Learning Goal:

To determine the maximum possible power transmission for acircular shaft and the minimum diameter required to avoid exceedingshear stress limits.

A rotating shaft can be used to transmit mechanical power fromone place to another. For example, a shaft can be connected to amotor at one end and a pulley at the other. The shaft can thentransmit power from the motor to the pulley. When the machine isoperating, the shaft will rotate at some angularvelocity ? and will be subject to atorque T. The power transmitted by the shaftis P=T?.

The shaft's rotation can also be expressed as afrequency, f, which represents the number ofrevolutions of the shaft per unit time. The frequency and angularvelocity are related by ?=2?f, sothe power can also be calculatedusing P=2?fT.

When designing a shaft, one consideration is limits on shearstress. The torsionformula ?allow=TcJrelatesthe allowable shear stress in a circular shaft with outerradius c to the torque T. Thepolar moment of inertiais J=?2c4 for a solidshaft.

In the SI system, the units of torque are newton-meters (N?m),and the units of power are watts (1W=1N?m/s). In the FPS system,the basic units of torque are foot-pounds (ft?lb), and the units ofpower are foot-pounds per second (ft?lb/s). However, power is oftenexpressed in horsepower, where 1hp=550ft?lb/s.

Part A: Transmitted power

A solid circular rod is used to transmit power from a motor to amachine. The diameter of the rodis D = 1.5 in and the machineoperates at ? = 170 rpm . If theallowable shear stress in the shaft is 11 ksi , whatis the maximum power transmissible to the machine?

Part B - Minimum diameter

A solid circular shaft is required totransmit P = 40 kW from a motorto a machine. The maximum allowable stress in the shaftis ?allow = 79 MPa . If themachine runs at ? = 18 rad/s ,what is the minimum diameter for the shaft?