Worm & worm gear questions.

Hi guys.
I'm missing all the worms & worm gears for my K&T 2CHL.
The ratios are. 1:96, 1:24 & 1:3.
Ramsay1 measured one gear for me and now I'm trying to figure out everything else.

I measured the center distance between the worm gears the best I could. I used gauge blocks between the 2 shafts and got 1.496 (each shaft is 1.312). Center is 2.808". I must be doing something wrong because using his measurements, I'm coming up with a different center dimension .
Center = 0.5(d+D)
[2.6860"]

OD of worm gear is 3.9" with 24 Teeth
DP---- 26/3.9 = 6.66666
CP---- 3.1415/6.6666 = .4712
PD----24/6.66666=3.6

I'm also trying to find the lead of the gear but every formula I'm looking at in the machinery's handbook has the helix in it....Is there a way to solve for the helix angle with the info I have?

Worm, OD is 2.215"
8 teeth

Dp = 4.5146
CP = .6958
PD = 1.7720

I've got lots of books and I'm trying to learn as much as I can but gears are new to me.
Any and all help is always appreciated.
Andy

Forget the second set of calcs as on the worm - you are using spur gear procedure for finding DP of worm - never happened

What you are interested in is its pitch dia and lead - which has to match the CP of the mating worm wheel

I'll look in Buckingham and see what I can come up with - if anything (nothing, just looked)

This is a usually CLEAR book - the worm gear section starts on page 310

Internet Archive: Error

Hobby Shop said:

Hi guys.
I'm missing all the worms & worm gears for my K&T 2CHL.
The ratios are. 1:96, 1:24 & 1:3.
Ramsay1 measured one gear for me and now I'm trying to figure out everything else.

I measured the center distance between the worm gears the best I could. I used gauge blocks between the 2 shafts and got 1.496 (each shaft is 1.312). Center is 2.808". I must be doing something wrong because using his measurements, I'm coming up with a different center dimension .
Center = 0.5(d+D)
[2.6860"]

OD of worm gear is 3.9" with 24 Teeth
DP---- 26/3.9 = 6.66666
CP---- 3.1415/6.6666 = .4712
PD----24/6.66666=3.6

I'm also trying to find the lead of the gear but every formula I'm looking at in the machinery's handbook has the helix in it....Is there a way to solve for the helix angle with the info I have?

Worm, OD is 2.215"
8 teeth

Dp = 4.5146
CP = .6958
PD = 1.7720

I've got lots of books and I'm trying to learn as much as I can but gears are new to me.
Any and all help is always appreciated.
Andy

Click to expand...

Start with the worm itself and measure the axial pitch- you can get close with calipers, but more accurately, use a comparator or mount the worm in a lathe, zero a test indicator on the worm flank at any depth you choose, move the cross slide out and move 4-5 leads and bring the indicator back in to the same depth as before while measuring the carriage travel- move the carriage to bring the indicator back to zero. your carriage travel divided by the number of leads you skipped is your axial circular pitch. (im assuming here you don;t have access to a lead checker.) Calculate the addendum for that circular pitch and use the worm od to calculate the worm pitch diameter. Now take that circular pitch and multiply it by the # of teeth in the worm wheel.
The result is the circumference of the worm wheel pitch diameter. Calculate the pitch diameter of the worm wheel (pi*pd= circumference).
Now you can calculate your center distance 1/2 worm pd + 1/2 worm wheel pd. This should be close to your measured centerdistance unless there is a profile shift in the worm wheel, which is entirely possible with several ratios fitting on the same centerdistance. Remember that the WORM PD and axial pitch dictates the lead of the gear set and the dimensions of the worm wheel. Hope that gets you started. Dan

Andy,
Unless you enjoy the project of calculating and building from scratch the worms and worm gears, I'd suggest to shop for a donor/acceptor machine or parts salvaged from one.
If, instead, you enjoy the challenge, I'd suggest you start from a scenario where you have the mating pair to measure: measure the distance between the shafts, make your calculations, and verify your results by checking the dimensions and angles on the existing worm and worm gear.

Paolo

Thanks John.
I'll do more reading. I have a copy of the 3rd edition and I didn't even think of referencing it. This might take me a while but I'll eventually get it.

Thanks Dan, lots of to digest there.
I don't have access to the original gear(s) so I'm winging it.
What I do have.... is a set of gears for a different LL box gears (5814). I'm hoping we hit a home run because all the worms are within 1/8" of being the same length but different OD's.

You gave me an idea. I have a Weldon air bar, what about mounting the worm like an end mill? Measure the start on the BP, rotate 360* & measure again with the readout. That would give me the lead. Work everything backwards from there for the helix angle. Does that sound reasonable? If not, I'll try the lathe.

Here are a few pictures of the gears I'm after. Once I get all the #'s to make them, I might send them to you or someone else to cut them. I know it won't be cheap but I want it be 100% correct.

Andy

As can be seen, the 3 to 1 has MULTIPLE starts, which means the LEAD will be much longer than the apparent "pitch"

24 and 96 are both single start

Paolo,
Not that it couldn't happen but finding the parts from a donor machine is going to be almost impossible. The gears are always the first things to get tossed. These gears are for the last attachment I needed to complete mill. The math isn't hard, a little algebra & trig. It's the terminology/nomenclature, It's all new to me. I think cutting the gears will be the real challenge. If it is and after the 2nd or 3rd set I mess up......I'll make the blanks and job out what's beyond my pay grade. I'm not on any time schedule to get this thing finished, it's a hobby for me and I enjoy learning new things.

Andy

Paolo_MD said:

Andy,
Unless you enjoy the project of calculating and building from scratch the worms and worm gears, I'd suggest to shop for a donor/acceptor machine or parts salvaged from one.
If, instead, you enjoy the challenge, I'd suggest you start from a scenario where you have the mating pair to measure: measure the distance between the shafts, make your calculations, and verify your results by checking the dimensions and angles on the existing worm and worm gear.

Paolo

Click to expand...

johnoder said:

As can be seen, the 3 to 1 has MULTIPLE starts, which means the LEAD will be much longer than the apparent "pitch"

24 and 96 are both single start

Click to expand...

That was some of my confusion. With 8 starts, I wasn't sure if it was still considered a worm or a helical gear.

Not to worry about names.

Helical gears have leads when you mill them in a Universal mill

Hobby Shop said:

That was some of my confusion. With 8 starts, I wasn't sure if it was still considered a worm or a helical gear.

Click to expand...

Has lead of worm been measured?

johnoder said:

Has lead of worm been measured?

Click to expand...

Not yet John, I'm going to clean up my numbers and repost everything later.

If you are going to measure the helix angle on a comparator, be aware that the angle changes with the diameter or radius. You can see this visually by looking at the angle at the OD and comparing it to the angle at the root. This is why its best to measure the lead and calculate the lead angle. FYI, the lead angle is always specified at the pitch diameter.

Dan from Oakland said:

If you are going to measure the helix angle on a comparator, be aware that the angle changes with the diameter or radius. You can see this visually by looking at the angle at the OD and comparing it to the angle at the root. This is why its best to measure the lead and calculate the lead angle. FYI, the lead angle is always specified at the pitch diameter.

Click to expand...

Unfortunately, I didn't see your post before I left and measured it. Looking at the gear, I see exactly what your talking about. I'll double check the (1:3, 8 thread worm) lead by measuring it. I measured the worms like this picture. This is my first gear. they're completely new to me. With everyone's help (thanks) and a lot of reading, I'm learing this as I go.

Andy

I measured the worm lead and lead angle on the shadow graph. This is what I have for the 1:24 worm/wheel. I'm within .0015" of the fixed centers on the 5814 box. I'll remeasure the worm and wheel but I'm pretty sure the numbers are good. I'm still working on the other gears.

Andy

I'd give up on the worms and install a planetary gear set (or two) from an automatic transmission and generate a new table of leads with a spreadsheet.

The range of leads on a KT low lead attachment are insanely broad. When did anyone need a 122 inch lead?

When you have a good solid worm lead - as Dan described the procedure for obtaining - you can run the numbers the other way from that

As it stands, you are basing your pitch on the wheel on assumptions, like 5 degrees, and obtaining the .534 lead on that (not that your tiny photos lend themselves to being legible)

As an example of the built in errors:

If lead was actually .53445 and PD of worm was actually 2.409, the angle would be nearer 4.04 than 5 degrees

Hobby Shop said:

I measured the worm lead and lead angle on the shadow graph. This is what I have for the 1:24 worm/wheel. I'm within .0015" of the fixed centers on the 5814 box. I'll remeasure the worm and wheel but I'm pretty sure the numbers are good. I'm still working on the other gears.

Andy

Click to expand...

Here is a larger (hopefully) image Andy emailed

johnoder said:

When you have a good solid worm lead - as Dan described the procedure for obtaining - you can run the numbers the other way from that

As it stands, you are basing your pitch on the wheel on assumptions, like 5 degrees, and obtaining the .534 lead on that (not that your tiny photos lend themselves to being legible)

As an example of the built in errors:

If lead was actually .53445 and PD of worm was actually 2.409, the angle would be nearer 4.04 than 5 degrees

Click to expand...

John and Andy,

If I have interpreted the equations from Brown & Sharpe, Formulas in Gearing, 1905 edition, and 20th edition of Machinery's Handbook here are a set or worm/wheel parameters for this example. This example is intended to be the same design that Andy is working on.

I have a simple spreadsheet which allows me to quickly modify the design parameters and find and correct errors in my interpretation of the terminology and formulas.

The goal of the spreadsheet was to create a design which generated a worm wheel that would fit through the 4.5" round opening in the LL gearbox housing.

As an aside, I found it difficult to post this type of material.

Bob


2H - 1 to 3 ratio 8 start Worm/Wheel Gear Set

Worm TPI, TPI ~ threads per inch (a single continuous thread), 0.232, Input(*)
Center Distance, C = ( D + d ) /2, 3.250, Input
Number of Teeth on Wheel, N , 24, Input
"Worm Multi-start, MS = 1,2,3, etc", 8, Input
Worm Lead or Axial Pitch, L = 1 / TPI ~ inches per (a single continuous thread), 4.307,
Wheel Circular Pitch same as Axial Pitch for Worm, CP = L / MS, 0.538,
Worm Addendum, S = 0.3183 * CP, 0.171,
Diametrical Pitch, DP = Pi / CP, 5.836,
Pitch Diameter of Wheel, D = N * CP / Pi, 4.113,
Pitch Diameter of Worm, d = 2 * C - D, 2.387,
Worm OD, o = d + 2 * S, 2.730,
Whole depth of Worm, W = 0.6866 * CP, 0.370,
Worm Helix Angle, B = ( 180 / Pi ) * atan( Pi * d / L) Degrees, 60.136,
Worm Lead Angle #12, La = (180/Pi) * atan( L /( Pi * d ) Degrees , 29.864,
Norm Pitch of Worm #(1), Pn = CP * cos( (Pi/180) * La ), 0.467,
Worm Thread tool Tip, T = 0.31 * CP, 0.167,
Wheel Throat Diameter, O = D + 2 * S, 4.455, K&T 2H Low Lead Housing Opening for Wheel ~ 4.5”
Gashing Angle of Worm Wheel, GA = 90 - B (degrees), 29.864,

Here are the all the worm & worm gear measurements for the K&T 5814 Low lead.

1:3
Worm OD = 2.740"
Gear OD=4.454"

1:24
Worm OD= 2.750"
Gear OD = 4.454"

1:96
Worm OD=2.250"
Gear OD = 4.495

Gear Box worm/wheel center = 3.262"