That's one of my favorite Wisdoms.
The more you know, the more you know you don't know.
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King 1440 and Craftex Threading
- Thread starter cuslog
- Start date
That's one of my favorite Wisdoms.
The more you know, the more you know you don't know.
You have no idea...
I taxed my brain and came to the conclusion that you are exactly right Rudy, thank you for doing the math for me. I was able to reverse engineer your conclusion and learned how to come to the same conclusion. It just took me a lot longer!
I have done some research about gear profiles and found that these are module 1.25 profile. They are 10mm wide and have a smaller diameter 10mm wide hub and a 19mm bore with a 5mm keyway. I can buy semi finished gears from Madler North America for about $80USD including shipping. The finish the bore and keyway when they arrive.
Or I could order a #6 module 1.25 gear cutter and attempt to make them myself. I've never made a gear and it sounds like a fun challenge so the cutter is ordered and I have lots of 4140 to make them from.
Woooo Hoooo. That's what I was hoping you would do! Please keep us in the loop so we all know how it goes! I suspect that there are a few threading/feed gears in my future too....
DPittman
Ultra Member
That's why I love being so damn ignorant, it makes me feel like a genius.
@John Conroy Is this new gear do that you can thread a specific size not currently available? Only reason I ask is I had some similar thoughts to achieve certain sizes, but quickly ran into the issue that the tooth count (pitch diameters) dictate the gear centers. So if the input/output shafts are fixed & is a dimensional mismatch, it requires something like the adjustment sector arm / idler gear, sub-assembly, not unlike my current / your old lathe. I'm sure you know all this but just in case. So far I'm batting 4 brain farts over 4 days, I just hope its not spreading LOL
I just assumed that the 120/127 was on a Banjo like mine. How else could you get the three different gears that are called out on that lathe to fit?
It's too late. It's already spread all the way to Ontario......
Ya, this one has been a bit of a ride.
On the plus side, the boss lady has agreed to let me go to the shop to count teeth on my lathe. That's how I chose to describe what I was doing. Her eyes glazed over as I explained why. She quickly decided that isn't exerting myself. Silly girl has no idea what happens once I get my hand into the cookie jar.....
There's tons of room for different size gears and a large range of adjustment.
Mine is quite similar. The drive gear a) turns one to one with the spindle. It can also be reversed or put in neutral. But it is ALWAYS 1:1 with the spindle. Then there is the 120/127 which is on a Banjo for adjustment. Then there is the driven gear b) that provides the input into the quick change gear box. Both a) & b) are on shafts that cannot be moved. As above, the a) gear is spindle output, and the b) gear is gear box input. The location of the 120/127 is adjusted on a Banjo to accommodate all the different gear diameters. In the photo, they are both 60Tooth gears. I marked both of them right on the casting to avoid confusion about which is which.
Not clear in the above photo is the fact that both a) and b) can be moved in or out by using a shaft collar to engage with either the 127 or the 120 gear.
In the photo below, they are both engaged on the 120 gear so the collar is positioned on the side of the gear furthest from the gear box. I've seen these gears with integrated collars, but with so many gears, that didn't make sense on my lathe.
@PeterT & @John Conroy & @RobinHood
As I suggested, I spent some time assessing my own lathe and on that basis I made a few assumptions about yours and created the following complete metric threading chart for your lathe using all the levers and filling in all the empty boxes. It is apparent why some were dropped - they are simply duplicates of others.
I also created a spreadsheet that would fill in the chart for ANY Top and Bottom Gear. It is the far right group of cells in the photo. You simply enter the gear tooth count for the two gears at the top and the spread sheet will calculate the metric thread pitch.
Id appreciate it if you guys could check it over. If you like it, I will create an Imperial Version.
The next logical step is a feed-rate chart. And I suppose one could also create a spreadsheet that will suggest gear combinations to achieve a given thread pitch.
One quick question: Are there any more levers on your lathe besides 1, 2, 3, and 6? What happened to 4 & 5?
As I suggested, I spent some time assessing my own lathe and on that basis I made a few assumptions about yours and created the following complete metric threading chart for your lathe using all the levers and filling in all the empty boxes. It is apparent why some were dropped - they are simply duplicates of others.
I also created a spreadsheet that would fill in the chart for ANY Top and Bottom Gear. It is the far right group of cells in the photo. You simply enter the gear tooth count for the two gears at the top and the spread sheet will calculate the metric thread pitch.
Id appreciate it if you guys could check it over. If you like it, I will create an Imperial Version.
The next logical step is a feed-rate chart. And I suppose one could also create a spreadsheet that will suggest gear combinations to achieve a given thread pitch.
One quick question: Are there any more levers on your lathe besides 1, 2, 3, and 6? What happened to 4 & 5?
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uhhmmm because I wasn't 100% clear if that's where it was being implemented. But maybe I'm selfishly looking at my own lathe. I think this is where I last left off my prior spreadsheet - seeing if any additional useful thread combinations would arise by using one of the common gears packaged with the MET 3mm version. On my 8 TPI lathe the included gears are 30,32,40,46 which allow the suite of IMP & MET threads mentioned. On the 3mm MET lathe the gears are 36,40,42,54,60,66 (which are typically not packaged with IMP lathe). So I just assumed 36T only makes sense for 3mm leadscrew, but may well be a function of the lathe.
Of I did my math right, the 36T does not provide me any missing threads. But that likely isn't John's situation. So rather than assume....
Dabbler
ersatz engineer
I noticesomething missing...
5mm metric coarse the pitch is .8 mm (and metric fine is .7mm) It seems that you cannot cut them on your lathe.... So 5mm is out for you?
Where is the 1/2" coming from? I don't get it.
My own lathe has both 0.8 and 0.7.
The chart I made is for the lathe that is the subject of this thread (King 1440 & Craftex). For that lathe, both those are indeed missing.
However, the proposed new 42 & 36 count gears that Rudy calculated to get the 1.75 pitch would also coincidentally add 0.7 to its capabities. I'm in bed now, but tomorrow I'll figure out what gears would need to be made to be able to cut 0.8 threads.
It's just my crazy brains way of explaining why a 127 tooth gear can be used to convert between metric and imperial.
1/2 inch is exactly equal to 1.27 cm. The 3 digits in 1.27 are 127. That's why a 127 tooth gear can be used to convert exactly between metric and imperial.
There are lots of other ways of explaining why it works. That's just my way. If you prefer other ways to look at it, you wouldn't be alone. My brain isn't wired to think the same way as most normal people. I've been told it's some kind of disease I have......
Nuts, I was hoping you would have the answer of why 127 has magical powers. I'm sure I even read somewhere but its not coming to me.
Everyone has their way of visualizing so I'll throw out my description FWIW. A 3mm pitch leadscrew traverses 0.118"/rev (rounding off). An 8 TPI leadscrew traverses 0.125"/rev. The ratio between them is 1.058. Turns out a gear combination of 127/120 yields exactly the same ratio (yellow shade). The 8 TPI now thinks its metric & metric can now cut imperial.
More generalized, if we happen to have a 10 or 6 TPI pitch, we need different gears, 150 & 90 respectively. But notice we still need 127. Its the marriage councilor between metric & imperial haha
Everyone has their way of visualizing so I'll throw out my description FWIW. A 3mm pitch leadscrew traverses 0.118"/rev (rounding off). An 8 TPI leadscrew traverses 0.125"/rev. The ratio between them is 1.058. Turns out a gear combination of 127/120 yields exactly the same ratio (yellow shade). The 8 TPI now thinks its metric & metric can now cut imperial.
More generalized, if we happen to have a 10 or 6 TPI pitch, we need different gears, 150 & 90 respectively. But notice we still need 127. Its the marriage councilor between metric & imperial haha
127T gear is the smallest number of teeth a gear can have and still give a true IN to MET (or vice versa) conversion. Why? Because 127 is a prime number.
One could use a 254T gear (or any multiple of 127 for that matter) to get a true IN to MET conversion as well - so long as the other gear on the same shaft is also proportionately sized to maintain the ratio.
Problem with a 254T gear: it would be HUGE; most lathes do not have the space required to have such a large gear in the same DP / MOD they use for the other change gears.
Lack of space is also why on some lathes they use an “approximate” IN to MET conversion because it is “close enough” for short threads.
For example, on Colchester Lathes (they patented their ratios!), they use:
6/7 x 8/11 x 12/19 to derive the 50/127 ratio. The error is only +1 unit in 36575 units! [ref: “Screwcutting in the Lathe“ by Martin Cleeve, Workshop Practice Series #3 from Argus Books, Table 5, pg48].
Almost all precision lead screws have a thread pitch error greater than that.
Only jig-borers need to be accurate to +/- one tenth of a thousands per 16 inches of feed [ref: “Holes, Contours and Surfaces” by Richard F. Moore & Frederick C. Victory. The Moore Special Tool Company, Bridgeport, CT.]
So the error in the thread being cut is from the lead screw itself and not the “approximated“ transposing ratio…
Yes there must be something about the minimum 127, but why? I thought about prime numbers, example below. Here I changed the rules, now a 2mm metric vs same 8 TPI.
Our familiar 127 works perfect with 80. But I tried a few random different primes, 67 & 97 for example, it doesn't compute a ratio match. Where's the programming kids when you need them? LOL.
Our familiar 127 works perfect with 80. But I tried a few random different primes, 67 & 97 for example, it doesn't compute a ratio match. Where's the programming kids when you need them? LOL.
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DPittman
Ultra Member
Hmnn makes an electronic lead screw all that more attractive?
I confess I am never sure what you are really asking Peter. That is NOT an insult. It's just recognition that your brain works quite different than mine. A darn good thing most would say. I would certainly agree. But it does mean that someone with a brain like mine is gunna have a problem trying to communicate perfectly with someone else with a brain like yours. And neither one of us is like everyone else! LOL!
Lord help anyone else reading this......
Rudy's explanation isn't the one I use for myself, but it's perfectly correct. But your question to him helps me understand what you are looking for...... I THINK...... LOL!
You are trying to understand the nuances of the 127.
Yes, 127 is a prime number. That means nothing else can be divided into it. In other words, IT IS THE SMALLEST number of integer teeth that can be used to convert between metric and imperial. Please remember that for a few paragraphs as I try to explain the nuances of the magic 127 gear.
To convert inches to metric in a machine, we can only use integer gears. No gear can have 1/2 of a gear or 1/3 of a gear or 2.6 or 1.3333333333 or 7.1 or 25.4. I am being a bit deliberately pedantic here for a reason that will become clear in a few paragraphs. Please bear with me.
Many years ago, the conversion factor between imperial and metric units of length was quite arbitrarily set by international agreement to be 1 inch = 25.4 mm. This is a complete number not an approximation. It's not roughly 25.4. It is exactly 25.4.
I know some will argue with that but please don't. It will not help this discussion to quibble.
If we want to convert a metric distance in mm to an imperial distance in inches, we have to multiply or divide one or the other by 25.4.
All threads - both metric and imperial are expressed in turns per revolution. Metric is a metric (mm between threads) distance per revolution, and imperial is a number of revolutions per Imperial unit of length (TPI or threads per inch). To convert metric threads to imperial threads we can use the following formulas:
mmPitch = 25.4 / TPI
OR
TPI = 25.4 / mmPitch
OR
TPI * mmPitch = 25.4
If our gear train produced 1 mm of movement on the lead screw per revolution (a pitch of 1mm) we would need another gear with 25.4 teeth to get one inch of travel. But we cannot make a gear with 25.4 teeth.
However, we can make one with 254 teeth. Then the 254 tooth gear would result in 10 inches of travel. Then we could use a 10:1 gear ratio to reduce that to 1 inch.
And a 32 tooth gear to get a 32nd, etc etc.
But as Rudy explained, 254 is a very big gear. Fortunately though, 254 is not a prime number. It can be perfectly divided by 2 to get 127. 127 is still a big gear but not a huge one. So, we don't really need a huge 254 tooth gear, instead we can use a smaller more practical 127 tooth gear and a 2:1 ratio to get back to our 254.
Unfortunately, 127 is a prime number so we cannot divide 127 by anything else. Therefore we cannot use a smaller gear than 127 without compromising on the precision of the conversion.
The prime number is not a requirement, it is a result. The simple fact is that the smallest whole number of teeth that can be used to convert between imperial and metric is 127. Once you hit a prime number, you cannot divide by any other smaller whole number - that's the definition of a prime number. In a very real way, the 127 tooth gear really is magic. But not because it is a prime number. It is magic because it is an even multiple of 2.54. No more, no less.
Once the conversion ratio of 2.54 has been introduced via the magic 127 gear, one can use other gear ratios 10:1, 5:1, 1:4, 1:8 etc etc to get anything else.
Note: the 1/2 inch I discussed earlier is just my way of skipping over the need for the 2:1 ratio and going straight to 127 instead of 254. But please forget about that for this discussion unless it helps you too.
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