Sprocket diameter, chain link pressure, transverse vibration

In summary, the student is trying to find the dimensions of a sprocket for a bike, but does not understand how to approach the third problem. The first two problems involve finding the dimensions of the sprocket and calculating the tensions in the chain. The third problem is designing and drawing the sprocket.
  • #1
r_prieto5
18
0

Homework Statement


Power=P, rotation speed n1, rotation speed n2, chain center distance c, life = Lh
All I need for this one is the formula for sprocket diameter. I have found calculators (https://www.rbracing-rsr.com/calcsprocketdiam.html) but no reference to the formula. Chain pitch and number of teeth given. Variables are say teeth=19 and pitch 15.875.

Chain link pressure, I guess calculated with simple surface pressure formulae.
Find resonance frequencies of transverse vibration.

Homework Equations


From DIN 8187 tables:
Width b2=13.28mm, pin diameter d2=5.08mm, bearing area A=2.02cm2, breaking load Fbmin=66700N, mass q=2.7kg

The Attempt at a Solution


Surface pressure p=F/A, I however, do not know the force that the sprocket will exert on it and I guess it is not the breaking load. I'm guessing there could be radial forces on it? Or is it only a tensile stress (σ=F/A) between links?
I have no clue how to approach the third one.
 
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  • #3
Each of the design guides above explains how to calculate sprocket diameters .

Calculation of tensions in the chain is based on sprocket diameter , rotational speed and power transmitted .

There is no way of calculating resonant frequencies just using the sparse information supplied with the question .

You could calculate the excitation frequencies - perhaps that is what is meant .
 
Last edited:
  • #4
@Nidum I could not find the equation in any of the three links but I managed to find them elsewhere

Pitch Diameter = P ÷ sin (180° ÷ N)

Outside Diameter = P × (0.6 + cot ( 180° ÷ N) )

Regarding the surface pressure on the chain link, would you have any diagrams or formulae I could use?
Regarding the resonant frequency, can't these kind of values be found from the properties of DIN 8187 standards?
 
  • #6
There is a lot of information on the sites I gave links to in post #2 . Perhaps you should look through them again .

I can only repeat that there is no way of calculating resonant frequencies just using the information supplied in the original question . It would be very difficult anyway even if comprehensive information was available .
 
  • #7
Nevermind, I simply could not find the necessary information from the links provided but I managed to find them from some solutions manuals. Here they are in case anybody needs them
Chain link pressure N=p⋅d2⋅b2
Resonance frequency ω=πN/cq⋅1/√(N/q+v2=2πƒ)
 

1. What is the purpose of measuring sprocket diameter?

Measuring sprocket diameter is important for determining the gear ratio of a chain-driven system. It also helps in selecting the appropriate size of sprocket for efficient power transmission.

2. How does chain link pressure affect the performance of a machine?

Chain link pressure is the force exerted by the chain on the sprocket teeth. It is important to maintain optimal chain link pressure to prevent wear and tear on the sprocket and ensure smooth operation of the machine.

3. What causes transverse vibration in chain-driven systems?

Transverse vibration in chain-driven systems can be caused by several factors such as misalignment of sprockets, improper tensioning of the chain, or worn out sprocket teeth. It is important to address these issues to prevent damage to the machine and ensure efficient power transmission.

4. How can sprocket diameter affect chain link pressure?

The larger the sprocket diameter, the lower the chain link pressure. This is because the chain has more teeth to distribute the force over, resulting in less pressure on each individual link. On the other hand, a smaller sprocket diameter will lead to higher chain link pressure.

5. What are some ways to reduce transverse vibration in a chain-driven system?

To reduce transverse vibration, it is important to properly align the sprockets, maintain the correct tension in the chain, and regularly inspect and replace worn out sprockets and chains. Using vibration-dampening materials or adding tensioners can also help reduce transverse vibration.

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