Abstract
In this paper, a solution is provided to solve the heat conduction equation in the three-dimensional cylinder region, where the laser intensity of the material irradiation surface is expressed as a Gaussian distribution. Based on the symmetry of heat distribution, firstly, the form of the heat equation in the common rectangular coordinate system is changed to another form in the two-dimensional cylindrical coordinate system. Secondly, the ADI with the backward Euler method and with Crank–Nicolson method are established to discretize the model in the cylindrical coordinate system, after which the simulation results are obtained, where the first kind of boundary value condition is used to verify the accuracy of these two algorithms. Then, the above two methods are used to solve the model with the third kind of boundary value condition. Finally, the comparison is performed with the results obtained by the MATLAB’s PDETOOL, which shows that the solution is more feasible and efficient.
Highlights
In the fields of advanced equipment manufacturing for example aerospace and new energy, hard and brittle materials such as beryllium, fused silica, and diamond are widely used to manufacture products and devices
The implementation of the alternating direction implicit (ADI)-finite-difference time-domain method (FDTD) and its convolution perfect matching layer (CPML) is divided into three steps
Matrix expression of ADI-FDTD method in three-dimensional cylindrical coordinate system is proposed by matrix transformation
Summary
In the fields of advanced equipment manufacturing for example aerospace and new energy, hard and brittle materials such as beryllium, fused silica, and diamond are widely used to manufacture products and devices. Some numerical methods had been proposed [3,4,5,6,7,8,9,10,11,12,13,14], such as the alternating direction implicit (ADI) finite-difference time-domain method (FDTD) and its convolution perfect matching layer (CPML). Transform the finite difference time domain method in the traditional three-dimensional cylindrical coordinate system into a matrix expression. Matrix expression of ADI-FDTD method in three-dimensional cylindrical coordinate system is proposed by matrix transformation. The existing methods directly give a three-dimensional cylindrical coordinate model in the electromagnetic environment, combined with the unconditionally stable ADI algorithm. We propose a three-dimensional heat conduction model of laser processing in the rectangular coordinate system, which is discretely transformed, simplified, and solved in three steps. The heat conduction distribution can be solved quickly and stably, which provides an effective calculation method for the optimization of related parameter
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