Clamped Joints

Clamped joints connect a hub, lever, collar, or bracket to a shaft by normal pressure created by tightening bolts. They avoid keyways and permit angular or axial adjustment.

Friction capacity

If the resultant normal force is \(N\), the available tangential force is approximately

$$F_t\le\frac{\mu N}{n_s}.$$

At an effective radius \(r_m\), torque capacity is

$$T_{cap}=\frac{\mu Nr_m}{n_s}.$$

For distributed pressure, use \(T=\int_A \mu p r\,dA\) and determine \(p\) from the real clamp geometry.

Design checks

Bolt preload must be sufficient without yielding the bolts or crushing the hub. Check hub bending, local pressure, split-lug stresses, bolt fatigue, slip, fretting, and loss of preload. Surface coatings and lubricants change friction and therefore both tightening preload and transmitted torque.

The joint should be tightened symmetrically, provide adequate split flexibility, and retain a reserve against vibration and temperature-induced relaxation.

Types of clamp connections

A split hub may have one slit and one or more tightening bolts, or it may consist of two separate halves. A collar can locate a component axially, while a clamping lever or hub can transmit both torque and axial force. Split constructions simplify assembly because they need not slide over the shaft end.

Relation between bolt force and contact pressure

The bolt force does not become useful normal force in a one-to-one ratio. Hub flexibility, slit position, lug geometry, bolt spacing, and local bending determine the pressure field. A uniform-pressure model is suitable only for preliminary sizing; refined analysis uses ring theory, contact mechanics, or finite-element verification.

Combined torque and axial force

If the interface simultaneously transmits torque \(T\) and axial force \(F_a\), a convenient preliminary interaction is based on the resultant tangential demand at the effective radius:

$$F_{res}=\sqrt{F_a^2+\left(\frac{T}{r_m}\right)^2}\le\frac{\mu N}{n_s}.$$

The actual direction and distribution of friction should be considered when loads vary independently.

Bolt and hub checks

Bolts are checked for preload, tightening stress, service fluctuation, fatigue, and thread stripping. The hub is checked at the slit, lugs, bolt holes, and thin wall over the shaft. Excessive tightening can close the slit, yield the lugs, or create an uneven pressure peak without meaningfully increasing capacity.

Fretting and surface condition

Microslip under fluctuating torque or bending produces fretting debris and can initiate fatigue cracks. Clean mating surfaces, adequate pressure, good alignment, and a suitable surface treatment improve resistance. Lubrication during assembly may change friction drastically and must be included in the specified tightening procedure.

Calculation sequence

1. Define torque, axial force, bending influence, duty, and required adjustment.
2. Select split-hub geometry, bolts, and effective contact length.
3. Estimate required normal force from friction capacity.
4. Relate normal force to bolt preload and hub deformation.
5. Check bolts, lugs, hub wall, shaft pressure, slip, and fretting.
6. Specify surface condition, tightening order, locking, and inspection.