The thermal analysis of cutting/grinding processes by meshless finite block method

Abstract

Development of the Finite Block Method (FBM) is presented, with the introduction of infinite elements for the first time, for predicting stationary and transient heat conduction in cutting/grinding processes. Utilizing the Lagrange series the first order partial differential matrix is derived, adopting a mapping technique, followed by the construction of the higher order derivative matrix. For linear stationary heat conductivity three free parameters including the velocity of the workpiece, the cooling coefficient and the inclined angle of the contact zone, together with their effects on temperature, are observed. For the transient heat conduction study, the Laplace transformation method and Durbin's inverse technique are employed. Numerical solutions are discussed and comparisons made with the finite element method and analytical solutions, demonstrating the accuracy and convergence of the finite block method.

Grinding temperature and its consequences on induced residual stresses during grinding of nickel-based superalloys: a review

“…A finite block method was proposed to measure the temperature in the grinding zone of the ground surface by analyzing the results of the transient heat conduction problem during the grinding process. This transient heat conduction problem is represented in terms of the partial differential equation, which is solved by the Lagrange series using the plotting method, and the results obtained from this method predict the temperature in the grinding zone [40]. In past years, research has been done associated with the problem of high heat generation in the grinding zone and its effect on the surface integrity of the ground surface during grinding of nickel-based superalloy.…”

Integrated modelling method of bonding strength and residual life prediction for selective repair structure of aluminium alloy

“…Many numerical calculations have been performed to analyse and predict the residual life, including the meshless method (MLM), [1][2][3] cohesive zone method (CZM), 4,5 finite element method (FEM) 6,7 and extended finite element method (XFEM). 8,9 Lu et al 10 analysed the fatigue crack propagation behaviour of Ti-6Al-4Valloy under uniaxial tensile load using an MLM and discovered that the crack trajectory predicted by the MLM was consistent with experimental data.…”