Full Sliding Adhesive-Like Contact of V-Belts

2002 ◽  
Vol 124 (4) ◽  
pp. 706-712 ◽  
Author(s):  
Go¨ran Gerbert ◽  
Francesco Sorge
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Power Transmission ◽  
A Priori ◽  
Belt Drive ◽  
Natural Boundary ◽  
Condition Problem ◽  
New Type ◽  
Wrap Angle ◽  
Natural Boundary Conditions

Analysis of power transmission in a belt drive consisting of, e.g., two pulleys might be treated as a boundary value problem. Tight side tension FT, slack side tension FS and the wrap angle α are the three natural boundary conditions. In the literature, theories are developed where seating and unseating as well as the power transmitting part of the contact are considered. The solutions presented so far don’t fulfill the boundary conditions properly, since a certain tension ratio FT/FS is associated with a certain contact angle and not an a priori specified one. It appears that a new type of full sliding solution must be introduced to handle the boundary condition problem. During part of the contact there is almost no tension variation in spite of the full sliding conditions. The designation adhesive-like solution is here introduced for that part. Conditions and character of the adhesive-like solution are outlined in the paper.

Full Sliding “Adhesive-Like” Contact of V-Belts

2000 ◽  
Author(s):  
Göran Gerbert ◽  
Francesco Sorge
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Power Transmission ◽  
A Priori ◽  
Belt Drive ◽  
Natural Boundary ◽  
Condition Problem ◽  
New Type ◽  
Wrap Angle ◽  
Natural Boundary Conditions

Abstract Analysis of power transmission in a belt drive consisting of e. g. two pulleys might be treated as a boundary value problem. Tight side tension FT, slack side tension FS and the wrap angle α are the three natural boundary conditions. In the literature, theories are developed where seating and unseating as well as the power transmitting part of the contact are considered. The solutions presented so far don’t fulfil the boundary conditions properly, since a certain tension ratio FT/FS is associated with a certain contact angle and not an a priori specified one. It appears that a new type of full sliding solution must be introduced to handle the boundary condition problem. During part of the contact there is almost no tension variation in spite of the full sliding conditions. The designation adhesive like solution is here introduced for that part. Conditions and character of the adhesive like solution are outlined in the paper.

DIFFRACTION BY EDGES

2008 ◽  
Vol 22 (23) ◽  
pp. 2287-2328 ◽  
Author(s):  
ANDRÁS VASY
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Boundary Conditions ◽  
A Priori ◽  
Differential Forms ◽  
Natural Boundary ◽  
Propagation Of Singularities ◽  
Natural Boundary Conditions ◽  
Manifolds With Corners

In these expository notes we explain the role of geometric optics in wave propagation on domains or manifolds with corners or edges. Both the propagation of singularities, which describes where solutions of the wave equation may be singular, and the diffractive improvement under non-focusing hypotheses, which states that in certain places the diffracted wave is more regular than a priori expected, is described. In addition, the wave equation on differential forms with natural boundary conditions, which in particular includes a formulation of Maxwell's equations, is studied.

Cooling Simulation of an Injection Mold with an Embedded Insert

2012 ◽  
Vol 580 ◽  
pp. 194-201
Author(s):  
Mi Ting Xu ◽  
Shi Xun Zhang ◽  
Xian Zhang Shi
Keyword(s):  
Boundary Condition ◽  
Boundary Element Method ◽  
Numerical Model ◽  
Boundary Conditions ◽  
Model Building ◽  
Attractive Alternative ◽  
Injection Mold ◽  
Natural Boundary Condition ◽  
Natural Boundary ◽  
Natural Boundary Conditions

This paper proposes a numerical model of cooling analysis of an injection mold that has an embedded insert. The Boundary Element Method (BEM) is employed because of its popular usage in this area. The key problem in model building is how to involve the independent surface between mold and insert into the BEM equations and how to give the natural boundary conditions on it. This problem is solved by using coupling BEM which provides an attractive alternative in that the natural boundary condition is shifted to the surface between part and mold. So, instead of using the finite differentiation method, the boundary condition can be determined analytically. This is useful in improving the accuracy of cooling analysis.

scholarly journals Elements of Bi-cubic Polynomial Natural Spline Interpolation for Scattered Data: Boundary Conditions Meet Partition of Unity Technique

2020 ◽  
Vol 8 (4) ◽  
pp. 994-1010
Author(s):  
Weizhi Xu
Keyword(s):  
Boundary Conditions ◽  
Spline Interpolation ◽  
Partition Of Unity ◽  
Scattered Data ◽  
Rectangular Domain ◽  
Natural Boundary ◽  
Natural Spline ◽  
Cubic Polynomial ◽  
Natural Boundary Conditions ◽  
Cubic Polynomials

This paper investigates one kind of interpolation for scattered data by bi-cubic polynomial natural spline, in which the integral of square of partial derivative of two orders to x and to y for the interpolating function is minimal (with natural boundary conditions). Firstly, bi-cubic polynomial natural spline interpolations with four kinds of boundary conditions are studied. By the spline function methods of Hilbert space, their solutions are constructed as the sum of bi-linear polynomials and piecewise bi-cubic polynomials. Some properties of the solutions are also studied. In fact, bi-cubic natural spline interpolation on a rectangular domain is a generalization of the cubic natural spline interpolation on an interval. Secondly, based on bi-cubic polynomial natural spline interpolations of four kinds of boundary conditions, and using partition of unity technique, a Partition of Unity Interpolation Element Method (PUIEM) for fitting scattered data is proposed. Numerical experiments show that the PUIEM is adaptive and outperforms state-of-the-art competitions, such as the thin plate spline interpolation and the bi-cubic polynomial natural spline interpolations for scattered data.

Meshless Integral Method for Analysis of Elastoplastic Geotechnical Materials

2010 ◽  
Author(s):  
Jianfeng Ma ◽  
Joshua David Summers ◽  
Paul F. Joseph
Keyword(s):  
Boundary Conditions ◽  
Function Approximation ◽  
Integral Method ◽  
Weak Form ◽  
Constitutive Law ◽  
Governing Equations ◽  
Natural Boundary ◽  
Pressure Sensitive ◽  
Support Domain ◽  
Natural Boundary Conditions

The meshless integral method based on regularized boundary equation [1][2] is extended to analyze elastoplastic geotechnical materials. In this formulation, the problem domain is clouded with a node set using automatic node generation. The sub-domain and the support domain related to each node are also generated automatically using algorithms developed for this purpose. The governing integral equation is obtained from the weak form of elastoplasticity over a local sub-domain and the moving least-squares approximation is employed for meshless function approximation. The geotechnical materials are described by pressure-sensitive multi-surface Drucker-Prager/Cap plasticity constitutive law with hardening. A generalized collocation method is used to impose the essential boundary conditions and natural boundary conditions are incorporated in the system governing equations. A comparison of the meshless results with the FEM results shows that the meshless integral method is accurate and robust enough to solve geotechnical materials.

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