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Sprocket diameter, chain link pressure, transverse vibration

  1. May 4, 2016 #1
    1. The problem statement, all variables and given/known data
    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.

    2. Relevant 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

    3. 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.
     
  2. jcsd
  3. May 5, 2016 #2

    Nidum

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    Last edited by a moderator: May 7, 2017
  4. May 5, 2016 #3

    Nidum

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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 .
     
    Last edited: May 5, 2016
  5. May 5, 2016 #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. May 6, 2016 #5

    Nidum

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  7. May 6, 2016 #6

    Nidum

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    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 .
     
  8. May 10, 2016 #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)
     
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