Sprocket diameter, chain link pressure, transverse vibration

[r_prieto5]

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.

 

[Nidum]

Design guide[PLAIN]http://www.renoldjeffrey.com/nmsruntime/saveasdialog.asp?lID=1019&sID=2750[/PLAIN] [Broken]

Designing and Drawing a Sprocket

http://www.renoldjeffrey.com/nmsruntime/saveasdialog.asp?lID=1019&sID=2750 [Broken]

 

[Nidum]

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 .

 

[r_prieto5]

@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?

 

[Nidum]

Ref_1 p13

Ref_2

 

[Nidum]

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 .

 

[r_prieto5]

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)