POWER TRANSMISSION REFERENCE GUIDE
Wave-spring specification
S
prings are flexible mechanical components to store and release energy or apply and release forces on machine axes. Wave springs combine flat (non-coiled) bow springs (as their waves) with traditional compressionspring coil geometry. For the design’s compactness (as a high force-to-work height ratio) and other benefits, some motion systems have migrated from traditional helical or coil springs to flat-wire wave springs. Design engineers typically work with manufacturers to customize wave springs to specific operating conditions by material, thickness, number of turns, and other geometric features. That helps address or avoid the following springinstallation challenges. Column buckling in springs occurs with long free lengths and spring ends that can’t evenly distribute load around the spring circumference. Buckling mainly depends on geometry and not spring material properties. Traditional springs tend to buckle when deflection (for a set free length) is excessive.
Such buckling is preventable by keeping the design to below critical deflection and length values. The former is the ratio of deflection to spring free length; critical length is the ratio of that length to the spring diameter. One rule of thumb for avoiding buckling in traditional springs is to keep free length to less than quadruple the spring diameter — and load to less than the product of spring rate, length, and buckling factor. Wave-spring buckling factors vary greatly, but the value is nearly always higher than those of other springs. That means they readily hold their centered cylindrical shape and often self-locate into assembly bores — even operating reliably in machined assembly features held to relatively loose tolerances. Spring surge is a potential concern in assemblies with a compression spring having one free end. Depending on the motion input, such springs can exhibit resonance that’s large enough to cause temporary loss of contact with the assembly housing — and damage surrounding machine elements. That’s an issue of highest concern if the spring material provides
Formulas for specifying a wave spring Here are basic formulas to narrow down the wave spring type, shape and size that best suit an application. Note that wave springs are helping today’s push toward design miniaturization. Smaller designs need shorter and smaller diameter wave springs. That’s spurred some developers to make wave springs less than 0.250 in. in diameter.
Operating stress S = (3πPDm)/4bt2N2
Fatigue stress ratio x = (s - s1/(s - s2)
Where: S = Operating stress P = Load, lb Dm = Mean diameter, in. b = Radial width of material, in. t = Thickness of material, in. N = Number of waves per turn
Where: s = Material tensile strength s1 = Calculated operating stress at lower working height (not to exceed s) s2 = Calculated operating stress at upper working height
Deflection f = ((PKZDm3)/(Ebt3N4)) x (ID/OD)
: Where: R = Spring rate, lb/in. P = load, lb f = Deflection, in. b = Radial width of material, in. t = Thickness of material, in. N = Number of waves per turn K = Multiple wave factor Dm = Mean diameter, in. Z = Number of turns
Where: f = Deflection, in. P = Load, lb K = Multiple wave factor Dm = Mean diameter, in. Z = Number of turns E = Modulus of elasticity b = Radial width of material, in. t = Thickness of material, in. N = Number of waves per turn
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DESIGN WORLD — MOTION
Waves Springs — Power Transmission HB 05.19 V3.indd 52
Spring rate R = (P/f) = (Ebt3N4)/(KZDm3) x (ID/OD)
5 • 2019
motioncontroltips.com | designworldonline.com
5/15/19 8:46 AM
