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I looking for help on a problem I am trying to solve here at work. I am not an ME, so my mechanics knowledge is low. This isn't helped by the fact that my mechanics class was 13 years ago. I have a label applicator that is not geared correctly, so it runs slower than the wrapper that it is supposed to be matched to. When it works, the labeler feeds a label on to a passing book, but with the labeler running slower than the wrapper the label sort of gets applied across two different books. Not good.

This wrapper uses a simple flat conveyor belt to move our products through it. The rubber roller that drives this belt is about 3.25" in diameter. On the same shaft as this roller is an 18 tooth 06B sprocket, pitch diameter = 2.15". This sprocket has a chain that goes to a 24 tooth sprocket, pitch diameter = 2.87", on a straight shaft. On the other end of this shaft is a 23 tooth sprocket, pitch diameter = 2.75". This sprocket then drives a 30 tooth sprocket, pitch diameter = 3.58". Bolted to this sprocket side to side is a 50 tooth spur gear, pitch diameter = 2.96". This spur gear turns a 40 tooth spur gear, pitch diameter = 2.37", via a shaft. This spur gear is on the same shaft as the feed roller on the labeler which is 2.365" in diameter.

I probably have my terminology wrong, but the linear surface speed of the label feed roller is supposed to be the same as the conveyor belt. That way the labels come of the backing the same speed as the book that they are being applied to. Unfortunately, this isn't the case. The best I can figure out, the labeler is about 1/2 the speed of the wrapper. That's just from watching it and visually seeing what the labeler is doing. I've uploaded a video of the labeler in action: http://www.flickr.com/photos/bluebeemerboy/sets/72157623177463001/ [Broken]

I'm having trouble figuring out the pitch diameter of the spur gears because I don't know if they are standard or metric. The machine is metric but all of the sprockets are standard. The best I can measure, the outer diameter of the 50 tooth spur gear is 3.082" (78.28mm).

Here's my math:

50 tooth spur gear:

Metric Module (M) = OD/(N+2) = 78.28mm/52 = 1.505

Pitch Diameter (PD) = M * N = 1.505 * 50 = 75.27mm=2.96in

40 tooth spur gear:

OD = M (N+2) = 1.505 * 42 = 63.21mm=2.49in

Pitch Diameter (PD) = M * N = 1.505 * 40 = 60.2mm=2.37in

06B sprockets: D = P / sin (π / N)

P N D(mm) D(in.)

9.525 18 54.85 2.16

9.525 23 69.95 2.75

9.525 24 72.97 2.87

9.525 30 91.12 3.59

So, the 3.25" OD roller turns a 2.15" PD sprocket that drives via chain a 2.87" PD sprocket on one end of a shaft and a 2.75" PD sprocket on the other. That drives via chain a 3.58" PD sprocket that turns a 2.96" PD gear that turns a 2.37" PD gear that turns a 2.365" OD roller. The surface of the 3.25" roller is supposed to be the same as the 2.365" roller.

I need to figure out which sprockets to change and what to change them to. Changing the 18 tooth is undesirable but possible and changing the 30 tooth sprocket is not possible. If the change can be made to either the 24 or 23 tooth sprockets, that would be ideal. The labeler can run slightly faster than the wrapper, maybe 5% or so, but not much. We DO NOT want it to run slower than the wrapper.

Thanks in advance!

Don

This wrapper uses a simple flat conveyor belt to move our products through it. The rubber roller that drives this belt is about 3.25" in diameter. On the same shaft as this roller is an 18 tooth 06B sprocket, pitch diameter = 2.15". This sprocket has a chain that goes to a 24 tooth sprocket, pitch diameter = 2.87", on a straight shaft. On the other end of this shaft is a 23 tooth sprocket, pitch diameter = 2.75". This sprocket then drives a 30 tooth sprocket, pitch diameter = 3.58". Bolted to this sprocket side to side is a 50 tooth spur gear, pitch diameter = 2.96". This spur gear turns a 40 tooth spur gear, pitch diameter = 2.37", via a shaft. This spur gear is on the same shaft as the feed roller on the labeler which is 2.365" in diameter.

I probably have my terminology wrong, but the linear surface speed of the label feed roller is supposed to be the same as the conveyor belt. That way the labels come of the backing the same speed as the book that they are being applied to. Unfortunately, this isn't the case. The best I can figure out, the labeler is about 1/2 the speed of the wrapper. That's just from watching it and visually seeing what the labeler is doing. I've uploaded a video of the labeler in action: http://www.flickr.com/photos/bluebeemerboy/sets/72157623177463001/ [Broken]

I'm having trouble figuring out the pitch diameter of the spur gears because I don't know if they are standard or metric. The machine is metric but all of the sprockets are standard. The best I can measure, the outer diameter of the 50 tooth spur gear is 3.082" (78.28mm).

Here's my math:

50 tooth spur gear:

Metric Module (M) = OD/(N+2) = 78.28mm/52 = 1.505

Pitch Diameter (PD) = M * N = 1.505 * 50 = 75.27mm=2.96in

40 tooth spur gear:

OD = M (N+2) = 1.505 * 42 = 63.21mm=2.49in

Pitch Diameter (PD) = M * N = 1.505 * 40 = 60.2mm=2.37in

06B sprockets: D = P / sin (π / N)

P N D(mm) D(in.)

9.525 18 54.85 2.16

9.525 23 69.95 2.75

9.525 24 72.97 2.87

9.525 30 91.12 3.59

So, the 3.25" OD roller turns a 2.15" PD sprocket that drives via chain a 2.87" PD sprocket on one end of a shaft and a 2.75" PD sprocket on the other. That drives via chain a 3.58" PD sprocket that turns a 2.96" PD gear that turns a 2.37" PD gear that turns a 2.365" OD roller. The surface of the 3.25" roller is supposed to be the same as the 2.365" roller.

I need to figure out which sprockets to change and what to change them to. Changing the 18 tooth is undesirable but possible and changing the 30 tooth sprocket is not possible. If the change can be made to either the 24 or 23 tooth sprockets, that would be ideal. The labeler can run slightly faster than the wrapper, maybe 5% or so, but not much. We DO NOT want it to run slower than the wrapper.

Thanks in advance!

Don

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