Shafts, Bearings, Gears & Power Transmission

Power transmission is a chain: motor shaft, coupling, belt or gear, driven shaft, bearings, and load. Size the chain, not isolated catalog parts.

If an ideal reducer has input speed \(\omega_i\) and output speed \(\omega_o=\omega_i/N\), output torque is \(T_o\approx \eta N T_i\), where \(\eta\) is efficiency. A 0.6 N·m motor through a 5:1 reducer at 90% efficiency supplies about 2.7 N·m. Acceleration and jam torque may govern above steady demand.

Shaft checklist

• combined bending and torsion across each load case;
• deflection and slope at gears, seals, and bearings;
• fatigue at shoulders, keyways, grooves, and threads;
• critical speed and imbalance response;
• axial location, thermal growth, fits, assembly, and service access.

Use shoulders and retaining features deliberately. A sharp shoulder raises stress; a large fillet may interfere with a bearing corner. Reliefs, spacers, chamfers, and catalog corner radii must coexist.

Bearing arrangement before bearing number

Decide how the shaft is constrained. A common locating/nonlocating arrangement fixes axial position at one bearing and permits thermal growth at the other. Two fully locating bearings can fight each other when housings expand or are misaligned. Preload can raise stiffness and remove clearance but also raises heat and sensitivity.

Choose the drive by behavior

• Gears: compact, accurate ratio, high stiffness; require alignment and lubrication.
• Timing belts: quiet, remote shafts, no slip; add compliance and tension loads.
• V-belts/friction belts: tolerate shock and can slip; ratio and preload vary.
• Chains: rugged and temperature tolerant; introduce polygonal speed variation, noise, and lubrication needs.
• Lead/ball screws: rotary-to-linear; compare efficiency, backlash, critical speed, buckling, and back-driving.

Transmission worksheet

For one axis, build a table from load to motor. At each element record speed, torque, efficiency, reflected inertia, radial/axial load, and failure mode. Add a jam case and loss-of-power case. This catches the classic mistake of selecting a motor from steady force while ignoring acceleration, screw buckling, bearing load, or brake duty.