Temperatures During the Heating Cycle

This article builds on the previous section and shows the temperature evolution of a nonferrous metal billet (i.e., a billet not affected by the Curie point) over time during a heating cycle.

The unstable phase during t corresponds to the curve for τ < 0.25 in Figure 13.2. After this phase, the surface and center temperature curves rise together until the power is disconnected at t. The temperature difference during t is determined by the effects of the limited penetration depth and the radiation discussed above. After time t, the process temperature reaches equilibrium.

The time provided takes into account all cooling processes between the billet leaving the induction coil and before use. If the surface cools exceptionally rapidly, a B-curve may be used, indicated by a dashed line.

Note that the hottest point is actually below the surface. In the case of an overheated aluminum billet, a locally molten ring of metal can be seen approximately 10 mm below the surface.

When calculating the power input, care must be taken to ensure that t is below the melting point and that the temperature difference of 0.1° is small enough to prevent stress cracking. Although no precise relationship has been established, a rule of thumb for nonferrous metals is a temperature difference of 1.1°C per millimeter of radius. In practice, the measured temperature profiles are experimentally measured using a chromium-nickel-chromium-aluminum thermocouple. These results generally agree with the calculated results. The difference between the hottest point and the surface temperature is often small and usually negligible shortly after heating begins, even for metals with low thermal conductivity. It is possible to measure the temperature distribution at the end of a billet, and sometimes even within the billet heating apparatus. The effects of the phase connections and coil design in a three-phase induction coil on the resulting temperature difference, as well as the heating rate, will be discussed later in this article.

Magnetic saturation and the Curie point complicate the temperature distribution in steel. Initially, when the metal is cold, magnetic saturation causes the magnetic flux to penetrate deeper than the penetration layer concept suggests. This alters the power distribution in the steel. Subsequently, when the surface reaches the Curie point and becomes nonmagnetic, the power density at the surface decreases. Internally, however, the steel remains magnetic, and the power input remains high. This influence is also affected by the steel's variable resistivity, which changes the power applied at different depths.

These effects have been graphically visualized as a "magnetic wave" moving from the surface to the interior. However, this is a simplified representation of the complex situation. More precise calculations can be performed using a computer. This article shows a typical temperature-time curve for a steel slab. The curve indicates the temperatures at the surface, the center, and at r = 0.73°. After an initial period of instability, the three points move in parallel until the surface reaches the Curie point. At the Curie point, the surface heating rate slows. As each layer reaches the Curie point, the slab gradually becomes nonmagnetic.