Computer-aided Analysis Of High Speed Scanning Induction Systems For Rail Heating Before Hardening - Petrica Taras, Virgiliu Fireteanu

Computer-Aided Analysis of High Speed Scanning Induction Systems for Rail Heating before Hardening P. TARAS and V. FIRETEANU POLITEHNICA University of Bucharest, EPM_NM Laboratory 313 Spl. Independentei, RO-060042, Bucharest, Romania http://amotion.pub.ro/~epm

Abstract The paper analyses induction systems for scanning heating of rails after the exit from the finishing rolling mill, in order to realize the optimum profile of temperature at the entry in the hardening zone of the rails production lines. Two configurations of modular transversal flux inductors for railhead heating are studied. The result analysis concerns the temperature chart along the rail and in the rail cross-section and the temperature transversal profile of upper and lateral sides of the railhead. Introduction An induction system for rails heating may be used to increase only the temperature of the head of the rail, thus insuring the optimal temperature value for hardening, or to compensate the thermal losses between the finishing rolling mill and the hardening installation. Only the first technology is considered in this paper. The high-speed scanning induction heating applications requires high levels of power, which can be achieved by using relatively long inductors. Such inductor must also ensure a uniform profile of temperature in order to obtain an uniform hardening profile all over the railhead circumference. This supposes a compromise between the dimensions of the magnetic core and coils in order to achieve the optimal flow pattern of the eddy currents in the rail. Since the rail transversal cross-section is very narrow towards the rail length, the 3D finite element models demands important memory and time computing resources. Consequently two-dimension models are used as a first approach in this paper to estimate some of the parameters of the inductor. The 3D models take those estimations as a starting point. Imposed values of the hardening depth  - thickness of the railhead layer to be hardened - are considered. At the end of the heating a surface layer of this thickness must have a temperature field optimum for hardening, higher or equal to a value depending on the rail steel hardening properties. Finite Element 2D Models of Rails Induction Heating The preliminary 2D analyses concern longitudinal flux inductors. The first model is in fact a 1.5 D model of single-shot induction heating in longitudinal flux, Fig. 1, which estimate the current, the induced power and the increase of the rail surface temperature in a given time. The second 2D model, Fig. 2, is a scanning induction heating model that gives a raw estimation of the heating time and inductor length for imposed value of rail speed. Both models take into account the temperature dependent properties of the rail material.

Air Air

Rail

Inductor Inductor

Fig. 1. The 1.5D finite element model of the rail heating

Rail

Fig. 2. The 2D finite element model of the rail heating

1.5D Single – Shot Magneto-thermal Model The simulations with this model consider the initial rail temperature 680 C and the final temperature f = 750 C at the hardening depth . The current I [A/cm] related the inductor unit length is varied over a range of values and the frequencies 200 Hz, 500 Hz, 1000 Hz and 3000 Hz are considered. This model provides the time interval tf[s] in which the temperature reaches the value f at the hardening depth , the surface temperature at the end of heating and the induced power p[W/cm2] related to the unit rail surface. The examples of simulation results in Figs. 3 and 4, concern the temperature variation in the rail depth and the time variation of the induced power in the railhead.

Fig. 3. Temperature variation in the rail depth (f = 1 kHz, tf = 1.5 s, I = 2 kA/cm)

Fig. 4. Time variation of active induced power (f = 1 kHz, I = 2 kA/cm)

Magneto-thermal 2D Model of Scanning Induction Heating To establish a base of comparison, common values of the heating time 1.0 s, 1.5 s and 2.0 s are imposed, two base frequencies, 500 Hz and 1000 Hz and the corresponding hardening depth 10 mm and 5 mm were selected. The model of scanning induction heating takes into account the value 1 m/s of rail speed. The simulation results presented in Table 1 are the temperature  at the depth  in the rail at the end of heating, which, as expected, is not so far from the reference value f , the temperature surf of the rail surface at the inductor exit, the length Li of the inductor, and the power induced in the rail, P2rail. The contour of the rail heat, respectively the depth of the 2D model is 130 mm. Table 1 f [Hz] 1000 500

 [mm] 5 10

 [C] 757.7 742.0

surf [C] 790 804

Li [m] 1.5 2.0

P2rail [kW] 772 1276

Transversal Flux Inductors for Railhead Hardening Two transversal flux systems called OO-LONG, Fig. 5, and OO-TRANS, Fig. 6, are studied. Two identical coils supplied with opposite currents are placed along the rail in this first case. The second heating system, Fig. 6, contains two transversal flux inductors. The short COIL-in-COIL_OO-TRANS inductor has two different coils, one for the upper railhead face heating and the second for lateral railhead faces heating. The long COIL-by-COIL OO-TRANS inductor, Fig. 6, contains two identical coils, for heating of the central area of upper railhead face, respectively of the lateral railhead faces.

Fig. 5. OO-LONG transversal flux heating system

Fig. 6. OO-TRANS transversal flux heating system

Magneto-harmonic 3D Model of Electromagnetic Field Computation, OO-LONG system Based on the scalar formulation of the quasi-static harmonic electromagnetic field, the finite element analysis of rail induction heating in transversal flux inductors, concerns the computation of induced currents, Fig. 7, and the corresponding volume density of induced power. Related to the integral along the rail of the power density on the railhead surface, the transversal profile, Fig. 8, shows a decrease with about 10 % of the induced power to the extremity of the upper face, followed by an increase of about 16 % in the upper part of the lateral face. After this maximum, the induced power decreases in transversal direction at about 50 % of the value in the center of upper railhead face. For 1 kHz for frequency and 5 for relative permeability, the induced power related to the unit length is 443.1 kW/m. If the rail steel is non-magnetic, the induced power decreases at 243.3 kW/m. Consequently, for heating under the Curie point, a rigorous evaluation of electromagnetic field must take into account the non-linearity of the rail steel.

Fig. 7. Density of induced current, OO-LONG system

Fig. 8. Transversal profile of induced power

Magneto-thermal 3D Models of Scanning Rail Head Heating, OO-LONG system The magneto-thermal model of scanning induction heating is a coupling between the electromagnetic field analysis in frequency domain and the step-by-step in time domain computation of thermal field. This model takes into account each time step a new position of the rail with respect the inductor dependent on scanning speed. For reasonable values of computation time, independent on temperature physical properties were considered. The steady state rail temperature and the corresponding temperature in the cross-section of the rail when the rail leaves the inductor are presented in Figure 9. The transient temperature variation in two middle points of the upper and lateral faces of the railhead, Fig. 10, shows a heating of the railhead surface of about 708 – 680 = 28 C, when the rail passes with the speed 1 m/s inside the OO-LONG inductor, 320 mm length.

Fig. 9. Steady state rail temperature, OO-LONG system The similarity between the transversal profile of railhead surface steady state temperature at the exit from the inductor, Fig. 11, and the transversal profile of the induced power, Fig. 8, is the result of reduced contribution of the thermal conduction phenomenon in the induction heating o rails for high values of scanning speed. Consequently, in high speed scanning induction-heating applications, the transversal non-uniformity of rail temperature at the inductor exit can be appreciated by the transversal profile of the induced power density integrated along the rail.

Fig. 10. Railhead temperature increase, OO-LONG system

Fig. 11. Transversal profile of rail heating, OO-LONG

Magneto-thermal 3D Models of Scanning Rail Head Heating, OO-TRANS System The steady state rail temperature and the corresponding temperature in the cross-section of the rail when the rail leaves the inductor are presented in Figure 12. The transient temperature variation in two middle points of the upper and lateral faces of the railhead, Fig. 13, shows a heating of the railhead surface of about 733 – 680 = 53 C, when the rail passes with the speed 1 m/s inside the OO-TRANS system, 1254 mm length.

Fig. 12. Steady state rail temperature, OO-TRANS system

Fig. 13. Railhead temperature increase, OO-LONG system

Fig. 14. Transversal profile of rail heating, OO-LONG

Conclusions Two modular variants of transversal flux inductors for high speed scanning heating of rails before hardening were evaluated. The results presented in the paper confirm the increasing interest in computer aided investigation and optimization of new devices based on finite element analyses and models developed with professional software. References [1] X. Zhan, S. Wang (2005), Proceedings of the Eastern Asia Society for Transportation Studies, Vol. 5, 263 - 271 [2] C. Shupe (1970), Rail Hardening machine and method, , US Patent no 4201602 [3] V. Fireteanu, M. Popa and P. TARAS (2009), 14th International Symposium on Electromagnetic Fields