Speed, Torque, and Power in a Simple Geartrain
The input shaft to the simple geartrain is driven by a motor that supplies 1 kW of power at the operating speed of 250 rpm. (See Figure 8.25.) (a) Determine the speed and rotation direction of the output shaft. (b) What magnitude of
torque does the output shaft transfer to its mechanical load?
Approach
To find the rotation direction of the output shaft, we recognize that the input shaft rotates clockwise in the figure, and, at each mesh point, the direction of rotation reverses. Thus, the 30-tooth gear rotates counterclockwise, and the
50-tooth output gear rotates clockwise. To determine the speed of the output shaft, we will apply Equation (8.17).
VR=\frac{output speed}{input speed}=\frac{\omega _{4}}{\omega _{1}}=\frac{N_{1}}{N_{4}}=\frac{N_{input}}{N_{output}} (8.17)
In part (b), for an ideal geartrain where friction can be neglected, the input and output power levels are identical. We
can apply Equation (8.5)
P = T\omega (torque) (8.5)
to relate speed, torque, and power.
