An analysis of the temperature field of the workpiece in dry continuous grinding

Abstract

The recent model for heat transfer during intermittent grinding described in Skuratov, Ratis, Selezneva, Pérez, Fernández de Córdoba and Urchueguía (Appl Math Model 31:1039-1047, 2007 is considered. This model is particularized to the case of continuous dry grinding, where an alternative solution is obtained in the steady state. This alternative solution is analytically equivalent to the well-known formula of Jaeger (Proc R Soc NSW 76:204-224, 1942) for the steady-state temperature field created by an infinite moving source of heat and proves to be very useful for evaluating the maximum point of the temperature.

Aplicaciones Del Modelado Matemático en Problemas Energéticos: Un Recorrido Desde La Investigación a La Creación De Empresas

“…La principal ventaja del modelo SV consiste en que consigue una solución analítica mucho más general que la ofrecida por el modelo clásico de Jaeger, pues se obtiene la dependencia explícita del tiempo para el caso de rectificado húmedo (con refrigerante) y fricción no continua. De hecho, se ha podido comprobar la compatibilidad entre ambos modelos particularizando el modelo SV a las hipótesis que sustentan el modelo clásico de Jaeger [9].…”

New Integrals Arising in the Samara-Valencia Heat Transfer Model in Grinding

“…New mathematical identities have been proved in this framework. For instance, comparing Jaeger's model with Samara-Valencia model, a new Dirac delta representation [8],…”

Calculation of Some Integrals Arising in the Samara-Valencia Solution for Dry Flat Grinding

“…Another example is the engineering problem of measuring the coastline, which initiates the study of fractals in mathematics [20]. In the framework of grinding, comparing Jaeger's solution with the Samara-Valencia one, a new representation of the Dirac delta [21] and two new nontabulated integrals [22] have been obtained recently. The scope of this paper is just to provide another two nontabulated integrals by using (0) theorem.…”