Western saws cut, and ugly teeth do smile, but japanese are better and we know it. Why? The secret is as usual a fragile balance between two opposite forces, and japanese craftsmen know to walk on the tightrope.
Let's start with a western saw pattern, projected onto two dimensions for the sake of simplicity.
The gullet space is where the saw dust goes once you start cutting, so the more space there is, the more you can cut with each tooth.
Say we instead of using a triangular file to sharpen, as in western world, we use one file for each side of the tooth, as is done in developed places like Chile.
That looks more like our mountains here. Which is better in the sense that gives you more space where to put the sawdust so you can cut more with each tooth. But, here starts the contradictory principle to play, as you make the teeth pointy they become also weaker. The strength of the material is proportional to the area (volume in 3D) of the teeth, so as you increase the angle they become weaker... something you don't want in your mouth, weak teeth.
Not clear? Well, let's solve the plane stress relation for a fixed material with different geometries and see if you get it. (Red is the deformed geometry, black the relaxed position)
I'm applying a force on the left facet of the teeth, always the same force, and checking the deformation of the teeth. As the teeth becomes more pointy, they also deform more in the tip. Eventually they can reach their breaking point and pluff. Cappicci?
So what you do? You can change the geometry of the teeth such that they are strong yet have plenty of room for the sawdust. How you do that?
Indeed, you create a third facet that increases the strength of the teeth since it supports it from the back, that's where the force of the wood on the teeth is going.
Like this:
Without the third top facet the tooth become weak and useless.
Now, since we have a strong tooth and plenty of space to put the sawdust, we can put more teeth per inch and remove the same amount of sawdust as the western pattern, only faster and easier.
This is maybe an exaggeration but you get the idea, as long as you have enough gullet space you can put more teeth and cut faster.
did you like that fem plot? Me too, I'm coding later a japanese teeth pattern and show you why it's better to cut chumasaru rake and what's the best angle for the top facet. And maybe in a few days we go 3D.
I will continue dwelling in saw sharpening for a while since it's been too long that I promised to make a write up and send a pdf of it to the guys who took the class in NL. Sorry for the delay but I was busy learning how to do this FEM analysis, amongst other things.
Very fun stuff Sebastian!
ReplyDeleteI needed to do some reading to familiarize myself with the basic concept of finite element analysis because I've seen those little stress pattern triangles before, and as expected, it's light years over my head mathematically, haha. No surprise there. I love this as a graphic tool to explain complex 3-dimensional deformations, and I would get a kick out of seeing you model the deformation caused to a saw plate getting kinked.....say, 2x compressive force, 0.75x lateral force, one end of the surface contained (ie: stuck in the kerf). I can see it in my head, but this would be a tool to help better visualize and display it.
I *REALLY* like the use of this to explore saw tooth geometries, but the simple act of cutting those muriad of wood fibres is complex. I think that a simplification of the input parameters will result in a tooth design that looks strikingly similar to every generic "Japanese" style tooth found on the commercially cheap saws.
Your favorite blue/yellow handled saw (I've lost it somewhere, you'll be pleased to hear, haha) has a tooth design identical to the ChoMasaru line of thought that we've been exploring. A short tooth for minimal lateral deflection, forward and reverse slope that gives a good shearing angle to the wood fibres both on the pull AND push stroke, and a relatively blunt upper facet for longevity (as you display so perfectly in this FEM display).
Just thinking about this, it makes me want to have a rack of saws, each optimized for individual wood species and condition. Thoughts to ponder.
Thanks for sharing this!
you need to specify a bit better your kinked saw, I cannot picture it. But it would be fun. It reminds me of the other plots I made (the one of the coloured hammer blows) and that I wanted to repeat with a proper simulation. There is some kind of plastic deformation going on there, I don't know yet how to model that though. What you are asking I think is a bit different no?
DeleteYou are totally right btw, wood is a complex material, but you can start to complexify (is that a verb?) your model little by little. Add anisotropy in one dimension to have rip and cross cut, then add the different densities in the rings... although the process is complex, the basic unit of modeling is a single tooth cutting some fibers, grabbing them out of a matrix at a certain energy cost, and moving that in a groove. Maybe you have a simple expression that relates the wood's young modulus to the tooth angles and that's the base for your species-specific saws.
gonna check the literature for some inspiration. Thanks for the inspiration
Great stuff! I've been working at hizumi on a couple of different saws with Marks help, its one of those things that is nearly impossible to codify into simple rules, especially as the deformations congregate and add together. I was at a point of focusing in too much on individual deformations, and Mark basically explained that you have to find a way to connect the flaws with your correction, and he went and banged all over the saw for like five minutes and made it better, after me sitting there for a couple of hours. Nuki is an especially interesting case, balancing stresses equally on both sides of the saw with a round faced hammer. There's no way to learn this but to go at it and see the results. Tooth shape is a whole different animal, and I loved to see you graphic analysis, really gets it in the mind.
ReplyDelete