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An Application to create dividing head tables

Anyone know of one. Free I hope

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Ajohnw11/05/2016 17:22:09
3631 forum posts
160 photos

There seems to be plenty of spread sheets about where the plate hole counts are entered plus the worm wheel tooth count and then some division ratio that is needed is entered and it calculates which plate and turns for that or comes back with a no can do.

Some seem to work with fractional degrees. I wonder if that is totally reliable because of the decimal precision where as a pure fractions of a circle method would be precise.

Anyway I wonder if anyone has come across an application that generates a table of all a set can do over some specified range of divisions.

John

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Andy Ash11/05/2016 18:22:18
136 forum posts
33 photos

I have the bog standard Myford head, but I didn't have the table so I did my own spreadsheet.

With that, I know how many turns on the wormscrew there are to make the head revolve once, and I calculate decimal; whole revs and part revs separately. (Integer and fractional parts). I do that for every division from one to as many as I need. Usually around 125 divisions. You can always do more division just by extending the number of rows down.

Then I have columns which know how many holes there are in the division plate circle. In each cell for the column I calculate how many holes is the closest to the fractional part of the number of divisions for that row. Finally, that cell uses conditional formatting so that it lights up yellow if it is within a given angular tolerance of a single division for that number of divisions.

The beauty of this, is that you can adjust the tolerance as you need. If you only have certain plates, then you can relax and/or tighten the tolerance to find out if you can reach a given number of divisions accurately enough.

What I found with the standard Myford plates is that they must have been fairly clever with their choice of hole circles. If you tighten the tolerances too much, the choices all drop away together. If you loosen the tolerance then you don't get much more benefit unless you can tolerate really gross errors.

There are four Myford plates, and No.1 plate gives the most possibilities with only 7 circles. No. 2 plate gives a lot of repeats and only a few a few more (perhaps half as many again) divisions with more hole circles. By the time you get to plates 3 & 4 you pretty nearly get only one extra division per hole circle (although they're not all primes). The Myford head shipped with No.1 and 2, you could buy 3 & 4 as extra if you needed the hard to get divisions.

**LINK**

Obviously it's a spreadsheet so you can tweak it to your worm and plates.

Edited By Andy Ash on 11/05/2016 18:25:37

Involute Curve11/05/2016 18:57:58
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337 forum posts
107 photos

I have an old Basic / DOS (Remember that!!) program for dividing head use, you input all the division plates you have, and the worm gear ratio 40, 60 or what have you, once this is done you run the program, input the divisions required, the program outputs all suitable setups you have based on your available division plates.

I've ran it on XP ok from the command prompt, if anyone wants a copy, pm me.

Perhaps it could be used as the basis of an android app!!

 

Shaun

Edited By Involute Curve on 11/05/2016 18:59:50

Michael Gilligan11/05/2016 19:42:58
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20113 forum posts
1044 photos

John,

If you look at that 'vintage' article of mine, which you recently referenced on another thread, you will find two very small programs ... one for CBM BASIC [Commodore 64] and one for the Psion Organiser XP.

They are pimitive by modern standards, but the underlying principle is sound.

If Neil & Diane wish to do so, I would be happy for the two little programs to be published here; as a starting point for development.

MichaelG.

Ajohnw11/05/2016 21:01:41
3631 forum posts
160 photos

Thanks Shaun but there are several spread sheets that will do that. One I think is hosted on here.

I can use Andy's saves me some work. I had started reading up on macro's in order to only produce a table that includes integer divisions that the plates and worm wheel can do. If I am feeling manic at some point I might give it a go. I use Libre Office so not sure if the result would be compatible with MS. I can load any MS spread sheet and also save in that format.

I don't think I have your vintage article Michael. I just saw a reference to it. I was hoping that you would comment on angling the worm to suit it's thread helix angles as if yours does work the info would be of use to others. I'm not suggesting it doesn't work either way seems to be ok but I have never cut a gear when the helix angle isn't matched

I do have a spreadsheet I did myself of sorts but only for partial revolutions of the handle. It's pure integer so can't go wrong. It may not the other way but there is always a chance when prime fractions are involved and converted to decimal as they are irrational numbers. The spread sheet produces numbers in no particular order by just using possible factors of the worm wheel and the factors in the plate hole counts. It just produces results like this - not the easiest to use.

brownandsharpplates60t.jpg

surpriseJust hope the maths is sound. It does seem to be. Using it needs a degrees of cutting and pasting and mental determination of the factors in the hole counts and worm wheel. Those plates were aimed at 40T wheels and I think loose some counts as a result but gain others. I don't have any permanent web space but in the rather doubtful chance that some one want's a copy I could put it on filebin.

Edit - I started wondering about other ways once I had calc'd a couple of clock gear ratio's. It turned out that I do have plates for a train I worked through but the plates currently don't fit my dividing head. sad

John

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Edited By Ajohnw on 11/05/2016 21:07:46

Michael Gilligan11/05/2016 22:52:25
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20113 forum posts
1044 photos
Posted by Ajohnw on 11/05/2016 21:01:41:

I don't think I have your vintage article Michael. I just saw a reference to it. I was hoping that you would comment on angling the worm to suit it's thread helix angles as if yours does work the info would be of use to others. I'm not suggesting it doesn't work either way seems to be ok but I have never cut a gear when the helix angle isn't matched

.

Sorry to disappoint you, John, but I think you will have a very long wait ... So far as I recall, I made no mention of worm-angling.

MichaelG.

Ajohnw12/05/2016 09:41:28
3631 forum posts
160 photos

I doubt if anyone is interested in the chart I posted BUT do notice that it's only correct for fractional turns of the handle. For divisions of less than 60 it isn't correct. It's just another way of doing it but needs repeating for 2, 3 etc turns of the handle for the lower number divisions.

Andy's spreadsheet is the best one I have come across and I doubt if working in decimal will go wrong in this case but in some similar areas it can. I'm reminded of the early days of banking software when some people became rich by sticking rounding errors in their own accounts, also me trying to compute zero slope in a function. It seemed to take a long time. When I looked I found a number with several hundred zero before it and the decimal point.

John

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Ajohnw12/05/2016 11:17:13
3631 forum posts
160 photos

surpriseI just put my plate hole counts in Andy's sheet and then noticed that if I set the precision to finer than 0.001 I get no results. As it's all integers really it just shows what decimal arithmetic can do with them, the more used the worse it gets. I doubt if it matters.

John

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Ajohnw12/05/2016 12:55:56
3631 forum posts
160 photos

I found an application that does it. It's here

**LINK**

I have it running under wine on linux. Display not entirely correct but usable. Maybe some one on windows could download it and virus scan it.

The set up results on Linux are a little odd. I ran it from the folder that has setup.exe in it setting that as the folder to run in using Q4Wine as it makes that easy. Nothing appeared to happen but looking in the application folder I found 3 versions. Ran Rotab.exe.deploy under Q4wine and it ran. I tried copy pasting a column of it's output into a word processor and no problem there either.

I've not checked any of the numbers.

John

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Andy Ash12/05/2016 13:27:55
136 forum posts
33 photos

Hi John,

I'm glad you found it useful, and figured out how to customise it for your dividing head.

My current job is developing manufacturing software. Before I did that spreadsheet, I had considered actually writing an application to do the job that the spreadsheet now does. I realised I could get everything I needed out of the spreadsheet so I never bothered with the application.

I read that you wanted an application and not a spreadsheet, and I wasn't going to post. When I then read what you had said about precision, I realised I should post anyway. Obviously, with the variable precision you can compromise if you want.

I would always recommend calculating out any choice that the spreadsheet helps you to find. This is just in case the spreadsheet has an error. As far as I know it's all-right.

If you decide to compromise and use a hole circle that doesn't give an integer result, don't forget that you can distribute the error around the full circle. If you calculate how far short/over 60 revolutions (or whatever for your input and worm) you would be with a hole circle that you know carries an error, then you can drop/add those holes gradually and evenly throughout division of the full revolution.

I'll admit that it's not the easiest of things to keep track of, but you only need to use a notepad and a pencil to keep track. It's perhaps a lot better than having to find/make a plate and hole circle that you only ever use once.

If you do it that way, the errors can be surprisingly small, and you still get what you want without the "correct" plate.

Glad to be of service.

Edited By Andy Ash on 12/05/2016 13:33:32

Howard Lewis14/05/2016 22:34:32
6040 forum posts
14 photos

Following problems with the chart supplied with the Vertex HV6 Rotary table, I made up an EXCEL spreadsheet for the three Division Plates for the HV6. Look for the thread on earlier pages of this Forum.

Neil said that he would post it on the Stub Mandrel website.

Although for a 90:1 ratio, it ought to be useable with a substitution of Number of Holes and/or Worm/Wheel ratio.

Howard

Ajohnw14/05/2016 23:35:29
3631 forum posts
160 photos

I use the application I posted a link to. Copy pasted the output from it into a word processor and used find - replace to convert it into a coma separated list. Then converted the list to a table so now have all divisions up to 200 for 4 plates, one column per plate. It will do 3 plates in one go and doesn't find duplicates on the same plate.

Biggest problem was getting the word processor to use columns the way I wanted.

laughAnother problem was me, I set it to do divisions from 2 - 200, With a 60T worm. I reckon I can cope with 4,5 and 6 in my head but I doubt if I can get above 200 divisions on 4 plates on one side of A4 so probably wont correct that.

Next with be divisions over 200 to some other number that can fit on the other side of the A4 sheet after I have checked that the output is correct !! I have checked a couple. A few more wont hurt. Probably set it for B&S plates, 40T worm and compare with Machinery's.

John

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Steven Vine15/05/2016 18:32:40
340 forum posts
30 photos

This topic has picqued my interest. I have written a VB.Net application that will calculate the rotations and hole plates. Shaun sent me a copy of the old program he had (Mklotz), and I consulted that during the build.

The app is up and running. It loads and saves data and performs the calculations. I am still checking that it is calculating correctly. It seems ok with the few numbers I have thrown at it. It is still under test (which I hope covers my behind if the calcs are wrongindecision 

You can download it from this location **LINK**

You can specify up to 10 dividing heads with up to 20 hole circles per dividing head.

Feel free to download it and have a play. It's all safe.

Steve

Bazyle17/05/2016 21:08:53
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6301 forum posts
222 photos

Andy, your excel file is great for adapting to other worm ratios and plates and giving alternative which might save swapping the plate sometimes. I was interested in your use of the MOD function as I haven't been aware of it.

However it seems to dislike the situations where the target division is a multiple of the plate so I modified it using the TRUNC function.
=IF((($D4*E$3)-TRUNC($D4*E$3))>$B$1,0,$D4*E$3)

This still gave errors due somehow to the calculations not being exact so needed a big error allowance.

Going to this long winded version seems to do the trick. B2 is the worm wheel size. Not sure if this was a variable in your version as I've fiddled around as one does.
=IF((($B$2*E$3)/$A4)-($C4*E$3)-TRUNC((($B$2*E$3)/$A4)-($C4*E$3))>$B$1,0,(($B$2*E$3)/$A4)-($C4*E$3))

Ajohnw17/05/2016 22:52:48
3631 forum posts
160 photos

I used the application I linked to and produced this via a word processor. I copy pasted the apps output into it and used find replace to change it to a coma separated list and then used a wp utility to put these into tables.

divisiontable.v01.jpg

I've checked several out manually and all have been ok so then did another page from 200 divisions that went up to the max divisions the plates can give - a bit short of 4,000.

Later when I have time I'll do a spread sheet as a check but using fractional arithmetic or maybe some variant of pure integers that does the same thing and can't have rounding errors and use this to check the application.

John

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Andy Ash17/05/2016 22:58:15
136 forum posts
33 photos

Roger that Bazyle.

I certainly think that making the worm an adjustable parameter is a useful thing if you're exploring division possibilities. I only have the one head so it never mattered to me. It would be quite a straightforward change to make.

The spreadsheet isn't actually that complicated mathematically. What's incredible is that the computer can do so many sums, so quickly that it can answer all the separate problems in the blink of an eye.

The worm sets the number of revolutions for a complete circle. The actual rotation of the handle for one division out of however many you want can be expressed as a fraction;

Worm revs / Number of Divisions = Actual rotations of worm for one division.

If you do that sum, then you get a number, say 2.456.

The two whole revs is easy. But you also have to get the 0.456 part. It's just added on, but the holes on the plate help to define it. If a hole circle has 46 holes and you use 35 of them, this too can be expressed as a fraction.

35 / 46 = 0.760.......

That is to say using 35 of 46 holes, you can define 0.760 of a revolution. We actually wanted 0.456 of a revolution and with our 46 hole circle we can ask how many holes makes 0.456 of revolution.

0.456 * 46 = 20.976 holes

Obviously this carries an error. The closest you can actually get is 21 holes. So you're left with an error of 0.024

My spreadsheet simply asks how many holes of each hole circle do I need to use to achieve complete accuracy. On top of that is an algorithm that rounds up or down and decides if the difference (proximity) between that nearest integer is bigger or smaller than the specified limit for the whole sheet of hole circles and divisions. If it is smaller, the results are hilighted, if larger they are zeroed and not hilighted.

NOTE: Watch out. The way the columns are aligned it may not always be evident that decimal values are being returned. If you have any doubts temporarily stretch the cell width. The wider you make it, the more precision you will see.

If you set the proximity bigger, you get more matches, but you will notice that more of the results are actually decimal values. The spreadsheet might say 0 full rotations plus 22.08 holes on the 46 hole circle. Obviously you can't have 22.08 holes. You can have 22 holes. I was aiming to get 125 divisions.

125 * (22 / 46) = 59.782

Over the whole circle I come up short. How short?

60 - 59.782 = 0.217 of a revolution.

So how many holes is that?

0.217 * 46 = 10 exactly.

So if we were to divide a circle into 125 divisions using 22 holes on the 46 circle; we'd get to the end of the 125 divisions and we'd be short of 60 revolutions, by 10 holes. It's still not precise, but you can achieve integral precision. All you do is add the extra ten holes gradually throughout the division operation. If you have 125 divisions you could normally use 22 holes on the 46 circle. Then every 13th division use 23 holes.

The differential precision still has a problem, but the integral precision is now fine.

The only way you can have both, is to use a hole circle that reports an integer number (nothing after the decimal point) on my spreadsheet. These integer numbers are those which are typically only reported by the manufacturers on the table that comes with the dividing head - say Brown and Sharpe.

You can make my spreadsheet so that it only shows the integer numbers, but I find the variable precision is more useful (because I only have a couple of plates) so I do it that way. I can get at things I wouldn't otherwise be able to get.

I have to go make some zeds right now. (I hope my worked example sums were right!!! I'm sure someone will say if not.)

I'll try to analyse your worksheet functions tomorrow Bazyle, and compare them with what I did originally. I'll let you know whatever I think.

Edited By Andy Ash on 17/05/2016 23:27:44

Ajohnw17/05/2016 23:58:33
3631 forum posts
160 photos

I suspect that the clue to doing it exactly is that the divisions have to be some fraction of 1/'worm tooth count. That might mean that some pre processing of the various numbers would avoid the problems with fractional arithmetic, common denominators etc. Ideally as 1/n is always needed as it's the division the 1/ part might even disappear.

If not I suspect that conditional statements will be needed and probably will be anyway, just more of them. The libre spreadsheet app will do these as it supports good old basic that as far as this sort of thing is concerned is much like the original dartmouth variant. I didn't do this on the first chart I posted because I didn't want to spend time picking up how they use it. Lots of the examples that are about use other languages.

Pretty busy at the moment. Cleared garage and the next thing was and still is freeing up rusted brakes on a car that hasn't moved for nearly 15 years. Most of 2 days and nearly done now. One more to go which should be simple but as it's the last one probably wont be.

John

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Involute Curve18/05/2016 08:38:57
avatar
337 forum posts
107 photos
Posted by Steven Vine on 15/05/2016 18:32:40:

This topic has picqued my interest. I have written a VB.Net application that will calculate the rotations and hole plates. Shaun sent me a copy of the old program he had (Mklotz), and I consulted that during the build.

The app is up and running. It loads and saves data and performs the calculations. I am still checking that it is calculating correctly. It seems ok with the few numbers I have thrown at it. It is still under test (which I hope covers my behind if the calcs are wrongindecision

You can download it from this location **LINK**

You can specify up to 10 dividing heads with up to 20 hole circles per dividing head.

Feel free to download it and have a play. It's all safe.

Steve

Steve that looks good, I gave it a quick try and it seems to work ok , I dont have time today to play with it much but I will over the next day or two.

good job

Shaun

Zebethyal18/05/2016 09:21:37
198 forum posts

I have a spreadsheet I wrote (still looking for somewhere I can post it so others can have access if they are interested).

It has 2 tabs, one where you list out the holes in your plates, set the worm ratio, enter the required division and it will show you which plates are capable of solving it.

Division1

The other tab is a huge table that has divisions down the left and plate holes along the top, this one shows every solveable division within that range, again, you just enter your worm ratio.

It shows both turns and holes to move in order to solve a given division, there is also a column at the end that shows, based on the plate holes provided, whether or not a particular division is possible.

The solve is possible if n1 ( 360/divisions ) divided by n2 ( 360/(holes*worm ratio) ) is an integer, this value is the number of holes to use in addition to the number of turns ( integer(n1/(360/worm ratio)) ).

Division2

Additional plate holes can easily be added (just an additional column)

The spreadsheet currently solves for every division from 1 to 360, additional divisions simply require more rows, or just a custom row that shows the division required.

Another thing to bear in mind is that just because you can't solve a particular division with the plates you have, does not necessarily mean that you can't make a plate that can solve it quite easily.

Using the above example of 125 divisions, my worm ration of 90 and my available plate hole sets of 15, 16, 17, 18, 19, 20, 21, 23, 27, 29, 31, 33, 37, 39, 41, 43, 47, 49, it would appear that I do not have a plate that can solve for 125, however I can easily make a plate, using the plates I already have.

125 divisions can be solved with 25 (0 turns and 18 holes) or 50 (0 turns and 36 holes).

25 divisions can be solved with 15 (3 turns and 9 holes) or 20 (3 turns and 12 holes), both of which are in my standard set.

50 divisions could also be solved with 15 (1 turn and 12 holes) or 20 (1 turn and 16 holes).

I intend to make a 4th plate for my dividing set that has 25, 63, 67, 68 and 71 holes, as these add additional useful numbers.

The main area where the intermediate aproach would break down is for prime numbers such as 67, 71 and 127, this is one of the reasons why I have made my Division Controller, (I need to make a 127 tooth metric translation gear for my lathe), which once up and running will largely render the division plates redundant.

Edited By Timothy Moores on 18/05/2016 09:41:30

Ajohnw18/05/2016 10:37:45
3631 forum posts
160 photos

You could upload it to filebin.net Timothy but it will only stay on there for a few months. I'd like a copy to use to compare with others. No nags or anything else from filebin. I've used it a number of times.

Your plates look like the ones to Brown and Sharp standard. They were aimed at 40T worm wheels the idea being to be able to obtain low division ratios closely and higher ones to a standard that allowed a lot of gear pair type ratio's to be obtained pretty closely. Cincinnati used a different standard, sort of B&S with bells on so more divisions but aimed at 40T again. That 4 plate table I posted is the plates from Maidstone Engineering. The divisions they give with 60T look pretty good to me so I am going to convert them to fit my dividing head.

I had hoped some one would download and virus check the app I linked to. No one has but that's forums for you. Well some of them.

Using that I had a play with various worm wheel tooth counts out of curiosity. A dividing head based on lathe change wheels has some interesting possibilities. Other than the plates and decent sector arms they are not that difficult to make. Screw cutting a worm to suit the change wheels may be a problem but it just needs to be very close rather than exact.

John

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