Geometry of woodturning

[Frank&Earnest]

One of the things I learnt in primary school is that "mathematics is no opinion". All the woodturning books I have seen describe the process but do not define it in geometrical terms. Plenty of opinions and few demonstrable facts.

It is understable that the recent commercial books aim at entertaining rather than educating, and a TAFE booklet I have is quite basic, but it seems reasonable to expect that an industrial process used extensively up until the first half of last century would have attracted some analytical study, probably long forgotten now.

Does anybody know of any source of this nature? (Does anybody else care? :wink: )

[hughie]

Hmm, not a lot around as you say.



Rob Wallace, Woodturner Info | Facebook (http://www.facebook.com/pages/Rob-Wallace-Woodturner/233605240761?v=info)
https://www.lylejamieson.com/tools/documents/AAWArticle-FearFactor-Winter06.pdf
Tips (http://woodturner1.net/Curt2010/Tips.html) [at bottom of page]

[groverwa]

If you are referring to the Golden Mean there is a start to the maths side of it at Golden ratio - Wikipedia, the free encyclopedia (http://en.wikipedia.org/wiki/Golden_ratio) and the Golden Angle at Golden angle - Wikipedia, the free encyclopedia (http://en.wikipedia.org/wiki/Golden_angle)

Hope this helps
Mike

[Frank&Earnest]

Thanks Mike, it has helped... to make me realise that I was not clear at all.

What I meant is an explanation of how a blade of any particular shape cuts depending on the angle it is presented to the surfaces of the wood cylinder and why.

Experienced woodturners would find "how" empyrically for each blade they have used for a long enough time, but because there are endless variations of shape and each woodturner has specific preferences, there are endless discussions because the "why" is not known in a systematic way.

I have a gut feeling that such an explanation, if it was ever developed, is now lost in the mist of the ages.

And I would bet at even better odds that there is not much interest in it anyway, because anybody can become proficient enough in a few tools to get reasonable results without needing to know whether the same results would have been obtained more effectively with different tools. As said, you can turn with a sharpened shovel. And probably become quite expert at using it, I suppose.

But I look forward to being proved wrong by the umpteen thousand members of this forum.

[colhu]

Hi all

With my (old) Mechanical Engineer's hat on, I would have to reckon there was some basic physics at work when we are playing with different shapes and angles of cutting edges.

As an obvious example, it is easy to see the difference in the quality of cut, and the forces involved on the tool tip, between a skew used in planing mode and in scraping mode.

Nearly 40 years ago I did my undergraduate thesis on forces involved in metal machining, based on different tool angles etc. Obviously in metal machining, optimizing cutting forces saves time and money. I've never had any reason to go looking for people who might have studied similar things in wood machining, but I would imagine the designers of router cutters would have looked at it.

Maybe I'll spend some time thinking about it ..... then again, maybe I won't.

cheers, Colin

[Frank&Earnest]

That's it Colin. Now that you have shown your hand, I know whom I am going to pester to test my theories! :D

[bookend]

Mike Darlow's books like The Fundamentals of Woodturning go into the science of cutting more than any other books I've seen. He seems to have a love of the technical elements of turning, which bores some people witless. :no:

I like it anyway. :D

[Frank&Earnest]

Mike Darlow's books like The Fundamentals of Woodturning go into the science of cutting more than any other books I've seen. He seems to have a love of the technical elements of turning, which bores some people witless. :no:

I like it anyway. :D

True, I have his "Woodturning Methods" and agree that he goes in some technical detail. Still not the sort of thing done for metal machining, as Colin was saying. Maybe the technology was already obsolete before the capacity to document it had reached an appropriate level. After all we do not have manuals for pyramid building!. :D

BTW, Colin, am I underestimating the complexity of such an analysis, if I say that the principles of solid geometry and physics involved do not exceed what most people would have picked up in high school?

[rsser]

What are we talking about? Cutting angle, clearance angle, cutting edge support etc?

+1 to Darlow's Fundamentals for a basic treatment.

The flatware folk can also shed some light; eg. Hoadley's type 2 and 3 chips and how and why you get them.

[Frank&Earnest]

Thanks Ern, yes, that's what we are talking about.

Quoting from Hoadley:

"The way in which a sharp blade interacts with wood to form a chip or shaving is classified using a system developed in the 1950s by Norman Franz for his doctoral thesis on machining wood. Dr. Franz described chip Types I to III. Later research by William McKenzie described an additional Type 0 chip.
The only account I have been able to find of their research is in Appendix I of Leonard Lee’s book The Complete Guide to Sharpening"

is evidence that some research of this kind was done and is now difficult to retrieve. . Hoadley picked up a few relevant concepts for his testing of planes. Range of variables: thickness of the blade, angle of the bevel, angle of the blade, direction of the grain, hardness of the wood. In woodturning there would be other variables: angle blade/ direction of rotation, direction of rotation of the grain. All of this for each one of the dozens of blade shapes, but for simplification let's say just straight or curved.

Will try to put my hands on the book you recommend to see how much is covered.

[artme]

The beginnings of another philosphical dissertation.!!

I think Darlow's books are excellent and good enough to work your way from his beginnings to a knowledge and technique of your own that will only come from experience and practice.

To in anyway compare this sort of work with what happens in metalwork is a bit eronious (spelling?).

Metals of known composition have known properties and are easil scientifically tested for the ideal cutting angles and speeds etc,

Timber is a different kettle of fish (&chips).Timber is mighty variable, even within the species. The only thing we can aim for, at best, is a line of best fit approach. I doubt the Europeans had Our hardwoods in mind when they drew up general conclusions as to what did and didn't work.

Still, it's an interesting - albeit esoteric - diversion.

[NeilS]

The Science and Engineering of Cutting, By Antony Atkins (http://books.google.com/books?id=sl3imKj8258C&printsec=frontcover&dq=The+Science+and+Engineering+of+Cutting:+The+Mechanics+and+Processes+of+...++By+Antony+Atkins&source=bl&ots=81DZOm8fSQ&sig=tnSAeee-Jujnm5O4vKXvTDQY32A&hl=en&ei=_qoQTN6fONqDcO-mic8H&sa=X&oi=book_result&ct=result&resnum=1&ved=0CBIQ6AEwAA#v=onepage&q&f=false)

Covers various materials, including wood.

.....

[colhu]

Wow - this discussion is really going to stretch the brain!

I agree our preferred medium is far more variable than metal or plastic, and so is our freehand tool handling technique, compared with tool mounted rigidly in a toolpost and fed via a handwheel or a feedscrew.

But ultimately what we are trying to do is apply enough force to the timber (or metal or plastic) to peel off a layer of the surface. The efficiency of that process is going to depend on the size and shape of the point of contact between the tool and the workpiece and the angle in which the force is applied.

I'm not any kind of expert in this stuff, but things do make more sense to me when I can understand the underlying physics.

I need to go and think about all this some more.

cheers, Colin

[Frank&Earnest]

Thanks guys, we are getting there.

Artme, with these people on board, the interest of the discussion is assured! :)

Neil, getting very close indeed, you are a research powerhouse.

Colin, we are exactly on the same page. :2tsup:

Even if nothing specific to woodturning comes up, with these two sources (Atkins + Darlow) it should be possible to extrapolate a lot that is relevant to it.

For example, test hypothesis #1:

"whatever the shape of the blade, first contact with the wood is one dimensional (at the tangent point) and the cut is bidimensional (along a linear section of the edge)."

[rsser]

As posted elsewhere, we face partic. challenges compared to flatware woodies. With a bowl we are cutting long grain, cross grain and end-grain and mixes of these. With one tool where they might use several or several set-ups. We almost inevitably will be cutting long grain but against the way it lies from time to time as well with resulting tear-out.

Just out of interest last night I was comparing the performance of a fettled Stanley 6 handplane against that of a Veritas bevel-up jointer. Both had A2 blades with both bevel planes polished to 8000 grit and 45* cutting angles. Both mouths were wide open to simulate a turning tool.

What was surprising was that cutting against long grain both tools performed well, the Stanley leaving visible but really rather minor tear-out in the early growth sections. At a guess there are two reasons for this: the blades were far sharper than the tools most turners use and the speed was crawling pace by comparison. The very small blade projection may also be a factor.

Anyway, I only offer this tale to indicate that while the geometry is clearly important there's other factors in the mix.

[rsser]

Just to add, Frank there is some practice wisdom out there about varying the bevel angle to suit particular timbers.

See this link (http://www.woodworkforums.com/f8/turning-qualities-timbers-81048/).

[artme]

Nothing like a bit of empirical research Ern! Good point.

It is interesting in this context to look at how planes such as those made by Terry Gordon perform on tough timbers when used with the blade set at a high cutting angle. The results with a sharp blade are brilliant. Just a question though
:When does cutting become scraping?

How is sheer scraping differently defined to sheer cutting?

Whar influence do cutting tools' metalurgy have one the angles at which they are sharpened and at which they cut most effectively?

So many questions, so few answers.:C

[rsser]

Yes, good questions.

Terry's high angle planes (also Muji, and LN and V. bevel up planes with high cutting angles as well) are designed to lift and break chips on interlocked grain before they can be lifted below the intended cutting line. You can attempt a similar effect with a Stanley if you put say a 10* back bevel on the blade but these blades are prone to flex and don't yield a good finish.

FWIW I regard scraping as a special case of cutting.

Others more expert than me will of course provide better opinion.

As for metallurgy, that's a book in itself. At a guess finer particles such as you get with powder metallurgy or cryo treatments provide a finer cutting edge (ie. less jagged with the tips less likely to break off) so more acute bevel angles can be used. That must mean less fibre crushing and earlier fibre severing in the sever/lift process.

[Frank&Earnest]

We almost inevitably will be cutting long grain but against the way it lies from time to time as well with resulting tear-out.
...
...while the geometry is clearly important there's other factors in the mix.

I am calling geometry also finding the angle between the blade and the direction of the grain - which changes at any given point of a curve and at opposite points of the rotation if turning with the grain. Hope this does not create problems of semantics...:)

Artme's question is an example of the things I would like to settle vith a definition: for me, cutting becomes scraping when the angle between the upper side of the blade and the surface of the wood becomes smaller than 90 degrees. There can be 1000s of descriptions, but this definition, if correct, should be true for all of them. And would deny that scraping "is a special case of cutting" because it means that its purpose is to break and burnish the fibres, not to cut them.

[NeilS]

FWIW I regard scraping as a special case of cutting.



Agreed, it's a scraping cut.



.... cutting becomes scraping when the angle between the upper side of the blade and the surface of the wood becomes smaller than 90 degrees.

Agreed, in a scraping cut the axis of the cutting face of the blade is presented at 90<meta http-equiv="Content-Type" content="text/html; charset=utf-8"><meta name="ProgId" content="Word.Document"><meta name="Generator" content="Microsoft Word 9"><meta name="Originator" content="Microsoft Word 9"><link rel="File-List" href="file:///C:/DOCUME%7E1/BRON%26N%7E1/LOCALS%7E1/Temp/msoclip1/01/clip_filelist.xml"><!--[if gte mso 9]><xml> <w:WordDocument> <w:View>Normal</w:View> <w:Zoom>0</w:Zoom> <w:DoNotOptimizeForBrowser/> </w:WordDocument> </xml><![endif]--><style> <!-- /* Style Definitions */ p.MsoNormal, li.MsoNormal, div.MsoNormal {mso-style-parent:""; margin:0cm; margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:12.0pt; font-family:"Times New Roman"; mso-fareast-font-family:"Times New Roman";} @page Section1 {size:612.0pt 792.0pt; margin:72.0pt 90.0pt 72.0pt 90.0pt; mso-header-margin:36.0pt; mso-footer-margin:36.0pt; mso-paper-source:0;} div.Section1 {page:Section1;} --> </style>° or less to the tangent that is formed at the point of blade/wood contact, where the tangent is aligned to the direction of blade travel. Skewing the face of the blade skews the tangent away from the direction of blade travel and, in effect, reduces the cutting angle without changing the axis angle.

Perhaps an accurate definition but not one that I would throw at a novice woodturner to confuse them or that useful for an experienced turner who knows all this intuitively from experience without thinking about it in this way, unless they were into designing their own woodturning tools....:U

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[Frank&Earnest]

No argument with your assessment of usefulness, Neil, I believe I said that much myself, using different words... :U

I am indeed confused by what you deem to be an expansion of my definition, though: whatever the woodturning skill of the reader :D the complexity of language would be daunting for many like me, who are still unsure about the correct terminology. Thanks for telling me that the "upper side" is actually the "cutting face", for example.

For "axis of the blade" I assume you are referring to the axis of symmetry, that is in common language the centre line along the shaft of the tool. If that is the case, there is a piece missing, both in your and my previous imprecise definition: the direction of such line in relation to the vertical and horizontal axis. I understand your definition of the angle that has to be <90o as the angle you hold the tool in relation to the (horizontal) axis of rotation of the lathe. Which to me is still cutting (which explains why you also consider it cutting) unless the definition of scraping is met: that the angle formed by the axis of the blade (whatever its orientation relative to the horizontal axis) and the vertical axis delineated by the circumference or the base of the rotating cylinder at the tangent point is <90 degrees.

In summary, thank you for teaching me the correct terminology and helping me refining the definition... but are we still agreed now? :)

[NeilS]

I am indeed confused by what you deem to be an expansion of my definition, though: whatever the woodturning skill of the reader :D the complexity of language would be daunting for many like me, who are still unsure about the correct terminology. Thanks for telling me that the "upper side" is actually the "cutting face", for example.

I have no wish to get into a terminology war, just using the most commonly used terms that I'm familiar with to describe what I understand to be happening.

For "axis of the blade" I assume you are referring to the axis of symmetry, that is in common language the centre line along the shaft of the tool.

Yes

If that is the case, there is a piece missing, both in your and my previous imprecise definition: the direction of such line in relation to the vertical and horizontal axis. I understand your definition of the angle that has to be <90o as the angle you hold the tool in relation to the (horizontal) axis of rotation of the lathe.

No, and that has highlighted a flaw in my definition. Oh, why in the heck did I let myself get into this.... :doh:

The phrase 'blade travel' can be interpreted in two ways. A bad thing in any definition! I was referring to the direction the wood travels past the blade, as it does in woodturning. A more precise way to say this is 'where the tangent is aligned to the direction of wood rotation'.

So, not <90 to the axis, but <90 to the tangent aligned to the rotation of the wood.

Sorry about causing confusion there.

... but are we still agreed now? :)

Yes, I think so, if we take the following words from your second last paragraph.

.... the angle formed by the axis of the blade... and the circumference .... of rotating... at the tangent point is <90 degrees.

Think I might take a Bex and have a good lie down the next time I get the urge to get into definitions .....:U

.....

[Frank&Earnest]

Yes, I think so, if we take the following words from your second last paragraph.

.... the angle formed by the axis of the blade... and the circumference .... of rotating... at the tangent point is <90 degrees.

Think I might take a Bex and have a good lie down the next time I get the urge to get into definitions .....:U

.....

Sorry to have caused you such discomfort, Neil, your contribution to this discussion is highly valuable. Next time we meet I'll offer you some more enjoyable liquid relaxant than Bex. :;

So Ern, given this definition, do you still think that scraping is a form of cutting?

[rsser]

Frank, I don't care much whether it is or isn't. There's a place for it, like cutting, which is to remove stock and to do so with maximum efficiency and minimal adverse effects.

Seems to me we've got a bit off topic.

Re geometry, there's the what and the why.

I think I have half a grip on the what and much less on the why.

Think I still have your email address Frank and will send you a scan of the what, acc. to one leading maker of bevel shaping machines ;-}

[Frank&Earnest]

Thanks Ern. With that and the books there should be more than enough to chew.

[Frank&Earnest]

My heartfelt thanks, Bookend, Rsser and NeilS, for your advice.

I know it is not the bloke's way, but in these two months I did read the instructions. :D
First of all, this exercise has proven the real value of the forum: to point out the right sources, not to waffle about opinions. Had I known before about Mike Darlow's book, I would not have had to reinvent the definition of scraping, (the good thing is at least that I did not make a fool of myself, for once,:D) I would just have answered Artme's question with: "as Mike Darlow says on page 42..."

This is indeed the most technical of the books addressed to the hobby woodturning public that I have seen, it answers most of the questions. The single point that I have found most helpful for my understanding is not there, though, but at least the practical descriptions of the book confirm its validity, so I feel confident expressing it.

What helped me making sense of how blade and wood interact is remembering a fact learned in primary school: that two lines intersect in one point. Whatever the shape of the tool and the wood, the circumference of the rotating piece and the edge of the tool are lines. Knowing where the point of contact is goes a long way towards understanding how the tool behaves: for example why the points of the skew or the wing of a gouge are harder to control than the axial centre of the tool.

Hopefully I will be able to use my recent learning to explain my theories about tool design... :;

[NeilS]

Glad to hear you have sorted that out, Frank.

I'll get you to sort me out as well on all of that, if you can, the next time we get together...:U

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[Frank&Earnest]

Glad to do that, Neil. Will be a good opportunity to swap observations about our own Dunning–Kruger effects...:U

[artme]

As for Mssers Dunning and Kruger I have no difficulties at all!!

I understand cognition and metacognition very well Just can't figure some thing out!:D:whistling2::whistling2::rolleyes:

[NeilS]

glad to do that, neil. Will be a good opportunity to swap observations about our own dunning–kruger effects...:u


as for mssers dunning and kruger i have no difficulties at all!!

I understand cognition and metacognition very well just can't figure some thing out!:d:whistling2::whistling2::rolleyes:

:d

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[robo hippy]

Oh, this makes my head hurt!!!!!!!!!!!!!

I don't think there is such a thing as a perfect cutting angle, and/or bevel because there are too many variables. Bevel angle is one thing, how the tool is presented is another. If you drop the handle, you change the angle, as you rotate the tool, you change the angle, similar I guess to what happens when you drive over a speed bump; hit it square on, and you get a bigger bump, hit it from a 45 degree angle, and you get a smaller bump.

Scraping is cutting, as I can get nice long shavings and leave a fair surface, but that quality depends on the particular wood, and grain orientation.

I see no difference between shear cutting and shear scraping, the end result is the same, and can be done with a scraper or a gouge.

robo hippy

[NeilS]

..... similar I guess to what happens when you drive over a speed bump; hit it square on, and you get a bigger bump, hit it from a 45 degree angle, and you get a smaller bump.



Must remember that one for the next time I try to explain shear cuts to someone.

I've often used the analogy of how you can use a wood plane with skew, but not everyone who has used a plane in that way understand what they are doing is reducing the effective cutting angle of the blade by skewing the plane.

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[Frank&Earnest]

Darlow page 42.:U:U:U