Belts, Gears, Couplings and Transmitted Power

Follow speed, torque and power through the drive

Power transmission connects a prime mover to a driven machine. A boiler-house motor might drive a pump through a flexible coupling, a ventilation fan through belts, or a conveyor through a reduction gearbox. Objective 9 requires understanding speed changes, transmitted power and efficiency. A speed reduction can increase available torque, but it cannot increase power. First identify the driving member, the driven member, the transmission ratio and where losses occur.

Rotational speed may be expressed in revolutions per minute, while angular velocity is expressed in radians per second. One revolution is 2π radians, so angular velocity equals 2π × rpm / 60. Shaft power equals torque multiplied by angular velocity. Use torque in N·m and angular velocity in rad/s to obtain watts. The 60 conversion belongs in the denominator when changing rpm to revolutions per second; forgetting it creates a sixtyfold error.

Belts and pulleys

In an ideal belt drive without slip, the tangential belt speed is the same at each pulley. Driver speed × driver pitch diameter therefore equals driven speed × driven pitch diameter. A small driving pulley turning a larger driven pulley reduces speed. Use the pitch diameters specified by the problem, rather than mixing outside diameter and pitch diameter. With significant slip, actual driven speed is lower than the ideal prediction.

An open belt drive gives the same rotation direction at both pulleys. A crossed arrangement reverses relative direction but introduces additional practical restrictions. V-belts grip the groove sides by wedging action; multiple matched belts distribute load. Synchronous toothed belts engage teeth to maintain a defined speed relationship. A flat or V-belt transmission may slip under overload, but a toothed drive is not a substitute for overload protection. The proper belt type, tension and alignment are equipment design decisions.

A 1,800 rpm motor with a 100 mm pitch-diameter pulley drives a fan pulley of 300 mm. Ideal fan speed is 1,800 × 100 / 300 = 600 rpm. Suppose the motor supplies 12 kW shaft power and belt efficiency is 90%. Useful fan shaft power is 10.8 kW. At 600 rpm the angular velocity is 62.832 rad/s, so fan torque is 10,800 / 62.832 = 171.9 N·m. Motor torque is 12,000 / 188.496 = 63.66 N·m. The torque increases by less than the speed ratio of three because the belt loses power.

Gears and chain drives

For two meshing gears, driver speed × driver tooth count equals driven speed × driven tooth count. Two external gears rotate in opposite directions. An idler between them changes the final direction and shaft spacing, while the overall speed ratio still depends on the first and final tooth counts. A compound train differs: two gears fixed to the same intermediate shaft share shaft speed, so the stage ratios multiply.

A 20-tooth pinion drives a 60-tooth gear, giving a 3:1 reduction. A second pinion on that intermediate shaft gives a further 4:1 reduction. Total reduction is 12:1; a 1,440 rpm input gives 120 rpm output. If each stage is 95% efficient, total efficiency is 0.95 × 0.95 = 90.25%, not 95% and not 190%. An 8 kW shaft input therefore gives 7.22 kW output. The difference, 0.78 kW, becomes losses including heat and sound.

Safe operating observations

A flexible coupling accommodates limited specified misalignment; it does not make alignment unnecessary. During permitted operating rounds, observe abnormal noise, vibration, temperature and lubricant leakage from a safe position. A loose guard, a frayed belt or a missing chain cover is a defect requiring reporting and appropriate isolation. Never reach through a guard, tension a moving belt, or use a hand to search for a hot or damaged rotating component.

Before drive maintenance, isolate all energy sources and consider rotation imposed by the driven process, gravity or stored mechanical energy. A stopped motor does not prove the connected fan or conveyor cannot move. After authorized work, guards, fasteners and lubrication must be restored and the approved return-to-service checks completed. For examination questions, distinguish the ideal geometric speed ratio from measured efficiency and from the separate safety requirements of the installation.

Source notes

Official scope and technical references checked 2026-10-17: Reference 1. Archived DOE handbooks are used for physical principles, not current Canadian legal requirements.