- #1
arokisbobcat
- 10
- 1
- Homework Statement
- Loads on a shaft with V-Belts
- Relevant Equations
- V-Belt Net Force: Fnet = T / (D/2) ; V-Belt Bending Force: Fb = 1.5 * Fnet
Hi,
In refreshing up on some topics regarding Mohr's circle, I came across this problem and can't seem to understand how the forces for the sheaves were obtained. The problem contains a shaft that has two V-belt sheaves rotating in opposite directions. The shaft has a Torque of 1100 lb-in and a diameter of 1.25 inches.
The purpose of the problem is to analyze combined stresses on the specified element. I understand that part but do not understand how the Forces, Fb and Fc, are obtained in diagram B.
I've tried a couple different approaches. The first is that I assumed each sheave is taking the Torque of 1100 lb-in. Using the V-belt Force (net) equation of [ T / (D/2) ], this would give a force of 1760 lbf. Therefore using the V-belt Bending Force this would be F (bend) = 1.5 * Force (net), which would be 2640 lbf. Per my FBD, I would assume that the reactions at the shaft ends would also be opposite since the sheave forces are equal and opposite. If I consider the center of my shaft and assume the loads from each sheave, since they aren't symmetrically positioned, contribute different load values, I still don't arrive at the values in the text. This would essentially be that sheave at B since it is closer to the Center Line would contribute 3/4 of the force than that of sheave C.
The second approach that I thought might get me to the answer is to assume that the 1100 lb-in Torque is split between the two sheaves. The calculated V-belt forces when I consider the distance from the Center Line of the shaft give me closer values to the text.
I would appreciate much if this problem could be clarified for me. I've searched for the solution and similar problems but haven't been able to pin point an exact solution. Chegg does have this exact problem solved but that would be a paid subscription fee. Link - https://www.chegg.com/homework-help...ries-two-v-belt-sheaves-tensions-be-q86762199
In refreshing up on some topics regarding Mohr's circle, I came across this problem and can't seem to understand how the forces for the sheaves were obtained. The problem contains a shaft that has two V-belt sheaves rotating in opposite directions. The shaft has a Torque of 1100 lb-in and a diameter of 1.25 inches.
The purpose of the problem is to analyze combined stresses on the specified element. I understand that part but do not understand how the Forces, Fb and Fc, are obtained in diagram B.
I've tried a couple different approaches. The first is that I assumed each sheave is taking the Torque of 1100 lb-in. Using the V-belt Force (net) equation of [ T / (D/2) ], this would give a force of 1760 lbf. Therefore using the V-belt Bending Force this would be F (bend) = 1.5 * Force (net), which would be 2640 lbf. Per my FBD, I would assume that the reactions at the shaft ends would also be opposite since the sheave forces are equal and opposite. If I consider the center of my shaft and assume the loads from each sheave, since they aren't symmetrically positioned, contribute different load values, I still don't arrive at the values in the text. This would essentially be that sheave at B since it is closer to the Center Line would contribute 3/4 of the force than that of sheave C.
The second approach that I thought might get me to the answer is to assume that the 1100 lb-in Torque is split between the two sheaves. The calculated V-belt forces when I consider the distance from the Center Line of the shaft give me closer values to the text.
I would appreciate much if this problem could be clarified for me. I've searched for the solution and similar problems but haven't been able to pin point an exact solution. Chegg does have this exact problem solved but that would be a paid subscription fee. Link - https://www.chegg.com/homework-help...ries-two-v-belt-sheaves-tensions-be-q86762199
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