induction-hardening

name	induction-hardening
description	Induction hardening process design — Lenz's law, skin depth, power density, frequency selection, case depth, quench parameters, distortion, residual stress, Jominy correlation, AMS 2304/2301, scanning vs. single-shot, tempering requirements, gear and shaft applications.
metadata	{"priority":7,"promptSignals":{"phrases":["induction hardening","induction heat treatment","induction case hardening","surface hardening induction","induction coil design","case depth induction"],"minScore":3}}

Induction Hardening — Complete Skill

Physics of Induction Heating

Lenz's Law and Eddy Currents

Principle: alternating current in coil induces eddy currents in workpiece (Lenz's law); eddy currents generate heat by Joule heating: P = I²R

Induced EMF: EMF = -N × dΦ/dt = -N × A × dB/dt [V; N = turns; Φ = flux; A = area; B = flux density]

Eddy current density: J(x) = J₀ × e^(-x/δ) [A/m²; x = depth from surface; δ = skin depth]

Skin depth (penetration depth): δ = 503 × √(ρ / (f × μ_r)) [mm; ρ = electrical resistivity [Ω·m]; f = frequency [Hz]; μ_r = relative magnetic permeability]

For steel (below Curie point ~768°C): ρ ≈ 2×10⁻⁷ Ω·m; μ_r = 50–200 (ferromagnetic; depends on field strength and temperature) δ ≈ 503 × √(2×10⁻⁷ / (f × 100)) = 0.225 / √f [mm; f in Hz; for μ_r = 100]

For steel (above Curie point — paramagnetic): μ_r = 1; ρ ≈ 1.2×10⁻⁶ Ω·m δ ≈ 503 × √(1.2×10⁻⁶ / f) = 0.55 / √f [mm; increases 2–4× when austenitic]

Frequency Selection

Case depth vs. frequency: Effective case depth ≈ 2–3 × δ (at operating frequency)

Frequency	Skin Depth (cold steel)	Typical Case Depth	Application
60 Hz	10–30 mm	10–25 mm	Large shaft bore heating
1 kHz	2.3–7 mm	5–15 mm	Large gear teeth, crankshafts
10 kHz	0.7–2 mm	2–6 mm	Gears, shafts, bearings
100 kHz	0.2–0.7 mm	0.5–2 mm	Small gears, cams, thin components
400 kHz	0.1–0.35 mm	0.2–0.8 mm	Thin cases, small parts, valves

Gear hardening frequency selection: For through-hardening of tooth: f < 1 kHz For case hardening of tooth flank only: f = 10–300 kHz For contour hardening (tooth profile follows hardened zone): dual frequency (DF) process DF process: 10–30 kHz + 150–400 kHz simultaneously → both tooth flank and root case

Power Density

Power density required to heat steel: P_specific = ρ_steel × c_p × ΔT / t_heat [W/m³; ρ_steel = 7,800 kg/m³; c_p = 502 J/(kg·K); ΔT = temperature rise; t_heat = heating time]

For ΔT = 800°C in t = 2 s: P_specific = 7,800 × 502 × 800 / 2 = 1.57 × 10⁹ W/m³ = 1.57 kW/cm³

Coil efficiency and coupling: Power to workpiece: P_work = η_coupling × P_input [η_coupling = 0.6–0.85 for typical setups] Gap between coil and workpiece: 2–5 mm typical; larger gap → lower η

Generator power sizing: P_generator = (P_specific × V_heated) / η_coupling × η_generator [kW; V_heated = heated volume in m³]

Case Depth and Hardness

Effective Case Depth (ECD)

Definition: depth below surface at which hardness equals 50 HRC (or equivalent per AMS 2304) AMS 2304: ECD = depth to 513 HV (HV is Vickers hardness; 513 HV ≈ 50 HRC) AMS 2301: 50% martensite rule (microstructural criterion)

Case depth range by application: Gears: ECD = 0.15–0.30 × module (SAE J1249); typical 0.5–2.5 mm Shafts (bending fatigue): ECD ≥ 0.3 mm (minimum for fatigue benefit) Crankshafts: ECD = 2–5 mm for journal surfaces Camshaft lobes: ECD = 1–3 mm (moderate case, hard surface) Bearing races: ECD = 0.5–1.5 mm

SAE J1249 case depth formula for gears: ECD_min = 0.15 × m_n [module in mm; ECD in mm] ECD_max = 0.30 × m_n

Hardness Profile

Surface hardness target: Steel ≥ 0.4% C: 55–62 HRC surface hardness achievable Minimum surface hardness for wear: 55 HRC (automotive gears) Typical profile: 60 HRC surface → gradient → 45 HRC at ECD → core hardness 28–45 HRC

Jominy correlation (prior hardenability governs core): Core is not quenched; core hardness = as-rolled or normalized hardness (typically HRC 25–35) Shallow case: core must have adequate toughness; don't use high-hardenability steel unnecessarily

Process Parameters

Scanning vs. Single-Shot

Single-shot (encircling coil): entire zone heated simultaneously; one-shot quench

• Uniform case; simpler fixturing; better for small parts
• Risk: thermal mass limits case depth uniformity in complex shapes

Scanning: coil moves relative to workpiece at controlled rate

• Scanning rate: v_scan = 1–30 mm/s (controls case depth and power density)
• For shaft journals: rotate while scanning → uniform circumferential heating
• Spray quench integrated with coil movement

Simultaneous quench (single-shot): quench immediately after coil power off Progressive quench (scanning): quench zone follows heating zone → prevents self-tempering

Quench Parameters

Quench media: Water: fastest quench; high distortion risk; used for low-hardenability steel (1045) Polymer quench (PAG, polyalkylene glycol): 5–20% concentration in water; reduced quench severity; lower distortion; preferred for gears and complex shapes Oil quench: slower; least distortion; for highly hardenability steels (4340, 8620 carburized) Air cool: insufficient for induction hardening depths > 2 mm (too slow)

Quench severity (Grossmann H factor): H = 0.2 (still oil) → H = 1.0 (agitated water) → H = 2.0 (brine/caustic) Polymer quench: H = 0.4–0.8 (depending on concentration and agitation)

Delay time (dwell before quench): Typical: < 0.5 s (minimize conduction from surface to core); longer dwell → deeper total case

Tempering After Induction Hardening

Mandatory: always temper to relieve residual tensile stress at surface-core interface and reduce brittleness Temper temperature: 150–220°C (low-temperature temper; preserves hardness ≥ 55 HRC) AMS 2301: temper within 4 hours of quench; at 150–175°C × 1–2 hours minimum

Self-tempering: residual heat from core flows back to surface after quench; can substitute for furnace tempering for thick parts if calculated properly

Laser tempering (selective): use laser to re-temper specific zones; useful for crankpins post-induction

Distortion and Residual Stress

Residual Stress Profile

Compressive residual stress at surface: key benefit of induction hardening Mechanism: martensite transformation expands volume at surface → core constrains → net compression at surface Typical: σ_residual = -200 to -600 MPa (compressive) at surface → tension in core for equilibrium

Effect on fatigue: Compressive surface residual stress raises effective mean stress toward compression → shifts Goodman line → fatigue life improves 2–5× vs. through-hardened

Torsional residual stress: For scanning direction: residual stress has axial and circumferential components Bending: surface compression increases fatigue limit 30–50% vs. un-hardened shaft

Distortion Sources

Thermal gradients: rapid heating/cooling → non-uniform thermal expansion → plastic deformation Transformation strains: martensite (BCC, 4% larger volume than austenite FCC) → expansion only in case Residual stress relaxation: if exceeds yield → shape change

Distortion control: Fixturing: rigid holding during heating and quench; mandrel for bores Quench timing: uniform quench onset; spray quench symmetry Pre-stress relieving: normalize or anneal before induction if cold-worked material Post-process grinding: typically 0.1–0.3 mm stock removal (profile and straightness)

Dimensional change prediction: Bore shrinks 0.01–0.05% per mm diameter after case hardening (martensite expansion is outer case, core doesn't transform) Shaft length: grows 0.01–0.03% per mm heated length; compensate by fixturing

Steel Selection for Induction Hardening

Required carbon content: ≥ 0.35% C for 50+ HRC surface (0.40–0.55% C optimal) Hardenability: DI (ideal diameter) sized for required core properties; induction hardening doesn't require high hardenability for case (surface cools fast regardless)

Common steels: 1045 (C45): simple, low-cost; core HRC 25–35; adequate for shafts, farm equipment 4140 (42CrMo4): better core strength (HRC 30–40); gears, crankshafts 4340 (36CrNiMo4): highest core strength (HRC 40–55); high-performance applications 8620: carburizing grade — also induction hardenable; good toughness 1070–1080: high-carbon; leaf springs, wear parts; excellent surface hardness; brittle core

Pre-hardened feedstock: QT (quench and temper) to ~HRC 28–32 before induction → improves core properties; reduces distortion vs. normalized

Coil Design

Single-turn encircling coil: high efficiency for uniform round parts (bearings, journals) Multi-turn coil: better coupling efficiency; for longer zones Internal (ID) coil: for bore hardening; current direction reversal; flux concentrators needed Profiled coil: shaped to gear tooth profile; hairpin coil for rack teeth

Flux concentrators: Soft magnetic flux concentrator (Fluxtrol, Ferrotron): guides field to specific zone Increases coupling efficiency by 20–40%; reduces stray heating of unintended areas

Coil material: copper tube (water-cooled); 1/4–1/2 inch OD; wall 1–2 mm; current density 30–80 A/mm² in coil

Quality Control

Hardness testing: Vickers (HV); Rockwell HRC; micro-Vickers cross-section traverse every 0.1 mm Case depth measurement: cross-section metallographic etch; measure hardened zone to ECD definition Magnetic Barkhausen Noise (MBN): non-destructive; sensitive to residual stress and case depth; used for 100% online QC Crack detection: magnetic particle inspection (MPI) per ASTM E1444; fluorescent MT for induction-hardened surfaces

Standards

Standard	Scope
AMS 2304	Induction hardening — case depth (50 HRC criterion)
AMS 2301	Heat treatment of steel — 50% martensite criterion
SAE J1249	Gear case depth requirements
ASTM E18	Rockwell hardness testing
ASTM E384	Micro-Vickers hardness testing
ASTM E1444	Magnetic particle inspection
ISO 15787	Technical specifications for heat-treated ferrous parts

Output

Provide: part type (shaft/gear/cam/bearing), material (grade and initial condition), target surface hardness [HRC] and ECD [mm], frequency selected [kHz] with skin depth δ [mm] justification, power density [kW/cm³] and generator power [kW], process type (single-shot/scanning, scanning rate [mm/s] if applicable), quench medium (polymer concentration [%] and H factor), temper temperature [°C] and time [min], distortion expected [mm/100mm] and mitigation, residual surface stress [MPa] (compressive), fatigue improvement factor vs. untreated, quality inspection method (MBN/MPI/cross-section hardness traverse), and applicable standard (AMS 2304, SAE J1249, ISO 15787).