A METHOD OF SIMULTANEOUS QUENCHING BY THE INDUCTION OF THE DRIVER'S TEETH
TEODOR LEUCA , GABRIEL CHEREGI
Key words: Electromagnetic field coupled with the thermal one, numerical shaping
This paper presents a method of simultaneous quenching of the eddy currents of the driver's teeth. The method has some evident advantages as compared to the individual treatment of the driver's teeth. Examination of the heated piece, which has been treated, requires thermal diffusion problem solving coupled with the problem of the eddy currents. The results obtained are being presented.
The diffusion of the thermal field is defined by the following equation,
(10)
where c is the volumetric heat capacity, l is the heat conduction and p is the density of the power volume, that coverts the electromagnetic shape into heat. To the equation are being added the limitation condition
l 
(11)
and the temperature initial condition: 
.
Time discretization of the equation (10) is done by Crank-Nicholson technique, and the space discretization, by the method of the finished element.
Material data of the eddy currents problem (B-H characteristic and resistivity) depend on the temperature, whereas material data of the thermal problem depend on the outcome of the eddy currents (power density) and the temperature (thermal capacity and conduction). For this reason, for each time frame allocated to the thermal problem, it comes back to the eddy currents and diffusion problems, the material data being corrected. If there is no major correction, another time spacing will be taken. If there is any time instability whatsoever, then the time spacing deminishes.
Simultaneous quenching of the driver's teeth has some significant advantages in comparison to their individual quenching:
- time required for quenching a driver diminishes N times, where N is the number of the driver's teeth;
- to the same value of the current, the supply votage increases N times, and this is agreed in order to produce the high-frequency supply equipment.
- due to the periodicity of the electromagnetic and thermal field, the quenching obtained is uniform for all teeth.;
- the produced heat in order not to be diffused useless to the neighbouring teeth, so the method is efficient. (nu are sens fraza) ??????
In case of the high gear module, an inductor was made with the agency of which a single tooth was queched. The new method of simultaneous quenching of the driver's teeth consists in creating a system of coils in order to wrap all the drivers' teeth, similar to the wrapping of the common mode engine rotor with N poles. It is conceived in such a manner to be possible to change one one gear with another. So, unlike the electrical engine case, the frontal part of the coil's heating system looks like a funnel that allows the driver to fit in (fig. 1).
Fig. 1 High-efficiency quenching appliance
Results obtained in case of the inductor coil with circulary section conductor
I have chosen the current density of 15 A/mm2, with the frequency of 8000 Hz. In case of the structure with the circulary inductor there will be a current of : 2649,45, because the the circulary area of the conductor is: 176,63 mm2.
In case of the circulary conductor gear we have the following field lines (Fig. 2), set out for the time t = 21,28 s, in the initial phase 0:
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Field lines, for the circulary conductor inductor |
Magnetic induction for the phase 0 set out for the time t = 21,28 s |
Temperature maps for the time 0.1 si 21.28 sec (Fig. 3):
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Maps of temperatures recorded in the tooth at 0.1 sec |
Maps of the temperatures recorded in the tooth at ............la timpul.??????? |
Results obtained in case of the inductor with rectangular section conductor
The same graphics are set up in case of the rectangular inductor (Fig. 4)
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Field lines for the rectangular conductor inductor |
Magnetic induction for the phase 0 set out for the time t = 21,28 s |
For the rectangular section inductor, we have the following maps of temperatures recorded in the tooth (fig. 5):
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Maps of temperatures recorded in the tooth at 0.1 sec. |
Maps of temperatures recorded ni the tooth at 20.78 sec. |
The numerical modelling of the superficial quenching process by the agency of the eddy currents is a complex problem, where two curvilinear field problems are being solved at the same time: that of electromagnetic field and of thermal diffusion. The curviliniarity of the eddy currents is given by B-H curvilinear relation, whereas that of the thermal problem is given by the dependency of the thermal data (thermal conductivity, heat capacity, coefficient of thermal transmittance).
The coupling of the two problems results in the powerful
dependency of the B-H relation with
the temperature, in the problem of the electromagnetic field and source of the
thermal field, due to the Joule losses, in the thermal diffusion. The
curvilinearity of the B-H relation
will be solved by accepting the pseudolinearity model, where 
, the magnetic permeability is iteratively corrected in
accordance with the magnetic induction. The model's big advantage arises from
adopting the sinusoidal mode and the complex images, the numerical form of the
field equations leading to a system of algebrical equations with complex
coefficients.
The coupling of the two field problems is solved by the time discretization procedure, where, for each time spacing, the iterative correction of the electromagnetic and thermal data is made.
REFERENCES
G. Paoli, O. Biró, and G. Buchgraber, "Complex representation in nonlinear time harmonic eddy current problems," IEEE Trans. Magn., vol. 34, pp. 2625-2628, Sept. 1998.
R. Pascal, Ph. Conraux, and J. M. Bergheau, "Coupling between Finite Elements and Boundary Elements for the numerical simulation of induction heating processes using Harmonic Balance Method," IEEE Trans. Magn., vol. 39, pp. 1535-1538, May 2003
G. R. Cheregi, "Contributions on the numerical analysis of the heating process through induction in the thermal treatments issues," doctoral thesis, 2006.
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