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.

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§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.

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§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.

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§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.

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§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.

T = p · A · r_m where A = k · N · h · L, r_m = D + d4, h = D − d2

Example 1 — an 8-tooth straight spline

Major diameter D = 30 mm, minor d = 26 mm, N = 8 teeth, engaged length L = 40 mm, allowable flank pressure p = 20 MPa, and a load-share factor k = 0.5 (only about half the teeth carry, from manufacturing spread). Mean radius r_m = (30 + 26)/4 = 14 mm; tooth height h = (30 − 26)/2 = 2 mm; engaged area A = 0.5 × 8 × 2 × 40 = 320 mm². Torque capacity T = 20 × 320 × 14 = 89 600 N·mm = 89.6 N·m — close to the 99.5 N·m the same-diameter solid transmission shaft carried on the Shafts page, but distributed as low flank pressure instead of concentrated at a keyway.

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.

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§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.

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§7Quick reference

The working core of the page on one card rack.

Forms

straight-sided · involute

serration = fine spline

Why spline

many teeth > one key

centres · slides under load

Torque

T = p·A·r_m

A = k·N·h·L

Load share

assume k = ¼ – ½

Fit

sliding · close · fixed

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Handbook application: from concept to controlled practice

Purpose. This expanded section turns the original page into a practical handbook. It preserves the supplied material and adds a repeatable way to apply, check and review Splines and Serrations. It does not replace a contract, legislation, a controlled standard, competent engineering judgement or specialist advice.

The operating aim is to carry the subject from function and assumptions through design evidence, verification and controlled release. Read the original explanation first, then use the workflow and checks below to convert knowledge into evidence.

Apply Splines and Serrations by beginning with the duty, not the component or software command. Convert the key ideas—splines, serrations, straight-sided, involute, many—into measurable requirements and interfaces. Record operating and non-operating environments, duty cycle, expected life, loads, energy sources, human interaction and reasonably foreseeable abnormal conditions. When a value is not a project requirement or verified supplier datum, identify it as an assumption or illustrative value.

Create a calculation and evidence trail that another competent person can audit. Every input should carry a source, unit, revision and uncertainty or tolerance where relevant. Every model should state its boundary conditions and limitations. Keep nominal capacity separate from design capacity, and keep verification margin separate from an arbitrary safety factor. If a code or standard governs the work, confirm the applicable edition and contractual status rather than copying a number from a secondary summary.

Design for manufacture, assembly, inspection, operation and maintenance at the same time. A technically valid geometry can still fail because it cannot be fixtured, measured, cleaned, guarded, reached or replaced. Review process capability, datum or reference strategy, tolerance accumulation, access, error-proofing and changeover. Where people interact with plant, apply the hierarchy of controls and consult those who will operate, clean, maintain and recover the equipment.

Plan verification before release. Define the characteristic, method, equipment, sample or test condition, acceptance criterion, record and responsible person. Validation then asks a different question: whether the resulting system is effective and suitable in the intended use context. A passed drawing check or analysis does not by itself validate usability, maintainability or production performance.

Step-by-step operating method

Define the duty. Capture the required function, interfaces, operating environment, life, loads and unacceptable outcomes.
Establish the model. Identify governing principles, units, material or process data, assumptions and uncertainty.
Develop alternatives. Compare feasible concepts against performance, manufacturability, safety, maintainability and cost.
Verify the design. Use analysis, test, inspection or demonstration with acceptance criteria defined before execution.
Release and learn. Baseline the design, control changes, retain evidence and feed operating results into the next revision.

Illustrative design review record

Illustrative values only. Build a one-page record with the required function, input sources, assumptions, governing load or process condition, failure consequences, selected concept, verification method and acceptance criterion. Mark every numerical input as project requirement, verified supplier data, measured value, calculation output or assumption. Review the weakest evidence first. If an assumption can change safety, compliance, interchangeability or capacity, it must be resolved before release rather than buried in a calculation note.

Evidence class	Question	Release expectation
Requirement	What must the design do and under which conditions?	Approved and traceable
Input	Where did the load, property, tolerance or process limit come from?	Source, unit and revision recorded
Analysis	Which model and assumptions connect input to result?	Checkable calculation or simulation
Verification	How will conformity be demonstrated?	Method and acceptance criterion agreed
Validation	Will the solution work for intended users and conditions?	Representative use evidence

Common failure modes and recovery actions

1. Watch for

Starting detailed design before interfaces and operating limits are agreed.

Recovery: Return to the governing definition or requirement and restate the decision in one sentence.

2. Watch for

Using catalogue or typical values as though they were certified project inputs.

Recovery: Separate evidence from assumption, assign an owner and set a date for validation.

3. Watch for

Checking nominal performance while ignoring tolerances, degradation and foreseeable misuse.

Recovery: Run a small counterexample, boundary test, pilot or independent check before proceeding.

4. Watch for

Confusing verification of requirements with validation of user need.

Recovery: Record the consequence, decision and rationale, then update the controlled baseline.

5. Watch for

Releasing drawings or procedures without configuration, inspection and change controls.

Recovery: Escalate when the issue affects safety, compliance, acceptance, material value or an agreed tolerance.

Review checklist

What function and failure consequence govern this decision?
Which inputs are measured, specified, assumed or illustrative?
How will conformity be demonstrated and recorded?
What change would invalidate the current evidence?
Are mandatory requirements distinguished from recommendations and illustrative values?
Are sources, assumptions, units, dates and versions recorded closely enough to reproduce the decision?
Have safety, legal, ethical, stakeholder and operational consequences been considered at the appropriate level?
Is there a named owner and a trigger for review, escalation, change or retirement?

Questions for deeper application

What is the most important distinction a practitioner must preserve when applying Splines and Serrations?