Dual Idler Gears 3

[61Lat]

I'm stuck on the problem of calculating the center distance between input and output gears in a dual idler system and still having the idlers mesh properly. I happened to find this picture that actually illustrates the issue extremely well. Any ideas?

 

[mfgenggear]

61Lat

I will take a shot in the dark. does the center distance have to be fixed. or can it be adjustable.
I seen this with gear trains in hobbing machines where you have to add an Idler to change direction.
but it does not affect the gear change ratio. a different idler can be used as long as it's within the
max & min center distance. A nut with thrust washers are used to lock the shaft in place.

I guess you can construct or fab some cheap gears to actually see what fits a set center distance.
then calculate it back arrive at the required formula. buy some cheap gears at Boston Gear or some other
off the shelve gears.

HTH


Mfgenggear
if it can be built it can be calculated.
if it can be calculated it can be built.

 

[61Lat]

mfgenggear

Changing the distance is fine. I would like a center distance between T1 and T3 of somewhere around 4" but if the final distance is 3.5" or 5" it doesn't really matter. Similarly, I don't really care about the distance between T2A and T2B. The main thing is trying to calculate some distance, whatever it comes out to be, that will allow the gears to mesh properly. I'm guessing that in the picture I posted, there are probably 5 or 6 center distances that will work. These will eventually have the bearing locations machined into a gear box housing so whatever the final number is, it needs to be accurate. It's also not very adjustable once it's made. I thought about buying cheap gears and laying them out like you suggested but I don't believe I'll be able to line them up and measure everything properly. The placement needs to be pretty exact for both idler gears to carry an equal load. If there's some way to calculate the T1-T3 center distance given the number of gear teeth, that would be ideal.

 

[tbuelna]

If you use fixed pitch centers for your gears it will create load sharing problems between the two idlers. One way to resolve this issue is to float the idlers:

 

[Windward]

Exactly, tbuelna. Great picture.

When the load is split, they will not fit. Float those gears and have some beers.

NASA tried to solve this problem in general, not just for idlers, with gear timing. I have no faith in it. It does not allow for unequal wear in gears and bearings, differential expansion from temperature change or effect of changing load. Gear timing may improve the situation a little, but there are better methods.

 

[tbuelna]

When the load is split, they will not fit. Float those gears and have some beers.

Your post puts Johnnie Cochran to shame!

Here an approach used on the Napier Saber gearbox to balance loads between two compound idler gears using a balance beam:

 

[Windward]

But Johnnie Cochran gets paid for it! Here is another arrangement using a balance beam, but it equalizes the loads on two branch shafts in a parallel shaft gearbox. Click on the illustration to enlarge, balance beam is on the left:

http://www.cres.gr/megawind/Wind_Turbine_Gearbox.htm

There are two US patents showing how to do this with four branch shafts: 2,225,863 and 2,863,324.

 

[gearguru]

Good discussion.
The theoretically exact location of those two idlers can be calculated using the given numbers of teeth.
Not simple, but not a rocket science either.
As Mfgenggear put it:
if it can be built it can be calculated.
if it can be calculated it can be built.

 

[61Lat]

I definitely agree with you guys that floating the idlers is the best way to balance loads but I'm still stuck with my original question. What formula do I use to calculate the center distance between the input and output gears? In the picture I posted, the bottom gear isn't meshing properly with the two idlers. Obviously I can move the output gear closer to the input gear or further away to get everything to line up but I'm stuck on coming up with a calculation to figure that out. Even the floating idlers in the picture of the cam drive that tbuelna posted have a set center to center distance.

 

[gearguru]

61Lat, it took me too a while to find the way to derive the calculation. If you are interested I can help, but it needs longer explanation, I prepare it and then I post it here.

 

[mfgenggear]

see attached on constrained Gear System
see page 6

http://www.khkgears.co.jp/de/gear_technology/pdf/gear_guide2.pdf

Mfgenggear
if it can be built it can be calculated.
if it can be calculated it can be built.

 

[Occupant]

I found a solution. I believe, it is the only one existing for the parameters given. I don't think, scaling will make a difference, but try it out.

 

[mfgenggear]

did you guys read my post? is that not the solution?


Mfgenggear
if it can be built it can be calculated.
if it can be calculated it can be built.

 

[61Lat]

Mfgenggear,

That's exactly what I was looking for. Thanks for the help

 

[gearguru]

Well, it looks like that I did not invent the wheel again. It happened to me before. But I found out on my own HOW the formulas were derived before I saw them, and that was fun too.
Nice 4th to all fellow Americans.

 

[tbuelna]

61Lat-

....The placement needs to be pretty exact for both idler gears to carry an equal load....

The approach in the document provided by mfgenggear will indeed tell you if your gears will assemble/mesh based on PCD and tooth counts. However, being able to assemble your gears and have them mesh without interference does not guarantee equal load sharing between the idlers. To illustrate the difficulty in getting equal torque split between your two fixed axis idlers, consider that even a difference of a few ten-thousandths of an inch between the mesh contacts of the opposing idlers can greatly alter the relative tooth loads. I've attached a table that gives load reduction factor recommendations for epicyclic planet gears based on tooth accuracy and mounting stiffness. While your case is slightly different than that of a simple epicyclic, the table still gives you some idea of how much effect tooth accuracy and structural stiffness can have on load distribution.

If you are against the idea of floating the idlers, then I would recommend performing an FEA study to establish the operating displacements in your gears/shafts/bearings/housings. You can use this information to modify your components for improved load distribution under operating conditions.

Lastly, there is one other approach you might consider using with your fixed axis idlers to help with load sharing. Take a look at using flex pins. Flex pins are a recent development being used on highly loaded epicyclic planet gears.

Hope that helps.
Terry