KEVOS® MAKEOS · Materials
Induction Hardening Plan (Reference Depth, Frequency for the Case, Heating Energy and Power)
For induction hardening a bar to a given case depth, does the generator frequency suit the case, what frequency would, and how much energy and power does heating the surface layer need?
Plan for induction surface hardening of a round bar: the electromagnetic reference (penetration) depth at the generator frequency from the steel's hot resistivity and relative permeability, its ratio to the case depth against your range, the frequency that would put the reference depth at the middle of that range, the bar diameter as a multiple of the reference depth, and the energy to heat the surface layer to the hardening temperature, with the power at the work and from the generator and the surface power density for the heating time you enter.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Part and case | ||
| Bar diameter | mm | Diameter of the round bar or shaft being hardened. |
| Heated length | mm | Length heated at once by the coil (for scanning, the length heated in the time entered). |
| Case depth required | mm | Hardened case depth required, from the drawing. |
| Heated depth as a multiple of the case depth | Depth that must reach the hardening temperature, as a multiple of the case depth, to allow for the transition below the case. | |
| Electrical | ||
| Generator frequency | kHz | Output frequency of the induction generator. |
| Steel resistivity at the hardening temperature | µΩ·m | Electrical resistivity of the steel at the hardening temperature, which is several times its room-temperature value. |
| Relative permeability while hot | Relative magnetic permeability of the steel while it is hot; it falls to 1 above the Curie point, where the hardening is done. | |
| Least reference depth as a multiple of the case | Least ratio of reference depth to case depth you accept for this work, from your practice or the equipment maker. | |
| Largest reference depth as a multiple of the case | Largest ratio of reference depth to case depth you accept. | |
| Least bar diameter as a multiple of the reference depth | Least ratio of bar diameter to reference depth for efficient heating, from the equipment maker's guidance. | |
| Heating | ||
| Hardening temperature | °C | Temperature the surface layer must reach for hardening. |
| Starting temperature | °C | Temperature of the part before heating. |
| Mean specific heat over the range | kJ/(kg·K) | Mean specific heat of the steel between the starting and hardening temperatures, from material data. |
| Steel density | kg/m³ | Density of the steel. |
| Heating time | s | Time the layer is heated for, from the process (often a few seconds). |
| Generator to work efficiency | % | Share of the generator output that ends up as heat in the work after coil and transformer losses. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
Part and case
What this means: Bar diameter
- What it is
- The diameter of the round bar or shaft being surface hardened.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 2000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 40 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the heated layer volume and the diameter to depth ratio.
- Get it right
- Use the diameter at the hardened zone.
What this means: Heated length
- What it is
- The length of the bar heated at once by the coil, or the length heated in the time entered when scanning.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Energy and power rise in proportion.
- Get it right
- For a scanning coil, use the coil length the bar passes in the heating time.
What this means: Case depth required
- What it is
- The hardened case depth the drawing requires.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 50 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the frequency range and the heated layer.
- Get it right
- Check how the drawing defines case depth, usually to a stated hardness.
What this means: Heated depth as a multiple of the case depth
- What it is
- How deep the layer heated to the hardening temperature must reach, as a multiple of the case depth, allowing for the transition zone below the hard case.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 10. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.5 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A deeper heated layer needs more energy and power.
- Get it right
- Base it on sectioned trial parts; 1.2 to 2 is a common range.
Electrical
What this means: Generator frequency
- What it is
- The output frequency of the induction generator, which sets how deep the induced current and its heat reach.
- Units and format
- Enter a number in kHz: kHz. The form accepts 0.01 kHz to 10000 kHz. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 kHz as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Higher frequency gives a shallower reference depth.
- Get it right
- Read it from the generator; many units can only run within a narrow band.
What this means: Steel resistivity at the hardening temperature
- What it is
- The electrical resistivity of the steel at the hardening temperature, several times higher than at room temperature.
- Units and format
- Enter a number in µΩ·m: µΩ·m. The form accepts 0.01 µΩ·m to 100 µΩ·m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.1 µΩ·m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The reference depth rises with its square root.
- Get it right
- About 1.0 to 1.2 µΩ·m is typical for carbon steels above about 800 °C; use material data for alloy steels.
What this means: Relative permeability while hot
- What it is
- The relative magnetic permeability of the steel while it is hot; above the Curie point it falls to 1.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 10000. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher permeability makes the reference depth smaller.
- Get it right
- Use 1 for hardening temperatures above about 770 °C; below that, steel is magnetic and the depth is much smaller.
What this means: Least reference depth as a multiple of the case
- What it is
- The least ratio of reference depth to case depth that your practice or the equipment maker accepts for this work.
- Units and format
- Enter a plain number with no unit. The form accepts 0.1 to 10. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only moves the lower edge of the frequency range.
- Get it right
- Use guidance from the equipment maker or your own proven processes.
What this means: Largest reference depth as a multiple of the ca…
- What it is
- The largest ratio of reference depth to case depth you accept.
- Units and format
- Enter a plain number with no unit. The form accepts 0.1 to 10. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only moves the upper edge of the frequency range.
- Get it right
- Use guidance from the equipment maker or your own proven processes.
What this means: Least bar diameter as a multiple of the referen…
- What it is
- The least ratio of bar diameter to reference depth for the coil to heat the bar efficiently.
- Units and format
- Enter a plain number with no unit. The form accepts 0.1 to 100. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only moves the bar size pass line.
- Get it right
- Take it from the equipment maker; small bars at low frequency heat poorly.
Heating
What this means: Hardening temperature
- What it is
- The temperature the surface layer must reach to harden on quenching.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts 0.000001 °C to 1500 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 900 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Energy and power rise with the temperature rise.
- Get it right
- Induction hardening uses higher temperatures than furnace hardening because the time is short; follow the process sheet.
What this means: Starting temperature
- What it is
- The temperature of the part before heating starts.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -50 °C to 500 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A warmer start lowers the energy needed.
- Get it right
- Room temperature unless the part is preheated.
What this means: Mean specific heat over the range
- What it is
- The mean specific heat of the steel between the starting and the hardening temperature.
- Units and format
- Enter a number in kJ/(kg·K): kilojoules per kilogram per kelvin. The form accepts 0.1 kJ/(kg·K) to 5 kJ/(kg·K). Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.6 kJ/(kg·K) as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Energy and power rise in proportion.
- Get it right
- Steel's specific heat rises with temperature; use a mean over the range from material data.
What this means: Steel density
- What it is
- The density of the steel, used to turn the heated layer volume into a mass.
- Units and format
- Enter a number in kg/m³: kilograms per cubic metre. The form accepts 1000 kg/m³ to 20000 kg/m³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 7850 kg/m³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Energy and power rise in proportion.
- Get it right
- About 7,850 kg/m³ for carbon steels.
What this means: Heating time
- What it is
- The time over which the layer is heated to the hardening temperature.
- Units and format
- Enter a number in s: seconds. The form accepts 0.000001 s to 3600 s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4 s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A shorter time needs proportionally more power.
- Get it right
- Take it from the process sheet; induction heating times are often a few seconds.
What this means: Generator to work efficiency
- What it is
- The share of the generator output that becomes heat in the workpiece after coil, transformer and lead losses.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 1% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 70% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A lower efficiency raises the generator power needed.
- Get it right
- Coil design and coupling distance affect it strongly; use the equipment maker's figure.
Method and formulas
- Reference depth δ = 503 √(ρ ÷ (μ_r f)) m, with ρ in Ω·m and f in Hz.
- Frequency for a target depth δ_t = ρ (503 ÷ δ_t)² ÷ μ_r, with δ_t at the middle of your ratio range times the case depth.
- Heated layer: an annulus of depth h = case × multiple; mass m = ρ_s π ÷ 4 (D² − (D − 2h)²) L; energy = m c_p ΔT.
- Power at the work = energy ÷ time; generator power = work power ÷ efficiency; power density = work power ÷ (π D L).
- Example: at 10 kHz the reference depth is 5.2787 mm, 2.6393 times the 2 mm case; about 30.96 kHz would suit it. Heating the layer in 4 s needs 51.62 kW from the generator.
Limitations
- The reference depth is an electromagnetic estimate for a uniform material; the hardened depth also depends on heating time, conduction into the core and the quench.
- Energy for the heated layer only; heat conducted into the core during heating and losses from the surface add to the real demand.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check whether an induction generator's frequency suits a case depth
- Find the frequency for a new case depth
- Estimate the power for a heating time
Who it is for
- Heat treaters
- Process engineers
- Manufacturing engineers
What you get
- Reference depth at the generator frequency and its ratio to the case
- Frequency for the middle of your ratio range
- Bar diameter as a multiple of the reference depth
- Energy for the heated layer, power at the work and from the generator, surface power density
Interpreting the result
- Higher frequencies concentrate the heat in a shallower layer, so frequency is chosen to suit the case depth and power to suit the heating time.
- Below the Curie point steel is magnetic and the reference depth is much smaller, which is why surface layers heat fastest early in the cycle.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 487–489, 467–470. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These KEVOS® Library readings explain the method this tool uses, with worked examples.
Method explained here · KEVOS® original book
Reference depth and the Curie point
In Induction Hardening by the Numbers
What it covers: How frequency, resistivity and permeability set the depth of induction heating, why steel's heating depth jumps when it passes its Curie point, and how to choose a frequency for a case depth.
Method explained here · KEVOS® original book
Induction and infrared heating
In Industrial Electric Heating by the Numbers
What it covers: Heat steel inside itself with induction, choose a frequency from the depth of penetration, size the power to heat a bar end, and use infrared emitters to heat surfaces by radiation.
Useful alongside · KEVOS® original book
Standard depth of penetration and choosing a frequency
In Eddy-Current Inspection by the Numbers
What it covers: How deep eddy currents reach in aluminium, copper alloys and steel, the three-depth thickness rule for conductivity tests, the stacking test, and choosing a frequency for each job.
Useful alongside · Library collection
Heat treatment and surface hardening explained for designers and buyers
In Machine Elements and Mechanical Design
What it covers: A drawing that just says "harden" invites cracked, distorted or soft parts. How heat treatment works, which process suits which part, and how to specify and verify the result.
KEVOS® tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.