Sprocket diameter, chain link pressure, transverse vibration

AI Thread Summary
The discussion focuses on calculating sprocket diameter, chain link pressure, and resonance frequencies related to sprockets and chains. The formulas for pitch diameter and outside diameter are provided, emphasizing the relationship between these dimensions and the number of teeth and pitch. Surface pressure on chain links is calculated using the formula N=p⋅d2⋅b2, but there is uncertainty about the forces involved. Resonant frequencies cannot be determined with the limited information given, highlighting the complexity of the calculations. Overall, the conversation underscores the need for comprehensive data to accurately perform these engineering calculations.
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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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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 .
 
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@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?
 
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 .
 
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)
 

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