Mechanisms of Rubber Abrasion in Unsteady State

1984 ◽  
Vol 57 (4) ◽  
pp. 755-768 ◽  
Author(s):  
S. W. Zhang
Keyword(s):  
Frictional Force ◽  
Sufficient Conditions ◽  
Unsteady State ◽  
Small Particles ◽  
Physical Processes ◽  
Rupture Length ◽  
Frictional Forces ◽  
Basic Characteristics ◽  
The Relationship ◽  
Quantitative Condition

Abstract Abrasion of rubber under the action of mechanical stress appears to involve two basic processes: micromolecular fracture and macrodelamination. The formation of ridges mainly results from the effect of tearing and tensile rupture, but the production of small particles is mainly due to the effect of microcutting. Ridge and small particle formation are basic characteristics of rubber abrasion. The physical processes during dry wear are gradual tearing leading to crack growth and also rupture of the tongue tip. A new concept of rupture length per revolution has been introduced, which is itself a function of the number of revolutions that have occurred during the unsteady state. Based on this, a quasi-theoretical relation for the rate of wear has been proposed. It reflects the influence of several factors on the rate of wear in a comprehensive way, and, it was verified by the experimental results. In the unsteady state of abrasion, the rate of wear and the spacing of the abrasion pattern not only depend upon the frictional force but also upon the number of revolutions. The relationship between the spacing and the frictional force is exponential. The influence of the rotational speed on the wear rate could be neglected when the speed did not exceed 18 rev/min. Oily wear was found at relatively small frictional forces (kN/F=0.24−0.41 m). The action of microcutting and the decomposition of the rubber are both prerequisites and sufficient conditions for oily wear to be produced. The same rubber shows two different modes of wear under different frictional forces. But a quantitative condition for the change from dry wear to oily wear is not yet clear.

Investigation of Abrasion of Nitrile Rubber

1984 ◽  
Vol 57 (4) ◽  
pp. 769-778 ◽  
Author(s):  
S. W. Zhang
Keyword(s):  
Steady State ◽  
Carbon Black ◽  
Crack Growth ◽  
Unsteady State ◽  
Small Particles ◽  
Physical Processes ◽  
Wear Rates ◽  
Rubber Compounds ◽  
Dominant Process ◽  
Particulate Wear

Abstract Abrasion of NBR appears as a dry (particulate) wear, similar to unfilled BR, NR, and SBR, and filled BR. The abraded surface seems textured on two scales: that of the ridges of the abrasion pattern and that of small particles of debris. The formation of macroridges on filled and unfilled NBR appears to involve two distinct ridges one formed after the other. First, fine and tightly spaced primary ridges, followed by rough and sparsely spaced secondary ridges. The abrasion pattern on unfilled NBR is relatively stable once steady state has been reached and the pattern has been fully developed. As for the filled NBR, both the scale and roughness of the secondary ridges are uneven, even if steady state has been reached completely. Wear rates of filled and unfilled NBR have been found to be proportional to an exponent n of the applied frictional work. The unsteady state rates of wear were also somewhat dependent on the number of revolutions of the test wheel. Both the proportionality coefficient k and exponent n are dependent upon the composition and also upon the wear state. The exponent n for unfilled NBR is greater than that for filled NBR, and for the unsteady state it is greater than that for steady state. Reversals in the relative rates of wear between filled and unfilled NBR are also observed at different severities of abrasion. This phenomenon perhaps reflects a competition between two different physical processes: crack growth and rupture of tongue tip. The dominant process may be crack growth at low severities of wear and rupture of the tongue tip at high severities of wear. Therefore, the fact that, at high severities, carbon black markedly reduces the rates of abrasion might be attributed to the tensile strength gain of rubber compounds due to reinforcement by carbon black.

scholarly journals Some Modifications of Pairwise Soft Sets and Some of Their Related Concepts

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1781
Author(s):  
Samer Al Ghour
Keyword(s):  
Topological Space ◽  
Sufficient Conditions ◽  
Soft Sets ◽  
New Concepts ◽  
Bitopological Spaces ◽  
The Relationship ◽  
Soft Topological Space

In this paper, we first define soft u-open sets and soft s-open as two new classes of soft sets on soft bitopological spaces. We show that the class of soft p-open sets lies strictly between these classes, and we give several sufficient conditions for the equivalence between soft p-open sets and each of the soft u-open sets and soft s-open sets, respectively. In addition to these, we introduce the soft u-ω-open, soft p-ω-open, and soft s-ω-open sets as three new classes of soft sets in soft bitopological spaces, which contain soft u-open sets, soft p-open sets, and soft s-open sets, respectively. Via soft u-open sets, we define two notions of Lindelöfeness in SBTSs. We discuss the relationship between these two notions, and we characterize them via other types of soft sets. We define several types of soft local countability in soft bitopological spaces. We discuss relationships between them, and via some of them, we give two results related to the discrete soft topological space. According to our new concepts, the study deals with the correspondence between soft bitopological spaces and their generated bitopological spaces.

The Maxslope Taxometric Procedure: Mathematical Derivation, Parameter Estimation, Consistency Tests

2004 ◽  
Vol 95 (2) ◽  
pp. 517-550 ◽  
Author(s):  
William M. Grove
Keyword(s):  
Parameter Estimation ◽  
Nonlinear Regression ◽  
Classification Accuracy ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Indicator Variable ◽  
Regression Slope ◽  
The Relationship ◽  
Mathematical Derivation ◽  
Made In

This article first explains concepts in taxometrics, including the meaning of “taxon” in relation to taxometric procedures. It then mathematically develops the MAXSLOPE procedure of Grove and Meehl which relies on nonlinear regression of one taxometric indicator variable on another. Sufficient conditions for MAXSLOPE's validity are set forth. The relationship between the point of maximum regression slope (MAXSLOPE point) and the HITMAX cut, i.e., the point on a variable which, if used as a diagnostic cut-off score, yields maximum classification accuracy, is analyzed. A sufficient condition is given for the MAXSLOPE point to equal the HITMAX cut; however, most distributions have different MAXSLOPE and HITMAX points. Equations and an algorithm are spelled out for making a graphical test for the existence of a taxon, estimating taxometric parameters, and conducting consistency tests; the latter serve as stringent checks on the validity of a taxonic conjecture. The plausibility of assumptions made, in deriving MAXSLOPE equations, is discussed, and the qualitative effects of violations of these assumptions are explained.

scholarly journals Modeling the dynamical sinking of biogenic particles in oceanic flow

2017 ◽  
Vol 24 (2) ◽  
pp. 293-305 ◽  
Author(s):  
Pedro Monroy ◽  
Emilio Hernández-García ◽  
Vincent Rossi ◽  
Cristóbal López
Keyword(s):  
Three Dimensional ◽  
Finite Size ◽  
Equation Of Motion ◽  
Particle Dynamics ◽  
Particle Sizes ◽  
Small Particles ◽  
Physical Processes ◽  
Mesoscale Simulation ◽  
Sinking Particles ◽  
Theoretical Results

Abstract. We study the problem of sinking particles in a realistic oceanic flow, with major energetic structures in the mesoscale, focussing on the range of particle sizes and densities appropriate for marine biogenic particles. Our aim is to evaluate the relevance of theoretical results of finite size particle dynamics in their applications in the oceanographic context. By using a simplified equation of motion of small particles in a mesoscale simulation of the oceanic velocity field, we estimate the influence of physical processes such as the Coriolis force and the inertia of the particles, and we conclude that they represent negligible corrections to the most important terms, which are passive motion with the velocity of the flow, and a constant added vertical velocity due to gravity. Even if within this approximation three-dimensional clustering of particles can not occur, two-dimensional cuts or projections of the evolving three-dimensional density can display inhomogeneities similar to the ones observed in sinking ocean particles.

scholarly journals Property $(w)$ of upper triangular operator Matrices

2020 ◽  
Vol 51 (2) ◽  
pp. 81-99
Author(s):  
Mohammad M.H Rashid
Keyword(s):  
Hilbert Spaces ◽  
Sufficient Conditions ◽  
Extension Property ◽  
Operator Matrices ◽  
Single Valued Extension Property ◽  
Triangular Operator ◽  
Upper Triangular Operator Matrices ◽  
Necessary And Sufficient ◽  
The Relationship ◽  
Number Of Authors

Let $M_C=\begin{pmatrix} A & C \\ 0 & B \\ \end{pmatrix}\in\LB(\x,\y)$ be be an upper triangulate Banach spaceoperator. The relationship between the spectra of $M_C$ and $M_0,$ and theirvarious distinguished parts, has been studied by a large number of authors inthe recent past. This paper brings forth the important role played by SVEP,the {\it single-valued extension property,} in the study of some of these relations. In this work, we prove necessary and sufficient conditions of implication of the type $M_0$ satisfies property $(w)$ $\Leftrightarrow$ $M_C$ satisfies property $(w)$ to hold. Moreover, we explore certain conditions on $T\in\LB(\hh)$ and $S\in\LB(\K)$ so that the direct sum $T\oplus S$ obeys property $(w)$, where $\hh$ and $\K$ are Hilbert spaces.

scholarly journals On the Formulation of Basal Debris Drag for the Case of Sparse Debris

1988 ◽  
Vol 34 (118) ◽  
pp. 259-264 ◽  
Author(s):  
E.M. Snoemaker
Keyword(s):  
Melting Rate ◽  
Physical Processes ◽  
Rock Friction ◽  
Rock Fragments ◽  
Ice Velocity ◽  
Basal Melting ◽  
The Relationship

AbstractTwo models are presented for the formulation of abrasion and basal drag due to rock–rock friction (debris drag) for the case of sparse debris entrained in the basal layers of a temperate glacier resting on a bedrock bed. The first model is formulated in terms of average basal melting rate, va, and the concentration, C, of basal debris fragments which make intermittent bed contact. The second model is formulated in terms of vn the component of ice velocity normal to the bed flowing around rock fragments contacting the bed, and Cc, the concentration of debris actually in contact with the bed. The relationship between the two models is given for the case of a sinusoidal bed. Generalizations are discussed as well as potentially important physical processes which remain to be investigated.

Insensitivity and reversed Markov processes

1983 ◽  
Vol 15 (4) ◽  
pp. 752-768 ◽  
Author(s):  
W. Henderson
Keyword(s):  
Markov Processes ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient ◽  
The Relationship

This paper is concerned with the relationship between insensitivity in a certain class of Markov processes and properties of that process when time is reversed. Necessary and sufficient conditions for insensitivity are established and linked to already proved results. A number of examples of insensitive systems are given.

A Study of Frictional Forces between Orthodontic Brackets and Archwires

1994 ◽  
Vol 21 (4) ◽  
pp. 349-357 ◽  
Author(s):  
Alison Downing ◽  
John McCabe ◽  
Peter Gordon
Keyword(s):  
Stainless Steel ◽  
Frictional Force ◽  
Nickel Titanium ◽  
The Other ◽  
Friction Testing ◽  
Beta Titanium ◽  
Polycrystalline Ceramic ◽  
Ceramic Brackets ◽  
Frictional Forces ◽  
Testing Assembly

The differences in magnitude of static and kinetic frictional forces generated by 0·022 × 0·030-inch stainless steel (Dentaurum®) and polycrystalline ceramic (Transcend®) brackets in combinntion with archwires of different sizes (0·018 inch and 0·019 × 0·025 inch) and materials (stainless steel, nickel-titanium, and beta-titanium) at a constant ligature force were investigated. A friction-testing assembly using the Instron machine was used. In all cases, the static frictional force was greater than the kinetic frictional force. There were no significant differences in the frictional forces generated by stainless steel and polycrystalline ceramic brackets. Beta-titanium archwires produced greater frictinal forces than the other two materials. Increasing the archwire diameter increased the frictional force.

scholarly journals A Coupled Model for Solution Flow and Bioleaching Reaction Based on the Evolution of Heap Pore Structure

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Shenghua Yin ◽  
Xun Chen ◽  
Chi Ma ◽  
Leiming Wang ◽  
Aixiang Wu
Keyword(s):  
Coupled Model ◽  
Small Particles ◽  
Copper Ore ◽  
Solution Flow ◽  
Pore Evolution ◽  
Main Factors ◽  
Set Up ◽  
Seepage Law ◽  
Leaching Reaction ◽  
The Relationship

Based on the basic seepage law, equations have been derived to descript the solution flow within the copper ore heap which is treated as anisotropy porous media. The relationship between heap permeability and pore ratio has been revealed. Given the consideration of cover pressure and particle dissolution, pore evolution model has been set up. The pore evolution mechanism, due to the process of dissolution, precipitation, blockage, collapse, and caking, has been investigated. The comprehensive model for pore evolution and solution flow under the effect of solute transport and leaching reaction has been established. A trapezoidal heap was calculated, and the estimated results show that permeability decreases with the decreasing of pore ratio. Therefore, the permeability of the heap with small particles is relatively low because of its low pore ratio. Furthermore, permeability and height are found to be the two main factors influencing the solution flow.

A Modified Monte-Carlo Potts Model for Dynamic Recrystallization

2015 ◽  
Vol 1096 ◽  
pp. 280-287 ◽  
Author(s):  
Jian Fu ◽  
Bi You Peng ◽  
Bin Xie ◽  
Yi Gen Ye
Keyword(s):  
Monte Carlo ◽  
Dynamic Recrystallization ◽  
Potts Model ◽  
Metallic Materials ◽  
Stored Energy ◽  
Modified Model ◽  
Grain Sizes ◽  
Basic Characteristics ◽  
Evolution Modeling ◽  
The Relationship

In order to improve the microstructure evolution modeling of dynamic recrystallization (DRX) in agreement with physical experiment, a modified Monte-Carlo (MC) Potts model for simulating DRX process was proposed in this paper under the consideration of the inhomogeneous stored energy distribution related to grain sizes, the nucleation criteria related to critical dislocation density, the site energy change related to grain preferred-growth, the combination of macroscopic thermo-mechanical parameters and microscopic material parameters, and the relationship between MC calculation steps and real DRX time. The results show that the modified model can better simulate the basic characteristics of dynamic recrystallization of metallic materials during forging, which the recrystallized grains nucleate mainly in the deformed regions with high stored energy and preferentially grow up by merging adjacent deformed grains with high stored energy.

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