model represented the experimental values adequately, it can be applied to the simulation and design of cooking processes of cereals grains, allowing for saving in both time and costs.

Analysis of Plastic Strain between Substrate and Micro-Cantilever under Different Deformation Characteristics

2013 ◽  
Vol 477-478 ◽  
pp. 21-24
Author(s):  
Hui Kai Gao ◽  
Jian Meng Huang
Keyword(s):  
Plastic Strain ◽  
Rough Surface ◽  
Three Dimensional ◽  
Equivalent Plastic Strain ◽  
Adhesive Contact ◽  
Contact Model ◽  
Deformation Characteristics ◽  
Element Analysis ◽  
Flat Substrate ◽  
Micro Cantilever

The contact between substrate and micro-cantilever simplified as an ideal flat substrate contact with a micro-cantilever rough surface. A three-dimensional adhesive contact model was established on isotropic rough surfaces exhibiting fractal behavior, and the equivalent plastic strain was discussed using the finite element analysis. The maximum equivalent plastic strain and its depth were presented with the different paths of rough solid when loading. The result show that the equivalent plastic strain versus different depth which at different locations showed different laws, in the top area of the asperities versus different depth, the maximum equivalent plastic strain occurs in the subsurface range about 0.5μm from the surface or on the surface. In addition, with different deformation characteristics, the degree of the equivalent plastic strain was different.. The contact model between micro-cantilever rough surface and flat substrate will lay a foundation to further research on the substance of the process of friction and wear.

Three-Dimensional Analysis of Closed-Die Forging Processes: Part 1: Formulation

1989 ◽  
Vol 203 (1) ◽  
pp. 33-37 ◽  
Author(s):  
C F Lugora ◽  
A N Bramley
Keyword(s):  
Theoretical Model ◽  
Energy Dissipation ◽  
Metal Flow ◽  
Three Dimensional ◽  
Total Rate ◽  
Die Forging ◽  
Closed Die Forging ◽  
Proposed Model ◽  
Optimum Velocity ◽  
Forging Load

In this series of papers, a theoretical model based on the upper bound elemental technique is presented for prediction of forging load and metal flow in three-dimensional closed-die forging processes. Three basic elements are introduced in order to partition a forging into simple elementary regions. An optimum velocity distribution within the forging is obtained by minimizing the total rate of energy dissipation using a simplex optimizing procedure. Applications of the proposed model are discussed in Part 2.

A Three-Dimensional Load Sharing Model of Planetary Gear Sets Having Manufacturing Errors

2015 ◽  
Author(s):  
Nicholas D. Leque ◽  
Ahmet Kahraman
Keyword(s):  
Three Dimensional ◽  
Planetary Gear ◽  
Load Sharing ◽  
Distribution Model ◽  
Gear Mesh ◽  
Position Errors ◽  
Proposed Model ◽  
Manufacturing Errors ◽  
Manufacturing Tolerancing ◽  
Planetary Gear Sets

Planet-to-planet load sharing is a major design and manufacturing tolerancing issue in planetary gear sets. Planetary gear sets are advantageous over their countershaft alternatives in many aspects, provided that each planet branch carries a reasonable, preferably equal, share of the torque transmitted. In practice, the load shared among the planets is typically not equal due to the presence of various manufacturing errors. This study aims at enhancing the models for planet load sharing through a three-dimensional formulation of N-planet helical planetary gear sets. Apart from previous models, the proposed model employs a gear mesh load distribution model to capture load and time dependency of the gear meshes iteratively. It includes all three types of manufacturing errors, namely constant errors such as planet pinhole position errors and pinhole diameter errors, constant but assembly dependent errors such as nominal planet tooth thickness errors, planet bore diameter errors, and rotation and assembly dependent errors such as gear eccentricities and run-outs. At the end, the model is used to show combined influence of these errors on planet load sharing to aid designers on how to account for manufacturing tolerances in the design of the gears of a planetary gear set.

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