| name | keyway-spline |
| description | Keyway and spline design — key types, key stress (shear/bearing), ANSI key dimensions, spline profiles (involute/straight-sided), torque capacity, hub-shaft fit. |
| metadata | {"priority":6,"promptSignals":{"phrases":["keyway","key design","spline","woodruff key","parallel key","key stress","key shear","key bearing"],"minScore":4}} |
Keyway & Spline Design — Complete Skill
Key Types
Parallel (square/rectangular): most common; square = w×w, rectangular = w×h
Woodruff key: semicircular; self-locating; common in tapered shafts
Gib-head taper key: driven in axially; high torque; harder to remove
Feather key: allows axial sliding (splines are preferred for this)
Pin (cross-pin, cotter): simple; low cost; limited alignment
ANSI Standard Key Dimensions (B17.1)
Shaft diameter range → Key size (w × h):
| Shaft dia [in] | Key w × h [in] |
|---|
| 0.375 – 0.4375 | 3/32 × 3/32 |
| 0.500 – 0.5625 | 1/8 × 1/8 |
| 0.625 – 0.875 | 3/16 × 3/16 |
| 0.875 – 1.25 | 1/4 × 1/4 |
| 1.25 – 1.375 | 5/16 × 5/16 |
| 1.375 – 1.75 | 3/8 × 3/8 |
| 1.75 – 2.25 | 1/2 × 1/2 |
| 2.25 – 2.75 | 5/8 × 5/8 |
| 2.75 – 3.25 | 3/4 × 3/4 |
| 3.25 – 3.75 | 7/8 × 7/8 |
| 3.75 – 4.50 | 1 × 1 |
Keyway depth in shaft: = h/2 (half of key height)
Keyway depth in hub: = h/2 (other half)
Key Stress Analysis
Transmitted Torque
T = F_t × r where r = shaft radius
F_t = 2T/d (tangential force at shaft surface)
Shear Stress (Key shears at shaft-hub interface)
τ = F_t / (w × L) where L = key length, w = key width
Safety factor: n_s = S_sy / τ = 0.577 S_y / τ (Von Mises) or 0.5S_y/τ (Tresca)
Bearing Stress (Side of key pressed against keyway)
σ_b = F_t / ((h/2) × L) [one side of key bears]
Safety factor: n_b = S_y / σ_b (bearing yield criterion)
Key Length Design
For given T, shaft dia d, key dimensions (w×h), material S_y:
From shear: L_min = 2T / (d × w × S_sy / n)
From bearing: L_min = 4T / (d × h × S_y / n)
Use max of two
Practical limits: L ≤ 1.5d (avoid too long) and L ≥ d (rule of thumb)
Worked Example (SI)
T = 1000 N·m, d = 60 mm, key = 18×11mm (ANSI near equivalent)
S_y = 350 MPa (key material, 1018 steel)
F_t = 2×1000/0.060 = 33,333 N
τ = 33,333/(0.018×L), required L for n=2: L = 33,333×2/(0.018×0.577×350×10⁶) = 0.0187 m = 18.7 mm
σ_b = 33,333/((0.011/2)×L), required L for n=2: L = 33,333×2×2/(0.011×350×10⁶) = 0.0347 m = 34.7 mm
→ Bearing governs: use L = 35 mm (round up to 40 mm practical)
Stress Concentration at Keyway
End-milled keyway: Kt = 2.14 (bending), Kts = 2.62 (torsion) — Shigley Table 7-1
Profile keyway (sled-runner): Kt = 1.6, Kts = 1.6 (less severe)
Recommendation: use generous fillet radius at keyway bottom (r ≥ 0.02d)
Shot peen keyway region to induce compressive residual stress (fatigue improvement)
Involute Splines (ANSI B92.1)
Tooth profile: same as spur gear involute, standard pressure angle 30°/45°
Major diameter D, module m:
N = number of teeth, D = m × N (module notation) or D = N/P (diametral pitch, in⁻¹)
Torque capacity:
T = π × n × m × D × L × (S_y/2) / 2 [approximate, all spline teeth sharing]
Or: T = (μ × P × D_pitch/2) × n_teeth (friction drive — interference fit)
Fit classes:
Class 1: loose-fit (fretting, dynamic; spline can slide)
Class 2: close-fit (precision, no sliding)
Class 3: press fit (permanent)
Straight-Sided Splines (SAE)
Standard: 4, 6, 10, 16 splines
4-spline: D_major/d_minor = 1.25 (square-ish)
6-spline: standard for general use
Torque capacity: T = τ × A_shear × r_pitch = τ × h × L × n × r
Woodruff Key (ANSI B17.2)
Semicircular in cross-section; number designation: W#×#
First number ×(1/32): key width; second ×(1/8): key dia
Example: #808 = 8/32 wide × 8/8 dia = ¼" × 1" diameter
Depth cut into shaft is larger than hub — weakens shaft significantly
Do not use Woodruff on small shaft diameters under bending
Max Kt,shaft ≈ 6.0 at Woodruff keyway bottom
Output
Provide: key size (w×h×L) [mm or in], shear stress τ [MPa], bearing stress σ_b [MPa], safety factors n_shear and n_bearing, Kt at keyway.
