Sprocket and Spur Gear Chain Drive Question

[bmwbykrydr]

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/

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

 

[shiftersteve]

Don,
You obviously put ALOT of effort into your post. Thats good. Remember that a gear ratio is a gear ratio- I might try this method instead of taking the complicated approach. Calculate or test the current belt speed in inches per minute. Once you have that, calculate the % difference between the current belt speed and the new desired belt speed. Use that % to reduce anyone of the gear ratios in system by the same percent difference.

Depending on the how the gear ratios are tied- (gear to gear, by chain or timing belt etc) the harder part of the job is to find out what combination of gearsets you can change to that will give you BOTH the desired belt speed AND physical ability to do so with available center distances between the drive sprockets - ie do you have enough room for the new size sprockets, can the chain lengths be altereed, is there enough adjustability in the tensioners to tension the chain properly etc etc. Chain and drive belt center distances are listed in catalogs from the likes of Martin or TB Woods.

If you cannot come up with the proper solution mechanically, you can always change out the motor and driver to a variable speed drive setup. - which can get expensive- but is often the best solution. That way you have a very fine tunable range to work with to give you the exact speed your looking for. This being a lable machine, I'm curious if the motors utilized are not speed adjustable by programming- stepper, or servo motors? If so, your solution might be as easy as a phone call to the machine's programmer.

Steve Frank
Apex Designs
Suwanee GA

 

[bmwbykrydr]

Thank you Steve. The engineer at this OEM and I have determined that changing the 24T sprocket to a 17T and the 23 T to a 32T will give us the correct ratio, or at least a usable ratio, at the feed roller, 1.129:1. We want the labeler to be slightly faster than the belt so there is no force applied to the label web as the produce goes by. Until the parts arrive I won't know FOR SURE, but I will post the results either way.

Don

Just to pat my own back, my math on calculating the original ratio was correct, .575:1, something the OEM engineer miscalculated at first. :-) Class of '96 rules!