bimetallic-strip

name	bimetallic-strip
description	Bimetallic strip (thermostat element) — differential thermal expansion mechanism, Timoshenko bimetallic strip equations (curvature, deflection, stress), material selection (Invar/brass, Invar/steel, Invar/copper, brass/steel), sensitivity (deflection per °C), snap-action disc (Belleville), thermostat calibration, hysteresis, creep and fatigue in bimetallic elements, and applications in thermostats, circuit breakers, automotive sensors, and ASTM B388 standards.
metadata	{"priority":7,"promptSignals":{"phrases":["bimetallic strip","bimetallic thermostat","bimetallic element","differential expansion","Invar bimetallic","thermostat strip"],"minScore":3}}

Bimetallic Strip — Complete Skill

Operating Principle

Differential Thermal Expansion

Mechanism: two metals with different CTEs bonded at interface; temperature change → differential length change → curvature Metal with higher CTE expands more → longer → forces strip to curve toward low-CTE metal side

Bending direction: If α₁ > α₂ (metal 1 on bottom): heating → bottom elongates more → strip curves downward (concave up) If cooled: strip curves the other way

Applications: Thermostats (HVAC, ovens, hot water): strip curves to make/break electrical contact at set temperature Circuit breakers (overload protection): bimetal heated by overload current → deflects → trips mechanism Automotive coolant temperature sensors (older designs) Precision instruments: temperature compensation in balance wheels, barometers

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Timoshenko Bimetallic Strip Theory

Curvature and Deflection

Timoshenko (1925) exact equation for curvature: κ = (α₁ − α₂) × ΔT × 6(E₁t₁E₂t₂)(t₁+t₂) / [3(t₁+t₂)² + (E₁t₁²−E₂t₂²)²/(E₁t₁E₂t₂)]

Simplified for equal thicknesses (t₁ = t₂ = t/2, where t = total thickness): κ = (α₁ − α₂) × ΔT × 6E₁E₂ × t / (t² × (3(E₁+E₂)² + 4E₁E₂)) Further simplified for E₁ ≈ E₂ = E: κ ≈ 3(α₁ − α₂) × ΔT / (2t) [κ = 1/R = curvature; R = radius of curvature; t = total thickness of bimetallic strip]

Most common simplified form (strips with equal or near-equal layers): κ = C_κ × (α₁ − α₂) × ΔT / t Where C_κ ≈ 1.5–2.0 (depends on modulus ratio n = E₁/E₂ and thickness ratio m = t₁/t₂) For equal moduli and equal thicknesses: C_κ = 1.5

Deflection of free-end cantilever strip: δ_tip = κ × L² / 2 = C_κ × (α₁ − α₂) × ΔT × L² / (2t) Where L = strip length; t = total thickness; ΔT = temperature change from reference

Example: Strip: brass (α₁ = 19×10⁻⁶/°C) bonded to Invar (α₂ = 1.2×10⁻⁶/°C); t = 1.0 mm total; L = 50 mm ΔT = 50°C; equal layers; E₁(brass)=100 GPa; E₂(Invar)=141 GPa; modulus ratio ≈ 0.71 Δα = (19 − 1.2) × 10⁻⁶ = 17.8×10⁻⁶/°C κ ≈ 1.5 × 17.8×10⁻⁶ × 50 / (0.001) = 1335 × 10⁻³ = 1.335 m⁻¹ → R = 0.749 m δ_tip = 1.335 × 0.050² / 2 = 1.335 × 0.00125 = 1.67 × 10⁻³ m = 1.67 mm

Sensitivity (deflection per °C per unit L²/t): S = C_κ × Δα / 2 [mm/°C per (L²/t); normalize by geometry]

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Stress Analysis

Bending Stress in Strip

Maximum bending stress (at bonded interface, at fixed end for cantilever): σ_max = E × (t/2) × κ [σ = E × y × κ; y = t/2 from neutral axis; for symmetric strip] σ_max = E × t/2 × C_κ × Δα × ΔT / t = C_κ × E × Δα × ΔT / 2

Example (continued): E_avg ≈ 120 GPa (approximate average); σ_max = 1.5 × 120×10⁹ × 17.8×10⁻⁶ × 50 / 2 = 1.5 × 120×10⁹ × 8.9×10⁻⁴ = 1.5 × 1.068×10⁸ = 160 MPa

Fatigue assessment: Cyclic thermal loading → fatigue at interface and at root of cantilever Brass endurance limit ≈ 80 MPa; σ_max = 160 MPa > σ_e → potential fatigue failure after many cycles Design remedies: increase thickness t; shorten length L; reduce Δα (different material pair); reduce ΔT per cycle

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Material Selection for Bimetallic Elements

Standard Material Pairs

ASTM B388 designations:

ASTM Code	High Expansion Layer	Low Expansion Layer	Deflection Sensitivity
B388 Class 1	72Mn (72%Mn)	Invar (64%Fe-36%Ni)	High
B388 Alloy 25	Yellow brass	Cold-rolled steel	Medium
TM10 (EN 12164)	Brass CuZn37	Invar 36	High
F-21 (Kanthal)	Fe-Ni-Mn alloy	Invar	Very high

Key materials: Invar (Fe-36Ni): α = 1.2×10⁻⁶/°C (near-zero); E = 141 GPa; low CTE side of high-performance bimetal Brass (CuZn37): α = 19×10⁻⁶/°C; E = 100 GPa; standard high-CTE layer 72Mn brass: α = 21×10⁻⁶/°C; even higher sensitivity than standard brass High-CTE nickel alloys (e.g., Permanickel): α = 13.5×10⁻⁶/°C with better corrosion resistance

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Snap-Action Discs (Belleville Thermostat)

Dish-Shaped Bimetallic Element

Principle: bimetallic disc formed with dome shape; at critical temperature: disc snaps through (bistable behavior) → fast-acting contact; no gradual drift Snap ratio: h/t ratio determines snap temperature differential (Belleville curve analysis) Snap force: significant; reliable contact make/break; resistant to vibration

Hysteresis in snap-action: Contact temperature T_make ≠ T_break (T_break < T_make for NC contact) Hysteresis: ΔT_hys = T_make − T_break = 5–25°C depending on disc design Reduces cycling frequency near setpoint (prevents rapid on-off chatter)

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Thermostat Design

Set Point Calibration

Mechanical adjustment: Pre-load spring against bimetal → shift contact-make temperature Adjustable screw changes free-end gap → changes deflection needed → changes ΔT required → shifts set point

Temperature range and calibration: Typical snap-disc thermostat: setpoint adjustable ±20°C from nominal; calibrated to ±1–3°C Industrial thermostat: factory-calibrated; ±1°C tolerance; replaceable element

Creep and drift: Long-term creep at elevated temperature → drift in set point Mitigation: use Invar/high-Mn alloy with good high-temperature creep resistance UL 60730: specifies drift limits for thermostats in appliances

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Applications

Application	Temperature Range	Strip Geometry	Function
Household thermostat	15–30°C	Long flat strip	HVAC make/break
Oven thermostat	150–250°C	Snap disc	Heater control
Circuit breaker	50–150°C trip	Crimped strip + heating coil	Overcurrent trip
Automotive radiator fan	85–100°C	Snap disc	Fan clutch engagement
Coffee maker	85–95°C	Strip + snap disc	Brew temp control
Compressor overload	Trip at 80–110°C	Disc	Motor protection

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Standards and References

Standard	Scope
ASTM B388	Bimetallic thermostat metal strip
EN 12164	Bimetal specifications (European)
UL 60730	Automatic electrical controls — thermostat safety
IEC 60730	Automatic electrical controls for household use
ANSI/ISA S37.1	Electrical transducer nomenclature

Output

Provide: application (thermostat type; T_setpoint [°C]; T_range [°C]; mechanical or electrical contact; force required [mN]), material pair selection (high-CTE: brass/Mn-brass/F-21; α₁ [μm/mK]; low-CTE: Invar/cold-rolled steel; α₂ [μm/mK]; Δα = α₁−α₂ [μm/mK]; ASTM B388 designation), strip geometry (t_total [mm]; t₁/t₂ ratio; L [mm]; width w [mm]; cantilever or disc), deflection (κ = 1.5×Δα×ΔT/t [m⁻¹]; δ_tip = κ×L²/2 [mm]; per °C sensitivity δ/ΔT [mm/°C]; meets gap requirement?), stress (σ_max = 1.5×E×Δα×ΔT/2 [MPa]; vs. endurance limit [MPa]; fatigue life estimate; reduce L or t if overstressed), snap-action (disc type: yes/no; h/t ratio; hysteresis ΔT [°C]; snap force [mN]), thermostat performance (setpoint accuracy ±[°C]; drift over life [°C]; adjustment range [°C]; UL 60730 compliance), and applicable standard (ASTM B388 for material; UL 60730 / IEC 60730 for thermostat safety; EN 12164 if European).