Calculating Power Distribution for Molybdenum Electrodes in All-Electric Melting Furnaces

The section most often skipped in electric melting furnace design is power distribution: many furnaces only discover local overheating or insufficient melting after they are built, and the root cause lies in geometry, conductivity and heat load not being reconciled at the calculation stage. What follows is a workable calculation chain for process and electrical engineers to check against. Get power distribution right, and both the life account and the output account of the molybdenum electrodes will hold up.

Four inputs to the calculation chain

The first step is to collect the basic data: the target melting rate and specific heat consumption; the conductivity of the glass at working temperature, where a typical soda-lime melt at around 1300 °C is on the order of a few tenths of a siemens per centimeter and varies markedly with temperature and recipe, so measured values must be used rather than generic handbook figures; the tank wall geometry and the electrode layout; and the current density set by the life target. Only when all four inputs are complete does the calculation mean anything; any one of them guessed will leave the result without constraint. Where measured conductivity is unavailable, it is better to measure the resistance of a small melt sample first than to apply generic handbook values.

From a single electrode to the whole tank

The current of a single molybdenum electrode equals the current density multiplied by the immersed cross-section. The equivalent resistance between a pair of adjacent electrodes is estimated by dividing the melt resistivity by the electrode spacing and multiplying by a geometric factor for the current path, the so-called cell constant. Voltage is the product of current and equivalent resistance, and power the product of the two. When several electrodes are connected in parallel, the current divides naturally according to differences in cell constant, and verification should rely on measured current. Although top electrodes carry a low share of the power, they directly determine refining quality and bubble rating and should not simply be allocated in proportion. The power of each electrode pair is distributed along the tank length and then adjusted to the thermal requirements:

On standards, electrode products are controlled to YS/T 1312-2019, Molybdenum Electrodes; molybdenum rods follow ASTM B387 / GB/T 17792; molybdenum plate and disc follow ASTM B386 / GB/T 3876; acceptance is based on the quality certificate and measured records.

The ranges in the table are indicative; the actual split should be verified against the heat-loss boundary conditions of the specific furnace.

Verification and iteration

For the electrical system and the process implementation of the furnace, see the preparation and process notes.

After the calculation, verify in both directions:

• plot temperature and current density along the tank length and check whether any local overheating exceeds the limits of the electrodes and refractories;
• check against the melting rate target whether the total power leaves more than 10% of adjustment margin;
• verify that the current density of each electrode falls within the range permitted for its life;
• check whether the power share of each tank zone matches its thermal task.

After start-up, correct the cell constant by regression against measured voltage and current, the glass temperature field and product quality, and build a design file so that the life expectation of the electrodes is realized. When WeiBeam.com takes part in a project, we make a habit of capturing this iteration data for reuse on furnaces of the same series, which is an effective way to shorten the ramp-up period of a new furnace.