Gearcutting

[rhankey]

Sorry John,

But if it's gearcutting then you do need dividing plates. The vernier on a rotary table is IIRC at best 10 secs of arc on the larger tables, on my Vertex 6" it is 20 secs.....so say 49 teeth

=360/49, = 7.346938776 deg = 70:20.081632653':48.97959184" rounding gives 70:20':49" or at best say 50 secs, then the error = 1.97959184*49 = 97 secs or 1.616 mins. On my Vertex the error is a minimum 8.979 secs or 7.34 mins!

I don't think you can afford the error the vernier will give for gearcutting.

Best Regards
Bob

Bob,

In using your example of cutting 49T, I can understand that the cumulative error of advancing the RT 7deg:20’:49” to get to the next tooth position could result in material error by the time you complete a full revolution. Wouldn’t it be way more accurate to compute a set of absolute deg:min:sec settings for each tooth (eg: n * 7deg:20’:49”) using Excel (or whatever method of your choice)? This way, individual teeth may be +/- a let’s say 50 sec based on the accuracy of your RT, but will average out to being fine. This might not be close enough for car differentials where they need to achieve crazy accuracy, but for our small engine gear cutting needs, I can’t imagine this being a big problem.

Certainly a set of dividing plates makes life a lot easier for gear cutting, but I can’t see why a RT without plates can’t be plenty accurate enough.

Am I missing something?

Robin

 

[Mainer]

Most certainly, you would figure out the deg-mini-sec for each tooth individually, and not just keep adding on and getting a cumulative error.

Also, consider what a minute of error is in terms of distance. A gear 1" in diameter has a pitch circle circumference of 3.14". A minute of angle is 1/3600 of a circle. 3.14/3600 is a distance error of 0.0009". A gear 2" in diameter would have a distance error of 0.0018" for a minute of angle. As Robin suggests, that is likely to be plenty close enough. In fact, gears could probably have even more error and work well enough for non-critical applications. They will just be noisy and have somoe amount of jerkiness.

An involute gear cutter is correct for only one tooth count in its range, anyway, so even if you get the angular position exactly correct the tooth form has a good chance of being incorrect to some degree.

Cut 'em and try 'em.

 

[mklotz]

Yes, as Robin points out, the cumulative error problem can be solved by computing a division increment to high accuracy in the computer and then multiplying to get the angle settings for each division. That is exactly what my ROTARY program does. The error for the division increment will be only the difference between the true value of 360/49 and the computer's internal approximation of that value, a value far, far smaller than one arcsecond. The dominant error in the setting will be due to our silly insistence on using Babylonian angle nomenclature. By rounding the calculated setting to the nearest arcsecond we incur an error of average value 0.5 arcsecond. Since this dominates the increment error, it's safe to say that the net error in any setting calculated as above is ± 0.5 arcsecond.

Now, I think what Bob is arguing is that, due to the vernier coarseness on the average RT, the setting calculated above can only be set with 10 arcsecond accuracy, a value which completely dominates the 0.5 arcsecond error. However, isn't it true that this error is reduced at the workpiece by a factor equal to the gear ratio of the table?

 

[Dinkum]

Thanks for all the input. Its amazing how many different approaches there are to one problem. Now I really am stuck for a decision.

How's this for a new approach: could I build a dividing head (like Harold Hall's) but use dividing plates that are meant for a RT rather than the direct gear indexing? Would I have to put a 90:1 reduction in it to be able to use the dividing plates or just use them differently?

 

[mklotz]

Yes, you could do that and no gearing would be necessary. You would need plates with hole circles that are integer multiples of the number of divisions you intend to make on your workpiece. Some economies are possible. A 24 hole plate can be used for 2,3,4,6,8,12, and 24 divisions. Prime number divisions require a hole plate with that number of holes (or an integer multiple). For example, 17 divisions requires a 17 hole plate or a 34 (2*17) hole plate or a 51 (3*17) or...etcan.

Remember, however, that the dividing head can't be used to mill curved profiles like a rotary table can. It's called a dividing head for a good reason - that's what it does and nothing more.

Plus, if you want to make your own dividing head hole plates, you're gonna need a - wait for it - rotary table.

For a home hobby shop not making parts for inertial guidance systems, the RT is the tool of choice for maximum utility.

 

[lensman57]

Thanks for all the input. Its amazing how many different approaches there are to one problem. Now I really am stuck for a decision.

How's this for a new approach: could I build a dividing head (like Harold Hall's) but use dividing plates that are meant for a RT rather than the direct gear indexing? Would I have to put a 90:1 reduction in it to be able to use the dividing plates or just use them differently?

Hi,
One last word before you male a decision, if you do decide to go for a rotary table make sure that you can mount the chuck straight from the lathe on to the RT, this is very important for concentricity and can make life very easy at times. The shining example of this is the USA made miniature Sherline machines where you can move the chuck between the lathe, the mill and the RT and hold concentricity, I am sure there are other makes that have this useful feature and it is worth keeping this in mind.

Regards,

A.G

 

[Maryak]

Now, I think what Bob is arguing is that, due to the vernier coarseness on the average RT, the setting calculated above can only be set with 10 arcsecond accuracy, a value which completely dominates the 0.5 arcsecond error. However, isn't it true that this error is reduced at the workpiece by a factor equal to the gear ratio of the table?

Help............if as in gear cutting, I am trying to move the circumference of a circle from point A to point B and the equipment I have is not up to the job, then I don't understand how the error is reduced when it is the known error at the start of the process. Would that make the stated error of 10" or 20" to in fact be 0.11" and 0.22" ??? ??? ???

A confused Bob

 

[mklotz]

If my program tells you to set the RT to a certain angle and you dial in that angle 10 arcseconds off the advised value because of the granularity in your RT crank vernier, the workpiece will be only 10/GR from the specified angle (GR = RT gear ratio).

If my program rounded the specified angle to the nearest integer arcsecond, said specified value can be in error by, on average, 0.5 arcseconds.

 

[steamer]

If my program tells you to set the RT to a certain angle and you dial in that angle 10 arcseconds off the advised value because of the granularity in your RT crank vernier, the workpiece will be only 10/GR from the specified angle (GR = RT gear ratio).

If my program rounded the specified angle to the nearest integer arcsecond, said specified value can be in error by, on average, 0.5 arcseconds.

your correct Marv....assuming the pitch error of the gear is small

 

[Maryak]

OK,

But I would have thought that the GR was already removed from the equation in the derivation of the vernier scale ??? As I see it the graduations on the hand wheel and hence the vernier move the table the equivalent degrees to those so marked and I don't see what the gear ratio has to do with this. If a 72:1 worm makes 5 degrees per turn and a 90:1 worm makes 4 degrees per turn then irrespective of which worm I use I still need to rotate the table the same amount to derive the same no of divisions around the circumference and my hand wheels and verniers would be graduated to suit the worm ratio I am using.

If I want 5 degrees of rotation then at 72:1 its 1 turn of the worm, at 90:1 its 1.25 turns of the worm or 1 turn + 1 degree on the hand wheel collar.

Best Regards and still confused
Bob

View attachment Divstodegs.xls

 

[steamer]

If the vernier scale is mounted to the table of the RT and is compared to the position of the table, your correct Bob.

If the vernier scale is mounted to the worm or dial....before the gear pair....your correct Marv


Mine is on the worm of dial.....most I have seen are mounted there.....but I'm sure there are some mounted the other way

Dave

 

[Maryak]

Guys,

I know I'm getting older and the brain cells have had more than their share of over indulgence but for me it's not a matter of whose right or whose wrong.......................I truly do not understand what is being said. As I said previously IMHO the scales on the handwheel, (attached to the worm), are so marked as to reflect the actual movement of the table. So if my best setting on those scales is 8secs off the required setting, how is this error reduced ???
when it has, I believe, moved the table 8secs more or less than it should have been moved.

Best Regards from a totally and absolutely confused

Bob

 

[MachineTom]

You will know when the last tooth you cut, is visibly wider or narrower than the rest.

That 8 sec. can be additive or subtractive or best of all BOTH. Now how many parts have you made that are .0005 oversize vs how many are undersized by .0005", If like me you tend to have undersized part.

The joy when using plates and a quadrant is the speed that is gained on a time consuming process as gear cutting. Save you money and buy a used dividing head, one with a chuck and tailstock, and a swivel too. Ellis units are often on ebay.

If you have not used a quadrant it is slick, set you hole count circle with the crank pin, set you quadrant to the number of holes per step. If the gear cut spacing figures to 1 turn + 19 holes, you cut the first tooth, then crank the handle 1 turn and continue until it gets to the quadrant leaf at the 19th hole, release the crank pin into the hole, rotate the quadrant till it hits the pin, its now set for another 19 hole spacing, cut gear, rotate 1 turn and continue until it gets tto the quadrant leaf again.

 

[Maryak]

Call me Bob Dolittle but I think I’ve got it.

With a 90:1 worm and wheel, 1 turn of the handwheel attached to the worm, will rotate the worm wheel 40 Thanks to the effect of the gear ratio, the error of this movement is a maximum of 4/900 or 0.044440 and so on.

In other words the smaller the distance the worm wheel is rotated by the worm the smaller will be the error of said movement.

Back to my original example of a 49 tooth gear:

The required movement of the worm wheel per tooth is 70 20’ 49” to the nearest arcsecond.

Setting up my 6” rotary table which has a vernier scale of 20” the closest I can measure to the required angular movement is 70 20’ 40” or a deviation of -9 arcseconds, using the gear ratio effect, the error of this movement will be -9/90” or -0.1 arcseconds. A gear cut using this will be a bit like a caterpillar with a wooden leg or:

GrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrTHUMP

Fortunately there may be a way to spread or even remove this error. Looking down my DMS list, tooth no 20 has a movement of 1460 56’ 20” to the nearest arcsecond.

So, we use this number for our indexing of the gear, i.e. the second tooth cut will be tooth 20 and the third tooth will be tooth 40 and the fourth tooth will be tooth 11 and on.

The high tech term for the above is "Block Indexing." I had forgotten about it until I did a quick flip through Machinerys Handbook.

Best Regards
Bob

 

[steamer]

Call me Bob Dolittle but I think I’ve got it.

With a 90:1 worm and wheel, 1 turn of the handwheel attached to the worm, will rotate the worm wheel 40 Thanks to the effect of the gear ratio, the error of this movement is a maximum of 4/900 or 0.044440 and so on.

In other words the smaller the distance the worm wheel is rotated by the worm the smaller will be the error of said movement.

Back to my original example of a 49 tooth gear:

The required movement of the worm wheel per tooth is 70 20’ 49” to the nearest arcsecond.

Setting up my 6” rotary table which has a vernier scale of 20” the closest I can measure to the required angular movement is 70 20’ 40” or a deviation of -9 arcseconds, using the gear ratio effect, the error of this movement will be -9/90” or -0.1 arcseconds. A gear cut using this will be a bit like a caterpillar with a wooden leg or:

GrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrTHUMP

Fortunately there may be a way to spread or even remove this error. Looking down my DMS list, tooth no 20 has a movement of 1460 56’ 20” to the nearest arcsecond.

So, we use this number for our indexing of the gear, i.e. the second tooth cut will be tooth 20 and the third tooth will be tooth 40 and the fourth tooth will be tooth 11 and on.

The high tech term for the above is "Block Indexing." I had forgotten about it until I did a quick flip through Machinerys Handbook.

Best Regards
Bob

Now I'm confused! Rof} :