Calculating duel idler gear centres 1

[GGear]

thread406-347690
Hello everyone
I am stuck with the same problem that 61Lat (thread406-347690) had calculating the centre distance between the input and output gears in a duel idler gear train. Does anyone have the formulas to calculate them? mfgengear and gearguru said they had the answer, not sure what I’m missing but I can’t seem to find them in the thread. I understand that the belt length (red line) must be divisible by the pitch but cant see how I can use that to calculate the centres. Any help?

 

[Occupant]

The attached is an (accurate) approximation for a solution based on the fact that the length of the blue line divided by the pitch has to be an integer (or close enough to be one). I used a fudge factor for the length of line be of 3, but you can change that based on your conditions - and the solution is metric, not a big deal, I hope.

 

[Occupant]

Used the wrong PDF.

 

[tbuelna]

Based on the small numbers of teeth you show for the gears (20/19/24), it will be difficult to get them to smoothly mesh without some serious tweaking. You also need to check whether the gear combination you describe will result in satisfactory load sharing between the opposing idler gears if they have fixed pitch centers.

 

[GGear]

I’m afraid I don’t follow how you calculated that answer. I understand how you get a and c but why did you use 3 for working out b? I also don’t understand the formula for working out theta. I am familiar with asin(b/a) but not the 180/pi part. Could you show your working out on this example so I can work it back to see how you did it. Thanks.

 

[Occupant]

a.) As I said 3 before (actually 3*modul) is a fudge factor to prevent the two idlers bumping into each other - you can make it anything you want based on your design.
b.) When you do e.g. angle = asin(x/y) in Mathcad, the result is in radians. So I convert it into degrees to use in the formula below.

 

[tbuelna]

GGear-

The arrangement you describe is a "torque split" gear mesh. Here is a short tech paper that provides an analytical solution for your case in section 3.3 .

As I noted above, obtaining satisfactory load sharing between the idlers can be quite difficult, so I'd highly recommend reading section 4 of the paper.

Regards,
Terry

 

[GGear]

Thanks I’ve got the formulas worked out now and have a centre distance that works.
Thanks for the tech paper Terry I have been worried about the load sharing and this will be a great help in resolving that.

Regards
Peter

 

[tbuelna]

GGear- Out of curiosity, do you have any concept of how you will get the two idlers to load share adequately?

 

[tbuelna]

Sorry, forgot to add that your combination of gear tooth numbers (20/19/24) presents a very difficult design case. With the small numbers of teeth used for each gear/idler, it will require some serious geometry modifications to get them to mesh smoothly. And getting the idlers to load share will be even more difficult.

 

[GGear]

I’m going to make a test set of ground gears, idlers will be ground in pairs for accuracy, and then I’ll see how they run. I think it’s going to be a bit of trial and error to start with but these are the parameters I’ve been given to work with so I’m going to give it a go and see how it works out. I’m hoping that by maintaining a tight tolerance the load sharing will be sufficient.

 

[tbuelna]

Using high precision gears alone won't ensure even load sharing between your idlers. You also need to do a careful analysis to see exactly how each gear and the bearings/housing supporting it moves under load. The you need to make adjustments to your bearings, gear pitch centers, housing structure stiffness, etc. so that the torque split between the idler gears is more balanced under operating loads. One of the most effective ways to address this problem is to float the idler gears.

Out of curiosity, what approach will you use to establish the operating torque split between the two idler gears? Will you strain gauge the gears?

 

[GGear]

I did recommend floating idler gears to the customer when I started the project but he wants to try without floating idlers and I am therefor leaving the testing up to him. Not sure how he is going to do it.