Study On Non-fourier Effects On Temperature Field Of Induction Quenching Processes

Electromagnetic induction quenching is one of the hardening techniques widely usedfor the crankshaft surface. In this paper, theoretical and numerical analysis on thenon-Fourier temperature field of the electromagnetic induction hardening process werecarried out, on the basis of in-depth understanding of the principle of electromageticinduction hardening and the actual quenching process. The main contents in this researchare shown as follows:The mathematical model for the one-dimension non-Fourier temperature field whichtook into account the internal heat source was derived in the Cartesian coordinate system,on the basis of analyzing the distributed heat of the Electromagnetic induction hardeningprocess, according to the engineering background of Electromagnetic inductionhardening process. The analytical solutions of the non-Fourier temperature field includingrectangular-distribution heat source and the one including linear-distribution heat sourcewere obtained on the Cartesian coord1inate system, through the using of Green function,Laplace transform and the inverse transform of Laplace. Comparison between thenon-Fourier and Fourier temperature fields shows that there is a significant shock in thetemperature before it is stable because of the limited heat propagation speed and that ittakes a longer time to reach a stable temperature, when taking into account thenon-Fourier effect. The influence of the pulse width of the heat source on the non-Fouriereffect was analyzed. Results show that the non-Fourier effect is related to the pulse widthand the larger the pulse width, the less obvious the non-Fourier effect. Comparisonbetween the temperature fields corresponding to the rectangular-distribution heat sourceand linear-distribution heat source shows that the temperature fields are basically thesame. Therefore, the linear-distribution heat source problem can be simplified to thecorresponding rectangular-distribution heat source problem, in order to improve thecomputation efficiency.The temperature governing equations for one-dimension non-Fourier transient heatconduction problem which includes internal heat source in cylindrical and sphericalcoordinates were derived from the Cartesian coordinates according to the rotating shaftequation. The temperature filed was obtained through the using of Green Function, dimensionless methods and discrete integral. Results show that the heat propagation incylindrical and spherical coordinates has spikes, which is different from the form ofrectangular square wave in Cartesian coordinates due to the difference of their shapes.Hence, the shock in cylindrical and spherical coordinates is more intense than inCartesian coordinates. Therefore, it can be predicted that in the same thermaldisturbances, the temperature fluctuation, maximum temperature, and the resultingengineering problem in cylindrical and spherical coordinates are more obvious, higher,and more serious than those in Cartesian coordinates, respectively.Finite difference method was utilized to study the two-dimension non-Fouriertemperature field. The explicit scheme was given and its stability was analyzed. Resultsshow that the explicit difference scheme for the two-dimension non-Fourier temperaturefield does not meet the stability requirement.