| 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
- Establish load F, bore/shaft dimensions (gives D_m limits)
- Establish free height H and working deflection δ_w
- Select N_t and N_w (more turns → softer; more waves → stiffer)
- Solve for t given constraints: k = F/δ_w
- Check bending stress at crest
- Check clearance (ID must clear shaft; OD must fit bore)
- 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.
