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# Analytical Solution of Transient Three-Dimensional Temperature Field in a Rotating Cylinder Subject to a Localized Laser Beam

[+] Author and Article Information
Mostafa M. Kashani

Precision Manufacturing Lab (PML),
Department of Mechanical Engineering,
Sharif University of Technology,
Tehran 11365-11155, Iran
e-mail: kashani@mech.sharif.edu

Professor
Mem. ASME
Precision Manufacturing Lab,
Department of Mechanical Engineering,
Sharif University of Technology,
Tehran 11365-11155, Iran
e-mail: movahhed@sharif.edu

Professor
Mem. ASME
Department of Mechanical Engineering,
Sharif University of Technology,
Tehran 11365-11155, Iran

Reza Shoja Razavi

Associate Professor
Department of Materials Engineering,
Malek-ashtar University of Technology,
Shahin Shahr,
Isfahan 83145-115, Iran
e-mail: shoja_r@mut-es.ac.ir

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received June 15, 2016; final manuscript received December 13, 2016; published online February 28, 2017. Assoc. Editor: Ali Khounsary.

J. Heat Transfer 139(6), 062701 (Feb 28, 2017) (8 pages) Paper No: HT-16-1387; doi: 10.1115/1.4035654 History: Received June 15, 2016; Revised December 13, 2016

## Abstract

Laser-assisted machining (LAM) is a growing trend in machining of hard to cut materials. In most experimental cases, LAM is carried out in two stages; first, laser and machine parameters are tuned to adjust the temperature at the material removal point ($Tmr$), and second, the cutting tool is engaged to cut the points that have already been heated by the laser. Alternatively, an analytical model for the prediction of temperature filed can replace lengthy experimentation needed for tuning the material removal temperature. This paper presents an analytical solution to the transient temperature field in a rotating cylinder subject to a localized laser heat source based on Green's functions. The analytical solution is validated by comparing the surface point temperatures to thermal experiments on DIN 1.7225 steel, which shows good agreement in trend and values. Furthermore, a finite element model is developed and verified by the results of the same experiments, providing a more detailed investigation on the performance of the analytical model. The developed analytical scheme can be used to readily calculate pointwise temperatures on workpiece surface and internal points which can be used as a tool for designing machining conditions.

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## Figures

Fig. 1

Configuration of workpiece, pyrometer, and laser head

Fig. 2

Flowchart of the analytical solution process

Fig. 3

Meshing of the core and outer regions

Fig. 4

Temperature distribution contours (°C). (t = 60.8 s, N = 300 rpm, f = 0.1044 mm/rev, PL = 300 W).

Fig. 5

Selected points inside the pyrometer measurement region

Fig. 6

Analytically determined temperature histories for points in the pyrometer focus circle

Fig. 7

Comparison between experimental and analytical results; analytical results calculated by upper and lower values of the absorption coefficient are shown with the dotted lines

Fig. 8

Averaged versus central point temperature histories from analytical results

Fig. 9

Analytical (left) versus FE (right) temperature contours (°C) for the instantaneous axial laser emission plane. (t = 38.4 s, Z = 20 mm, N = 300 rpm, f = 0.1044 mm/rev, PL = 300 W).

Fig. 10

Analytical (top) versus FE (bottom) temperature contours (°C) at the instantaneous transverse laser emission plane. (t = 38.4 s, f = 73 deg, N = 300 rpm, f = 0.1044 mm/rev, PL = 300 W).

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