Power, Torque and Speed Relation

The following calculations show the relationship between power, torque and rotational speed as the rotational motion passes through the gearbox, with power in kW equal to P.

Pin = Pout + Gear losses

Gear losses = 1% per stage. With this being ignored an ideal case can be assumed.

The general equation of power is then applicable:

P = Tω


With ω as rotational velocity in radians/sec, T is torque in N.m, and n is rotational speed in rpm.

The principle is best explained with an example. If there is a rotational speed reduction of 25 through the gearbox with a standard input speed for an electric motor of 

n = 1475rpm:

Then for:

Pin = Pout = Tω

Thus, as rotational speed decreases through the gearbox, torque increases, and vice versa. The torque change through the gearbox is equal to the multiple of the gearbox ratio.

Hansen Transmissions specialize in supplying reducer solutions for many industries with specific emphasis on:

Hansen transmissions offers a range of specifically designed gearboxes to suit any application that would require a link between a driving motor and a driven system. Couplings are also supplied for specific application requirements, for example rigid couplings for high torque transfer and shaft mounted gearboxes, fluid couplings for gradual smooth startup, and flexible couplings where slight misalignment is present.