# Speed Transmitting Between Motor Gearbox and Sprocket Chain length: 1400mm.

Pitch of the chain:12,7 mm
Diameter: Ø55 For z=12
Diameter: Ø71 For z=16
Diameter: Ø87 For z=20

Hello friends,
Can someone who has knowledge of how to calculate the speed transferred to the sprocket wheel can help in such systems with various gear numbers (z = 20, 16)? Even if you do not know this system, can you at least give some information on how to proceed.

Here, a speed of about 1400/15 to 93.33rpm is transferred from the reducer to the gear wheel with 20 teeth. How can I do the calculations after this stage? My goal is, for example, how many times the chain comes to the starting point in 1 minute.

I would be very happy if you could give an idea.

Thanks.

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## Answers and Replies

Lnewqban
Gold Member
We need the diameter of the sprokets, which can be calculated if you provide the pitch of the chain.

• hutchphd
We need the diameter of the sprokets, which can be calculated if you provide the pitch of the chain.

Pitch of the chain:12,7 mm
Diameter: Ø55mm For z=12
Diameter: Ø71mm For z=16
Diameter: Ø87mm For z=20

hutchphd
Science Advisor
Homework Helper
We need the diameter of the sprokets, which can be calculated if you provide the pitch of the chain.

The diameter of the sprockets makes no difference whatsoever. All that matters is the number of teeth.

Lnewqban
Gold Member
Pitch of the chain:12,7 mm
Diameter: Ø55mm For z=12
Diameter: Ø71mm For z=16
Diameter: Ø87mm For z=20
Thank you.
Sorry, I missed the information shown in the posted picture about gear size.
The shaft of the driving sprocket should turn at 1400/15 = 93.33 rpm, which we can call rotational speed.

According to this on-line calculator:
https://rbracing-rsr.com/calcsprocketdiam.html

...the radius or distance from the center of the shaft to the center-line of the rollers is 3.196/2 = 1.59 inches = 40.59 mm.

The tangential velocity of your chain around the sprocket is also its linear speed, which can be calculated as V=ωr.

##V=(93.33~rpm / 60~seconds)(2π)(40.59~mm)## (result would be in mm/s)

Once you have the value of the linear speed of the chain, you can calculate how many times 1400 mm of chain go by any fixed point of the system in one minute.

Thank you.
Sorry, I missed the information shown in the posted picture about gear size.
The shaft of the driving sprocket should turn at 1400/15 = 93.33 rpm, which we can call rotational speed.

According to this on-line calculator:
https://rbracing-rsr.com/calcsprocketdiam.html

...the radius or distance from the center of the shaft to the center-line of the rollers is 3.196/2 = 1.59 inches = 40.59 mm.

The tangential velocity of your chain around the sprocket is also its linear speed, which can be calculated as V=ωr.

##V=(93.33~rpm / 60~seconds)(2π)(40.59~mm)## (result would be in mm/s)

Once you have the value of the linear speed of the chain, you can calculate how many times 1400 mm of chain go by any fixed point of the system in one minute.

Thank you a lot. It is really clear reply for me. I just want to ask you one thing. While calculating the how many times it will come to starting point in one minute, Should i use the chain length or number of chain roller?

Lnewqban
Gold Member
Thank you a lot. It is really clear reply for me. I just want to ask you one thing. While calculating the how many times it will come to starting point in one minute, Should i use the chain length or number of chain roller?
You are welcome. You can try your 110-link roller chain as a rope of lenght=1400 mm.

##Time=Distance/Velocity=Lenght~of~chain/Linear~speed##

##Number of cycles per minute=Calculated time/60~seconds##

Please, let us know your result.

Lnewqban
Gold Member
The diameter of the sprockets makes no difference whatsoever. All that matters is the number of teeth.
In the case of sprockets for roller chains, there is a geometrical dependence among the pitch (or distance between rollers), number of teeth of the sprocket and the radius of the centerline of the chain rollers on the sprocket.

All Z=20 sprockets have an angle of 18° between two consecutive roller's seats.
Therefore,
##r=Pitch/2sin(18°/2)##

Rotating at same rpm, a Z=20 driving sprocket for 1.0-inch roller chain will induce higher tangential velocity than a Z=20 driving sprocket for 0.5-inch chain.

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You are welcome. You can try your 110-link roller chain as a rope of lenght=1400 mm.

##Time=Distance/Velocity=Lenght~of~chain/Linear~speed##

##Number of cycles per minute=Calculated time/60~seconds##

Please, let us know your result.

Dear my friend , firstly thank you so much for your attention, and I tried two ways to solve, which one is correct for you. Your way result became so low values.

I tried the way that you explained to me:
Time= 1400 mm(Length of chain) / 396,5 mm/s (linear speed) = 3,53seconds
Number of cycles per mins= 3,53(calculated time) / 60 seconds =0,058 (in this case, result is so low value.)

and then In my opinion I tried different way:
Total way per one minute = Linear speed(mm/s) * 60seconds = 396,5mm/s * 60 seconds = 23790 mm
Number of cycles= Total way per one minute / Length of chain = 23790mm / 1400 mm = 16,99
I'm gonna be waiting your feedback and thoughts, thank you Lnewqban
Gold Member
I tried the way that you explained to me:
Time= 1400 mm(Length of chain) / 396,5 mm/s (linear speed) = 3,53seconds
Number of cycles per mins= 3,53(calculated time) / 60 seconds =0,058 (in this case, result is so low value.)
From the perspective of any fixed point, it takes 3.53 seconds from the first to the last link to go by.
That period of time fits 16.99 times within one minute.
Therefore, the calculation of the number of cycles per minute should be 60 / 3.53.

• baris45
From the perspective of any fixed point, it takes 3.53 seconds from the first to the last link to go by.
That period of time fits 16.99 times within one minute.
Therefore, the calculation of the number of cycles per minute should be 60 / 3.53.

I got exactly now. Thank you a lot for your helping and your time.

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• Lnewqban
hutchphd
Science Advisor
Homework Helper
Rotating at same rpm, a Z=20 driving sprocket for 1.0-inch roller chain will induce higher tangential velocity than a Z=20 driving sprocket for 0.5-inch chain.
But the relationship for the driven and driving chain is equivalent. And one revolution is Z teeth regardless. So this makes no difference. Any bicyclist knows this.