|Some Theoretical Issues|
|Copyright (c) 2002-15, Brent Beach|
While free and relatively simple (for a 3D drawing program), Sketchup models are accurate in scale and let you view the model from every angle.
By accurate in scale, I mean that if you specify that a rectangle (for example) has a specific size, then it has exactly that size (within the accuracy of single precision floating point numbers). If the modeller gets it right, the model is accurate.
And there in lies the rub. To make a model of a saw filing (the exact shape of the teeth for a given rake, bevel and slope, and the frame of reference in which each rotation is made (more below)) takes me about 20 minutes. In that 20 minutes there are perhaps 400 operations of one kind or another - click, drag, specify size, specify orientation. An error in any step produces an accurate scale model, but not the one intended. If any of the models in these pages seems to be out of whack with your intuition, let me know - you may be right.
If done correctly, the models let us compare the tooth shape for various filings. They also let us compare the un-tooth shape - the gullet shape.
The goal of adding these models to my saw filing pages is to produce drawings that mean something. You will see elsewhere in these pages drawings taken from various books - some the official publications of a famous saw company (Disston). Those drawings are not to scale. Some appear to depict saws which cannot be prepared with a triangular file.
For even more simplicity, almost all models show saws that have no set. While set is crucial in saws, it does not change the cutting action very much. Rather, it provides clearance for the saw by cutting a wider kerf that the actual thickness of the saw plate. Putting set in a model adds about 50% to the time taken to build the model.
In all models I assume the use of a triangular file. In all cases, both sides of the file are in contact with the tooth on either side of the gullet at the same time. Other filings can be achieved using different types of files - files with a narrower included angle at the corner that goes into the gullet (a cant file).
The drawing on the left shows the saw teeth from the front - what you see when you look down the line of the teeth from the handle toward the toe. You cannot see much in this view but you can see one very important angle - the front included angle at the tip of the tooth. This angle - 49.2 degrees in this case - is a measure of how sharp the saw is. By sharp I mean how well the teeth slice the fibres of the wood. This is quite a sharp saw.The side view on the right shows many of the other angles that define the tooth shape. None is as important as front included angle.
What you can see are:
For each saw model, I will include these measurements.
I use two different size files - one for 11 ppi cross cut saws, one for 6 ppi rip saws.
File shape may well vary from manufacturer to manufacturer and over time. I measured three files:
|File name||Corner width||Side width|
|7" extra slim||0.024"||0.31"|
|5" XX slim||0.016"||0.18"|
This drawing then corresponds roughly to a 5" double extra slim file. I use this file model for all the cross-cut saw models.
The file used in the rip saw models is exactly twice as big as the cross cut file model.
To produce a particular filing, I turn the file three times. In most models the order is bevel, slope, rake.
Some models use a different order - for example, rake, bevel, slope. The result is a different tooth shape.
In addition to rotation order, the plane in which the rotation is done is important.
This is a confusing point and one on which I will not dwell after showing the following two models. The models have exactly the same nominal filing - rake 30 degrees, bevel 30 degrees, slope 0 degrees.
In the first model, the file was turned as follows:
In the second model, the sequence is:
The two models are discussed in detail below.
One way of controlling rake is by using a wooden block on the end of the file, similar to the jig Woodnut4 uses. The rake in this model is 30 degrees. While you might use a wooden block, in sketchup I do a rotation operation about the lower corner of the file.
You also have to control the bevel angle while filing. You might do this by laying a template on the saw vice with lines drawn at the bevel angle you want. The bevel in this model is 30 degrees. In sketchup, I rotate the file in the horizontal plane. (Rotation of an object in a plane is a simple sketchup operation.)
The angle you see from the front view of the tooth is actually one of the most important angles there is - although it is rarely mentioned directly.
Front included angle at tooth tip in this model is 49.1
This is the sharpness of the saw - how fast the tip cuts down through the wood fibres.
When you think of a cross cut saw as a series of knives slicing the wood fibres, this angle is the one that determines how sharp that knife is.
The importance of the front included angle is discussed later.
From the side view, I get a number of important angles and lengths.
Rake: front 33.7, back 33.7
Bevel: front 30, back 30
Side included angle at tooth tip 67.4
Tooth height: .079"
How does this happen? Is it an error in model making? An error in sketchup?
In fact, the model is accurate. The change in rake angle with increasing bevel handle happens because the second rotation changes the effect of the first rotation.
Rotating the file to get the 30 degree bevel has increased the effective rake on the tooth. This happens because the line of contact between the tooth and the file is no longer straight up the side of the file. The line of contact is in this case 16.1 degrees from the line square to the side.
This drawing shows a file in a saw plate. The dotted line is square to the side from the base of the gullet. The actual contact line is 16.1 degrees away from vertical.
Second, the rake angle was set by rotating the file about its lower edge until the side came to rest on the equivalent of a slider with a front face sloped at 30 degrees. That is, the rake is set with respect to the saw face rather than simply rotating the file. The actual rotation for an effective 30 degree rake is only 26.6 degrees. (You could get this result by changing the angle in the block of wood you use on the file tip to 26.6 degrees.)
This is the filing you get if you use my jig and set the file angles by proper construction of the slider (which controls bevel and slope) and use of a block of wood on the teeth to set the rake angle.
From the front view:
Front included angle at tooth tip 49.2The angles and lengths, from the side view:
Rake: front 30, back 37.3
Bevel: front 30, back 30
Side included angle at tooth tip 67.3
Tooth height: .078"
In my opinion, aside from number of teeth per inch and amount of set, both of which are outside this discussion, the two main characteristics of a saw tooth that affect performance are the front included angle and the gullet volume.
Sawing cross-cut involves two separate actions. First, the tooth tip slices across the wood fibres. Second, the inside of the tooth pushed the severed wood toward the other side of the kerf. The next tooth cuts the other end of the fibre and pushes the chip back this way. Alternate teeth push the chip back and forth until the chip breaks off as saw dust.
|"Now the sharper each tooth is -- that is the more bevel on the point -- the deeper it will cut; but it must not cut any deeper than will crumble out across to the point of the other tooth. This is the difference between saws for soft or hard wood; if a saw for hard wood is too much bevel on the point, it will score deeper into the wood than it can carry out the chip, so that it will keep moving up and down in the same scores, and not accomplish anything."|
|More on this discussion of tooth shape in the Sloping Gullets page with reference to the 1850's book The Art of Saw Filing by H. W. Holly.|
A sharper tip will cut faster. Will it clear the sawdust? A faster slicing action means more wood pressing against the inside of the tooth. A smaller front angle means the tooth displaces the chip a short distance for a given depth sliced. This determines the ability of the saw to clear the chips.
If the slope is wrong for the wood, the chips will not clear and the saw will slide back and forth in the already sliced furrows. More downward pressure will move the saw deeper, which means more side to side movement of the chip and it could mean breaking the chips up. It is not however how we like to saw - by letting the saw do the work.
If a saw works well in softwood but not as well in hardwood, you might consider decreasing the slope (increasing the front included angle). If it works well in hardwood but is not as fast as it could be in softwood, consider increasing the slope (decreasing the front included angle). If you only every cut hardwoods, slope may not be important to you.
This model shows the volume involved. The red surfaces are the walls of the gullet volume. I did not draw in the remaining line so the inside of the volume could be visible.
One of the standard reasons for using sloping gullets is to increase the volume of the gullets. Larger gullets increases the amount of sawdust the saw can collect. If the gullet fill, the saw tips will lift off the wood and stop slicing the wood fibres.
Having larger gullets for a given number of teeth per inch means you can cut wider boards. Alternately, increased gullet size allows you to use a saw with more ppi for a given board thickness. More teeth per inch normally results in a smother cut (the surface left by the saw is smoother).
You can see from the above that the volume of the gullet increases by almost 16% as the slope increases from 0 to 30 degrees. This means you can saw a 16% wider board before the gullets fill with sawdust and stop cutting. This may or may not be a factor in your work. Most people cross cutting hardwood for woodworking projects would probably not notice a gain.
If you do think the gullets are filling and slowing the cutting action, you can increase the angle of the saw to the wood. Most people have the line of the saw teeth at about 60 degrees to the face of the wood. For wide or thick boards, increasing this angle will reduce the length of the kerf.
Where this is most likely to be important is for mitre saws. When you cut wide boards, does the cut take longer than you expect? If 4" wide board takes more than twice as long as a 2" wide board, you may be having a problem with gullets filling with sawdust. Try sloping the gullets when you file your mitre saw.
This filing has rake 30, bevel 30, slope 30. The tooth height measured to the gullet on the left in the picture, the upper end of the sloping gullet is much less than that measured to the right gullet, the lower end of the sloping gullet.
Sloping gullets produce taller teeth, using the larger measure. These taller teeth are more flexible because of their increased height. Does this increased flexibility matter?
The result? The tooth is more flexible. That means it can bend, in or out, affecting the width of the kerf. Which direction will it flex? The answer is the tip will move out, if it moves at all!
When we compare the forces on the inside of the tooth to those on the outside, we see that the forces inside are greater. The inside forces act against the inside bevel. Because this inside bevel is angled, the forces has two components. The first component is upward, resisting the downward movement of the teeth tips into the wood. The second component is outward, widening the kerf. The smaller the front included angle the greater is the outward force.
The outside has no bevel so wood pushing on that side exerts no force that would push the tooth inward.
How great is this effect? How much more will a tooth that is 10% taller flex outward during use? Well, that is pretty complicated. In fact, to calculate the amount of deflection we have to consider that the height of the tooth can be measured in two ways. In the right hand image, the height is shown from the tip to both gullets. The height to the left gullet is actually less than the tooth height when the gullet slope is zero.
This gets complicated but interesting. There are two ways to file a saw. When using sloped gullets, it matters. If you file with the file tip toward the toe of the saw and file up the gullet, then the short side of the tooth is on toe side. That is, the short side of the tooth is the side that cuts on the push stroke. Because the tooth is shorter, the force on the wood on the front bevel will have less bending power because it is acting over a shorter distance.
In any case, because teeth will only bend out, the only possible result is a wider kerf. This may mean removing a little more wood - doing a little more work. However, you would have to be pushing the saw pretty hard to make this effect significant.