Sprocket diameter, chain link pressure, transverse vibration

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Discussion Overview

The discussion revolves around the calculations related to sprocket diameter, chain link pressure, and resonance frequencies of transverse vibration in mechanical systems. Participants explore formulas, design guides, and the underlying principles necessary for these calculations, with a focus on theoretical and practical applications in engineering design.

Discussion Character

  • Homework-related
  • Technical explanation
  • Exploratory
  • Debate/contested

Main Points Raised

  • Post 1 raises the need for a formula for sprocket diameter and expresses uncertainty about calculating chain link pressure and resonance frequencies.
  • Post 3 suggests that calculating tensions in the chain depends on sprocket diameter, rotational speed, and power transmitted, but questions the ability to calculate resonant frequencies with the provided information.
  • Post 4 provides specific formulas for pitch diameter and outside diameter of the sprocket, while also asking for diagrams or formulae related to surface pressure on chain links.
  • Post 6 reiterates that calculating resonant frequencies is not feasible with the information given and emphasizes the difficulty even with more comprehensive data.
  • Post 7 shares formulas for chain link pressure and resonance frequency derived from solutions manuals, indicating a potential resolution for some aspects of the discussion.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the ability to calculate resonant frequencies based on the initial information provided. There are competing views on the availability and applicability of design guides and formulas for sprocket diameter and chain link pressure.

Contextual Notes

Participants express uncertainty about the force exerted by the sprocket and the nature of stresses involved. There are limitations in the information provided, particularly regarding the calculation of resonant frequencies and the specifics of surface pressure on chain links.

r_prieto5
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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)