A simple electric thermostat can use a bonded bimetal strip to move a contact as temperature changes. This model shows a straight strip clamped at one end and an adjustable contact near its free end. Explore how strip length, thickness, material flexivity and temperature rise affect its free deflection and the calculated point of first contact.
Electric Thermostat Interactive Calculator
Explore a simple bimetal contact. Adjust strip geometry, flexivity, temperature rise and contact gap; compare free deflection with the first-contact condition.
Equation Used
- Initially straight, uniformly heated and perfectly bonded strip.
- Constant entered flexivity and negligible pre-contact loading.
- No constrained contact-force, snap-action or hysteresis model.
- Computed contact temperature may exceed the valid range of a real material.
Free-strip geometry only; no snap mechanism, contact force or switching rating.
A strip, a clamp and an adjusting contact
Hiscox movements 733 and 734 show a bimetal strip supported in an insulated frame with an adjusting contact screw. The animation uses that simple arrangement, rotated horizontally for visibility. It does not add a snap spring or a mercury switch.
The bonded layers have different thermal expansion. For uniform heating and an initially straight, unconstrained strip, the ideal centreline bends into a circular arc. The high-expansion layer is on the outside of this bend.
The drawing heats from zero to the entered temperature rise and cools back. It stops deforming at first contact because the constrained shape after touching requires a different mechanical model. The enlarged inset makes a small remaining gap visible.
Inputs that determine the model
Length is the unbent centreline length from the clamp to the free end. Thickness is the combined thickness of both bonded layers. Temperature rise is relative to the straight reference condition.
Flexivity relates curvature change to temperature change and total thickness. Enter it in micro per kelvin, using a material value appropriate to the temperature interval. The default 30 µ/K is an illustrative input, not a universal property of bimetal.
The gap is the vertical separation between the free end in its straight reference condition and the adjusting contact. The screw is placed at the calculated horizontal location of first touch. Material stiffness, layer ratios and temperature dependence are not independently solved here.
Curvature and exact arc geometry
With flexivity F converted from µ/K to 1/K and thickness t in millimetres, curvature is κ=FΔT/t in inverse millimetres. For centreline length L, the end rotation is θ=κL radians.
A circular arc then gives horizontal tip position x=L sin(θ)/θ and vertical free deflection δ=L[1−cos(θ)]/θ. At zero temperature rise, x=L and δ=0. For small rotations, δ≈FΔT L²/(2t).
The ideal first-contact angle is found by solving δ(θ)=gap on the monotonic interval from zero to π/2. Its temperature rise is θt/(FL). Free travel minus gap is δ−gap. Positive margin means the free strip would pass the contact location; the actual constrained strip cannot do that.
The displayed end rotation describes the unconstrained strip at the entered temperature rise. A freely bending strip has no snap-time prediction without a spring, force, inertia and damping model.
Compare the default dimensions
A 50 mm strip, 0.30 mm total thickness and flexivity 30 µ/K at a 15°C rise have θ=0.075 rad, or approximately 4.30°. Free end deflection is approximately 1.874 mm.
For an initial 1.3 mm gap, first contact occurs at about 10.40°C rise under the same constant-flexivity assumption. The displayed strip stops at that first-contact pose even while the temperature indicator continues toward 15°C.
At small rotation, doubling length approximately quadruples deflection. Doubling flexivity or temperature rise approximately doubles it, while doubling thickness approximately halves it. Exact arc expressions are used in the calculator.
Limits of the strip model
Results assume a perfectly bonded, initially straight strip, uniform temperature, constant flexivity and negligible external loading before contact. They do not include gravity, initial curvature, contact pressure, insulation temperature or thermal lag.
The first-contact rise is a geometric extrapolation using constant flexivity. A value beyond the entered cycle or beyond a material’s characterized temperature range is not a usable thermostat rating. The calculator does not identify a qualified material or predict hysteresis, contact life or electrical switching capacity.
Layer thicknesses, screw and contact pads are enlarged in the drawing for readability. The strip centreline follows the computed arc, while the contact inset explicitly magnifies vertical separation.
Bimetal thermostat questions
Why does the strip stop moving before the temperature stops rising?
It has reached the fixed contact. Continued deformation would require calculating contact force and the constrained shape, which this free-strip model does not do.
What determines how far the strip bends?
Strip length, thickness, material flexivity and temperature rise determine the bend. The model calculates constant curvature and the resulting circular-arc geometry.
Is this snap action?
No. This is a gradually moving contact. A snap-action thermostat needs additional geometry and force relationships.
Does a positive travel margin mean the contacts overlap?
No. It compares the unconstrained tip deflection with the original gap. Physical contact prevents that free motion.
References
- Gardner D. Hiscox, Mechanical Movements, Powers, Devices and Appliances (1901), printed page 195, movements 733–734 — insulated strip frame and adjusting contact.
- Engineered Materials Solutions, Thermostatic Bimetal Designer’s Guide, pages 5 and 14–15 — uniform curvature and the definition of flexivity. Arc position and contact calculations on this page are derived from that curvature relationship.
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