This simulator puts two spur gears in mesh and lets you change everything that matters: how many teeth each has, how fast the driver turns and how much torque it gets. The gears are drawn in proportion to their tooth counts, so the gear ratio is visible, and the readouts show the output speed, output torque and pitch diameters that result.
• A driver gear (blue) and a driven gear (orange) meshed on their pitch circles, each labeled with tooth count, turning in opposite directions. • Sliders for driver speed, driver teeth, driven teeth and input torque. • Readouts for gear ratio i, output speed n₂, output torque T₂ and pitch diameters d₁ and d₂ (module 2 mm). • Notes, formulas and a worked example. The animation runs at 5 percent of true speed so the teeth stay readable.
Gear ratio is the driven tooth count divided by the driver tooth count, i = N₂ / N₁. Output speed is the input speed divided by the ratio, and output torque is input torque times the ratio times mesh efficiency, which the lab sets at 97 percent. With a 20-tooth driver at 1,000 rpm and 100 N·m driving a 60-tooth gear, the ratio is 3, output speed is about 333 rpm and output torque is about 291 N·m. Pitch diameter is the module (2 mm) times the tooth count.
Gears trade speed for torque: a larger driven gear turns slower with more torque, and a smaller one turns faster with less. Each external mesh reverses the direction of rotation. Real gear trains combine several stages, because ratios multiply from stage to stage, and lose a few percent at each mesh to friction. This model covers a single external spur pair with a fixed efficiency; it does not include backlash, helical or bevel geometry, or tooth stress.
Divide the driven gear's tooth count by the driver gear's tooth count. A 20-tooth driver meshed with a 60-tooth driven gear has a ratio of 3:1, meaning the driven gear turns at one third of the driver speed.
Power is speed times torque, and a gear pair passes nearly constant power apart from friction. If the output turns three times slower, it can deliver about three times the torque. The simulator multiplies torque by the ratio and by a 97 percent efficiency factor.
In an external mesh, the teeth of the driver push the teeth of the driven gear in the opposite rotational sense. To get the same direction you would add an idler gear or use an internal gear.
It covers one spur-gear pair with a fixed 97 percent efficiency. It does not model multi-stage trains, idlers, helical or bevel gears, backlash, lubrication, contact stress or tooth strength. See the Planetary Gearset lab for a compound arrangement.