Everyday mechanical engineering calculations
Five calculations that come up in every workshop and design office, with the formulas, typical values and the mistakes that cause failures.
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Speed and torque trade off
Gears and belts can't create power: they trade speed for torque. A 3:1 reduction gives a third of the speed and three times the torque, minus losses. That is why a small, fast motor with a gearbox can lift what a large slow motor would.
Size a motor from the load
Work out the torque the load needs at the output, divide by the gear ratio and efficiency to get motor torque, then use hp = lb·ft × rpm ÷ 5,252 at motor speed. Add 20 to 30% margin for starting and wear.
Torque a bolt for clamping force, not for torque
Joints fail when the clamping force is too low, letting parts slip and the bolt fatigue. Choose the preload first, typically 75% of proof load, then calculate the torque for the actual lubrication.
Typical mistakes
- Using outside diameter instead of pitch diameter for pulleys and gears.
- Applying a dry torque value to oiled or anti-seize threads.
- Forgetting that a cylinder pulls with less force than it pushes.
- Ignoring efficiency in worm gear drives, where it can be under 60%.