How do you design Belleville springs for specific load-deflection characteristics?
Answer
Belleville (disc) springs follow: P = (4E/(1-nu^2)) x (t^3/MRd^2) x [(h-delta)(h-delta/2).t + t^3], where P is load, E is modulus, t is thickness, h is cone height, delta is deflection, Rd is outer radius, M is a constant. h/t ratio controls characteristic: h/t < 0.4 gives linear, h/t approximately equals 1.41 gives flat portion (constant force), h/t > 1.41 gives negative rate region (snap-through). Stack in parallel for higher load (add forces), in series for higher deflection (add deflections). Widely used for preloading bearings, bolted joints, and overload protection. Material: spring steel, Inconel for high temperature.
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