Center to Center Distance in Power Transmission

[Aren Siekmeier]

I didn't see any search results addressing this specifically so I figured I'd create a thread as a reference for others among us with these questions:

In designing power transmission systems using gears, chains and sprockets, belts and pulleys, and numerous other types of mechanisms, a very important consideration is the center to center distance (here on out referred to as CD) between gears, sprockets, or pulleys to maintain chain/belt tension or a good mesh and therefore maximize efficiency and product life, particularly if looking to eliminate tensioning mechanisms to reduce complexity. I was hoping to get some input from those with lots of experience doing exactly this.

Gears are probably the easiest the deal with. You are given the pitch diameter of the gears you are working and you simply need to make them mesh at that distance. But it's not quite that simple. In FRC experiment, people have found it useful to add a few thousandths to the CD because we don't have a chance to wear our transmissions into a good mesh with the short period of use. Also, what kind of tolerance typically needs to be maintained on this distance?

The next simplest is chain and (timing) belt stages with two pulleys or sprockets of equal size. If the number of teeth is even, it's apparent that each sprocket uses half of its teeth in belt at any given time, and its pretty simple how that can be extended to sprockets with odd numbers of teeth (for large enough sprockets). This basic approach leads to a CD of the belt or chain length minus teeth on one of the sprockets, all divided by two (CD = (length - pulley size)/2 (in teeth) ) appropriately converted via the pitch. This means that the CD should be an even multiple of the pitch. But what tolerance matters in this case? Would experts typically undershoot by that tolerance or some percentage to ensure it is not over tight? Are there other considerations that should be taken into account?

It gets more complicated when the sprockets are no longer the same size. It is no longer trivial to assume how many teeth may be on each sprocket at any time, and also to determine the distances between the points of tangency with the sprockets. Basic trig would make this reducible if the sprockets have enough teeth that the behavior is not much different from two perfectly round sprockets. But with sprockets with very few teeth, the deviation seems quite significant to me, and the problem is much less tractable. What methods have teams found useful in determining an effective CD to maintain tension in such a situation? Is the variation due to acircular sprockets a big deal?

And then of course there is the situation of a non synchronous belt on perfectly round sprockets, in which case the trig above can be employed, but there remains the question of relevant tolerances. I don't think this type of transmission is used nearly as much in FRC, but is still of some interest.

So I'm just wondering if there is some general wisdom from experience or insight as to how to handle these different situations. What works? What doesn't? What are some common practices? What are some of the known tolerances on tension and the center to center distance?

EDIT: This thread will probably end up being relevant to the timing belt part of this discussion.

Also, I remembered after posting this that Dr. Joe posted this once upon a time, which looks like it does take into account the non circular nature of sprockets, though I haven't yet bothered to figure how. Have others found this tool accurate for these smaller sprockets?

[Adam.garcia]

Originally Posted by compwiztobe

What are some of the known tolerances on tension and the center to center distance?

I can only speak for the area where I have experience. I've spoken to many people around the FIRST and CD community, and they have said that it is a general rule of thumb to follow these tolerances:
Single-Speed Gearbox: +.000 - +.001 in.
Multi - Stage Gearbox: +.002 - +.003 in.

You can find more information about tolerances (and even a Center to Center Distance Calculator) here:
http://wcproducts.net/how-to-gears/

Hope this Helps!

[Aren Siekmeier]

I'll speak to some our own team's specific experiences:

Our 2012 intake was driven by a 1:1 timing belt (16t XL sprockets) from a P60, and the center to center distance was calculated assuming circular sprockets and their published pitch diameter, as well the outer loop distance of the belt (not sure why). We ended up with a belt that could have been any tighter, which was probably not efficient or very healthy for the mechanism (though I have a relative lack of experience with belts). I don't think the tolerance was particular good in this case, however... And sorry I don't have more numbers, I have none of the CAD in front of me at the moment.

On an off season project last summer we had a chain reduction between 10t and 42t sprockets (#25 chain). We used the center to center distance given by a chain path in Solidworks (using the pitch diameters supplied by Andymark) that was a multiple of the pitch (.250). This was of course also assuming circular sprockets. We wound up with very loose chains that would not have functioned properly without tensioners (perhaps as expected because of the irregular 10t sprocket). The tolerance on this should have been excellent as we had the plates done by CNC (probably .001 or 2, but I wasn't directly involved in that spec).

[artdutra04]

For timing belt center to center distances, I've always used the SDP-SI Belt Calculator to easily run through various options of available belts and sprocket sizes. The timing belts used in FRC don't stretch any appreciable distance, so I always use the exact CTC distance and have never had to use a tensioner.

[chadr03]

I have measured a few AndyMark gears for tooth thickness and they have all allowed for .005 to .010 of backlash at standard centers which is about where you want to be these types of transmissions. I would recommend a -.000 to +.003” CD tolerance on gearing.

Just remember a little bit of backlash is a good thing. You will destroy a gearset quickly if they are in a tight mesh.

[Andrew Zeller]

Originally Posted by compwiztobe

The next simplest is chain and (timing) belt stages with two pulleys or sprockets of equal size. If the number of teeth is even, it's apparent that each sprocket uses half of its teeth in belt at any given time, and its pretty simple how that can be extended to sprockets with odd numbers of teeth (for large enough sprockets). This basic approach leads to a CD of the belt or chain length minus teeth on one of the sprockets, all divided by two (CD = (length - pulley size)/2 (in teeth) ) appropriately converted via the pitch. This means that the CD should be an even multiple of the pitch. But what tolerance matters in this case? Would experts typically undershoot by that tolerance or some percentage to ensure it is not over tight? Are there other considerations that should be taken into account?

I am designing a drivetrain and I am trying to design the center distances from the center wheel to each outside wheel so that no chain tensioners will need to be used. I think I am doing this right but can you check it?

Both wheels will have 22 tooth AM sprockets with #35 chain. The pitch diameter of the sprockets is 2.638" and the pitch of the chain is 3/8"

Now distance= ((#chainlinks*chainpitch)-sprocketdiametral pitch)/2

Since I want my distance to be approximately 16", I solve for # of chain links and get 92. Then I put 92 in for #chainlinks and find my center distance to be 15.931"

Is this the right way to do it? Will this make the chain at a perfect tension when it is put on?

[Phalanx]

You can look at this thread here for more options in calculating.
http://www.chiefdelphi.com/forums/sh...ad.php?t=98758

The formulas can be found here with an excel spreadsheet calculator:
http://www.chiefdelphi.com/forums/sh...03&postcount=3

[Brian Selle]

For belt C-C, I've been using a free program from Gates called Design IQ 3. It's a little quirky at first but once you figure it out it works well. It can handle different size pulleys and multiple tensioners and has a list of standard size belts. I've also used the SolidWorks belt/chain feature and the results match the Gates program.

[Aren Siekmeier]

Originally Posted by boarder3512

I am designing a drivetrain and I am trying to design the center distances from the center wheel to each outside wheel so that no chain tensioners will need to be used. I think I am doing this right but can you check it?

Both wheels will have 22 tooth AM sprockets with #35 chain. The pitch diameter of the sprockets is 2.638" and the pitch of the chain is 3/8"

Now distance= ((#chainlinks*chainpitch)-sprocketdiametral pitch)/2

Since I want my distance to be approximately 16", I solve for # of chain links and get 92. Then I put 92 in for #chainlinks and find my center distance to be 15.931"

Is this the right way to do it? Will this make the chain at a perfect tension when it is put on?

Using my approach that you quoted:

You are taking the sprocket's [b]circumference[\b] (an integer number of teeth) into account when calculating center to center distance. If you have two equally sized sprockets with N teeth each, each will take up N/2 links of chain. Then the length in the middle has to total an even number of links, unless you're fine with using a half link, so the separation between the sprockets should be an integer multiple of the pitch.

So in your case, 16" is not a multiple of 0.375" (#35 pitch), so the chain will not be tight. You would want to go with 15.75" or 16.125". If you want exactly 92 links in your chain for whatever reason, it would be (92-22)/2 times the pitch for the c-c, which is only 13.125".