Investigation of the temperature field developed by a spinning beam in laser processing

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I.

INTRODUCTION

HIGH powered CO2 lasers have been used for metallic surface hardening, alloying, and incorporation of hard particles to modify surface properties normally using a stationary beam.[1–7] The advantages of using a spinning beam have been reported previously for titanium alloys and include the production of a smooth surface and a uniformly thick Ti-SiCp MMC layer by incorporation of hard particles in the Ti-6Al-4V alloy surface[8] and a smooth surface obtained in titanium alloy nitriding.[9] Spinning the beam is also considered to provide a more effective stirring of the melt than the stationary beam. However, the interaction time between the laser and the surface is considerably shorter with a spinning than a stationary beam. For example, when the beam is spinning at 1000 rpm in a 5-mmdiameter circle, the interaction time is 0.025 that of a stationary beam when the same specimen velocity is used. Therefore, to produce melt depths similar to those obtained with a stationary beam, it is necessary to increase the energy input when using a spinning beam. Hu and Baker[9] achieved this by using the laser closer to focus, with a 5to 10-mm defocus above the focal point, while retaining the same laser power. A similar situation would exist with an oscillating beam arrangement. Therefore, the development of a practical model to estimate the temperature profile and then to predict the optimum conditions when a spinning beam is used is necessary, so that the data already collected can be used to extend the range of experimental parameters and allow their optimization. Approaches to modeling the temperature field induced by a laser beam moving over the surface of a semi-infinite solid (equivalent C. HU, Senior Research Fellow, and T.N. BAKER, Professor of Metallurgy, and are with the Metallurgy and Engineering Materials Group, Department of Mechanical Engineering, University of Strathclyde, Glasgow G1 1XN, United Kingdom. Manuscript submitted January 3, 1996. METALLURGICAL AND MATERIALS TRANSACTIONS A

to a specimen traversing below the laser beam) include the integral of the solution of a point source over the area of the beam[10] and numerical procedures[10–17], which are rigorous but complex and difficult to use in practice. More recently, a simple model was given by Steen et al.,[18] which predicted the depth but not the profile of the melt. A different approach was used by Ashby and Easterling,[19] who developed an approximate solution for the entire temperature field produced by a Gaussian beam, based on the work of Bass,[20] where analytical temperature field equations were originally presented. Shercliff and Ashby[21] reworked Ashby’s earlier model[19] in dimensionless terms and used the superposition of Gaussian sources for a non-Gaussian beam (rectangular-uniform). This extended the application to a wide range of laser processing. Hu and Baker[22] used line sources together with the superposition of Gaussian sources, and therefore overcame the difficulties of the determination of the locations and profi