The Homotopy Perturbation Method (HPM) is used to solve the Burgers-Huxley non-linear differential equations. Three case study problems of Burgers-Huxley are solved using the HPM and the exact solutions are obtained. The rapid convergence towards the exact solutions of HPM is numerically shown. Results show that the HPM is efficient method with acceptable accuracy to solve the Burgers-Huxley equation. Also, the results prove that the method is an efficient and powerful algorithm to construct the exact solution of non-linear differential equations.

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h i g h l i g h t s • A virtual machining system is presented in order to create machined parts. • Geometrical errors of three-axis milling machine tools were modeled. • The real errors are enforced to the nominal machining G-codes by developed software. • To validate the system, surfaces of virtual and real machined parts are compared.

Virtual manufacturing systems carry out the simulation of manufacturing processes in digital environment in order to increase accuracy as well as productivity in part production. There are different error sources in machine tools, such as tool deflection, geometrical deviations of moving axis, and thermal distortions of machine tool structures. The errors due to tool deflection are caused by cutting forces and have direct effects on dimensional accuracy, surface roughness of the parts, and efficient life of the cutting tool, holder, and spindle. This paper presents an application of virtual machining systems in order to improve the accuracy and productivity of part manufacturing by monitoring and minimizing the tool deflection error. The tool deflection error along machining paths is monitored to present a useful methodology in controlling the produced parts with regard to desired tolerances. Suitable tool and spindle can also be selected due to the ability of error monitoring. In order to minimize the error, optimization technique based on genetic algorithms is used to determine optimized machining parameters. Free-form profile of virtual and real machined parts with tool deflection error is compared in order to validate reliability as well as accuracy of the software.

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The Friction stir welding (FSW) is recently presented so to join different materials without the melting process as a solid-state joining technique. A widely application for the FSW process is recently developed in automotive industries. To create the welded components by using the FSW, the plunged probe and shoulder as welding tools are used. The Finite Element Method (FEM) can be used so to simulate and analyze material flow during the FSW process. As a result, thermal and mechanical stresses on the workpiece and welding tool can be analyzed and decreased. Effects of the welding process parameters such as tool rotational speed, welding speed, tool tilt angle, depth of the welding tool, and tool shoulder diameter can be analyzed and optimized so to increase the efficiency of the production process. Material characteristics of welded parts such as hardness or grain size can be analyzed so to increase the quality of part production. Residual stress, strain, deformation, and estimations of the temperatures in the welding area can be predicted using the simulation of FSW in the FEM software. Heat generation, thermal, and thermomechanical analyses can also be implemented on the welded parts to analyze the distribution of temperature and strain in the heat-affected zone (HAZ). Moreover, welding operations of dissimilar metals can be analyzed using numerical simulation to increase the capabilities of the welding methodology in different industrial applications. In this article, a review of the FSW process is presented. As a result, the research filed can be moved forward by reviewing and analyzing recent achievements in the published papers. This article is part of a Special Issue on Lightweighting Materials for Automotive Applications.