wave-spring

name	wave-spring
description	Wave spring design — flat wire, multi-turn, Smalley wave springs, load-deflection, space-saving vs coil spring, material selection, applications.
metadata	{"priority":7,"promptSignals":{"phrases":["wave spring","Smalley spring","flat wire spring","wave washer"],"minScore":3}}

Wave Spring Design — Complete Skill

Types

• Single-turn wave spring (wave washer): one turn, 3-5 waves; compact
• Multi-turn wave spring: multiple turns stacked; acts like coil spring but shorter
• Nested wave spring: multiple single-turn springs nested; very compact
• Crest-to-crest: waves alternate peak-to-trough between turns

Geometry

D_m = mean diameter [mm] b = wire width [mm] (radial) t = wire thickness [mm] (axial) N_t = number of turns N_w = number of waves per turn (typically 3–6) H = free height [mm] δ = working deflection [mm]

Load-Deflection (Smalley / Wahl)

Spring rate (multi-turn): k = E b t³ N_w⁴ / (2π N_t D_m³)

More common form (Smalley catalog notation): k = E b t³ N_w⁴ / (2π³ D_m³ N_t)

Note: N_w per turn; total waves = N_w × N_t

Working load: F = k × δ

Stress

Bending stress at crest: σ = 3π F D_m / (4 N_w b t²)

Allowable: σ_allow = 0.65 S_y to 0.80 S_y (set removed); limit per Smalley recommendations

Space Savings vs. Coil Spring

For same load and deflection, wave spring typically:

• 50% shorter free height vs. equivalent coil spring
• Same or slightly larger OD/ID to fit bore/shaft

Application niche: bearings, seals, retaining ring preload, limited axial space

Materials

Material	E [GPa]	Max Temp	Notes
302 SS	193	260°C	Most common
17-7 PH	196	315°C	Higher strength
Inconel 718	200	540°C	High temp
Carbon steel	207	120°C	Low cost

Standard sizes (Smalley / stock): D_m range: 5–500 mm (catalog) t = 0.10–2.50 mm; b = 0.5–6 mm

Shim (Single-Turn) Wave Washer

Used for light preloading of bearings, seals, end play removal Load range: 2–450 N typical (stock sizes) Operating deflection: 0.1–2 mm

Force calculation: same formula but N_t = 1

Design Procedure

1. Establish load F, bore/shaft dimensions (gives D_m limits)
2. Establish free height H and working deflection δ_w
3. Select N_t and N_w (more turns → softer; more waves → stiffer)
4. Solve for t given constraints: k = F/δ_w
5. Check bending stress at crest
6. Check clearance (ID must clear shaft; OD must fit bore)
7. Verify from Smalley catalog — use nearest stock size

Bearing Preload Application

Common use: preload angular contact bearings in spindles Preload force ≈ 50–200 N typical Axial space: 3–8 mm for a wave spring vs. 15–25 mm for coil spring

Fatigue

For cyclic compression applications: Modified Goodman at crest bending stress Endurance limit ≈ 0.35–0.45 S_u (302 SS: S_u ≈ 1000 MPa → σ_e ≈ 400 MPa)

Output

Provide: D_m [mm], b × t [mm], N_t, N_w, H_free [mm], k [N/mm], F at working deflection [N], σ_max [MPa] vs. σ_allow, material, nearest catalog size recommendation.