Reference no: EM132416695

To determine the maximum possible power transmission for a circular shaft and the minimum diameter required to avoid exceeding shear stress limits.

A rotating shaft can be used to transmit mechanical power from one place to another. For example, a shaft can be connected to a motor at one end and a pulley at the other. The shaft can then transmit power from the motor to the pulley. When the machine is operating, the shaft will rotate at some angular velocity ω and will be subject to a torque T. The power transmitted by the shaft is P=Tω.

The shaft's rotation can also be expressed as a frequency, f, which represents the number of revolutions of the shaft per unit time. The frequency and angular velocity are related by ω=2πf, so the power can also be calculated using P=2πfT.

When designing a shaft, one consideration is limits on shear stress. The torsion formula τallow=TcJ relates the allowable shear stress in a circular shaft with outer radius c to the torque T. The polar moment of inertia is J=π2c4 for a solid shaft.

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 of power are foot-pounds per second (ft⋅lb/s). However, power is often expressed in horsepower, where 1hp=550ft⋅lb/s.

a) A solid circular rod is used to transmit power from a motor to a machine. The diameter of the rod is D = 1.75 in and the machine operates at ω = 200 rpm . If the allowable shear stress in the shaft is 11.8 ksi , what is the maximum power transmissible to the machine?

b) A solid circular shaft is required to transmit P = 48 kW from a motor to a machine. The maximum allowable stress in the shaft is τallow = 70 MPa . If the machine runs at ω = 16 rad/s , what is the minimum diameter for the shaft?