Discussion: “A Statistical Polyhedron Model of Abrasive Grain” (McAdams, H. T., 1963, ASME J. Eng. Ind., 85, pp. 388–393)

1963 ◽  
Vol 85 (4) ◽  
pp. 393-394
Author(s):  
J. Peklenik
Keyword(s):  
Abrasive Grain ◽  
Polyhedron Model

A Statistical Polyhedron Model of Abrasive Grain

1963 ◽  
Vol 85 (4) ◽  
pp. 388-393 ◽  
Author(s):  
H. T. McAdams
Keyword(s):  
Cutting Tools ◽  
Cutting Performance ◽  
Abrasive Particles ◽  
Abrasive Grain ◽  
Abrasive Cutting ◽  
Particle Geometry ◽  
Polyhedron Model

A statistical polyhedron model of abrasive grain is developed and its application to the design of abrasive cutting tools indicated. The model incorporates particle geometry and orientation with respect to the workpiece into a single concept useful in the prediction of cutting performance. Projective properties of the statistical polyhedron are exploited in a proposed method for measuring axial ratios of abrasive particles.

Relationships Between the Friction and Viscoelastic Properties of Rubber

2000 ◽  
Vol 28 (3) ◽  
pp. 178-195 ◽  
Author(s):  
N. Amino ◽  
Y. Uchiyama
Keyword(s):  
Viscoelastic Properties ◽  
Skid Resistance ◽  
Grain Sizes ◽  
Abrasive Grain ◽  
The Coefficient Of Friction ◽  
Tan Δ ◽  
Silicone Carbide ◽  
And Storage ◽  
Wet Skid Resistance ◽  
Frequency Curves

Abstract In this study, the relationships between friction and viscoelastic properties such as loss tangent tan δ and storage modulusE′ were examined. Wet skid resistance was measured using the British Pendulum Tester. The rubber specimens were rubbed againstfive silicone carbide cloths of differing abrasive grain sizes. The viscoelastic properties of the rubber specimens were measured with a viscoelasticspectrometer. From the data on wet skid resistance and viscoelastic properties, it is found that the coefficient of friction μ varies as follows:           μ = a + b · tan δ/E′ where a and b are constants. Tan δ/E′ was related to the hysteresis term of friction, and the μ-frequency curves were compared with the tan δ/E′ –frequency curves.

scholarly journals Data-based polyhedron model for optimization of engineering structures involving uncertainties

2021 ◽  
Vol 2 ◽  
Author(s):  
Zhiping Qiu ◽  
Han Wu ◽  
Isaac Elishakoff ◽  
Dongliang Liu
Keyword(s):  
Linear Programming ◽  
Convex Polyhedron ◽  
Linear Optimization ◽  
Optimal Solution ◽  
Composite Plates ◽  
Convex Polyhedra ◽  
Chebyshev Inequality ◽  
Engineering Structures ◽  
Load Bearing ◽  
Polyhedron Model

Abstract This paper studies the data-based polyhedron model and its application in uncertain linear optimization of engineering structures, especially in the absence of information either on probabilistic properties or about membership functions in the fussy sets-based approach, in which situation it is more appropriate to quantify the uncertainties by convex polyhedra. Firstly, we introduce the uncertainty quantification method of the convex polyhedron approach and the model modification method by Chebyshev inequality. Secondly, the characteristics of the optimal solution of convex polyhedron linear programming are investigated. Then the vertex solution of convex polyhedron linear programming is presented and proven. Next, the application of convex polyhedron linear programming in the static load-bearing capacity problem is introduced. Finally, the effectiveness of the vertex solution is verified by an example of the plane truss bearing problem, and the efficiency is verified by a load-bearing problem of stiffened composite plates.

3D Dynamic Finite Element Simulation Analysis of Single Abrasive Grain during Profile Grinding with Axial Feed

2013 ◽  
Vol 680 ◽  
pp. 410-416 ◽  
Author(s):  
Jun Ming Wang ◽  
Fu Yuan Tong ◽  
Xiao Xue Li
Keyword(s):  
Finite Element ◽  
Finite Element Simulation ◽  
Simulation Analysis ◽  
Tangential Force ◽  
Profile Grinding ◽  
Software Analysis ◽  
Dynamic Finite Element ◽  
Abrasive Grain ◽  
Element Simulation ◽  
Force Increase

By simplifying the geometric shape of abrasive grain in a cone-shape, the authors conduct the 3D dynamic finite element simulation on profile grinding with axial feed by single abrasive grain using deform-3D software. Analysis is made on the influence upon the grinding forces in case of the same grinding speed, the same grinding depth and the same friction factor between wheel and workpiece at different axial feed. The results show that the normal force and the tangential force increase with the increase of axial feed, but the axial force decreases with the axial feed.

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