Sprocket diameter, chain link pressure, transverse vibration

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SUMMARY

The discussion focuses on calculating sprocket diameter, chain link pressure, and resonance frequencies of transverse vibration in mechanical systems. Key formulas identified include the Pitch Diameter as P ÷ sin (180° ÷ N) and the Outside Diameter as P × (0.6 + cot (180° ÷ N)). Chain link pressure is calculated using the formula N=p⋅d2⋅b2, while resonance frequency is determined using ω=πN/cq⋅1/√(N/q+v2=2πƒ). The conversation emphasizes the need for comprehensive data to accurately compute resonance frequencies.

PREREQUISITES
  • Understanding of mechanical engineering principles
  • Familiarity with DIN 8187 standards
  • Knowledge of chain drive systems and their components
  • Proficiency in using formulas for tension and pressure calculations
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  • Research the application of DIN 8187 standards in sprocket design
  • Learn about the calculation of excitation frequencies in mechanical systems
  • Explore advanced topics in vibration analysis for mechanical components
  • Investigate software tools for simulating chain drive dynamics
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Mechanical engineers, students in mechanical design courses, and professionals involved in the design and analysis of chain drive systems will benefit from this discussion.

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)