The gear train with a ratio of 271:1, an input speed of 7,117 rpm, and input power of 0.2 hp has an output torque of approximately 54.107 Nm.
To find the output torque of a gear train, we can use the formula:
Output Torque = Input Torque * Gear Ratio
Here are the steps to find the output torque:
1. Convert the input speed from rpm to rad/s:
Input Speed = 7,117 rpm = 7,117 * (2π/60) rad/s = 746.92 rad/s
2. Convert the input power from hp to watts:
Input Power = 0.2 hp = 0.2 * 745.7 watts = 149.14 watts
3. Calculate the input torque using the formula:
Input Torque = Input Power / Input Speed
Input Torque = 149.14 watts / 746.92 rad/s = 0.1997 Nm
4. Calculate the gear ratio:
Gear Ratio = 271:1
5. Calculate the output torque using the formula:
Output Torque = Input Torque * Gear Ratio
Output Torque = 0.1997 Nm * 271 = 54.107 Nm
Therefore, the output torque of the gear train is approximately 54.107 Nm.