| 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
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]
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
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
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)
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
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 |
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).
