Slewing the Compound

[martyn nutlandParticipant @martynnutland79495]

I wonder if someone could explain in very very simple arithmetical terms how this works.

I wanted to take some very light cuts on my lathe to get a male and female spigot to mate fairly snugly.

I looked up such icons of knowledgeability on the internet as Tubal Cain and they tell you to incline the compound to the bed axis by x degrees – 30 or 60 in some cases 5.75 – 6.00 says one guru.

This then reduces (by half?) the amount the tool is advanced by the handle and as measured on the vernier.

I've puzzled endlessly how this calculation works mathematically and am at a total loss!

Martyn

[martyn nutlandParticipant @martynnutland79495]

What’s the Maths?

[Les Jones 1Participant @lesjones1]

Hi Martyn,
The direction of travel of the top slide is the hypotenuse of a triangle. If we measure the angle between this and the axis of the lathe (0 Deg when it is parallel to the axis.) and multiply the amount the top slide moves by the sine of the angle it gives the effective distance moved at right angles to the axis. As the sine of 30 Deg. is 0.5 then if the top slide moves 10 thou then the component of this at right angles to the axis is is 5 thou. (So you would reduce the diameter by 10 thou.) If you only want the tool to move in by 1/4 of the amount the top slide moves the look up the angle who's sign is 0.25 this turns out to be 14.477 Deg. They do teach useful stuff a school even if you don't think so at the time.

Les.

[JasonBModerator @jasonb]

And a sketch to illustrate what Les has just said

[pgk pgkParticipant @pgkpgk17461]

If you consider a right angle triangle where one side is parallel to the centreline of the lathe, the base side is the direction of the cross-slide and the hypotenuse is the angle of the compound then extending that hypotenuse at the apex and dropping a new perpendicular to the base has moved the base towards the lathe centreline… but by less than the distance the hypotenuse was extended.

Play with simple trig and you will see how that changes for a change of angle between base and hypotenuse.

If we play with very simple 3,4,5 triangles and change that hypotenuse from 5 to 10 then it has increased 5 units for a 3 unit change on base distance (from 3 to 6). in the case of a 3,4,5 triangle the angle between base and hypotenuse is just over 53deg.

In the case of a 60deg triangle all sides are equilateral of course.. say 10 units. To turn that into a rt triangle we cut it in half. Hypotenuse remains 10, base becomes 5

Now use an equilateral triangle of say 12 units and do the same…hypotenuse remains 12 and base becomes 6

So for 2 units increase in cross slide you have 1 unit increase towards lathe centreline

[martyn nutlandParticipant @martynnutland79495]

Yes…now I think I see, or I will when I re-read with a piece of paper and pencil.

Many, many thanks for elucidating; and in advance to anyone else who explains.

And yes, I do think we learn useful things at school, although it's a pity no one tells us at the time why that might be so. However, I doubt whether my aging maths mistress knew this theory was applicable to lathes!

Thanks again.

Martyn

[Michael GilliganParticipant @michaelgilligan61133]

Posted by martyn nutland on 02/06/2015 08:16:30:

… we learn useful things at school, although it's a pity no one tells us at the time why that might be so.

.

Martyn,

That has to be my "Quote of the Day"

… You are absolutely right.

MichaelG.

[GarryCParticipant @garryc]

Hi Martyn

We were lucky through school to have an ex wales rugby coach for maths teacher, not only did he teach me maths but also how to stay in one piece on the rugby field, great days.. I remember him as one of the best teachers in the school..

If you use an iPhone Martyn you may be interested in the free app that I use **LINK** – although I've found understanding the number theory is one thing – I've not yet been able to put it into practice very well..! .. Soon I think..

Hope it may be of help, I've found it great, very quick and easy to use – you just enter the numbers..

Regards

Garry

[Martin KyteParticipant @martinkyte99762]

For small angles the set over angle you want is 1rad x dividing factor. 2Pi rads in 360deg so a radian is 57.29deg.

If you want 10 thou travel on the topslide to 1 thou on the radius you need 57.29/10 which is 5.729 degrees. (somewhere around 6 will do)

1:20 is 2.8 degrees

To simplify and so you can remember it's Heinz 57 x 10 for tenths ( one thou on the cross slide dial is a tenth on the radius)

regards Martin

[Bob Brown 1Participant @bobbrown1]

It tends to all fall down when you are working to a shoulder and using a saddle stop as every time you advance the tool in you also advance the tool along. That said I have a micrometer saddle stop so I suppose it would be possible to adjust it as the tool is moved in but could get very confusing.

Bob

[Mike PooleParticipant @mikepoole82104]

I have found that the most inspirational teachers I have had are ones who have worked in industry, I went to a grammer school where all the teachers had degrees from top 10 universities except for the metalwork teacher. He was a great guy who had started work aged 14 hand sanding buses in a factory, I still have the passion from those lessons 47 years ago. At tech college I had a lecturer for electronics who had worked in industry, his anecdotes about the practical applications brought the subject alive and made his lectures ones not to miss. Trigonometry has been the most useful thing I ever learned in maths, finding almost daily tasks for it in the workshop. I think it would be a very good thing if the teaching profession were able to attract more people from industry or business to inspire the young with their experience.

Mike

[KWILParticipant @kwil]

This should also apply to politicians (of all parties) If they had a real job (or two) before entering politics they would appreciate the real world better. PPE should not be a degree to enable you to work in politics.

Edited By KWIL on 02/06/2015 11:24:04

[HopperParticipant @hopper]

If you want best control over tight clearances, set the topslide at 6 degrees (or just under).

That way, the geometry works out that every .001" graduation on the topslide collar moves the tool inwards by one tenth, or .0001".

Depends on what lathe you are using and its condition, though. Generally on a good lathe, you should be able to machine a spigot to within half a thou or less using the conventional cross slide in the normal manner. Trick with spigots is to machine the hole first, then turn the OD of the male spigot to fit the hole. Machining the OD is easier to do accurately than machining the ID.

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