Bodger Bill’s screwcutting issues

[Neil WyattModerator @neilwyatt]

Posted by Brian Wood on 14/10/2016 16:23:10:

So, there is a permanent 40 tooth gear at the start of the chain as Bazyle says. How bizarre, that would seem to me to be extremely limiting. Being a Myford man that kind of limitation simply doesn't apply. Is that true for both imperial and metric versions of this lathe?

Being creditable, rather than a limitation (easily overcome by starting the gear chain with a 40T gear) think of it as an opportunity to get other pitches by popping a different gear in that extra space

N.

[SillyOldDufferModerator @sillyoldduffer]

I'm still experimenting with ways of doing this, not just for Bill, but because I want to understand it as well.

My Chinese lathe has a fixed 40t headstock. This is bad news if you want to use an online calculator. I haven't found one yet that directly covers that eventuality.

Working back from a target tpi to find a suitable gear chain from first principles is – I think – quite difficult. Sparey says "don't calculate it – find a table". The sums are extra hard if you're not completely sure of the leadscrew!

So I'm approaching the problem the other way by calculating a table of all the pitches/tpi that can be obtained from a given set of gears with a 40t headstock, and a given leadscrew value.

Calculating such a table manually would be tedious and error-prone. As Bill has lots of extra gears, it would be extra hard in his case. Fortunately, touch wood, I have the programming skills needed to mechanise the process. It will still need careful checking though – I am the Weakest Link.

Dave

[Brian WoodParticipant @brianwood45127]

Hello Dave,

​I'm glad someone else has picked up the torch, well done. I fear I lost interest very soon after Jason added his complication of the final multipliers to the mix which up until then had been hidden information.

You have a personal interest in understanding it all, I was just hoping to be helpful.

​However, establishing the leadscrew pitch is fortunately easy, even with it concealed; just measure the carriage displacement per turn. It will either be 0.0833 inches (2.117 mm) for the 12 tpi imperial leadscrew or a straight 2 mm for the metric version.

​So, over to you now

​Regards
​Brian

[SillyOldDufferModerator @sillyoldduffer]

Posted by Brian Wood on 16/10/2016 12:59:09:

…

​So, over to you now

​Regards
​Brian

Thanks Brian. Watch this space – I've nothing in the bag so far and you may yet see me defeated by this one.

Dave

[Bill AndrewsParticipant @billandrews30971]

Hi All,

Please find a link to the image for a thread and feeding table for lathe (WM240).

https://fnjrha-ch3302.files.1drv.com/y3mykzPYkNjT6YIYd_GiS9YiTeILB_JmQnPIzuizD-qGRWdE7vc5EzzoqMHsA1hTw65VSRi7Odfbgko2ubumlBJ9drIhmXr5svGmjrJBdq5zJ64SvIczrB_kHydkfXC_3Dvdfr9FRX5mEZD4Dspl0IN1cA2k7t81s8-W8AUktd_F9M/SCAN0001.gif?psid=1

Hopefully, this will provide context.

Regards,

Bill

 

 

Edited By JasonB on 17/10/2016 18:24:16

[SillyOldDufferModerator @sillyoldduffer]

Posted by Bill Andrews on 17/10/2016 17:57:01:

Hi All,

Please find a link to the image for a thread and feeding table for lathe (WM240).

…

Bill

Thanks Bill. I've written a program to tabulate gear configurations. It works for my lathe and now I have a description I'll see if I can get it to do the same for yours.

That double 40 arrangement at top of the chain is new to me. Keep your fingers crossed.

Cheers,

Dave

[JasonBModerator @jasonb]

Checking it using the gear train for 24tpi seems to confirm you have a 12tpi leadscrew.

So I would go with what Silly old Duffer said that the hand written geartrain is wrong and the 52T on the leadscrew (bottom line)should actually be 55. That makes sense as you only have one 52T and one 55T gear in the set.

J

[Neil WyattModerator @neilwyatt]

The formula is

PITCH = 12 * (driven gear 1 * driven gear 2) / (driving gear 1 * driving gear 2 x 40)

Perhaps more useful:

PITCH / 0.3 = (driven 1 * driven 2) / (driver 1 * driver 2)

NOTE: Any gear that drives and is driven (i.e. idlers) should be left out.

Neil

[SillyOldDufferModerator @sillyoldduffer]

Hi Bill,

I've produced a pdf with nearly 54000 gear combinations for your delectation. I friended you in the hope of being able to send you a PM but it might be easier for you to use this link to DROPBOX.

You'll see that the table contains many different ways of generating a much smaller number of useful tpi.

It isn't a complete list: your lathe uses some set-ups like that for 12tpi that I haven't modelled.

Hope it's useful,

Dave

[SillyOldDufferModerator @sillyoldduffer]

Just in case anyone wants to see the code (Python3) here it is. Making it public guarantees it's wrong …

import itertools # supports permutations
import fractions # for rational arithmetic

metric = [ 20, 30, 45, 50, 60, 60, 65, 70, 75, 80, 85 ]
imperial280 = [ 20, 25, 30, 40, 45, 50, 55, 60, 63, 65, 70, 75, 80, 80 ]

imperial = [ 40, 90, 75, 50, 60, 66, 70, 80, 65, 42 ]
extras = list( range( 25, 95, 5 ) )

gears = imperial + extras

headstock = 40

if gears == metric:
leadscrew = fractions.Fraction( 3, 1 ) # WM280 Metric
else:
#leadscrew = fractions.Fraction( 1, 8 ) # WM280 Imperial
leadscrew = fractions.Fraction( 1, 12 ) # WM240 Imperial

# Basic gear chain formula. NB 40 is the fixed headstock gear on some lathes
# 40 A C
# ratio = — . – . – . Leadscrew
# A B D

possibles = []

# calculate the ratio of each permutation and add to the possibles list
for a,b,c,d in itertools.permutations( gears, 4 ):
ha = fractions.Fraction( headstock, a )
ab = fractions.Fraction( a, b )
cd = fractions.Fraction( c, d )
ratio = ha * ab * cd * leadscrew
possibles.append( (a,b,c,d,ratio) )

# Remove duplicates by converting the possibles List to a Set
possibles = set( possibles )

# Sort the set of possibles by ratio
possibles = sorted( possibles, key=lambda possibles : possibles[4] )

# Output the results
print( "{:2s} {:2s} {:2s} {:2s} {:^8s} {:^6s} {:^6s}".
format("A","B","C","D","ratio","metric", "tpi&quot)

for a,b,c,d,r in possibles:
if gears == metric:
print( "{:2d} {:2d} {:2d} {:2d} {:^8s} {:6.4g} {:6.4g}".
format(a, b, c, d, str(r), float(r), float(r) * 25.4 ))
else:
print( "{:2d} {:2d} {:2d} {:2d} {:^8s} {:6.4f} {:6.4g}".
format(a, b, c, d, str(r), 25.4 * float(r), 1/float(r) ))

[JasonBModerator @jasonb]

Thats a long list Dave!

It may be a bit shorter if you could omit any gear trains that use two of the same gear as Bill only has one of each as far as I can see.

J

[SillyOldDufferModerator @sillyoldduffer]

Posted by JasonB on 17/10/2016 20:10:58:

Thats a long list Dave!

It may be a bit shorter if you could omit any gear trains that use two of the same gear as Bill only has one of each as far as I can see.

 

J

Yes, and it would be even longer if I knew how just many 'spares' Bill has! Of course many of the possibilities are probably useless, and listing combinations like 60 60 60 60 would be a fat lot of pointless. Good job the list doesn't need to be printed on paper, or calculated manually.

I intend to simplify the list for use with my WM280 by eliminating 'odd' values and superfluous duplicates. There may also be gear combinations that won't physically fit into the banjo.

One thing has already made the exercise worth it. My manual doesn't give a combination for producing metric 0.7 threads. Luckily the program suggests combinations for 1.4 from which 0.7 is easily derived using the permanent gearbox.

Upwards and onwards,

Dave

 

 

Edited By SillyOldDuffer on 17/10/2016 20:56:59

[Brian WoodParticipant @brianwood45127]

Hello Dave,

​As you can see, I am still taking some interest in the outcome of this thread. With the advantage of the chart that Bill has provided I can understand things at last, although there is no mention of the further multiplier that Jason talked about; maybe that is a feature of larger versions of the lathe.

​Working out Bill's values gives a result of 24.582 tpi (0.0407 inches pitch and an equally useless 1.034 mm pitch) for a 12 tpi leadscrew.

The same figures give a pitch of 0.9763 mm which is 26.016 tpi from a 2 mm pitch leadscrew. Bill has clearly got those figures off the metric machine.

Regards
​Brian

[Bill AndrewsParticipant @billandrews30971]

Good morning Bazyle Thanks for your post of the 14th. I had reached the 60/30 stage myself but from there I couldn't make it work. It didn't once occur to me to place a 40 on the leadscrew. I've not had time this weekend to try out any of the ideas but I'll try to get to it today. I'll keep you posted.

Thanks again to everyone, Rgds Bill.

[HopperParticipant @hopper]

Posted by Bill Andrews on 17/10/2016 17:57:01:

Hi All,

Please find a link to the image for a thread and feeding table for lathe (WM240).

https://fnjrha-ch3302.files.1drv.com/y3mykzPYkNjT6YIYd_GiS9YiTeILB_JmQnPIzuizD-qGRWdE7vc5EzzoqMHsA1hTw65VSRi7Odfbgko2ubumlBJ9drIhmXr5svGmjrJBdq5zJ64SvIczrB_kHydkfXC_3Dvdfr9FRX5mEZD4Dspl0IN1cA2k7t81s8-W8AUktd_F9M/SCAN0001.gif?psid=1

Hopefully, this will provide context.

Regards,

Bill

 

 

Edited By JasonB on 17/10/2016 18:24:16

So, what does gear E engage with in this train? Is there another gear on the end of the leadscrew that engages with gear E? That would need to be entered into the calculation wouldn't it?

Or is it just a place-holder for non-compound gear trains? It would seem to be, as the train for cutting 12tpi is charted as 40-x-x-40, giving a 1:1 ratio for 12 tpi.  Likewise, 40-x-x-80 gives 24 tpi.  The first 40 of course being the fixed gear on the head stock and x-x being idlers of whatever size fills the gap and totally irrelevant to the ratio.

So it seems you should be able to calculate any gear train by the conventional method, using 40 as the headstock gear in all cases. Shouldn't be a problem should it?

+1 on the 52T gear being a slip of the pen for cutting 26TPI.

According to my favorite calculator a 55 in its place will give you 26.000TPI.

A	B	C	D	Thread Pitch	Percent Error	Error in 1" of Thread
40	52	33	55	26.000 TPI	0.000%	0.0000 in
40	55	33	52	26.000 TPI	0.000%	0.0000 in

Where

A = Headstock spindle gear. B and C = two gears compounded on one stud. D = leadscrew gear.

You can then add whatever idlers are needed to bridge the gaps in the train. Including that fixed second 40T gear that runs up against the the 40T headstock spindle gear and make no difference to ratio calculations.

Edited By Hopper on 18/10/2016 13:11:49

[SillyOldDufferModerator @sillyoldduffer]

Posted by Brian Wood on 18/10/2016 11:16:01:

Hello Dave,

​As you can see, I am still taking some interest in the outcome of this thread. With the advantage of the chart that Bill has provided I can understand things at last, although there is no mention of the further multiplier that Jason talked about; maybe that is a feature of larger versions of the lathe.

​Working out Bill's values gives a result of 24.582 tpi (0.0407 inches pitch and an equally useless 1.034 mm pitch) for a 12 tpi leadscrew.

The same figures give a pitch of 0.9763 mm which is 26.016 tpi from a 2 mm pitch leadscrew. Bill has clearly got those figures off the metric machine.

Regards
​Brian

Hi Brian,

I think we all got confused with the unusual arrangement at the headstock of this lathe.

Quite a lot of lathes, including mine, have a fixed 40t gear on the headstock that has to be taken account when calculating the gear ratios. Bill's lathe has an extra stud mounted 40t gear between the headstock and the banjo. I had to play with the numbers to get my head round it.

The good news is that the extra gear doesn't alter the ratios – it's just an idler. I guess it's only there to suit the layout of the gear chain on that particular model.

Jason was referring to the built in gearbox that many of the bigger members of this lathe family have: it adds 1:2, 1:1 and 2:1 to whatever the gear-chain is producing. The WM240 doesn't seem to have it.

Only Bill can explain where the pencilled numbers for 26tpi came from. It may be a mistake, or as you suggest, it's a metric approximation.

Bill's made himself loads of extra gears for his lathe and in consequence my program churned out a raft of possibilities for 26 tpi (The list is from approx Page 263 of the 916 page pdf! )

...
66 80 60 65   1/26   0.9769     26
25 40 30 65   1/26   0.9769     26
35 65 30 40   1/26   0.9769     26
42 40 30 65   1/26   0.9769     26
90 80 60 65   1/26   0.9769     26
35 80 60 65   1/26   0.9769     26
40 80 60 65   1/26   0.9769     26
90 40 30 65   1/26   0.9769     26
55 65 30 40   1/26   0.9769     26
42 65 45 60   1/26   0.9769     26
40 60 45 65   1/26   0.9769     26
55 80 60 65   1/26   0.9769     26
90 65 60 80   1/26   0.9769     26
45 65 30 40   1/26   0.9769     26
42 65 30 40   1/26   0.9769     26
25 80 60 65   1/26   0.9769     26
55 65 45 60   1/26   0.9769     26
66 40 30 65   1/26   0.9769     26
55 60 45 65   1/26   0.9769     26
60 60 45 65   1/26   0.9769     26
60 65 45 60   1/26   0.9769     26
70 40 30 65   1/26   0.9769     26
45 80 60 65   1/26   0.9769     26
50 65 60 80   1/26   0.9769     26
50 65 45 60   1/26   0.9769     26
35 65 60 80   1/26   0.9769     26
66 60 45 65   1/26   0.9769     26
66 65 60 80   1/26   0.9769     26
75 65 60 80   1/26   0.9769     26
90 60 45 65   1/26   0.9769     26
55 65 60 80   1/26   0.9769     26
25 65 45 60   1/26   0.9769     26
80 65 45 60   1/26   0.9769     26
70 80 60 65   1/26   0.9769     26
70 65 60 80   1/26   0.9769     26
60 40 30 65   1/26   0.9769     26
...

Spoilt for choice apparently although I don't know how many of the combinations will physically fit into Bill's lathe.

I see the formula I used got mangled in the formatting of an earlier post. It is:

40   A    C   1
—  x  –  x –  x –  = ratio
A     B    D   12

edit: still mangled!

I've also noticed that in typing up my program I left out a few of Bill's gears. I'll put them in and generate an even longer list of combinations.

Nothing is ever easy is it…

Dave

Edited By SillyOldDuffer on 18/10/2016 13:06:46

Edited By SillyOldDuffer on 18/10/2016 13:08:24

[JasonBModerator @jasonb]

Hopper Gear E and F are both positions on the leadscrew, depending on the train one or the other will have a spacer so they are really the last driven gear.

Dave, when you have got the chart for the 280 done I would be interested in a copy for use on myown 280.

[SillyOldDufferModerator @sillyoldduffer]

Posted by JasonB on 18/10/2016 13:26:08:

…

Dave, when you have got the chart for the 280 done I would be interested in a copy for use on myown 280.

No problem, I'll put a copy in the dropbox folder when it's ready.

I'm metric, do you need imperial?

Dave

[Brian WoodParticipant @brianwood45127]

Hello Bill,

​It's an impressive list, but I am willing to bet you will find many duplicates or rearrangements in it; you are also very likely to find that some of the choices may suit the mathematics but could prove impossible to set up practically.

​Things like wheels not reaching each other, big wheels fouling stud positions and so on. All of these will allow a heavy cull to be made and leave a central core of working values that can be assembled, meshed as required and capable of producing the desired result.

​The next one to list will be for the metric version of the same lathe.

Regards
Brian

[JasonBModerator @jasonb]

Posted by SillyOldDuffer on 18/10/2016 13:42:48:

I'm metric, do you need imperial?

Dave

If it is not too much trouble I have an imperial machine 8tpi leadscrew, set of gears in 5T steps 25 to 80 and a 63T

[SillyOldDufferModerator @sillyoldduffer]

Posted by JasonB on 18/10/2016 18:25:36:

Posted by SillyOldDuffer on 18/10/2016 13:42:48:

I'm metric, do you need imperial?

Dave

If it is not too much trouble I have an imperial machine 8tpi leadscrew, set of gears in 5T steps 25 to 80 and a 63T

No problem. I'll put up a link when it's ready.

Dave

[SillyOldDufferModerator @sillyoldduffer]

Jason,

This link should take you to a folder containing three versions of the table for your lathe:

• wm280jason.txt (raw data)
• wm280jason.odt (open document text)
• wm280jason.pdf (pdf)

My 280 manual suggests the imperial version has a 20t and no 35t. Let me know if the gear list is wrong, it doesn't take long to add or delete them.

Dave

[JasonBModerator @jasonb]

Thatnks Dave and you are almost right, exact set of gears now that I have checked are:

20, 25, 30, 40, 45, 50, 55, 60, 63, 70, 75, 80, 80 (no 35 or 65)

[SillyOldDufferModerator @sillyoldduffer]

OK Jason, I'll re-run it tomorrow morning.

[Thor 🇳🇴Participant @thor]

Hi Dave,

Any chance of you compiling a table for the metric version of the 280, and supplying a link?

Thor

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