Metric Threads

I have been assiduously studying the Colchester Bantam manual, whilst I wait for it to arrive Particularly the parts which describe the settings for screw-cutting. Primarily because this is something of which I have no experience at all. The imperial nameplate illustration I understand, I also understand the equation examples for non-standard threads.
What I don't understand is the metric equivalent: which range from 0.5 - 0.6 - 0.75 right through the various increments to 6.0.

Do these figure relate to the pitch of the thread? Or do they relate to the number of pitches contained within one millimetre?
And finally, what are D.P. threads?

TIA
Jack

Jack,

Metric threads are specified by pitch.

D.P. stands for Diametral Pitch ... and relates to [Imperial] gears and WormWheels. A thread made to match such a wheel will inevitably have "threads per inch" that includes Pi. ... Much simpler to express the D.P. that it fits.

Hope that makes sense.

MichaelG.

Metric threads are given as pitch in millimetres.

D.P. threads - are you really sure you want to know

'D.P. threads' are those which engage with a gear wheel of the same D.P. or 'diametric pitch'. D.P. is defined as the 'number of teeth per inch of pitch circle diameter'.

So, for example, a 20 DP gear of any diameter has 20 teeth for every inch of its pitch circle diameter (a circle passing roughly half way through each tooth face used as the base for all gear calculations and is the size that the gear would be if all teh gears in a train were replaced by plain wheels, just touching.

A 40-tooth 20DP gear will have 40 teeth, for example.

How do we make a screw thread to engage with such a gear? (assuming the gear has helical teeth to allow it to engage in line with the screw!) A 20 tooth gear has a 1 inch PCD and therefore a circumference of PI. The pitch of the teeth will therefore be pi/20.

So that's your answer DP threads have a pitch of pi/D.P. and allow threads to be made that will engage with gears. Not a great help as most gears have straight cut teeth and need to engage the screw at its helix angle, and this requires a shorter pitch, which reduces the helix angle requiring a... so it's quite an involve calculation as anyone who reads George Thomas' dividing device for the Myford bull wheel and J.A. Radford's revision of the same will appreciate.

I bet you're really sorry you asked now...

Neil

<and I am praying I got that right because if not the facial egg will be flying thick and fast...>

Edited By Neil Wyatt on 14/07/2014 21:29:51

.

No he's sorry you answered it .

Thank you both - for clarifying the metric thread question.

Neil - thank you also for the explanation of diametric pitch [D.P.]
I shall delve more deeply into this - and source the Thomas & Radford publications.
I'm a retired structural engineer, so physics and maths engage me. [quite sad, I appreciate, but that's the way I'm made I'm afraid]

A 40-tooth gear will have .... er .... well .... 40 teeth

That must be right then. A unanimous agreement !!

To get the DP, just add 2 to the tooth count and divide by the outside diameter (inch)
of the gear. So, 42 divided by 3.49 is 12 etc (jiggle equation as required)

Metric 25.4 / 0.5 = 50.8 TPI (25.4mm / inch) etc

It's just worth adding that Metric Gears & Clock Wheels are expressed in Module

Just like with pitch vs tpi, and litres per Km vs mpg ...

Module is expressed "the other way up" to D.P.

MichaelG.

Edited By Michael Gilligan on 14/07/2014 22:54:22

...........so you can get Module threads as well...................for example a 1 Mod screw has a pitch of about 3.141592653589793238462643 mm

Edited By Bazyle on 14/07/2014 23:54:01

.

Which makes the facility to screw-cut "25.4 DP threads" nice if you can get it.

MichaelG.

Jack: To be precise the pitch on a gear wheel is known as the circular pitch as it is measured on an arc, not a line. If the number of teeth on the gear is an integer then the circular pitch will be irrational.

I think that what Neil is saying about helix angles is that a worm has two pitches. One, the axial pitch is simply the linear distance from one thead to the next along the axis of the worm. The worm also has a normal pitch which is the same, but is taken orthogonal to the thread flanks. The two are related by the cosine of the lead angle. From a practical point of view if the lead angle is less than 15° or so then the errors are small. For example I was refreshing my memory the other night on the maths behind a worm and worm wheel I made last year. The worm is single start and 1/2" axial lead, and pitch. The lead angle is 7.8°, giving a difference between the axial and normal pitches of less than 1%. Cutting DP threads will be an approximation anyway, the accuracy of which depends upon the accuracy of the gear ratio that the designers chose for pi.

Regards,

Andrew

Andrew, can you please show us a picture of a gear with a non-integer number of teeth?

Regards, Frank

(and into which number system falls the c.p. then?)

Edited By Frank.N Storm on 15/07/2014 09:19:33

Somewhere, I have two books which were bequeathed to me by my father. I had no idea why at the time.
Now I'm beginning to understand. I shall have to go through my library and find the Machinery Handbook, at least.

Machinery Handbook 21st Ed. &   Smoley's Metric Four Combined Tables.
Smoley's is well used - by my father and by myself too.

Thank you each for your input. It all helps to provide understanding.

Edited By Jack Foreman 1 on 15/07/2014 09:18:35

I would not worry too much about DP threads,since I started work in 1958 I have only cut one dp thread,that was on my colchester triumph,the lathe was 20 years old when I purchased it and I wondered if this the only dp worm it had ever cut.,though on the triumph its easily selected on the gearbox ie no change wheels,on my master it requires an extra changewheel and these are always missing and I have never seen a spare for sale,have to make one someday. The worm I cut was for a 1930s Petter stationary with a mechanical "calibrator lubricator" the engine must have stood neglected for years as water had got inside it and was level to the horizontal axis of the worm and it had corroded the bottom half of the steel worm completely and I was presented with half a worm by a customer,"can you make one of these?". I would think that if the gear mating with the worm was thin,similar to a Meccano worm and the larger gears,there would be no need for pitch correction.