# Sprocket diameter, chain link pressure, transverse vibration

## 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
Gold Member
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:
@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
Gold Member
Nidum