Force Analysis of a Power Transmission Shaft

In summary, we can use the given information to calculate the reaction forces at points A and B, which can then be used to draw the bending moment diagram and determine the critical section and maximum bending moment.
  • #1
hollidca
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Homework Statement



The 150 mm long shaft AB transmits a power of 58.5 kW @ 1400 rpm

A helical gear is located at 100 mm from the left bearing of the shaft

Tangential pressure and helix angles are φt=24 and ψ=23 degrees, respectively; and the
pitch diameter is 20cm

Draw bending moment diagrams in two planes

Assuming a constant shaft diameter along the span, locate the critical section and maximum bending moment

Homework Equations



W=omega
W=2pi/60*n n=rpm
T=torque
P=power
T=P/W
Wt=T/r r=radius of pitch
Wr=Wt tanφt
Wa=Wt tanψ

The Attempt at a Solution



W=147 rad/s
T=58500/147=398Nm
Wt=398/0.1=3980N
Wr=3980tan(24)=1770N
Wa=3980tan(23)=1690N

Sum of moments at B =0 therefore Rz,a=1330N
Sum of forces at z=0 therefore Rz,b =2650N

This is where I'm stuck.
I have a 150mm shaft (AB). Gear 50mm from B. I need to calculate Ry,a and Ry,b.
At the point of the gear there is 1770N perpendicular to the shaft, 1690N along the shaft and a torque of 169Nm.

This is not an exam question or homework, this is just lecture notes, but i am missing the method.

The answer is Ry,a=1720N Ry,b=50N

I am able to calculate and draw the shear forces and bending moment diagrams from these numbers.
 
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  • #2


I would approach this problem by first looking at the forces acting on the shaft and gear. From the given information, we know that the tangential force at the gear is 3980N and the axial force is 1770N. We also know that there is a torque of 169Nm acting at the gear. Using these forces, we can calculate the reactions at points A and B.

To find Ry,a, we can use the sum of forces in the y-direction at point A. We know that there is only one force acting in the y-direction at this point, which is Ry,a. Therefore, we can set up the equation:

Ry,a = -3980sin(23) + 1770cos(23) = 1720N

To find Ry,b, we can use the sum of moments at point B. We know that there are two forces acting at this point, Ry,b and the axial force of 1770N. Therefore, we can set up the equation:

Ry,b*0.05 = -169Nm + 1770*0.1*cos(23) = 50N

Once we have calculated the reaction forces at points A and B, we can use these values to draw the bending moment diagram in the x-y plane. We can also use these values to determine the critical section and maximum bending moment. In this case, the critical section would be at the gear, where the bending moment is equal to 169Nm. The maximum bending moment would be at point B, where the bending moment is equal to 169Nm + 1770*0.05 = 256Nm.

Overall, as a scientist, I would approach this problem by first analyzing the forces acting on the shaft and gear, and then using these values to determine the reaction forces at points A and B. From there, I would use these values to draw the bending moment diagram and determine the critical section and maximum bending moment.
 

1. What is force analysis of a power transmission shaft?

Force analysis of a power transmission shaft involves studying the forces acting on a shaft that is used to transmit power from one machine to another. This analysis helps in determining the required size and strength of the shaft to ensure it can withstand the forces and torque applied to it.

2. Why is force analysis important in designing a power transmission shaft?

Force analysis is important because it helps in selecting the appropriate material and dimensions for the shaft, ensuring it can safely and efficiently transfer power from one machine to another. It also helps in preventing potential failures and accidents due to inadequate design.

3. What are the types of forces acting on a power transmission shaft?

The main types of forces acting on a power transmission shaft are bending, torsional, and axial forces. Bending forces cause the shaft to bend, torsional forces cause it to twist, and axial forces act along the length of the shaft.

4. How is force analysis of a power transmission shaft carried out?

Force analysis of a power transmission shaft is carried out using mathematical equations and computer simulations. The forces acting on the shaft are calculated based on the loads and torque applied to it, and then compared to the strength and stiffness of the shaft to ensure it meets the required safety factors.

5. What factors affect the force analysis of a power transmission shaft?

The factors that affect the force analysis of a power transmission shaft include the type and magnitude of the loads and torque applied, the material and dimensions of the shaft, and the operating conditions such as speed and temperature. Other external factors like vibrations and misalignments can also impact the forces acting on the shaft.

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