Frequency, power and case depth

Three variables, not one

People ask for a case depth and expect it to be a single machine setting. It is not. It is the outcome of three things that interact, and changing any one of them moves the answer.

• Frequency sets the depth at which energy is deposited.
• Power density sets how fast that layer reaches austenitising temperature.
• Heating time sets how far heat conducts inward before you quench.

A shallow case comes from high frequency, high power density and a short time: get the surface hot before the heat has a chance to travel. A deep case comes from lower frequency, lower power density and a longer time: let conduction do the work. Get the combination wrong in one direction and you overheat the surface; wrong in the other and you never reach transformation temperature at depth.

Reference depth against frequency

Reference depth is the depth at which the induced current density has fallen to about 37 percent of its surface value. Roughly 86 percent of the heating happens within it. It follows the relation below, and for steel it changes dramatically as the part passes the Curie point, because the steel stops being magnetic.

Two things to take from this table. First, the roughly seventeen-fold jump between the cold and hot columns. That is the Curie transition, and it happens partway through every hardening cycle on steel. It is that large because two things move at once: resistivity rises by about seven and a half times, and relative permeability collapses from around 40 to 1. Depth follows the square root of their ratio, so the two multiply rather than cancel. Second, the shape of the frequency relationship: quadrupling frequency halves the depth, so moving from 10 kHz to 40 kHz does not give you a quarter of the depth, it gives you half.

Calculate this for your own material

Reference depth is not case depth

This is the distinction that causes the most confusion, so it is worth stating flatly:reference depth tells you where the energy goes in. Case depth tells you how deep the metallurgy changed. They are related but they are not the same number.

Case depth is measured after the fact, by sectioning a part and running a microhardness traverse from the surface inward. The case ends where hardness falls to a defined limit. What determines it is how deep the steel actually got above its austenitising temperature before the quench arrived, which depends on the heat that conducted inward as well as the heat generated in place.

In practice, a useful working case is usually deeper than the hot reference depth, because conduction has had time to work. But the relationship depends on the steel, the geometry, the power density and the cycle, which is why case depth is developed on real parts and verified by hardness testing rather than calculated and assumed.

Power density and heating time

Power density is power per unit of heated surface area, usually stated in kilowatts per square centimetre. It is a more useful number than total power, because a 100 kW supply feeding a large coil and a 100 kW supply feeding a small one produce entirely different results.

High power density with a short time gives a steep thermal gradient: hot surface, cold core, shallow case. Low power density with a long time gives a shallow gradient: heat has time to conduct, so the case is deeper but the total heat input is higher and so is the distortion risk.

On a scanning machine the equivalent of heating time is scan speed. Slow the traverse and each point on the shaft spends longer under the coil, so the case deepens. This is the parameter an operator is most likely to be given control of, and it is why the PLC holds it constant.

The frequency bands in practice

Manufacturers describe frequency in bands rather than exact figures, because the right number depends on the part. The bands and what they suit:

• Medium frequency. Deeper penetration. Used for billet heating, bar and end heating for forging, shrink fitting, pre-heating and any case where you want the section heated through rather than a hot skin.
• High frequency. Shallower penetration. Used for hardening auto components, tractor parts, hand tools and agricultural tools, and for brazing.
• Ultra high frequency. Very shallow, very fast. Used for fine brazing work, small joints and thin sections where a lower frequency would heat too much surrounding metal.

How we select your machine

We select the frequency together with power, coil geometry and cycle time. Our PLC controlled vertical scanner covers the following operating range.

We select the frequency for your component and required case depth. A power rating alone does not define the heating process.

How to specify it

When you ask for a quotation, these details help us specify the machine, in the order they matter:

1. The part. A drawing is worth a page of description.
2. The material. Grade and condition. C45, EN8, EN19, EN31, 4140 and so on.
3. The surface to be treated. Which feature, over what length, and what must stay soft.
4. The required case depth and surface hardness, with tolerances, and the standard they are measured to.
5. The production rate. Parts per hour, and whether that is a shift figure or a peak.
6. What happens before and after. Prior heat treatment, and whether tempering is in scope.

With those six you get a machine specification. Without them you get a price for something that may not do the job.

The quote form asks for exactly these