A spline connection is a high-precision, usually backlash-free shaft-hub connection created by the positive connection of teeth on an external profile into identical gaps on an internal profile.

Its greatest advantage is the combination of high power transmission, maximum precision and yet simple assembly. It is a premium solution for demanding mechanical applications for the transmission of torque within an axis.

A gearing has a dimensional limit that must be checked and an attributive limit that must be checked. The dimensional limit is referred to as the actual limit and the attributive limit is described as the effective limit. Effective means the largest or smallest permissible envelope gearing. A hub must not be too small in terms of its effective dimension and too large in terms of its actual dimension. A shaft must not be too large in terms of its effective dimension and too small in terms of its actual dimension.

Fully toothed gauges are used for the effective limit, while sector-toothed rejection gauges are used for the actual limit. Alternatively, a measurement can be taken instead of using rejection gauges.

The running gear teeth manufactured on the workpiece are rolled together with a master gear in a corresponding inspection device.

The master gear should be manufactured by a gauge manufacturer with as few deviations as possible from the ideal geometry—preferably zero deviations. Rolling inspections are divided into single-flank and double-flank rolling tests. See the corresponding explanations for SFP (single-flank rolling test) and DFP (double-flank rolling test).

The term involute originates from Latin.

According to DIN 5480:

Unlike other gauges, a test force is permissible and necessary for spline gauges. The dead weight of the gauge alone is often insufficient. However, the test force should not exceed 15 daN. (1 daN numerically corresponds to 1 kg mass.)

According to DIN ISO 4156:

Composite spline gauges shall be used without excessive force to prevent damage or distortion to the component or gauge.

Running gearing:

The main task is to achieve an appropriate speed and/or corresponding torque. Transmission occurs from one shaft to another.

Spline gearing (fit spline):

The primary task is to connect a shaft with a hub and transmit torque within a common axis.

A gear consists of uniformly distributed teeth around the circumference with gaps between them. Each tooth has a right and left flank, whose profile follows an involute curve over the tooth height.

Running gearing transmits torque from one shaft to another. The shafts are often parallel but may also intersect at an angle (e.g., differential gears) or be spatially offset (e.g., worm gears).

Spline gearing transmits torque within one axis. Shaft and hub are assembled together; torque and speed remain identical.

A spline is a positive shaft–hub connection transmitting torque within a common axis.

A coupling is a machine element that provides a temporarily disengageable connection between two rotating components (e.g., between engine and gearbox).

Gear wheels:

The involute allows smooth meshing between gears, resulting in low noise. Noise behavior is a key quality characteristic. Further modifications beyond the involute optimize noise behavior.

Spline:

Only the involute provides true surface contact between external and internal flanks and is rotationally symmetric.

The involute is the only profile that remains geometrically unchanged when rotated about its base circle center. This enables proper surface contact between mating flanks. There is no true alternative solution.

A cylindrical base body with evenly distributed external or internal teeth. The flanks follow an involute profile, allowing smooth meshing.

Transmission of torque and achieving an optimal speed-to-torque ratio.

Spur gears transmit torque between usually parallel shafts.

Bevel gears transmit torque between shafts arranged at an angle, typically 90°.

1. Gear wheels – torque transmission between shafts
2. Splines – torque transmission within one axis
3. Face serration spline – torque transmission via face surfaces
4. Other systems – torque transmission via belts or chains

The pitch diameter is a theoretical (calculated) diameter:

d = z × m

It serves as a reference diameter for defining tooth thickness, space width, pressure angle, and helix angle.

Colloquially, the involute shape of one flank. Deviations are called profile deviations.

In gear terminology: “the module” (masculine in German).

Module is a ratio:

m = d / z

Unit: mm.

Examples:

• Tooth height (running gear) ≈ 2 × m • Tooth height (spline) ≈ 1 × m • Tip clearance ≈ 0.25 × m • Pitch = π × m

Meshing gears must have identical modules.

i=z1 / z2

Example: 60 teeth driving 20 teeth → ratio 3:1.

Direct gear contact avoids additional elements like belts or chains, reducing potential weaknesses.

Example: worm gear. Torque applied at the output cannot drive the input.

It describes how well a process result conforms to tolerance requirements.

Repeatability and Reproducibility test.

Statistical evaluation of measurement system capability (Gage R&R).

Roundness = form deviation.

Runout = positional deviation relative to a reference.

The angle at which two gears mesh.

Standard: 20° (running gears).

Splines: 30°, 37.5°, or 45° depending on standard.

It attempts to detect wear in a GO ring gauge but is ineffective due to uneven wear distribution.

Recommendation: use a second GO ring gauge while the first is inspected.

No. They are approx. 0.005–0.010 mm larger due to geometric deviation superposition.

The diameter up to which the involute profile must be present and verifiable.

The diameter up to which the involute is functionally used by the mating tooth.

Verification of gear measuring machines using certified reference standards by accredited laboratories (DIN EN ISO/IEC 17025).

Ratio between available path of contact and base pitch.

Contact ratio > 1 means multiple tooth pairs are engaged simultaneously.

Not directly measurable:

• Number of teeth
• Module
• Pressure angle

Directly measurable:

• Tip diameter
• Root diameter
• Tooth thickness (via measurement methods)

Advanced methods:

• Single-/double-flank rolling tests
• Gear measuring machines
• Roll scanning

Noise, Vibration, Harshness analysis.

Often tested at end-of-line gearbox testing.

Single-flank rolling with FFT analysis is effective for individual gears.

Intentional geometry adjustments:

• Tip relief
• Root relief
• Profile crowning
• Lead crowning

Used to improve noise, load distribution, and durability.

Higher contact ratio → smoother running.

However, axial forces occur.

Double helical (herringbone) gears cancel axial forces.

1. Parallel flank splines
2. Serration splines
3. Involute splines (most common in automotive)

Whenever torque must be transmitted within a common axis (drive shafts, clutch hubs, actuators).

Generally very durable; failures due to wear are rare.

Depends on material, load, and fit type. Often other machine elements fail first.

Two limits:

• Actual limit (dimensionally measured)
• Effective limit (envelope condition via GO gauges)

According to DIN 1319: determining the extent to which requirements are fulfilled.

Includes measuring and gauging.

Radian measure describes an angle:

radian = length of arc / radius

Arc length is a portion of a circumference (e.g., tooth thickness at pitch diameter).