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1

Topics for Today• Principles of Sharpening • Sharpening Angles• Types of Stones• Grinding Wheels• Guides/Jigs/Systems• Tips for Specific Tools/Blades• Hardness Rating• Types of Tool Steel• Master at Work

2

Sharpening 101

3

Definition of “Sharp”

Basically, an object is sharp when two geometric planes (the back and bevel, or two bevels) intersect with relatively little, or

zero, radius.

Zero radius is a theoretical ideal.

For woodworking, the angle at which the two planes intersect on various tools may differ, but is VERY important.

4

Sharp vs. Dull

• Difference:

5

Common Shop Tests for Sharpness

• Check for glint of light reflecting off edge; if you can’t see it, it isn’t sharp

• Feel (don’t slide across) blade with thumb• Slice Paper• Shave hairs• Slide on fingernail• Slice wood ---- look for continuous thin curl• Slice plastic ballpoint pen• Nylon paint brushes

6

Two Groups

• Let's divvy up the tools/blades into two groups:

1) Rough outdoor tools you can sharpen well enough with a file, and

2) Finer blades that need more specialized care……Today’s Discussion!!

7

File and Stones

• Certain tools (rough outdoor tools such as axes, shovels, lawn mower blades, etc.) need only be sharpened with a file

• Finer tools such as planes, jointer blades, chisels, lathe tools, knives, etc. are sharpened and/or polished with stones, steels, ceramics, or diamonds

8

Sharpening Axiom No. 1

• Sharpen single-beveled tools ONLY on the beveled side

You can ruin the cutting edge of the tool otherwise!!

9

Sharpening Axiom No. 2

• In general, sharpen the bevel at the same angle that was already there.

In other words, if you can tell what angle the manufacturer or

prior sharpener used, follow it.

If you can't tell, move on to:

10

Sharpening Axiom No. 3:

• Sharpening at a steep angle gives a more durable edge; sharpening at a low angle gives a sharper edge.

11

Sharpening Axiom No. 4:

• Sharpen until you raise a burr.

12

Sharpening Axiom No. 5:

• After sharpening…..polish and hone.

13

Stropping

• The purpose of stropping is not to abrade more metal, but rather to continue bending, flexing, fatiguing, and burnishing off the miniscule metal strands still clinging to the edge of the blade after the burr breaks off.

• If you sharpen with water stones and use a "gold" 8000 grit stone as a final step, stropping is not necessary.

14

Stropping

• Strop the bevel and back of the tool using a smooth firm piece of leather (very hard machine-belt leather is not good). Do not use abrasive dressings on leather - they are coarser than the Arkansas stone and will remove its effects. Wipe honing oil off the tool before stropping. Strop on clean, undressed leather only. Strop in one direction only.

15

Secrets to Sharpening

• “The first part of the secret is that you must maintain a constant angle between the knife blade and the hone. This is something which most mortals can't do without some sort of a fixture.”

• “The rest of the secret is that you must grind a relief until you get a burr, then you must grind a secondary edge until you get a burr. That's it, that's all there is. If you understand this you can put a sharp edge on any knife every time.”

--- Mike Casey

16

Use Two Abrasive Surfaces

• What is important is that you have two abrasive surfaces: a coarse one to get the hard grinding done faster and a fine one for the finish sharpening.

• A coarse stone wears material away quickly until the blade angle is what you want it to be, but if you continue to use it past that point, it'll take off your sharp edge rather than finish it.

• The fine one gives you that final keen, smooth edge.

17

Common Error

The most common error in using abrasives is not starting with a sufficiently coarse grit to efficiently do the necessary material removal to prepare the tool for sharpening.

This grit must do all the necessary shaping or flattening and edge defect removal. The task of all subsequent grits is simply to remove the scratches of the previous grit.

18

Common Mistakes

• The mistakes commonly made in knife sharpening are uncontrolled edge angles, failure to establish a new edge, and leaving the edge too rough. The following methods address each of these mistakes.

• The keys to success are:

• 1) Use an angle guide to control the edge angle, • 2) Sharpen until you raise a burr, and • 3) Hone or polish the edge smooth.

19

No Agreement! – Do What Works

• Use Jig --- Don’t Use Jig• Use Wet Stone ---- Use Dry Stone• Direction of Tool When Sharpening• Grit of Stone or Grinding Wheel• Type of Stone to Use• Exact Angle of Bevel for a Particular Tool

20

Speed vs. Sharpness

• Relationship:

21

One Bevel or Two?

• Some tools may have one bevel:• shovels, hoes, spades, pruners, scissors • chisels, planer blades, router bits• lawn mower blades, jointer blades

• Some tools have two bevels:

• axes, razor blades, knives*

* - some knives have only 1 bevel

22

Bevel Angle

23

Blade Angle

• A factor effecting edge sharpness is the angle it is sharpened. The lower the angle, the sharper the blade becomes. However, the lower the angle, the weaker the edge becomes. Very low angle blades like a razor blade or a fillet knife will ultimately have a sharper edge than high angle tools such as an axe.

24

Angle

• Most important of all—you've got to keep the same angle on the blade with each and every stroke. That's usually the real

problem.

• If you keep changing the angle as you work (ever so slightly, ever so unintentionally), you'll keep hitting edge to stone at different points and, in effect, rounding off the edge of the

blade, making it dull instead of sharp.

26

AnglesType of Knife or Tool Recommended Angle

Cleaver

Machete30-35 degrees

Hunting Knives

Pocket Knives

Survival Knives

Sport Knives

25-30 degrees

Chef's Knives

Kitchen Knives

Smaller Knives

Boning Knives

Carving Knives

18-25 degrees

Fillet Knives

Paring Knives

Razors

X-Acto Knives

12-18 degrees

27

Sharpening Knife Blade

• Figure 1 shows the cross-section of a typical knife as it comes from the factory. There is no relief and a secondary edge is ground into the edge of the knife. Each time you sharpen the secondary edge the knife will become blunter.

28

Sharpening Knife

• Grind a relief using a coarse stone. Since your relief has such a small angle, the edge of the blade will be weak and dull easily. We will take care of that later when we add the

secondary edge.

29

Sharpening Knife

• Grind a burr on both sides

30

Sharpening Knife

• Add Secondary Edge

31

Sharpening Knife

• Double Edge the Knife – Grind Primary Edge into Secondary Edge

32

Blade Variations

• Knife Blades (Cross Section)

33

Common Knife Grinds

• The four most common grinds used for knife blades:

Semi-Hollow - Creates a nice balance between a sharp edge and overall blade strength. It is the most common grind used today.

Full Hollow - Produces the thinnest and sharpest edge but is the most vulnerable to abuse.

34

Common Knife Grinds

Flat Grind (Rolled Edge) - Produces the strongest blade, the cutting edge becomes thicker after repeated use and re-sharpening. It's a little harder to re-sharpen.

Flat Grind (V-Grind) - Produces a very sharp cutting edge with reasonable blade strength. Easy to re-sharpen.

35

Knife Grinds

36

Common Sharpening Stones

• Understanding the Differences in Materials• The three most common types of sharpening stones are:

• Oil stones

• Water stones

• Diamond stones.

• Each of these stones has its own advantages that can help users achieve their sharpening goals.

37

Oil Stones

• Oil stones are the traditional Western stones that many people grew up using. These stones are made from one of three materials:

• Novaculite

• India Stones (Aluminum Oxide)

• Silicon Carbide

These use oil for swarf (metal filing) removal.

38

Novaculite Stones

• These natural stones (almost pure quartz) are quarried in Arkansas and processed to make what we call Arkansas Stones. These stones are separated into different grades related to the density and the finish a stone produces on a blade. The coarsest of them are called Washita. The finer grades are called Soft Arkansas, Hard Arkansas and Hard Translucent Arkansas. These are sedimentary rocks.

• These natural oil stones can produce a polished edge, but tend to cut more slowly than man-made stones.

39

Oil Stones

• Novaculite Stone– Arkansas Stones

• Washita (coarsest)• Soft Arkansas• Hard Arkansas• Hard Translucent Arkansas

40

Norton Stones

Norton sharpening stones are available in three different abrasives-

• Crystolon® • India® • Arkansas

Each designed to meet specific needs

41

Crystolon Stones

• Crystolon stones:

• Made of silicon carbide electric-furnace abrasive, gray or black in color. This fast-cutting abrasive is harder than any natural abrasive except diamond, and does an outstanding job finishing carbide tools or removing metal, when moderate tolerances are acceptable. Crystolon is the choice where speed of sharpening is most important, or as the first step in sharpening badly worn cutting edges. Available in

coarse, medium and fine grits.

42

India Stones

• India stones are made of aluminum oxide electric furnace abrasive, brown or orange in color. This abrasive is preferred for producing exceptionally keen, long-lasting edges, and for high-quality steel tool work. The choice over Crystolon where close tolerances and smooth cutting edges are required. Available in coarse, medium and fine grits.

43

Arkansas Stones

• Arkansas natural abrasive stones are made of Novaculite, white to black in color.

• Hard Arkansas (ultra fine grit), with its very dense, close construction, is recommended for final honing where the sharpest precision edges possible are needed.

• Soft Arkansas (super fine grit), with its less dense and more open construction, is ideal for producing final finishes after prior sharpening with electric furnace abrasives.

44

India Stones

• The next fastest cutting oil stone is called the India stone. The India stone is made of Aluminum Oxide. These stones can cut fast, and can also produce a fine edge on tools and knives. The grading system for these stones is generally labeled fine, medium and coarse. These stones are often brown or orange

in color.

45

Silicon Carbide

• The fastest cutting oil stones are made of Silicon Carbide. The silicon carbide stones made by Norton are called Crystolon stones. These stones are also labeled fine, medium and coarse. They are usually gray in color. While these stones won't produce an edge as fine as the India or natural stones, the fast cutting make them ideal for initial coarse

sharpening.

46

• Aluminum oxide (Corundum)

• Silicon Carbide (Carorundum)

47

Oil Stones

• The main disadvantage of the oil stone is its slower cutting rate. Of the three main stone types, the oil stone is the slowest.

• The fact that oil is used to remove the swarf is also messier to clean up than water.

48

Water Stones

• A natural stone consisting of microscopic particles of quartz suspended in a clay matrix. When sharpening, the clay slowly dissolves away exposing fresh quartz particles. The advantage of the system is that the quartz particles are always fresh and sharp, hence the stones are somewhat softer and

cut faster than Arkansas stones.

• Natural water stones are sedimentary rocks.

49

Water Stones

• Synthetic water stones are generally made of Aluminum Oxide. This is the same abrasive material used in the India stones. However, the difference is the binder that holds the abrasives in the water stone together. Water stones are softer than India stones, which promotes faster cutting because the old abrasive material breaks away and is replaced

with fresh sharp material.

50

Water Stones

• Fast cutting is clearly an advantage of the water stone. The other obvious advantage is the use of water rather than oil to remove the swarf from the stone. However, the water stone is not perfect. The softness that promotes fast cutting also wears the stone down more quickly. This tends to wear the stone unevenly, which requires flattening to bring the stone back into shape.

51

Water Stones

• Grades of Japanese water stones:

• Historically, there are three broad grades of Japanese sharpening stones: the ara-to, or "rough stone", the naka-to or "middle/medium stone" and the shiage-to or "finishing stone". There is a fourth type of stone, the nagura, which is not used directly. Rather, it is used to form a cutting slurry on the shiage-to, which is often too hard to create the necessary slurry.

52

Water Stones

• Converting these names to absolute grit size is difficult as the classes are broad and natural stones have no inherent "grit number".

• As an indication, ara-to is probably (using a non-Japanese system of grading grit size) 500 – 1000 grit. The naka-to is probably 3000 – 5000 grit and the shiage-to is likely 7000 – 10000 grit.

53

Diamond Stones

Made from industrial diamonds. Diamond powder is bonded to either a steel or plastic substrate. In use the stones can be lubricated with water.

54

Diamond Stones• There are two main types of diamond stone styles.

The more common style contains holes in the diamond surface to capture the swarf. These stones cut very fast and are very simple to use.

• The next type is the continuous diamond surface. These stones are preferred when you are sharpening tools with points that might get caught in the recesses of the non-continuous diamond surface.

• Both types of diamond stones are available in mono-crystalline and poly-crystalline diamonds. The mono-crystalline diamonds are more desirable as they will last longer. The poly-crystalline are cheaper.

55

Diamond Stones

• The two greatest advantages of the diamond stone are the very fast cutting that the diamonds provide and the flatness that is retained by the diamond stone. In fact, coarse diamond stones are often used to flatten oil or water stones.

• The main disadvantage of the diamond stone is its initial cost. While these stones are the most expensive, they will also last a long time, so the long-term cost can be comparable to other stones.

56

Ceramic Stones

Several manufacturers have introduced hard ceramic stones into the market. The stones are made of the same aluminum oxide used to make Japanese water stones but the material is bonded together into a hard mass. The stones use water, not oil.

57

Soft vs. Hard Stones

• Remember that a soft stone is more abrasive than a hard one.

• The fine, glasslike surface on a hard stone is for finishing.

58

Grinding Wheels

• Vintage Grinding Wheels

59

Grinding Wheel

• Most lathe tools will be made out of either carbon steel or high-speed steel. It is important to remember the material of each of your lathe tools, because you will want to use different grinding wheels for each.

• You will want to use silicon carbide wheels for carbon steel and aluminum oxide wheels for high-

speed steel.

60

Grinding Wheel

• It is easy to tell the difference between the two types of wheels. Silicon carbide wheels are dark gray in color. They are also commonly known as carborundum wheels. Aluminum oxide wheels are

much lighter in color, almost white.

• You can use aluminum oxide wheels for both types of steel.

61

Grinding Wheel

• Norton Blue Wheel --- I- Grade

This wheel is a softer I-grade suitable for high carbon steel.

62

Grinding Wheel

• Norton Blue Wheel --- K-Grade

• This is the wheel that wood turners have been asking us about. The K-Grade of this wheel means it is a harder wheel. The harder grade is great for sharpening high speed steel tools without wearing grooves in the wheel. If you're a turner, you

know what we're talking about.

63

Grinding Wheel

• Norton White Wheel --- J-Grade

• The white aluminum oxide is the standard for grinding cutting tools such as chisels and plane irons. Unlike the gray wheels that come with most bench grinders, these wheels help keep your tool much cooler so your tool doesn't overheat and weaken your cutting edge. Our medium 60 grit is a good way to grind your initial bevel. Our 100 grit provides a finer edge. After grinding, a few strokes on a bench stone and your tools are ready for use.

64

Scary Sharp System

Use abrasive sheets to substitute as single-use stones. One glues progressively finer sheets of sand paper onto a flat surface and then sharpens until the

paper wears out.

65

Shapton’s GlassStone System

• Shapton's all new ceramic on tempered glass abrasives are the perfect answer to your sharpening needs (picture and link)

• Shapton has pioneered a totally new concept for diamond abrasive technology. Marrying microchip production methods with diamond abrasive technology, Shapton has built the

worlds first diamond on glass lapping plate.

67

Sharpening Guide

• Chisel Guide

68

Sharpening Guide

• Homemade

69

Sharpening Guide

• Homemade

70

Tormek Wheel• Newer System

71

Oneway Wolverine Jig

• Flat Tool Sharpening and Honing Jig

                                  

              

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Oneway Wolverine Grinding Jig

73

Oneway Skew Grinding

• Attachment

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Wolverine Veri-Grind

• Attachment

                         

     

75

Work Sharp Wood Tool Sharpener

                                  

              

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Recommendation

Bench Chisels

Water stones

Diamond stones

Oilstones

Honing guides

Plane IronsWater stones Diamond stones Oilstones Honing guides Replacement blades

78

Recommendation

Router Bits Carving Tools

Diamond Folding Hone Carving Slips

Diamond Mini Hone Diamond stones

Diamond Folding Hone Oilstones

Strops

Pastes and Compounds

79

Recommendation

Carbide Tipped Saw Blades Scrapers

Diamond Mini Hone Burnisher

Diamond Folding Hone Water stones

Diamond stones

Oilstones

Mill Files

80

Sharpen Router Bit

• 2. Glide the bit with light pressure along the stone. To maintain balance repeat the same number of strokes on other wing. Usually only 5-30 strokes.    

1. Always sharpen the flat side, never the profile.

Using diamond sharpening stone/tool:

81

Sharpen Saw Blade

• Use diamond tool/stone:

1. Keep diamond surface flat to the inner face of saw tooth.  2. Use the same number of light, smooth, back and forth

strokes on each tooth. 

TIP: Mark the first tooth sharpened with chalk to avoid dressing twice.

82

Sharpen Serrated Blade

• Best to use ceramic or diamond tool:

83

Mohs Hardness Scale

• Devised by German mineralogist Friedrich Mohs in 1822, the Mohs Scale grades minerals on a comparative scale from 1 (very soft) to 10 (very hard).

What the scale means is that a mineral of a given hardness rating will scratch other minerals of the same rating, as well as any minerals of a lower hardness rating. For example, rubies and sapphires, which are composed of the mineral corundum and have a Mohs rating of 9, will scratch each other, as well as topaz (rating 8) and quartz (rating 7). But they will not scratch diamonds, which are rated 10.

84

Mohs Hardness Scale

10 Diamond

9 Corundum (Ruby and Sapphire)

8 Topaz

7.5 Beryl (Emerald)

6.5-7.5 Garnet

7 Quartz (Amethyst)

6 Feldspar

5 Apatite

4 Fluorite

3 Calcite

2 Gypsum

1 Talc

85

Mohs Hardness Scale

• What the scale does not make obvious is that the numeric values assigned to each interval of hardness are not equal. Some stones are disproportionately harder than others:

Stone Mohs Rating Results

Diamond 10 Approx. 90 harder than corundum

Ruby/Sapphire

(Corundum)

9 Approx. 5 times harder than topaz

Topaz 8 Little difference between topaz and quartz

86

Hardness Ratings on Mohs Scale

• Novaculite - 6.5 (a bit harder than file steel)

• Aluminum oxide - 9.2

• Silicon carbide - 9.5

• Ceramic -- 9.5 (will sharpen anything except carbide tipped tools)

• Diamond - 10

87

Rockwell Hardness Tester• Sample:

                              

                                                                           

89

Types of Tool Steel

• Most lathe tools will be made out of either carbon steel or high-speed steel. It is important to remember the material of each of your lathe tools, because you will want to use different grinding wheels for each.

• You will want to use silicon carbide wheels for carbon steel and aluminum oxide wheels for high-speed steel.

• You can use aluminum oxide wheels for both types of steel.

90

Types of Tool Steel

• For the past two centuries the best steels for woodworking in the West were made from what was called "Cast Steel".

• This process became extinct around the Second World War and various alloy steels came in vogue.

91

Carbon Steel

• Carbon steel, also called plain carbon steel, is a metal alloy, a combination of two elements, iron and carbon, where other elements are present in quantities too small to affect the properties. The only other alloying elements allowed in plain-carbon steel are manganese (1.65% max), silicon (0.60% max), and copper (0.60% max).

92

Carbon Steel

• Steel with a low carbon content has the same properties as iron, soft but easily formed. As carbon content rises the metal becomes harder and stronger but less ductile and more difficult to weld. Higher carbon content lowers steel's melting point and its temperature resistance in general.

93

Types of Carbon Steel• Mild (low carbon) steel: approximately 0.05–0.29% carbon content

(e.g. AISI 1018 steel). Mild steel has a relatively low tensile strength, but it is cheap and malleable; surface hardness can be increased through carburizing.

• Medium carbon steel: approximately 0.30–0.59% carbon content (e.g. AISI 1040 steel). Balances ductility and strength and has good wear resistance; used for large parts, forging and automotive components.

• High carbon steel: approximately 0.6–0.99% carbon content. Very strong, used for springs and high-strength wires.

• Ultra-high carbon steel: approximately 1.0–2.0% carbon content. Steels that can be tempered to great hardness. Used for special purposes like (non-industrial-purpose) knives, axles or punches. Most steels with more than 1.2% carbon content are made using powder metallurgy and usually fall in the category of high alloy carbon steels.

94

High Speed Steel

• Alloy of steel introduced in 1900. It doubled or trebled the capacities of machine shops by permitting the operation of machine tools at twice or three times the speeds possible with carbon steel (which loses its cutting edge when the temperature produced by the friction of the cutting action is above about 400°F, or 210°C). A common type of high-speed steel contains 18% tungsten, 4% chromium, 1% vanadium, and only 0.5 – 0.8% carbon.

95

High Speed Steel

• High speed steel (often abbreviated HSS) is a material usually used in the manufacture of machine tool bits and other cutters. It is often used in power saw blades and drill bits. It is superior to the older high carbon steel tools used extensively through the 1940s in that it can withstand higher temperatures without losing its temper (hardness). This property allows HSS to cut faster than high carbon steel, hence the name high speed steel.

• At room temperature HSS and high carbon steel have an equivalent hardness; only at elevated temperatures does HSS become advantageous.

96

High Speed Steel

• Tungsten is the major alloying element but it is also combined with molybdenum, vanadium and cobalt in varying amounts. Although replaced by cemented carbides for many applications it is still widely used for the manufacture of taps, dies, twist drills, reamers, saw blades and other cutting tools.

97

About Steel

• “The three qualities that most effect the selection of a steel for a hand-tool application are edge-holding, sharpenability, and corrosion-resistance. For metallurgical reasons, you can only have two of the three. We at HOCKTOOLS feel that in woodworking, corrosion-resistance is the least important of the three, and prefer an edge that is easily sharpened and long lasting.”

• from: www.hocktools.com

98

About Steel

• “A steel's carbon content determines its ability to harden with heat treatment. That hardness determines a tool's ability to hold a sharp cutting edge under abrasive pressure (wear). Generally, the harder the metal the better its edge holding, but it will be more brittle. Tempering reduces that brittleness, although it also reduces the tool's hardness and wear resistance. So a balance must be struck to decide how hard a blade should be. Our blades are hardened to Rc62 for long edge life. This is harder than most available replacement blades yet not as hard or brittle as most Japanese blades.”

• from: www.hocktools.com 

99

About Steel

• "Tool Steel" refers to a class of steels that are metalurgically very "clean" and fall within strict limits for alloy proportions. Vanadium, tungsten, and molybdenum are often added to tool steels to make the steel resist annealing (softening) when used in "high-speed" (high heat) applications. Chromium is added in very large quantities for corrosion

resistance ("stainless").

• from: www.hocktools.com

100

About Steel

• “High-speed steels are essential in metal-working tools (drills, milling cutters, etc.) and "stainless" steels can be cost effective by resisting rust during the manufacture, shipping, and storage of the tool itself. Correctly heat-treated, tools made from high-speed, stainless, and "chrome-vanadium" steels may hold an edge well in woodworking applications, but, due to the large, hard carbide particles that form during hardening, they are difficult to sharpen and cannot be honed as sharply as a blade of plain high-carbon steel.”

• from: www.hocktools.com

101

About Steel

“Our choice of High-Carbon Tool-Steel (.95% Carbon) offers the finest, sharpest edge possible. Its chromium and vanadium additions amount to only 1/2% each allowing quick, clean honing with traditional techniques. High-carbon steel holds and

takes an edge better than anything else.”

from: www.hocktools.com

102

A2 Steel

• More recently, toolmakers have been experimenting with fairly complex alloys, the most popular called "A2" steel.

• (The “A” refers to it being Air Hardened.)

103

A2 Tool Steel

• These steels have a common trait of being able to hold a very fine edge but also retain toughness against wear - so the blade lasts longer between sharpenings.

• Some experts believe that A2 steel, due to its crystaline structure is incapable of being sharpened as finely as older steels but the new alloys have become very popular.

104

A2 Tool Steel

• Sharpening them takes slightly longer and the harder abrasives of water stones are an advantage. However, Arkansas stones still work well, but a bit more slowly and, of course, have the feature of

remaining flat.

105

About A2 Tool Steel

• A2 differs from our usual High Carbon Steel with the addition of significant amounts of chromium and molybdenum. While “stainless” amounts of chromium (12% or more) make tool steel “gummy” and hard to sharpen, the modest amount of chromium in A2 (5%) improves its toughness and abrasion resistance, but imparts only a slight measure of corrosion resistance (like High Carbon Steel, it will rust and appropriate preventative care must be taken.)

• from: hocktools.com

106

About A2 Tool Steel

• “A2 is one of the steels that respond well to Cryogenic Treatment. This extreme cold treatment (-320F) increases the steel’s toughness without any decrease in hardness. You get increased wear resistance without any increase in brittleness so a Cryogenically treated blade will hold its edge longer. You can keep working instead of sharpening.”

• “We’ve differentiated these blades to avoid mixing them with our other blades by cutting the top corners with a 45-degree chamfer instead of our usual rounded corners. And they're marked "A2 Cryo".

• from: www.hocktools.com

107

Sharpening Japanese Sword

108

Sharpening Japanese Sword

109

Sharpening Japanese Sword

110

Sharpening 101

THE END

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