This calculator evaluates a selected continuous two-stage force law. Before nesting begins, F = k1x. After x1, F = k1x1 + k2(x − x1), where k2 is the selected post-nesting tangent rate. Stored energy is the exact integral of that piecewise force law.
Volute Strip Spring and Load Calculator
Evaluate a selected continuous two-stage spring load law before and after a nesting transition.
Equation Used
- The selected force law is continuous at x1.
- k1 and k2 are tangent rates for their respective stages.
- Stored energy is the exact integral of the selected force law.
- Material, contact friction, hysteresis, stress, fatigue and ratings are excluded.
k2 is the selected post-nesting tangent rate; effective rate is the secant ratio F/x.
Continuous tapered strip
The animation shows one continuous flat strip wound into a tapered helix. As its height decreases, the smaller turns telescope within the larger turns. Selected deflection sets the maximum illustrated compression. The selected force-law transition does not determine turn contact in the drawing, and the rates are not calculated from its strip dimensions.
What the calculator determines
Select the initial tangent rate, post-nesting tangent rate, transition deflection and evaluation deflection. The calculator reports exact energy and force under that selected law, secant rate F/x, and deflection beyond the transition.
Continuous piecewise law
For x ≤ x1: F = k1x and U = ½k1x². For x > x1: F = k1x1 + k2(x − x1) and U = ½k1x1² + k1x1(x − x1) + ½k2(x − x1)².
Selected-input arithmetic
At k1 = 120 N/mm, k2 = 900 N/mm, x1 = 45 mm and x = 150 mm, the selected force is 99.9 kN and nested stroke is 105 mm.
Selected law, not a spring design
The model excludes strip width and thickness, coil count and contact sequence, material modulus and yield, stress, fatigue, friction between nested turns, hysteresis, buckling, manufacturing tolerances and ratings.
Questions
Is k2 a secant rate?
No. It is the selected post-nesting tangent rate. The reported effective rate is the secant F/x.
Does the visual derive spring capacity?
No.
References & Further Reading
Gardner D. Hiscox, Mechanical Movements, Powers, Devices and Appliances (1901), page 279, figure 1144: single volute helix spring.
- Wikipedia contributors. Volute spring. Wikipedia
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