Bimetallic Strips

Overview

Engineering reference data for Bimetallic Strips in material science and properties.

Key Formulas

Stress

$\sigma = \frac{F}{A}$

Force per unit area.

Strain

$\varepsilon = \frac{\Delta L}{L_0}$

Change in length per original length.

Hooke's Law

$\sigma = E \varepsilon$

Stress proportional to strain in elastic region.

Thermal Expansion

$\Delta L = \alpha L_0 \Delta T$

Length change due to temperature.

Variables

References

• Original Source

Working Principle

Bimetallic strips convert thermal energy into mechanical displacement through differential expansion. When heated, the metal with a higher coefficient of thermal expansion elongates more than the metal with a lower coefficient. Since the two metals are rigidly bonded, this difference in expansion forces the strip to bend toward the metal with the lower expansion coefficient. This predictable bending is the core operating principle behind thermostats and other thermal actuators.

Bending Calculation

The bending displacement $s$ of a bimetallic strip is calculated using the formula derived from differential thermal expansion:

$$s = \frac{\alpha \cdot L^2 \cdot dt}{t}$$

where:

• $s$ = bending displacement (m)
• $\alpha$ = differential thermal expansion coefficient (K⁻¹), typically between 13 × 10⁻⁶ and 19 × 10⁻⁶
• $L$ = length of the bimetallic strip (m)
• $dt$ = temperature change (°C or K)
• $t$ = total thickness of the bimetallic strip (m)

Example Calculation

For a bimetallic strip with:

• $\alpha = 14 \times 10^{-6}$ K⁻¹
• Length $L = 50$ mm = 0.05 m
• Thickness $t = 2$ mm = 0.002 m
• Temperature change $dt = 100$ °C

The bending is calculated as:

$$s = \frac{(14 \times 10^{-6}) \cdot (0.05)^2 \cdot 100}{0.002} = 0.00175 \text{ m} = 1.75 \text{ mm}$$

This result demonstrates the practical, measurable displacement achieved under typical operating conditions.

Working Principle

Bimetallic strips convert thermal energy into mechanical displacement through differential expansion. When heated, the metal with a higher coefficient of thermal expansion elongates more than the metal with a lower coefficient. Since the two metals are rigidly bonded, this difference in expansion forces the strip to bend toward the metal with the lower expansion coefficient. This predictable bending is the core operating principle behind thermostats and other thermal actuators.

Bending Calculation

The bending displacement $s$ of a bimetallic strip is calculated using the formula derived from differential thermal expansion:

$$s = \frac{\alpha \cdot L^2 \cdot dt}{t}$$

where:

• $s$ = bending displacement (m)
• $\alpha$ = differential thermal expansion coefficient (K⁻¹), typically between 13 × 10⁻⁶ and 19 × 10⁻⁶
• $L$ = length of the bimetallic strip (m)
• $dt$ = temperature change (°C or K)
• $t$ = total thickness of the bimetallic strip (m)

Example Calculation

For a bimetallic strip with:

• $\alpha = 14 \times 10^{-6}$ K⁻¹
• Length $L = 50$ mm = 0.05 m
• Thickness $t = 2$ mm = 0.002 m
• Temperature change $dt = 100$ °C

The bending is calculated as:

$$s = \frac{(14 \times 10^{-6}) \cdot (0.05)^2 \cdot 100}{0.002} = 0.00175 \text{ m} = 1.75 \text{ mm}$$

This result demonstrates the practical, measurable displacement achieved under typical operating conditions.