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A shaft carries rotating parts (gears, pulleys, fans, rotors) and transmits torque between them. Bearings hold the shaft in place and let it turn with very little friction. Together they make up the backbone of every gearbox, pump, motor and spindle, and they are usually the first thing designed after the drive itself.
Shafts
What loads a shaft
- Torque from the motor or driving gear twists it, causing shear stress.
- Bending from gear tooth forces, belt tension and the weight of the parts it carries bends it between the bearings.
- Axial loads from helical gears or thrust push it along its axis.
Because the shaft rotates, a point on its surface goes from tension to compression and back every revolution. Bending stress in a rotating shaft is therefore fully reversed, and most shaft failures are fatigue cracks that start at shoulders, keyways and grooves.
Locating parts on a shaft
A shaft is stepped so that each part slides on from one end and stops at a shoulder. Other features hold the parts in place:
- Keys (or splines) pass torque from the shaft to a gear or pulley.
- Circlips (retaining rings) in grooves stop parts sliding off.
- Locknuts and spacers clamp bearings and gears axially.
- Interference fits hold bearing inner rings and some hubs without keys.
Only one bearing should locate the shaft axially (the fixed bearing); the other is allowed to slide slightly (the floating bearing) so the shaft can expand with temperature without overloading either bearing.
Sizing a shaft
For a first estimate of a solid shaft under combined bending and torsion, use the equivalent torque:
| Symbol | Meaning | Unit |
|---|---|---|
| Largest bending moment | N·m | |
| Torque | N·m | |
| Allowable shear stress, low enough to cover fatigue and keyways (about 30–50 MPa for medium carbon steel in a first estimate) | Pa | |
| Shaft diameter | m |
Assumptions: solid round shaft, maximum shear stress theory, steady loads. A final design checks fatigue properly (for example with the DIN 743 method or a Goodman diagram), with stress concentration factors at each shoulder and keyway, and checks deflection at the gears and bearings.
Bearings
Plain bearings
A plain bearing (bush or journal bearing) is a sleeve the shaft turns in, lubricated by oil, grease or a self-lubricating material such as sintered bronze or PTFE-lined polymer. Plain bearings are simple, compact and quiet and take shock loads well. Oil-film journal bearings carry the largest loads at high speed, in engines and turbines.
Rolling-element bearings
Balls or rollers roll between an inner and an outer ring, so friction is low even when starting. They are standard, interchangeable parts bought from a catalogue.
| Type | Loads | Features | Typical uses |
|---|---|---|---|
| Deep groove ball | Radial, moderate axial both ways | Most common; cheap, fast, quiet | Motors, gearboxes, fans, wheels |
| Angular contact ball | Combined radial and axial (one direction) | Used in pairs; precise | Machine tool spindles, pumps |
| Cylindrical roller | Heavy radial, little or no axial | High load capacity, allows axial float | Gearboxes, motors (floating bearing) |
| Tapered roller | Heavy radial and axial | Used in pairs, adjustable preload | Car wheel hubs, gearbox output shafts |
| Spherical roller | Very heavy radial, some axial | Self-aligning; tolerates shaft bending | Conveyors, crushers, heavy machinery |
| Needle roller | Radial, very compact | Small radial height | Gear pumps, universal joints, rocker arms |
| Thrust ball or roller | Axial only | Turntables, vertical shafts, screw jacks |
Bearing life
Rolling bearings eventually fail by fatigue of the rolling surfaces. Their basic rating life is the number of revolutions that 90 % of a large group of identical bearings will reach:
| Symbol | Meaning | Unit |
|---|---|---|
| Basic dynamic load rating (from the catalogue) | N | |
| Equivalent dynamic load on the bearing | N | |
| 3 for ball bearings, 10/3 for roller bearings | none | |
| Speed | rev/min |
Typical targets are 8000–15 000 hours for machines used intermittently and 20 000–50 000 hours for machines running a full shift every day.
Worked example: the output shaft of a gear reducer
The 120 mm gear from the gear guide example carries 96.8 N·m and a tangential tooth force of 1650 N. It sits midway between two bearings 200 mm apart. Size the shaft (C45 steel, τ_allow = 40 MPa) and check the life of a 6006 deep groove ball bearing (30 mm bore, C ≈ 13.8 kN) at 483 rev/min.
Step 1: total tooth force. With a 20° pressure angle there is also a radial force, so the total force is:
Step 2: bending moment for a central load on a simply supported span:
Step 3: equivalent torque and diameter.
The minimum is 25.5 mm, so a 30 mm bearing seat and a slightly larger gear seat give a sensible margin.
Step 4: bearing life. Each bearing carries half the force, P = 878 N.
In small gearboxes like this one, the bearings are often chosen by the shaft diameter rather than by load, and their calculated life is very long. In heavily loaded or high-speed machines, the bearing life calculation decides the bearing size.
Good practice
- Put bearings close to the gears and pulleys to keep bending moments small.
- Use generous fillet radii at shoulders (but smaller than the bearing’s corner chamfer, so the bearing sits square).
- Follow the bearing maker’s recommended fits: usually an interference fit on the rotating ring and a looser fit on the stationary one.
- Seal the bearings against dirt and water; most bearing failures come from contamination and poor lubrication rather than fatigue.
Key points
- Shafts carry torque and bending; rotating bending makes fatigue the main failure mode.
- Shoulders, keys, circlips and fits locate parts; one bearing fixes the shaft, the other floats.
- Choose ball bearings for general use, roller bearings for heavy loads, plain bearings for shock and compact designs.
- Bearing life L₁₀ = (C/P)³ million revolutions for ball bearings.