For any given task with any given steel/HT, some edge geometries are going to work better than others, and for any given metric of goodness, there is going to be a best geometry.
Now of course, this 'goodness metric' depends on the task being performed, the hands performing it, the steel, the heat treat, the individuals preferences for sharpness, the preferences about sharpening, etc. Given that, there are still some things that are obviously bad for all the above. For example, for any cutting task FFG cuts much better than a thick saber grind, and if you grind it to a zero edge, you're going to be stuck with an edge that won't stay together, or a thick wedge you have to forcefully press through the material you're cutting.
With all that intro/disclaimer BS out of the way, we can talk about the types of geometries that generally rank high in preferences. A blade that chips out at the base of the primary bevel is worse than one that chips when 10 microns thick, so there should be a higher margin of safety built in as the blade gets thicker.
For a crude model to begin with, I suggest modeling the blade as some shape that goes from some finite thickness "t" at x = 1 to 0 thickness at x = 0 that is held to be horizontal at the spine, and is pushed upwards at the very edge.
Since flexural strength goes with the square of the thickness (2x thickness gives 2x area and 2x the lever arm) and torque goes linearly with distance from the fulcrum (edge) the shape that gives equal stresses has a thickness that goes with sqrt(x) which is a sideways pointing parabola and has a final edge angle of 180 degrees
The first flaw in this model that jumps out is that we can't have an edge angle that is 180 degrees- I'm not willing to bite that bullet for this model. If your edge deforms into the material at all before getting much side load, then the force is effectively acting at 0+deltaX and the bevel should probably be flattish and come to a point after this.
In addition, since we want a larger safety margin as the blade gets thicker, the thicker parts get thicker faster than a parabola (plus you need stiffness in the other direction).
This crude model, while clearly lacking, still suggests very low angles until near the edge where they get considerably more obtuse.
If you expect the cutting force to be roughly proportional to sin(theta)*thickness, the tiny bevels don't cost you much cutting ability anyway, but they can make the edge significantly stronger.
So what real world data do we have?
My full hard M2 knife is hollow ground down to about 10-15mils and is ground at 13 degrees down to the last 50 microns, where it picks up to 30 degrees and the last 10-15 microns are ground at 35 degrees (all included angles).
Final edge angles of 28 would form 10 micron thick chips under typical every day stuff, but this problem seems to have gone away now that I run a steeper microbevel. The only time I chipped into the secondary bevel was when cutting fiberglass/polyester resin. It cut most of it fine, but when cutting through a thicker piece I had an 8 mil thick chip taken out.
Since the 2nd and 4th bevels are just above failure in my typical use, these seem close to optimal. Maybe I can make the third a bit more acute.
Taken from Craig on rec.knives:
He's talking about initial edge retention due to deformation/microchipping.
Please share your thoughts on the theory as well as experience in minimum angle/thickness needed for your knives to hold up!
Now of course, this 'goodness metric' depends on the task being performed, the hands performing it, the steel, the heat treat, the individuals preferences for sharpness, the preferences about sharpening, etc. Given that, there are still some things that are obviously bad for all the above. For example, for any cutting task FFG cuts much better than a thick saber grind, and if you grind it to a zero edge, you're going to be stuck with an edge that won't stay together, or a thick wedge you have to forcefully press through the material you're cutting.
With all that intro/disclaimer BS out of the way, we can talk about the types of geometries that generally rank high in preferences. A blade that chips out at the base of the primary bevel is worse than one that chips when 10 microns thick, so there should be a higher margin of safety built in as the blade gets thicker.
For a crude model to begin with, I suggest modeling the blade as some shape that goes from some finite thickness "t" at x = 1 to 0 thickness at x = 0 that is held to be horizontal at the spine, and is pushed upwards at the very edge.
Since flexural strength goes with the square of the thickness (2x thickness gives 2x area and 2x the lever arm) and torque goes linearly with distance from the fulcrum (edge) the shape that gives equal stresses has a thickness that goes with sqrt(x) which is a sideways pointing parabola and has a final edge angle of 180 degrees
The first flaw in this model that jumps out is that we can't have an edge angle that is 180 degrees- I'm not willing to bite that bullet for this model. If your edge deforms into the material at all before getting much side load, then the force is effectively acting at 0+deltaX and the bevel should probably be flattish and come to a point after this.
In addition, since we want a larger safety margin as the blade gets thicker, the thicker parts get thicker faster than a parabola (plus you need stiffness in the other direction).
This crude model, while clearly lacking, still suggests very low angles until near the edge where they get considerably more obtuse.
If you expect the cutting force to be roughly proportional to sin(theta)*thickness, the tiny bevels don't cost you much cutting ability anyway, but they can make the edge significantly stronger.
So what real world data do we have?
My full hard M2 knife is hollow ground down to about 10-15mils and is ground at 13 degrees down to the last 50 microns, where it picks up to 30 degrees and the last 10-15 microns are ground at 35 degrees (all included angles).
Final edge angles of 28 would form 10 micron thick chips under typical every day stuff, but this problem seems to have gone away now that I run a steeper microbevel. The only time I chipped into the secondary bevel was when cutting fiberglass/polyester resin. It cut most of it fine, but when cutting through a thicker piece I had an 8 mil thick chip taken out.
Since the 2nd and 4th bevels are just above failure in my typical use, these seem close to optimal. Maybe I can make the third a bit more acute.
Taken from Craig on rec.knives:
He's talking about initial edge retention due to deformation/microchipping.
Please share your thoughts on the theory as well as experience in minimum angle/thickness needed for your knives to hold up!
