Apex Bevel Geometry cross-sectional

[bluntcut]

I've been tinkering around with edge geometry, there are many ways to create/scrulpture an edge. After many long stared at conceptual models, a cross section image of a simplified Apex Bevel Geometry always hold my attention the longest. Would be fun to have/rent a SEM to see what's going on.


Notes - a complete geometry would includes X&Y changes over Z-axis. Excluded back bevels.

Thinking out loud ...

From edge durability viewpoint, convex & V are obviously stronger than wire & burr because thicker steel below the apex can withstand more from rolling/lateral(X direction) force. Forces from Y&Z directions exceed steel limits (tensile,ductility,etc..) will deform (sometime fracture/chip) the edge, to keep it simple - let's ignore Y&Z forces.

To create a submicron apex thickness(average) many of us use strop (compound charged and or bare/silicate). Experienced sharpners know a wire/burr edge is weak. For discussion, a wire edge defines as the thickess of the blade below the apex is less or equal to the apex thickness. Let's look at a scenario

ex) Initial -a perfect convex apex bevel with apex thickness=200nm, hair whittling goodness.
If we over strop this edge using lower than usual pressure+angle and or low flex backing and or long grain backing, we could end up with a wire. This wire edge is weak, more readily roll than the initial edge.

Stropping is an art of techniques heavily dependence on steel, geometry, abrasive, forces and touch. ugh can we simplify this? or better way to scrulpting an durable edge? I can hone an edge to standard straight razor shaprness but could not achieve tree-top without stropping YET. btw - to me, stropping = repeat exclusive edge trailing strokes.

Your thoughts?

[bluntcut]

Please over look my lack of language skills, I just want to share ideas where many others over the years already thought of & exercise.

Objective: To remove the problem parts in 'red'.



Conventional working knowledge (outside of knife sharpening) tells us to directly remove those 'red' parts and leave 'green' good parts alone. If these figures represent edges of aluminum sheet where the 'red' part is 3mm thick, simply we would just file the 'red' part off. For a knife, the 'red' part usually less than 40um (all the way to submicron) thick but somehow the removal technique deviated from common/file method. Why? Let's see

a) Steeling - Abrading component is more or less filing the 'red' part off. The burnishing component also affect the good 'green' part.

b) Strop - Fine for fig1 but for fig2&3, one must be careful not to scrape strop or stone. The good 'green' part directly affected.

c) Sharpen - For fig2&3 problem. deburr for fig1. The good 'green' part directly affected. Improper sharpening may end up with fig1 problem.

a) b) c) approaches are affecting the good 'green' parts in a lack of total control manner. The end result edge 'green' is altered into new shape or same shape but minutely shorter blade height.

***
Using conventional/file method.

1) For fig1, use a flat piece of wood bent(file/scrap perpendicular to edge) the wire over, changed problem into fig2. Treat fig2 & fig3 problems as fig3.

2) Hold the knife with edge facing you. Use flat stone(or round stone for recurve) and file away the 'red' part at the target angle.
* Abrasive selection is important, use abrasive 1/3 to 1/10 the thickness of the 'red' part worked well for me.

3) Use a flat pieace of wood (mdf and or balsa) to file/scrap the remnant of wire to bent over the opposite side, repeat 2) & 3) until done. Done when edge is free of wire/rolled/burr.

This approach directly attacks the problem 'red' area and with more control, while leaving the good 'green' area mostly intact.

For filing 90% of the time, I use DMT diasharp EF/EEF. For the rest 10% - dealing with super fine edges, I use home-made files with grit range from 12microns down to 0.1micron.
***

Whew, don't you glad I'm not rambling about cosmo physics

[richard j]

bluntcut, send me an email. rje196021@gmail.com

[Obsessed with Edges]

Hey blunt,

I like the graphics here (did you do these?), and I think your language skills will do fine here, so no worries.

This will hopefully 'bloom' into another very informative thread. It'll keep me watching (& thinking)...

[bluntcut]

bluntcut, send me an email. rje196021@gmail.com

gmail sent.

Hey blunt,

I like the graphics here (did you do these?), and I think your language skills will do fine here, so no worries.

This will hopefully 'bloom' into another very informative thread. It'll keep me watching (& thinking)...

Yes, I drawed those graphics/models (were mostly for my own staring sessions). Thanks.

[gga357]

I hope this does 'bloom' into a in-depth discussion.

[bluntcut]

A practical example: Create a coarse & stout edge using filing method.

1) work up a burr (oneside then the other) on whatever toothy grit (165 to 45 microns) you want your edge be

2) use wood to bent burr over on 1side (or opposite from the side you just filed off)

3) use 12 micron (e.g. dmt EF) with edge leading file stroke to remove rolled/bent-burr, repeat 2) until done (see previous post). optionally cont to 4).
* if you are not reprofiling, steps 1 thru 3 could be done in less than 5 minutes.
* at this stage, the apex should be thin + toothy and surprisingly sharp.

4) optional keep apex clean while refine. Use 3 micron (e.g. dmt EEF) with edge leading light pressure file stroke until scratches are uniformly consistent from 3microns.

5) optional for smoother edge. do 5 full strokes per side on 3micron, use 95% lateral(push saw motion) + 5% edge leading light pressure stroke. Lateral movement increases the effective-grit of the stone. Lateral movement has the same effective grit increase for edge-trailing/strop stroke as well.

I use diamond abrasive (very aggressive) because it can easily abrades with all type of steels+carbides (including VC, WC).

Try it, if it works, please discuss...

lol - I didn't want a 'doh' on my part, so I just hastily reprofiled a brandnew cheapy Elk Ridge 5.5" blade bowie (440A steel): reprofile using dmt XC to 40*incl, then file burrs off using EF. The edge can cross slice newsprint smoothly, push cut haltingly. This test took me ~ 7 minutes to complete. I'm heading to the backyard to hack some branches.

edit: after 30 minutes of chops, batons, slashes wood & branches and then broke down over 14 cardboard boxes, minor rolled on some part of the edge. A quick 20 seconds filing with dmt EF, got it back to slice newsprint.

[bluntcut]

We could brainstorm together to come up with good analytical reasons for strenght & weakness of different edge shapes/profiles? I'm slowly plodding along whenever time permits but with many smart brains in this community, we could speed thing up. Currently (ahem, perhaps my ignorance), there are plenty of annecdotal evidences & empirical-knowledges about edge shapes excel/fail for general or specific tasks, which addressed the 'experience' part of skills. Investing in understanding 'what and why', voila we've priceless skills.

Let's use these specs:
s0) available shapes: convex, v, hollow. Double and single bevel grind
s1) well heat treated m390 for general uses...please don't blink (pick your own steel), keep open mind
s2) ignore earthly abrasive, yoda gave us baryonic particles (and my grammar broken)
s3) ignore forces from Z direction (defer 3D, it's already quite complicated in 2D)
s4) 100% control over forces from X&Y directions
s5) omniscient eyes allow us to see atomic structure, arrangement and state
*) tbd

Neurons fire at will!

[FortyTwoBlades]

Let me think on this for a bit and see if I can come up with anything to contribute. A lot of this stuff can be very difficult to explain and can give one a headache just trying to figure out where to start or what to say! Very nice graphics, and good thoughts!

[gga357]

Not too sure how much the macro view pertains, but arches have always been very efficient structures. I see that as a reason convex grinds have a slight advantage. Now micro structures and steel matrix is not my area, so that may be more important.

[wouldestous]

i have a practical question and thought id just leave it here.

got an opinel #7 carbon. ive worked on it a little with a medium or maybe slightly coarse stone. i notice that now i can hone it on the bottom of a coffee cup and its way plenty sharp for my needs. but ill cut one or two little things and it will still be sharp but not way plenty sharp. honing it on a coffee cup gets it way plenty sharp again. but then cutting one or two little things will heavily reduce the edge. rinse and repeat.
does this sound like i have a wire edge as bluntcut describes above which is getting rolled during cutting and then straightened when i hone on a coffee cup?
ive observed a similar phenomena when filing down the edge on a new machete.
if i am continually rolling and straightening a wire edge then what will help getting a sturdier, longer lasting edge?

[bluntcut]

i have a practical question and thought id just leave it here.
...
if i am continually rolling and straightening a wire edge then what will help getting a sturdier, longer lasting edge?

No, you will end up with even a weaker edge because of fatigued steel. A burr/wire free edge is stronger.

Try these steps:
1) scrape your knife edge at about 80* (almost blade is almos vertical/perpendicular) to a rollup newspaper or a piece of wood - the idea is to bent/roll burrs or wire over to 1side.
2) use edge leading strokes into the bottom ring of a ceramic coffee cup at the bevel angle until you feel (with fingers) that rolled burrs/wire are gone. Repeat 1) bent remnant burrs/wire to the opposite side. do 2) again. repeat with less pressure each time (would take more than 1 or 2 times do completely clean up burr/wire).

Validations (to cover my 'doh'):
knives: a box cutter & opinel #9 carbon. my opinel is hair whittling sharp at ~26* inclusive back bevel, 36* convex 1mm cutting bevel.

Round 1)
dull 'em: made multiple cuts into a piece of flat granite until edges failed to slice printer paper.
sharpen: edge leading stroke using ceramic coffee cup -> slice newsprint at 45* (semi-cross grain) smoothly

Round 2)
dull 'em: made multiple cuts into a piece of flat granite until edges failed to slice printer paper.
sharpen:
i) worked up burrs with dmt fine.
ii) repeat steps 1) & 2) above
iii) -> slice newsprint at 45* (semi-cross grain) smoothly

[bluntcut]

My brain has been running a lot of simulations on interaction between edge geometries in variable cutting scenarios. Analyzed a few of today existing designs, especially those outstanding & curiously-successful geometries, resulted in a brain full of conjectures/ideas, although lacked of coherency. Out of many mental images, one struggled through with some resemblance of the envisualized image:


Edge Durability and Performance are the two interwoven variables, I will attempt to discuss (heheh, hands waving) each seperately.

Durability (for given steel properties - molecular+grain bond strenght, ductility, etc.. - St represents failure thresholds per steel unit 2D area):

D1) When forces (X+Y) exceed edge St value = Damage

a) Mitigate - increase steel area, essentially increased the size 'impact zone', to reduce dent/roll/deformation area and diffused forces into larger area to avoid locally focused steel failure - fracture/chip. Note - fracturing force can propagate/translate along the grain (weaker molecular lattice bonds) line to cause failure in area away from impact zone.

b) Control - reposition steel (geometry) to accomplish a)

c) Redirect - increase the bevel chest (curvature and or thickness) to channel forces from impact-zone to pressure-zone. The picture above shown abit of this. Optimally, we want to wedge just below tearing point then allow the cutting edge seperate the material with minimal force, and the 2 seperated parts move away from the edge, thus lowered the lateral/Fx force near apex.

d) Steer (when oneside of the seperated part is thin or falling away) - bias bevel curvature favoring the rigid side, so the edge steers (dampen) away from Fx solid direction. Impact zone is smaller because less overall Fx and same Fy.

D2) Edge roll - A biggest failure for edge that too thin and or poor steering, where Fy effectively turned into Fx (from the edge perspective). Mostly it became D1) situation. Aha, sound like a self-inflicted but correctable problem

a) Thicker edge - obviously.

b) Larger cutting angle - a stronger/thicker (behind the apex), add apex rigidity, reduce steering. e.g. micro-bevel.

c) Mitigate - stop cascade roll (over time) by stair stepping St. e.g. A micro mohawk on convex edge.

More next time...

[FortyTwoBlades]

Keep it up, man--you're explaining this stuff better than I could, by far!

[bluntcut]

Thombrogan just posted(20120926) on FoodieForums The authors are Mahvash and Hayward and the paper is titled "Haptic Rendering of Cutting: A Fracture Mechanics Approach" link. A great attempt to scientifically render sharp-interaction where it touches both performance & geometry.

My interests are in cutting interactions driven by parameters: cutter material+geometry; subject properties; forces vectors; etc.. Ultimately if there are enough interests and collaboration, we can come up with a multi dimensions & variables simulation which can generate reasonable prediction for any given set of parameters. Standard output values (over all, per dim/vector) can be very helpful for operational situation, values such as: global & local minima, maxima, saddle points. Hopefully, this topic/thread starts to bloom. We?

edit: it's easy to lose-touch with reality while abstracting/masking a compex interaction. An analytic (hand-waving, fixed use equations) model could be as useful and actually more relevant in everyday lives.

[wouldestous]

...
Try these steps:
1) scrape your knife edge at about 80* (almost blade is almos vertical/perpendicular) to a rollup newspaper or a piece of wood - the idea is to bent/roll burrs or wire over to 1side.
2) use edge leading strokes into the bottom ring of a ceramic coffee cup at the bevel angle until you feel (with fingers) that rolled burrs/wire are gone. Repeat 1) bent remnant burrs/wire to the opposite side. do 2) again. repeat with less pressure each time (would take more than 1 or 2 times do completely clean up burr/wire).
...

i got a wooden cigar box and a coffee cup and tried this; worked great. thanks, man.

[bluntcut]

Cut = edge seperates subject cleanly. Tear; rupture; displace and etc are excluded as non-cut.

Velocity(V) = Cut speed through material

Displacement Unit(D) = A measure unit of material thickness to be cut. It can be define as 1 molecular or 5mm or whatever reasonable thickness.

Time(Td) = D / V (displacement divides by velocity). It's more simple to use a time-window than a complete interaction which involves dynamic accelerations & decelerations (velocities).

Force(Fd) = cutting force per D

EdgeLimits(EL) = deformation thresholds at various interaction impulse-forces. Energy waves propagation through edge in displacement-time-window Td, directly translate to the size of impact area. Damage occurs when energy waves boundaries/crests is beyond the material instrinsic static deformation limits.

Total Work(W) done = Sum(D) until the edge no longer cut

Performance(P) = W / Average(Fd). A higher value indicates higher performance. So to get better performance, we can either by increase W and or reduce Fd.

Remarks:

Take a scenario - velocity in a chopping motion is much higher than a normal slice. Smaller Td could exceed EL by first impact or rapid cummulative/subsequence impacts. As the edge deteriated, more Fd is required per D cut, therefore end up with a poor performance.

Work-done can be large but still perform poorly if it took alot of forces sum(Fd) to get that amount of work-done. ex: cut throught a solid block of rubber, where friction+wedge sapped most of the cutting force while actual cutting takes very litte force.

*** Now with definitions out of the way (I'll admend to the list as time goes) ***
I) Sharp = performance most important factor

Let's look at sharp and then make it sharp ...

[bluntcut]

There are many good posts & explainations about sharpness on the internet. In this context, sharp qualified as an edge(apex geometry) cutting ability toward a target subject in a particular environment.

E.g. 1)
subject = paracord 550
env = strung in the air
sharpness = maximum apex thickness is 2 microns (wag)

E.g. 2)
subject = paracord 550
env = lay flat on wood, which allow more localize vertical compression and horizontal stretch
sharpness = maximum apex thickness is 4 microns (wag)

E.g. 3)
subject = man whiskers
env = shave on face
sharpness = maximum apex thickness is 1 microns (a painful shave)

E.g. 4) theoretical
subject = cells block
env = laboratory, slice sub-micron cell layer
sharpness = maximum apex thickness is sub 100nanometer

For each example, a minimum sharpness is required.

If we figure/deduce/theorize a feasible sharp that yields great(notice: I avoided the word 'best') performance, we need comprehensive sharpening skills to fulfill the target sharpness requirement. A comprehensive technique (a component of skill) would covers 95% of cutleries materials, where working-knowledge technique (bag-of-tricks) only covers a small sub-set of cutleries materials. With proper execution and regardless of material type, we should able to get the sharpness on first try. Reader: 'Oh hey, this sounds like crazy speak ...'. Hang on your flame thrower until the end of this post. Here's more fuel:

It's madness to use the same process to resolve problems that caused by it. That process is edge trailing (strop) stroke, while burr and wire are the problems. Trailing stroke with varying pressure and angle unfortunately made this process more indeterminate (unpredictable) and will likely get smaller burr/wire formation(if not rounded the edge).

Please blast away at crazy ideas/speaks (be mindful of bfc personal insult rule).

Coming up, a comprehensive step-by-step technique to sharpen 95% of cutleries materials near their thinness limits, producing a high sharpness edge practically free of burr & wire. And without using a nano-probe to construct the edge at 1 atom at a time.

Tell me if I am talking to myself. I will bottom-up a cup of st**f**

[Lagrangian]

Thombrogan just posted(20120926) on FoodieForums The authors are Mahvash and Hayward and the paper is titled "Haptic Rendering of Cutting: A Fracture Mechanics Approach" link. A great attempt to scientifically render sharp-interaction where it touches both performance & geometry.

Thanks for that reference! I'll definitely read it.

There are some books on the science of cutting and knives, although I haven't seen too many.

_The Science and Engineering of Cutting: The Mechanics and Processes of Separating, Scratching and Puncturing Biomaterials, Metals and Non-metals_
by Tony Atkins (2009)
ISBN-13: 978-0750685313
http://www.amazon.com/gp/product/075...ls_o03_s00_i00

_Messerklingen und Stahl_ ("Knife blades and steel")
by Roman Landes (2006)
ISBN: 978-3-938711-04-0
https://www.morebooks.de/store/gb/bo...-3-938711-04-0

The first book I have only just started to read. It's written at the undergraduate level it seems (uses a touch of calculus here and there). The second book seems fascinating, and is about scientific research conducted by the metallurgist Roman Landes, but unfortunately it is only available in German.

In addition to the above, there are other books, studies, and research papers on cutting metal because of it's engineering applications in manufacturing. These may not be relevant to us, in that we don't use our knives to cut steel. Even so, they might be useful to read about them to learn what concepts and methodologies they used to study cutting.

There are some papers on the study of cutting wood (also for manufacturing). I don't have a reference for this, but there was an engineering study about wood-chip formation during cutting. This study was briefly mentioned in this book (but did not go into details of the study):

_The Complete Guide to Sharpening_
by Leonard Lee (1995)
ISBN-13: 978-1561581252
http://www.amazon.com/The-Complete-G...+to+sharpening

I'm not an engineer, but as a physics major, the subject seems incredibly complicated to me. It may involve everything from surface-physics and tribology, to the material-science and strength-of-materials of the knife as well as the material being cut. Potentially, that is everything from chemistry to stress-analysis.

I'm quite curious about it though, so I hope the discussion continues. Please let us know what you find!

Sincerely,
--Lagrangian

"What grit sharpens the mind?" --Zen Sharpening Koan

[bluntcut]

Thanks for that reference! I'll definitely read it.

There are some books on the science of cutting and knives, although I haven't seen too many.

_The Science and Engineering of Cutting: The Mechanics and Processes of Separating, Scratching and Puncturing Biomaterials, Metals and Non-metals_
by Tony Atkins (2009)
ISBN-13: 978-0750685313
http://www.amazon.com/gp/product/075...ls_o03_s00_i00

I read the abstract, it sounds very fascinating -> inserted into my read-list.

_Messerklingen und Stahl_ ("Knife blades and steel")
by Roman Landes (2006)
ISBN: 978-3-938711-04-0
https://www.morebooks.de/store/gb/bo...-3-938711-04-0

I've seen many references made to this book... yup, would be great if I can read German.

_The Complete Guide to Sharpening_
by Leonard Lee (1995)
ISBN-13: 978-1561581252
http://www.amazon.com/The-Complete-G...+to+sharpening

I'll stay inside my ignorant bubble for now.

I'm not an engineer, but as a physics major, the subject seems incredibly complicated to me. It may involve everything from surface-physics and tribology, to the material-science and strength-of-materials of the knife as well as the material being cut. Potentially, that is everything from chemistry to stress-analysis.

My background is compsci and pure-math and that was over 20yrs ago - a rust major now. Pretty much everything has more variables/elements than we know what to do with them. After a few bouts of lost/bogged by complexity, I gave up formal analysis and adopted hand-waving.

I'm quite curious about it though, so I hope the discussion continues. Please let us know what you find!

I will gladly continue with my rambling, unless I miss your subtle hint

Thanks for the response.