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Peter_Hudlicky
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Join Date: Feb 2018
Posts: 6

Rear Sprocket Design

02/05/2018 2:25 PM

Hi,

I am a mechanical engineering student at the University of Waterloo on the student design team Waterloo Formula Electric SAE.

I'm designing a sprocket for a rear half shaft on our vehicle and was wondering if anyone has experience designing sprockets.

Trying to find the back tension on each tooth of the sprocket, I found the following equation cited in multiple online sources:

Tk=T0*(sinⱷ/sin(ⱷ+2B)^k-1

Tk is the tension on a given engaged tooth

T0 is the maximum tension experienced by the chain

ⱷ is the minimum pitch angle (17-64/N, N being the number of teeth of the sprocket)

2B is a little misleading, thought there is a variable B, the entire expression 2B seems to have a constant value of 360/N

k is the number tooth of the sprocket that is engaged

I have a couple of issues with the equation, aside from the ones mentioned above, I do not understand how it can be applied as it seems that using this equation, the first tooth engaged would take all of the tension of the chain as k-1 --> 1-1 = 0 --> Tk= T0*(sinⱷ/sin(ⱷ+2B)^0 = 1--> Tk = T0

Does anyone know this equation/can you corroborate its accuracy, and or clarify some of my questions about its application?

Thank you!

Peter
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SolarEagle
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#1

Re: Rear Sprocket Design

02/05/2018 2:45 PM

Well just shooting from the hip, I would want each tooth to be capable of carrying the entire torque load as a robust design detail...and probably 3 times that in the final spec...What would you do different?

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lyn
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#2
In reply to #1

Re: Rear Sprocket Design

02/05/2018 4:17 PM

Sometimes you can lose a toe by shooting from the hip.

I think the lad is looking for a mathematical/engineering solution.
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SolarEagle
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#7
In reply to #2

Re: Rear Sprocket Design

02/05/2018 5:26 PM

That may be so, but I seem to do okay....

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Jpfalt
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#13
In reply to #2

Re: Rear Sprocket Design

02/06/2018 1:58 PM

Interesting statistic: More officers were shot pulling their Colt 1911A1 pistol from the holster when it was "locked and loaded" than by enemy action during the Korean conflict.
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Peter_Hudlicky
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Join Date: Feb 2018
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#4
In reply to #1

Re: Rear Sprocket Design

02/05/2018 4:38 PM

That makes complete sense, and I agree with you. But I'm looking for an equation that could help me with applying loads in FEA.
Thanks!
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Doorman
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#3

Re: Rear Sprocket Design

02/05/2018 4:29 PM

This paper describes the application of FEA for chain and sprocket.

You're on the right track, just keep going.

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Peter_Hudlicky
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#5
In reply to #3

Re: Rear Sprocket Design

02/05/2018 4:40 PM

That is actually one of the papers that I have looked at, however, it seems to be incomplete (or perhaps I am just not understanding it properly), as the questions I have regarding the interpretation of the equation are still not answered by it.

Do you have any ideas as to how the equation they talk about in their paper can be applied?

Thanks!
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Doorman
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#6
In reply to #5

Re: Rear Sprocket Design

02/05/2018 5:02 PM

So, for tooth #4:

Tk=T0*(sinⱷ/sin(ⱷ+2B)^k-1, or with #4 substituted

T4=T0*(sinⱷ/sin(ⱷ+2B)4-1

Is this how you are applying? Ten times, once for each of the first ten?

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Peter_Hudlicky
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#8
In reply to #6

Re: Rear Sprocket Design

02/05/2018 6:01 PM

Thanks that makes sense, but do you see how if you were to use the first tooth engaged, you would get a value of 0 for the exponent, thus making Tk=T0, meaning the entire tension of the chain is being held by the first tooth, which can't be possible...unless I'm mistaken.
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Tornado
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#9

Re: Rear Sprocket Design

02/05/2018 9:15 PM

I think you need to assume that only the first pin/bushing of the chain is in full engagement with just one tooth of the sprocket.

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Peter_Hudlicky
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#10
In reply to #9

Re: Rear Sprocket Design

02/05/2018 11:11 PM

Thanks I'll Try that
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Jpfalt
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#11

Re: Rear Sprocket Design

02/06/2018 10:48 AM

Roller chain is always run with a very slight amount of slack in a rigid setup or with a spring loaded idler against the slack side of the chain. The chain also wears and stretches, increasing the pitch length of the chain over time (the first few seconds of operation and then for the rest of the life of the chain). As a result, the first roller carries the entire load, unless you do something very special like resiliently mounting the rollers on the roller axle pin. That's life with roller chain.
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Peter_Hudlicky
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#12
In reply to #11

Re: Rear Sprocket Design

02/06/2018 1:17 PM

Thank you! That actually explains the equation.
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RAMConsult
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#14
In reply to #12

Re: Rear Sprocket Design

02/10/2018 11:01 AM

And thank you for providing an excellent example of how a (student) thread should be handled. You stated the problem, showed your work, then clarified where you were stuck; and like magic, someone who had worked through that exact problem came to your assistance!

Welcome to CR4, and good luck with your studies.

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Doorman (2); Jpfalt (2); lyn (1); Peter_Hudlicky (5); RAMConsult (1); SolarEagle (2); Tornado (1)

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