Worm gears

If your lathe does not cut module threads then you can use a standard screw thread pitch and use the calculations for circular pitch. Below are tables of screw pitches and the equivalent metric module and diametrical pitches. The screw pitches are taken from my lathe, your lathe may differ.



Metric Pitch	TPI    Metric Module   Diametrical Pitch
1.00 0.318 79.7965
24 0.337 75.3982
22 0.368 69.115
1.20 0.382 66.497
1.25 0.398 63.8372
20 0.404 62.8319
1.40 0.446 56.9975
18 0.449 56.5487
1.50 0.477 53.1976
16 0.505 50.2655
1.60 0.509 49.8728
15 0.539 47.1239
1.75 0.557 45.598
1.80 0.573 44.3314
14 0.578 43.9823
13 0.622 40.8407
2.00 0.637 39.8982
12 0.674 37.6991
2.25 0.716 35.4651
11 0.735 34.5575
2.40 0.764 33.2485
2.50 0.796 31.9186
10 0.809 31.4159
2.80 0.891 28.4987
9 0.898 28.2743
3.00 0.955 26.5988
8 1.011 25.1327
3.20 1.019 24.9364
7 1/2 1.078 23.5619
3.50 1.114 22.799
3.60 1.146 22.1657
7 1.155 21.9911
6 1/2 1.244 20.4204
4.00 1.273 19.9491
6 1.244 18.8496
4.50 1.432 17.7325
5 1/2 1.470 17.2788
4.80 1.528 16.6243
5.00 1.592 15.9593
5 1.617 15.708
5.50 1.751 14.5084
5.60 1.783 14.2494
4 1/2 1.797 14.1372
6.00 1.910 13.2994
4 2.021 12.5664
7.00 2.228 11.3995

I only have formula for 14.5 and 20 degree pressure angle AGMA (American Gear Manufactures Association) worm gears. The AGMA seem to recommend 14.5 degree pressure angle for 1 and 2 starts with 20 degree pressure angle for 3 and 4 starts on the worm. I do not have any information for ISO worm gears but the AGMA formulation should make very workable metric worm gears. The biggest difference between the various standards I have looked at and other sources suggest that the worm wheel width has a useful range, with this in mind I opted to calculate the width with the middle values. The worm wheel width no matter which calculation is used are close to each other. Each method uses a different base diameter as a starting point, OD, pitch diameter and root diameter of the worm that is then multiplied with a constant.

A word on worm wheel blanks.
(According to the Machinery's Handbook) For fine pitch worm gearing there is little to be gained by concave radius of the outside diameter of the worm wheel blank especially when used for positioning rather than power transmission. A flat outside diameter if much easier to make. If the worm drive you are making is carrying a heavy load you could be better to buy a gear set of the double envelope type.

Worm Wheel face styles
There are two basic styles of worm wheel faces, flat faced and radiused face.

 


Flat faced
This face style is suitable for light drives and indexing purposes.
There is a slight variation sometimes seen where there is a shallow radius in the centre of the worm wheel face. This can be achieved by making the worm wheel 0.01 - 0.02 inches or 0.25 to 0.50 mm larger in diameter and sinking the hob extra deep by half the increased diameter.

Radiused faced
This face style is suitable for heavier drives and could used for indexing purposes.
If you plan on this style of worm wheel face then make the OD without the radiused face. The calculated depth to sink the hob will cut the radius for you.

 

Grinding your lathe tool bit.
If you grind your lathe tool bit to a sharp point you can measure the overall length of tool bit. As you grind the flat on the tool nose, measure the tool bit frequently and grind until the tool bit is shorter by "H  height" value. This will give the correct width of nose flat.

Backlash
The calculations for nose flat width is based on all the backlash is obtained by narrowing the the thickness of the worm thread. Steel being stronger than bronze.

If the thread on the hob is cut first then the nose flat can be reground a little more to shorten the tool bit to the value of "H  height". This way you only need one tool bit.

I have read on the internet of people making the worm and the hob thread on a single piece of steel and then cutting a portion off to make the worm with the remainder to be the hob. This is not a good idea because a) the hob will not cut the necessary clearance in the root of the worm wheel nor will there be any clearance at the root of the worm threads and b) there is no provision for backlash. In order to make this work the working center distance will have to be larger than the design center distance.

Clearance angles
Clearance angles are based on the helix angle of the worm thread +- 6 degrees. If you round the clearance angle to the nearest degree it will work well. Where the clearance angle is negative, a clearance angle of 0 degrees will work well.

Cutting the thread
If you try to cut the thread with the toll bit ground to the correct form the tool pressure is quite high and causes trouble. The easy way to cut this type of thread is a three step process.

1) Cut a "V" thread in the normal manner. Ensure that you do not cut to deep so that you do not cut away what will be the flat top of the worm thread.

2) Grind a parting tool so that its thickness is a bit less than the "W width" value. You will need to pay attention to the clearance angles. The parting tool needs as much support as we can get. Adjust the tool with the half nuts engaged so that the tool nose is centered in the grove of the "V" thread. Cutting the "V" thread first reduces the cutting load from the parting tool. Cut a square thread that is a little less than the "Thread depth" value.

3) With the half nuts engaged set up your worm thread forming tool so that it is centered on the groove of the square thread. There should be the remnants of the "V" thread and the flat nose of the worm threading tool can be on this. Cut to the depth of the "Thread depth" value and the job is done.

This three step process may seem like a lot of work but regrinding broken tools and or re making the worm or hob is far more work. Use cutting fluid and you should end up with a nice shiny accurate thread.

Fluting the hob
The hob does not need big wide flutes, narrow but more flutes is better. Most important is that before one set of teeth disengage from the worm wheel another has engaged otherwise the worm wheel teeth will be ruined. Consider using a fairly thick slitting saw about 0.060 inches thick (1.5 mm) to cut a flute (gullet) that has this shape. Lots of small  flutes. This will help the lack of clearance on the cutting teeth. There is not much material to remove and flute clogging should not be a problem.



gear cutter



Gashing the worm wheel blank.
You must gash the blank or you will make a piece of scrap metal. Gash to a depth that is just a little less than "Thread Depth". Cut the gash with a slitting saw, fly cutter, it is not important what you use. Ideally you will cut the gash at the helix angle or fairly close to the helix angle. Some people have cut the gash with no angle and that seems to work.

Crowning
Crowning the worm wheel is important. Crowning allows lubrication to be carried into the gear mesh where non crowned gear sets have a tendency for the worm wheel teeth to wipe the lubrication off the worm teeth. A crowned worm wheel allows for a little misalignment on the center lines without binding, this also makes assembly easier as precise assembly alignment is not necessary. Another consideration is if you have your worm on an eccentric to allow quick disengagement as this will eliminate any possibility of binding. There are two common methods of crowning. The most used (commercially) is to use an over sized hob as the hob can be sharpened many times before becoming to small. If you want to use this method tick the "Crown cutting" tick box. The other method is to use a standard hob diameter but to initially cut the worm wheel teeth a bit of the center line (0.01 - 0.02 inches or 0.25 to 0.50 mm) and then mill sideways double the initial offset. This makes a short section of helical gear that is often found in dividing heads.

If you are making a really light drive consider using a standard tap in place of a hob. This does work, I have made two worm wheels with a tap.  See this web page for more information Machining Technique for Worm Drives.