Keyed and Splined Joints

Keys and splines transmit torque between a shaft and hub by contact of their side surfaces. A key is simple and economical; splines distribute load among several teeth, improve centering, and may permit axial sliding.

Key forces and stresses

The tangential force at shaft diameter \(d\) is

$$F_t=\frac{2T}{d}.$$

For a key of width \(b\), working height \(h_w\), and length \(l\), preliminary checks are

$$\tau=\frac{F_t}{bl}le[\tau],\qquad p_b=\frac{F_t}{h_wl}le[p_b].$$

The usable length excludes rounded ends and other unloaded portions.

Splines

For \(z\) teeth, mean radius \(r_m\), working flank area per tooth \(A_f\), and load-distribution factor \(\psi_z<1\),

$$p_b=\frac{T}{z\psi_zA_fr_m}.$$

Actual load sharing depends on pitch error, alignment, hub stiffness, fit, and flank modification.

Design considerations

Keyways and spline roots weaken the shaft and create fatigue stress concentration. Check shaft and hub sections, fretting, wear in sliding splines, axial retention, manufacturing tolerances, and assembly. Avoid assigning axial location to a key unless a separate retaining element is provided.

Key types and application

Parallel keys are common for fixed hubs; taper keys can create radial wedging and may affect centering. Woodruff keys accommodate assembly and angular adjustment but require a deep shaft recess. Feather keys permit axial sliding while transmitting torque. The key type must match the required positioning and assembly method.

Load distribution along a key

Nominal formulas assume uniform shear and bearing, but hub and shaft deformation concentrate pressure near the entering end. Chamfers, end shape, key fit, and hub length influence the effective working length. Two keys do not necessarily double capacity because equal load sharing is difficult to guarantee.

Spline geometry and centering

Straight-sided, involute, and serrated splines differ in manufacturing and load behavior. Centering may occur on flanks, major diameter, or minor diameter. Involute splines provide favorable tooth geometry and self-centering under load, but accuracy and fit still govern load sharing.

Fixed and sliding splines

A fixed spline is designed mainly for torque and fatigue. A sliding spline must also resist flank wear, fretting, and seizure during axial motion. Misalignment produces edge loading; crowning or flank modification can improve contact. Lubrication and contamination control are essential in moving joints.

Shaft and hub strength

Keyways and spline roots reduce the net section and raise local stress. Check torsion, bending, and combined fatigue at groove ends and diameter transitions. The hub is checked for radial splitting, tooth or key bearing, and minimum wall thickness. Hardened flanks may improve wear resistance but require compatible core toughness.

Calculation sequence

1. Determine design torque, axial motion, centering, and assembly requirements.
2. Select a key or spline standard and preliminary dimensions.
3. Calculate tangential force and nominal bearing and shear stresses.
4. Account for unequal tooth or lengthwise load distribution.
5. Check shaft fatigue, hub strength, wear, fretting, and axial retention.
6. Specify fit, tolerance, heat treatment, lubrication, and inspection.