Finding the force on a shaft when given Watts - shaft design

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SUMMARY

The discussion focuses on calculating the force acting on a shaft in a power transmission mechanism, specifically when given power in watts and rotational speed in RPM. The user initially miscalculated the torque by using frequency in Hz instead of radians per second. The correct calculation shows that at 300 RPM, the angular velocity is 31.42 rad/s, leading to a torque of 47.7 N*m when 1500 W is transmitted. This confirms the importance of using the correct units in mechanical calculations.

PREREQUISITES
  • Understanding of torque and its relationship to power and rotational speed
  • Familiarity with unit conversions between RPM, Hz, and rad/s
  • Basic knowledge of mechanical design principles for shafts and bearings
  • Proficiency in applying equations of motion in rotational dynamics
NEXT STEPS
  • Study the relationship between power, torque, and angular velocity in mechanical systems
  • Learn about the design considerations for shafts and bearings in power transmission
  • Explore unit conversion techniques for rotational motion and power calculations
  • Investigate the effects of different gear ratios on torque and force transmission
USEFUL FOR

Mechanical engineers, students in mechanical design courses, and professionals involved in power transmission system design will benefit from this discussion.

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Homework Statement



I think I did this right, but for some reason I am second guessing myself. I don't need help with the whole question, just this part:

The question says "In this exercise, you will design and analyze a shaft and the bearings for use in a power transmission mechanism. You are to produce a detailed drawing of the shaft, including all features necessary to retain the shaft in the bearings and attach the gear. Include all tolerances and dimensions required to manufacture the shaft.

The gear has a 150 mm pitch diameter, and the shaft transmits 1500 W at a speed of 300 rpm."

There is a gear at one end of the shaft, then two bearings, then an end point where it is attached to some component not specified.

So I want to find the force in torque acting on the shaft so that I can actually design it.

Homework Equations


1 W = 1 (N*m)/s

The Attempt at a Solution



300rpm = 5hz (1/s)

5 hz * X N*m= 1500 W

Solve for X, it equals 300 N*m

So then since the radius of the gear is .075m,

300/.075 = 4000N
Is that a valid way to go from Watts when given RPM to force?

Thanks!
 
Last edited:
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I think I found my error, I need to use rad/s not hz.

so 300 rpm = 31.42 rad/s

31.42*X=1500W

X = 47.7 N*m

But I thought hz is 1/s so when you multiply it by watts it would cancel out the seconds and give you N*m, why does this not work?
 
I worked it using a different approach, and got the same answer. I can't see anything wrong with your work.
 

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