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Chapter 1: Problem 60

A press delivers a force of \(8000 \mathrm{~N}\) throughout a distance of \(18 \mathrm{~mm}\) each stroke. Select a number of strokes per minute and determine the rate of work output per second. If the press efficiency is \(90 \%\), what average torque must be provided by a 1750 -rpm driving motor?

Short Answer

Expert verified
The work done per stroke of the press is \(144 \mathrm{J}\). Assuming an operation rate of 60 strokes per second, the rate of work output per second or power is \(8640 \mathrm{W}\). Given the 90% efficiency, the motor must provide an average torque of \(474.334 \mathrm{Nm}\).

Step by step solution

01

Calculate the Work Done per Stroke

Work done is calculated using the formula: Work = Force x Distance. Here, the force is \(8000 \mathrm{~N}\) and distance is \(18 \mathrm{~mm}\) or \(0.018 \mathrm{~m}\). Let's calculate the work done.
02

Calculate the Power Output

Power is work done per unit time. Here, the unit time is 1 second. So power can be calculated by dividing the work done by one second. As the problem doesn鈥檛 specify the number of strokes per minute, a suitable number like 60 can be assumed for simplicity.
03

Convert Power to Watts

The original power unit in this case is Newton meter per second, but it's more meaningful in context to express it in watts, since 1 Watt equals 1 Newton meter per second.
04

Calculate Torque

To calculate the torque, first the output power of the motor is calculated, which is higher than the output power of the press due to the efficiency. Then torque is calculated using the formula for power and torque related to rotational motion, with given rounds per minute.
05

Convert Torque to Newton Meters

Finally, the torque is simplified from its much larger original unit (Newton millimeters) to the more convenient and commonly used Newton meters.

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