Splines and Serrations

§1Many teeth, not one key

A splined connection is a set of teeth cut integrally around a shaft, engaging matching grooves in a hub, so the two turn together. It is the heavy-duty alternative to a key.

The key, covered on the Shafts page, does the same job with a single square bar in a keyway — simple and cheap, but it concentrates the whole torque at one place, cuts a stress-raising slot into the shaft, and can work loose. A spline spreads the load across many teeth symmetrically, so it carries far more torque for the same diameter, keeps the hub automatically centred, and — because the teeth run axially — lets the hub slide along the shaft while still transmitting torque. That sliding-under-torque ability is why splines connect gearbox shafts, drive the sliding gears of a manual transmission, and join a vehicle’s propeller shaft to its axle.

§2Straight-sided splines

The older form has teeth with parallel, flat flanks — square-edged ridges around the shaft, standardised in counts of 4, 6, 10 and 16 teeth.

They are defined by a major (outside) diameter, a minor (root) diameter and the number of teeth, and are centred either on the major diameter or on the flanks. Straight-sided splines are simple to inspect and were long the automotive standard, but their square-cornered roots concentrate stress, and centring on the diameters is less precise than the involute form allows. They remain common where the design is established and loads are moderate.

§3Involute splines

The modern form gives the teeth the same involute flank as a gear — short, stubby gear teeth, typically at a 30°, 37.5° or 45° pressure angle.

The involute flank brings the gear’s advantages to the spline: a rounded, stronger root that resists fatigue far better than a square corner, and automatic self-centring as the flanks seat — the teeth wedge the hub concentric under load. They are made on the same hobbing machines as gears, so precision and cost are favourable at volume. For any highly-stressed or precision spline the involute form is now the default, and everything the spur page says about the involute and its pressure angle applies directly to the spline tooth.

§4Serrations

A serration is simply a very fine spline — many small vee-shaped teeth, used where a small-diameter part must lock angularly rather than carry large torque.

Because the teeth are numerous and fine, serrations allow the hub to be assembled at many closely-spaced angular positions, which suits adjustable levers, control arms and the shafts of instruments and potentiometers. They transmit only light torque — their value is precise, fine angular location and a secure press or clamp fit, not power transmission.

§5Torque capacity

A spline’s torque limit is set by the pressure the tooth flanks can bear: torque equals that pressure acting over the engaged flank area, at the mean radius.

The load-share factor is the honest part of the calculation: because no spline is made perfectly, the teeth do not all touch at once, so design practice assumes only a quarter to a half share the load. Doubling the engaged length is the simplest way to raise capacity, since torque scales directly with L.

§6Fits and sliding

Splines are specified with a fit class, just like the shaft fits on the tolerances page, chosen for how the hub must behave.

Three broad classes cover the field: a sliding fit, where the hub must move axially along the shaft under load (the transmission case); a close fit, located but removable; and a fixed or press fit, where the spline simply transmits torque and never moves. The fit governs the clearance between mating teeth and therefore the balance between free sliding and angular backlash — a sliding spline needs enough clearance to move without binding under the tooth loads, while a fixed one is drawn tight to eliminate lash. As with any fit, the class is chosen from the function first, then the tolerances follow.

§7Quick reference

The working core of the page on one card rack.