Understanding Roller Pressure: Effect of Angle on Sheave Force Distribution

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In summary: Based on the above calculations, it can be concluded that the force acting on each roller will differ depending on the angle at which the cable is pulling. In summary, the tension on the rollers will vary depending on their position on the sheave and the angle at which the cable is pulling, with the rollers on the ends experiencing greater tension than those in the middle.
  • #1
barvas11
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Hi Guys,
I have a sheave with 7 rollers spread evenly on 180° radius. There is an equal amount of force on each end of the sheave pulling down.
My question is will the force acting on rollers be the same for all rollers or will it differ depending on the angle?
I have attached the picture for better illustration.
Thanks for your advice
 

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  • #2
barvas11 said:
Hi Guys,
I have a sheave with 7 rollers spread evenly on 180° radius. There is an equal amount of force on each end of the sheave pulling down.
My question is will the force acting on rollers be the same for all rollers or will it differ depending on the angle?
I have attached the picture for better illustration.
Thanks for your advice

Start by assuming that the individual rollers are friction-free and that the cable mass is negligible. If the cable mass is not negligible then the calculation becomes a little bit messier.

Given the above assumptions, the tension throughout the length of the cable must be equal to the amount of force on each end of the sheave. Call this F.

Consider one of the interior rollers (roller 2 through roller 6). Draw a free body diagram. There are three forces on this roller: Tension pulling rightward, tension pulling leftward and the outward support force from the sheave. Since the roller is not moving, these forces must sum to zero.

What angle do the cables make with the horizontal?
What is the vertical component of the tension on the left hand side? Can you write it as a formula involving force F and angle theta?
Repeat for the right hand side? What is the vertical component of tension?
What is the total of these two tensions in the vertical direction?
[For compleness] What is the total of the two tensions in the horizontal direction?

Now consider roller 1 or roller 7. Draw your free body diagram again. Rotate it 90 degrees so that the roller's support is vertical. What angle does the left hand cable make with the horizontal? What angle does the right hand cable make with the horizontal? What is the net vertical component of tension? What about the horizontal?
 

1. What is the importance of understanding roller pressure and its effect on sheave force distribution?

Understanding roller pressure and its effect on sheave force distribution is important because it helps in designing efficient and safe roller systems. By understanding this concept, engineers can determine the optimal angle for rollers to distribute load evenly and prevent excessive wear and tear on the system. This also ensures the safety of workers operating the equipment.

2. How does the angle of the roller affect the distribution of force on the sheave?

The angle of the roller affects the distribution of force on the sheave by changing the contact point between the roller and the sheave. As the angle increases, the contact point moves towards the outer edge of the sheave, resulting in a smaller contact area and higher force distribution. On the other hand, a smaller angle results in a larger contact area and lower force distribution.

3. What factors influence the roller pressure on a sheave?

The roller pressure on a sheave is influenced by several factors such as the material properties of the roller and sheave, the angle of the roller, the weight and velocity of the load, and the surface conditions of the roller and sheave. These factors can affect the friction between the roller and sheave, resulting in different pressure distributions.

4. How can roller pressure be calculated for a specific angle and load?

Roller pressure can be calculated using the formula P = W/tan(θ), where P is the pressure, W is the load, and θ is the angle of the roller. This formula assumes a uniform distribution of force on the sheave. However, in real-world scenarios, other factors such as surface conditions and material properties should also be taken into account.

5. What are the potential consequences of incorrect roller pressure and sheave force distribution?

If the roller pressure and sheave force distribution are incorrect, it can lead to uneven wear and tear on the system, causing premature failure of the equipment. It can also result in safety hazards for workers operating the equipment, as excessive force distribution can cause the load to shift or the roller to slip, leading to accidents. Therefore, it is important to understand and properly calculate roller pressure and sheave force distribution for optimal performance and safety.

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