Garden Goodies

Here are a couple of photos showing some of our garden produce.

The top photo is a bowl-full of Aji Limon peppers.  They are spicy with a fair amount of "sneaker heat", and, in addition to the yellow color, they actually do have a nice citrus-like flavor.  I turned these into a fermented brined-pepper mash.  Very tasty, and a good way to preserve garden produce for the winter.

The second photo shows the winter squash we got this year.  There are several varieties shown here:  Cinderella pumpkin (the large orange guys), Kuru (small orange), Buttercup (small dark green), Sweet Meat (medium-sized gray-green), Butternut (oblong tan fruits), and Queensland Blue (medium sized gray-green, ribbed).  The Kuru and Queensland Blue were new to us this year.  We like the Kuru -- we put it in a batch of Mussaman Curry last night.  The Queensland Blue is very hard and dense, but the flavor is not as good as the others.  Our overall favorite winter squash:  Sweet Meat.  Best keeper:  Butternut.

Rocking Toy Part 2

Summer activities -- gardening, playing, etc. have delayed part 2 of my rocking toy post.  We're canning tomato juice right now, which involves some basic hanging around to do the hot water bath -- so I have some "spare" time to do part 2.

In part 1 I explained the basic principle of a pendulum or other simple mechanical oscillators.  My first photo shows the can opener that first got my attention:

 It's a simple old-fashioned "church key" with a punch on one end and a crown cap remover on the other.  In the context of a rocking toy, the opener rocks on the point of the punch and the arc of the cap remover.

 The above photo shows the church key with some added weights -- a stack of small neodymium magnets.  The idea was to raise the overall center of gravity so it was closer to the center of rotation.  This in turn would reduce the oscillation frequency, which it did -- the new oscillation frequency was about 1 hertz.

And now, my version of the rocking toy.  The main piece is about the same length.  I drilled and tapped a hole on the left for the pivot, which is a bolt whose end was formed into a taper using my lathe.  The right side has an arc machined into it, using my milling machine and rotary table.  I smoothed the arc with some 220 grit wet/dry sandpaper.  I also needed to bend the right-hand end down, to replicate the church key.  To make sure the bend was exactly perpendicular to the long axis of the bar, I cut a slot (again, with my mill) from the top to bottom of the bar.  It is about halfway through the bar.  Then I put it in a vise and bent it until it was about the same angle as the church key.

The end result is a mechanical oscillator that, again, has a surprisingly low frequency -- although for some reason as yet undetermined, my version oscillates at a slightly higher frequency.  Anyway, it is a fun "twiddler" to play around with.

If I was going to make another one, I would use cold-rolled steel instead -- it has a much nicer finish.  And refine the corners on the left side so it has a more refined appearance.  But those are just aesthetics.

First food post

Something that should be clear by now is we have a broad range of interests.  That includes food.  My wife and I have a 1600 square foot vegetable garden.  In some years we have extracted about 1,000 pounds of winter squash from it, in addition to quarts of tomato sauce, myriad zucchini, peppers, cucumbers, leaf vegetables, beets, basil, and on and on.

But we've been aging cheese, as well.  A well-aged Tillamook cheddar can  beat just about any other cheese, and, if you have the space in your 'fridge (or a separate refrigerated cheese vault), you can enjoy some really flavorful cheese for a very cost.  We have aged cheddar, in its original wrapper, for well over 10 years.   The acid level of the cheese, plus the salt content, does a good job of preserving it.  And the aging process produces lots of flavor components (like glutemates) that really ratchet up the flavor.

As an experiment, we bought a 2 pound brick of Tillamook "colby" cheese awhile back.  It is a milder sorta-cheddar/jack cheese.  But the price was right, and we had the space to store it awhile.  Well, that aging time turned into 15 years (!).  We rediscovered it, observed some potential issues, so decided to open the package and taste it.  Well, it is just fine -- some might say terrific.  Because this style of cheese often has some added red pigment, it looks a little odd --pink-- but it tastes great.  By the way, a well-aged Tillamook that has absorbed some truffle flavor from some Oregon white truffles, is amazing.

The main issue with preserved food is either the hydration level (think jerkey on the good side) or acid.  If the acid level produces a pH level of 4.3 or lower, clostridium botuliun can't grow, so the food is safe to consume.  Not to say it's tasty, that depends on other fermentation parameters.  Fermentation is not just about beer or wine, it helps make sauerkraut, kimchi, pickles, and artisan sausages.  It converts part of the food product to (typically) lactic acid.  Acids reduce the pH of food, and most putrefying bacteria don't like low pH.  So they are more stable.

Fermentations like this are used to produce (as mentioned above), sauerkraut, pickles, kimchi and sausages.  It also is used to make bread, cider vinegar, wine, beer, sake, miso, soy sauce, fish sauce, and many other foods found across the world.  In most cases, the fermented foods have more nutritional benefits than the original input biomass.  This it not an opinion.  Additional nutritional benefits are well documented.

Just say'in.

An unusual cooling system idea

Sorry, no drawings or photos in this post.  Brain work only.

In warm seasons like this one, my thoughts sometimes turn to DIY air conditioning (AC).  In our climate, AC is one of those rarely-needed things so buying some off-the-shelf solution doesn't appear to be a very cost effective solution.  I'd much rather spend lots more time and less money on something that works well enough to take the edge off the heat when it occasionally occurs.  I've seen approaches using evaporative cooling, but our climate also has an additional challenge -- relatively high humidity.  So-called "swamp coolers" work best in regions where the relative humidity is low.  They're more efficient, and the added moisture to the air is welcome.  On the other hand, when you start with 60% relative humidity, the cooling action isn't as good:  and the increased humidity due to the swamp cooler can actually make you LESS comfortable, even if the temperature is slightly lower.

There are indirect cooling approaches where a heat exchanger comes into play, cooling inside air without adding moisture.  The heat exchanger is an added complexity, and also has its own impact on efficiency.  What if we could start with much-cooler water, cooler than can be achieved using evaporative cooling?  If we can get that, perhaps we can live with less-than-perfect heat exchanger technology.

There may be a way to do this.

Long ago I performed an experiment to see if it would be possible to make my own turbomolecular vacuum pump (I refer you to Google to get educated on this type of vacuum pump). I mounted two thin mylar plastic disks on an axle. They were spaced a few tenths of an inch apart. Then I spun them up, using either a Dremel tool or an electric drill (this WAS a long time ago so I don’t remember that part all that clearly). Centrifugal force would pull the disks into flat planes, but, if some pumping action were taking place, the space between the disks would be at a lower pressure so the disks would be pushed together. I observed that the disks were indeed pushed toward each other so some pumping action was going on. I could not increase the speed enough to get the disks to touch, due to instability and vibration problems, but this problem probably could be solved with some refinement.

If the axle was made from a tube, and we drilled some holes in it between the two disks, it is likely that some sort of pumping action would occur that would pull gas down the tube toward the disks: but now we’re faced with making a good rotary seal. The angular velocity of the tube would be less than the outer edges of the disks, but it still is a nontrivial problem if you want a reliable vacuum pump.

So that approach languished for a long time. But I recently had an idea where the scheme could still be useful. As a chiller. In point of fact, it would function as a single-pass refrigeration system. In this approach, the spinning tube is dipped into a water reservoir. The tube also has a restrictor to reduce the water flow so the water doesn’t completely fill the pump. If the water does fill the pump, I believe the water probably will boil in the disk portion of the pump and screw up the cooling cycle (see below). If sufficient vacuum is developed the water will boil, extracting heat from its surroundings. The water vapor is ejected by the spinning disk pump, where it immediately re-condenses (and liberates the heat it absorbed when it boiled).

In its simplest form, the rotating tube would be submerged in the water so the expansion of liquid water into water vapor would cool the water on the immediate exterior of the tube, which could then be circulated into a secondary heat exchanger. Efficiency could be improved by increasing the surface area of the submerged tube, perhaps with aluminum or copper disks (but they can’t be too large or frictional forces would limit the maximum RPM, and also heat the water).

The advantage of this method is that the minimum-achievable temperature is not determined by the relative humidity of air, unlike a standard evaporative air conditioner. The minimum temperature would be the freezing point of water (0C/32F).

NOTE: this scheme could be foiled by the buildup of minerals from the water feedstock, since the minerals would be concentrated by the liquid-vapor conversion.  Some type of purge or ballast-water approach would be needed for a commercially viable system.

Also NOTE: while one might think the water vapor exiting the pump would be cold & therefore useful for cooling purposes, in fact it will re-condense as soon as its pressure returns to room pressure. When this happens, it will release the heat it absorbed.  Now, of course, the water will be very finely dispersed and some to all of it will evaporate in the ambient air – again cooling down in the process. But there won’t be any “gain” offered by the pump, and the ultimate minimum-low temperature will be determined by the dew point of the ambient air – much higher than the freezing point of water.

So it appears the energy input of the spinning-disk scheme is best used as a way to implement a single-pass refrigeration system.  I use the term "single-pass" because the input fluid, water, is available without any special condensor.  Unlike a classic closed-system refrigeration system.

 

Rockin' out, part 1. An observation and pendulum theory.

Some time back I was playing with an old-fashioned bottle opener, commonly known as a "church key".  At one point I placed the opener down so the rounded and pointed ends were facing down, touching the counter top (polished granite).  Here's a photo of the opener:

  When I put the opener down, I noticed it rocked back and forth surprisingly slowly.  Intrigued, I looked more closely at what was going on.  I saw that the opener rocked back & forth across the curved end, and in that configuration the opener was pretty stable.  It would eventually tip over if pushed over too far.

And then I tried an experiment to see if I could further increase the period of this simple mechanical oscillator.  We have some small (~1/8" square) super-magnets that are used to hold photos, coupons etc. on our refrigerator.  I stacked several of them together to raise the overall center of mass of the system, and put the stack on the opener.  Sure enough, the opener rocked even more slowly.  See below (sorry, no videos yet):

I was able to increase the period to about 1/2 second/cycle, pretty amazing considering the relatively small size and mass of the system.  Due to the relatively poor finish on the rounded end of the opener, it rocked in an irregular fashion.

I started thinking about making an "improved" version of this,  for a fun little machining project.  I did finally make one, with one false start.   But at this point, rather than just showing what I did I want to start by explaining the physics behind the mechanical oscillator, and what determines its frequency.   I will start with the pendulum, as shown below (two different positions of the sphere are shown).

The sphere is hanging on a cord of "R" length.  So what causes the sphere to swing back & forth?  Take a look at the right-hand drawing of the pendulum.  The sphere has moved over, and, due to the fact that the cord is a constant length, the sphere rises slightly.  Since the force of gravity always points down but the cord is at an angle, a restoring force appears which opposes the deflection of the sphere (this assumes that the forces due to gravity and acceleration are transmitted along the cord at angle "w").  In a dynamic situation the system exhibits a periodic transfer of energy between potential energy (due to the lift "H") and kinetic energy.  What determines the oscillation frequency?  If the cord is lengthened, for a given angle "W" "H" becomes smaller, and the restoring force becomes less.  The effect is to slow the pendulum oscillations down.  If we increase the mass, the acceleration decreases due to the relationship F = Ma where M is the mass of the sphere and a is the acceleration.  Solving for acceleration:  a = F/M.  Therefore the mass accelerates more slowly under the influence of the restoring force.  So frequency also decreases as mass increases.

Another way to look at the pendulum is as a system with a center of mass that is constrained to move around a given radius of curvature.  In these terms, the oscillating bottle opener is a similar type of mechanical oscillator.  Increasing the mass (by putting magnets on top of the the opener) decreased the oscillation frequency, just as it does for a pendulum.  We could continue to add mass until the center of mass is above the center of radius.  At that point the system would become unstable and flop over.  Unlike a pendulum.

Next time:  some implementation considerations with my rocking toy.

4x6 Bandsaw modifications

I recently completed some modifications to my Harbor Freight 4x6 bandsaw. 

I added a collection chute for saw swarf, vise jaw extensions so I can saw shorter pieces of stock, two jack "screws" to help keep the movable jaw from tilting backwards when clamping, and a jack rod to stabilize the movable jaw in the other axis.

The above photo shows the chute on the right.  I used some scrap sheet metal left over from our house project and a small metal bender (also purchased at Harbor Freight) to form the sides.  I drilled a couple of holes in the casting and chute to bolt the chute to the saw.  This arrangement doesn't capture all the swarf but it's far better than my previous setup, which was a paper bag taped to the base with duct tape.  It didn't take long for the tape to get crudded up with swarf and cutting oil, so I had to re-attach the bag every time I wanted to use the bandsaw.

You also can see two brass #10-32 "jack screws" on either side of the 14mm bolt used to attach the movable jaw to the screw nut.  They are used to stabilize the jaw so it doesn't rotate away from the stock as much when clamping it.  I faced off the ends of the screws to maximize the contact area between the screw and bandsaw table; and the brass won't scratch or mar the cast iron (I hope).  Finger tight is good enough for this.

The jack rod, on the left side of the jaws, is used to keep the movable jaw from rotating away from stock on the other axis.  In use, after the stock is lightly clamped the rod is run up to the fixed jaw and clamped in place.  Then the jaw is tightened down to secure the work.

 
This is a different view showing the jack rod and how I hold it in place.  I drilled a 1/2" hole in the plate, then used the band saw to cut a slot from the bottom of plate up to the hole.  There are two steel blocks mounted to the plate, on either side of the slot.  A 1/4" bolt feeds through the block that is visible in the photo and threads into the other block.  Tightening the bolt closes the slot and pinches the rod in place.  Actually, I had to widen the slot using a carbide end mill -- otherwise there wasn't quite enough closure to securely hold the jack rod.  If need be I can remove the rod for large items I'm cutting -- nothing else protrudes past the surface of the 1/4" thick plate.  There is a lot of mechanical advantage at work here -- the screw and the lever action -- so once the bolt is tightened that jack rod is going nowhere.

I'm using a piece of scrap aluminum rod, no need to use steel in this application.

Harbor Freight wire welder modification

Something I haven't done much with yet is welding/brazing to fabricate items.  I've done a lot of soldering, which is pretty similar to brazing so that doesn't present much of a challenge (so he sez).  Welding is a different story, and looks to be a very handy skill to have.  I started looking into inexpensive learning-level welders and found some info about modifying cheap Harbor Freight  welders, from pretty crappy AC to sort-of-OK DC current welders.

The basic approach is to take your HF alternating-current welder and turn it into a DC welder, using a high current diode bridge and large-value electrolytic capacitor.  This requires some serious mod work, cutting wires and installing the rectifier/capacitor inside the welder.  I bought the rectifier and capacitor on ebay (BTW, this type of modification is described on a number of web sites so I don't think it is necessary to go into much detail here). 

I also got some 10 gauge multi stranded wire and spade type connectors to match, to make sure the connectors and wire would not limit the current available for welding.  Wire this size is pretty stiff so it is necessary to think about the physical arrangement of the wires/diode bridge/capacitor so you are not exposing the device terminals to excess stress.

I finally completed the mods but was not totally confident that everything was wired up correctly.  To verify the wiring I performed an incremental power-up test.  I began by using an external 40V power supply.  I used it to bias up the capacitor and (hopefully) back-bias the diode bridge (it should look like an open circuit).  Everything looked OK so I plugged the welder power cord in, took a deep breath and flicked the power switch.  Nothing, nada.  Well, not all bad -- no smoke.  But not great, either.  So I cussed and opened the welder back up, and discovered I had not reconnected a connector on the controller board.  Well, that's better than an egregious wiring error I guess. 

After plugging the connector back in, the welder powered up OK.  Some trial runs produced results that clearly showed I need some practice making a good bead -- not too surprising there, but I got some good metal puddles that show promise. 

I started out with the slowest wire feed rate and just got "bangs" as the capacitor charged up and blew out the welding wire.  Now I'm up to about the halfway point on the feed-rate dial (whatever that means in physical terms) and get a more or less continuous arc.  I ran some beads across the surface of some iron plate I had for the testing.  The next thing to try:  gluing some metal pieces together to see how well this metal glue gun works.

Fun stuff.

By the way, while doing the welding tests I wore protective gear, including a welding helmet with eye protection.  The ultraviolet light from arc welding is hazardous!  Heed all warnings that come with your welder.

Improving the mini lathe tailstock

The first time I tried using my mini-lathe's tailstock I realized it needed help.  The drill bits were far from the center of the work-- so much so that I broke the tip of my center drill when I tried to start a hole!

I sort-of addressed the problem by making a toolpost mount for a drill chuck -- but it requires alignment every time I use it.  Plus, the forces tended to lift the carriage.  So there still were reasons to work on the tailstock.

The first thing to do was to get the top of the base parallel to the lathe bed, and the vertical boss exactly perpendicular to the bed.  I began by measuring the variation in height from the front to the back of the base.  I found the back was higher by .010".  This measurement would come in handy later on in the machining procedure.

Since the "vee" in the base establishes the alignment of the base relative to the bed, I arranged things so I could align the base with respect to the vee.  I did this with a precision-ground linear rod -- see below:

The DTI is a .0001, and I was able to align the rod/base to within about .0002".  If you look closely, you can see that the right side of the base has already been milled.  The photo shows the base being set up to mill the left side.  Also, before rotating the base to mill the ends, I milled the boss (the vertical "fin" in the middle of the base).  This ensured that the surface of the boss was exactly perpendicular to the lathe bed.  At this point I did not mill the top surface of the base, because I needed to establish the same front-to-back .010" height variation.  I needed to make an adjustable-height fixture, which is shown below.

The fixture is next to the moveable jaw of the vise, and is just a #10-24 bolt screwed into a threaded plate.  I turned the end of the bolt down to a rounded point, thinking this would ensure the base would ONLY align itself to the rod.  I adjusted the bolt until the top of the base had the same .010" slope, then milled the base.  This ensured that the top of the base was parallel to the lathe bed.

Next, I moved on to the top of the tailstock.  In this case, I extended the quill and clamped it in the vise, using the horizontal "vee" in the moveable jaw to establish the horizontal plane.  I also checked the alignment using a DTI and found it was OK.  I then adjusted the tailstock (bumping it with a dead blow hammer) until the mating surfaces were parallel to the milling head.  See below.

A quick check with the DTI showed that the two surfaces were not on the same plane, which would affect the vertical alignment.  So I milled off enough to equalize the two surfaces.  I also milled the vertical face that contacts the base.  This ensured that the quill would be parallel to the lathe bed.

After doing all this, I found that the tailstock was too low, to the tune of about .080 inch.  To address this I machined a couple of spacers.  This in itself was an "interesting" exercise because the spacers needed to be the same thickness.  I did it by machining a large spacer and cutting it in half.  I machined both sides of the stock to minimize the effects of warp due to stress relief (and also to address any tram related issues).

The tailstock alignment substantially improved after these mods.  It was a bit of a pain to set the alignment, but, since I'm not planning on turning any tapers, I have no plans at this point to add a tailstock adjuster.

Mini Mill Fine Feed Z Axis Crank

Every time I use the boring head on my mini mill I've told myself I need to make a crank for it.  The stock knob for the fine feed is pretty small so it's a pain to run the cutter down & then back up.  I had held off because I had been thinking about a crank that's similar to the X and Y axes.  Then I realized that I just needed a longer lever (and a handle) to get what I wanted.  After that, I got to work and made this:

The crank is made of flat aluminum stock.  I made the handle out of brass and polished it up a bit using some quadruple-0 steel wool.  I used an off-the-shelf shoulder bolt so the handle could spin freely, and eased the head a bit using my lathe and ball turning attachment.  The crank is attached using a couple of drilled/tapped holes in the fine feed knob.

The ball turner turned into a project as well -- I figured out that its design really required a mod to the lathe so I could manually drive the lead screw (to drive the carriage).  So the first crank I made turned out to be for the lathe.  Of course, the handle isn't nearly as nice because I did not have a functioning ball turner at that point.

I had thought the crank would be in the way too much to leave it installed all the time, but it has turned out to be so handy that I haven't removed it.  When the fine feed is not engaged the crank hangs down, as shown in the photo.  I suppose if it gets too annoying I could come up with something to hold it in some other orientation.  But to date it hasn't been a problem.

Knife Sharpener Prototype (?)

Implementing my knife sharpener took longer than expected, at least partly due to the surprising number of different machining steps it needed.  The knife holder needed three drilled/tapped holes and a 1/2" hole for mounting it on the base.  It also needed a recess milled to accommodate the thickness of a washer used with the mount.  The mount is a 1/2" diameter aluminum rod that was cut down to 7/16" and threaded so it could be bolted to the base.

The mast also required some machining -- in this case, a 1/2-20 threaded portion to bolt it to the base.  The pivot piece was machined from Acetal, and needed some machining so it could be attached to the mast (and also permit the sharpening rod to pivot).

The sharpening rod has two Acetal blocks screwed to it.  They are used to hold the sharpening stone.  I also had to fabricate a handle and place it correctly so the operator could not be cut by the knife.  Making the handle took a number of steps, too, but it turned out pretty nice.  I used brass for a bit of eye candy.

Anyway, here is the result:

The photo shows the knife installed in the holder.  It is not clamped down -- there is a recess on the back of the holder where the back of the blade fits, so it is held securely enough while it is being sharpened.  In use, the sharpening rod rides in the slotted piece that is attached to the mast.  The height is adjusted to get the desired bevel angle (in this case, 20 degrees).

After using this on a couple of knives (starting with an inexpensive one I didn't care about much), I have figured out that I need to make a couple more pieces.  First, I need another rod/stone holder assembly, for a honing stone.  Right now I've got my water stone installed, and after that I hone the knife using a freehand approach.  I also will make another pivot assembly that will be installed above the first one.  In combination with my honing stone I should be able to produce a nice secondary edge that will last a long time.

By the way, the base is a hunk of oak veneer plywood left over from our house project.  The feet are wood dowels that were turned to size on my lathe, then some rubber floor-protector feet were installed over them to protect the counter top.  Since I've got bolts projecting from the bottom of the base I definitely had to have SOMETHING to elevate the base above the counter and this approach seemed the simplest to implement.

At this point I have less than $50 invested in this (including the stones).  That may go up a bit after I make the additional rod/stone assembly.

Anti-Backlash mill modification revisited

It didn't take long for me to become unhappy with the design of my anti-backlash mod.  Due to the large amount of friction, I became concerned about excess wear of the lead screw.  A lot of nonuniform wear could cause problems when traversing to the extremes of the table.  So I started working on a scheme similar to the approach Sherline took on their CNC mill.  Their approach uses an external feed screw nut that is snugged up against the table to remove backlash.  To keep the nut in place, its outer perimeter has a rather coarse knurl.  A thick washer, also knurled on its outer perimeter, engages the external nut.  The external nut is turned via the washer until the backlash is reduced to a low value (while keeping the drag relatively low), then the washer is fixed in place with a bolt thru its center.

Below you can see my version of this:

The round piece is the external nut (fabricated from a feed screw nut I bought from Little Machine Shop).  I drilled a 1/16" hole in the nut, to engage a wire.  The bracket is bolted to the end of the X-axis table.  The slotted piece holds a 1/16" piece of piano wire that was bent to fit into the nut, and is fixed in place with a standoff/bolt combination.

Here's a photo of the installed pieces:

In use, the bolt is loosened so the nut can be rotated clockwise in order to remove any backlash, then tightened.  Since the only force the standoff, slotted piece and wire experience is the frictional torque between the nut and feed screw, they don't need to be very heavy-duty.

With this setup I was able to reduce the uncontrolled table "slop" to about .001", and the mechanical turns dial vs. DRO indicate I have about .002-.003" of backlash.  Before, there was about .005" of slop and about .010" of backlash.

The only thing I would change at this point would be to replace the Philips-style screw with an socket head screw.  Right now, to adjust the backlash I have to remove the feed screw bracket to gain access with a screwdriver.

Knife sharpener geometry -- spreadsheet

I have created a spreadsheet to illustrate the geometry I described in my previous post on the subject.  It can be found at: knife geometry.xls. 

Variables to play with are the radius of the arm (actually, the distance from the pivot point to the knife holder), length of the knife and the rotation angle of the knife.  If the radius is changed you will need to figure out the height of the pivot above the blade, to give you the desired bevel angle.

The spreadsheet has some warts -- some of the parameters have to be entered in several places.  To help figure out what goes where, the spreadsheet parameters are as follows:

Arm radius = 18"
Length of knife blade = 8"
Knife is rotated 12.75 degrees.

To determine the error in bevel angle halfway down the blade, just change the value in cell I50.  Right now it is set to show what the error is at the tip of the blade.  Changing it to 4 inches will show what the error is at the halfway point (in cell B46).

FYI, the angle calculations use the dot product of two normalized vectors.  If you take the dot product of two vectors whose magnitude is 1.0, the result is the cosine of the angle between the vectors.  Vectors can be normalized by dividing each component by the magnitude of the vector, which is given by:  sqrt(x^2 + y^2 + z^2), where x, y and z are the components of the vector in 3 dimensional space.

Dot products are very useful beasts, having a wide range of applications, from calculating the Fourier Transform to computer generated graphics.

Knife sharpening fixture

This entry contains some preliminary work I've done to build a knife sharpening fixture.  No photos as yet, but there probably will be some in a future post.  This time I'm just outlining the geometry of the fixture, variations in the bevel angle along the blade due to the geometry, and approaches to minimize the variations.

Below is a simple figure showing the basic fixture from the side:

 

The vertical mast has a pivot (the circle) whose height can be adjusted.  The line passing through the pivot depicts a rod, whose opposite end has a sharpening stone attached to it (the green line).  The knife is shown in magenta.  Hardware for holding the knife is not shown.  The whole thing is assembled on a base, shown by the thick horizontal black line.

The basic idea is as follows.  The pivot is above the plane of the knife by a distance dictated by the desired bevel angle and distance between the mast and knife.  We can calculate the bevel angle using this:  tan(theta) = H/L, where theta is the desired angle, H is the height of the pivot above the knife, and L is the distance from the mast to the edge of the knife.  If we know theta and L, then H = L*tan(theta).  Caution:  many spreadsheets assume radians, not degrees, are the argument to trig functions.  To convert degrees to radians, remember that 2*pi radians = 360 degrees.  (2*pi/360) * degrees gives you the radians.

There is an interesting aspect of this.  My online searching revealed that most everyone seems to be building fixtures that create a specific half-angle -- not the full angle between the two sides of the bevel.  So, if you're sharpening a knife to a "20 degree bevel", the angle between the two sides of the bevel is twice that -- 40 degrees.  Not that it matters, it's just different relative to the usage found in general machining practice.

Anyway, back to the fixture.  While it might seem to ensure you are sharpening your knife to a specific bevel, that is incorrect.  Take a look at the diagram below.

 The diagram shows the fixture looking down from the top.  The magenta rectangle is the knife and the thin black lines show the position of the rod (plus sharpening stone) over two positions on the knife.  Observation tells us that the bottom line is the shortest line and the top line is longer.  The difference depends on the size of the knife.  This variation in distance causes a variation in the effective bevel angle that will be ground into the knife.  How much of a difference are we talking about here?

Let's do some calculations based on a fixture design I found on the web.  In that design, the shortest distance was set to 10 inches.  Probably to keep the fixture small and easily transported.  If we want a 20 degree bevel, trig tells us that the pivot point must be 3.65 inches above the knife blade.  If we are sharpening an 8" chef's knife, the tip of the knife is further away from the pivot, and as a result the bevel angle is reduced to 15.9 degrees!  Ouch.

How can we improve this situation?  The easiest approach is to increase the distance between the pivot and knife.  Let's increase the distance to 18 inches.  We have to raise the pivot point to 6.55 inches to get a bevel angle of 20 degrees.  This change reduces the variation in bevel angle to 1.6 degrees.

But we can do better than this if we want.  Since the change in bevel angle is due to the increased distance, let's rotate the tip of the knife toward the pivot point to reduce the distance.  It turns out that a rotation of 12.8 degrees will reduce the error to close to zero.  Nice, huh?  Not so fast.  What about the bevel angle at the midpoint of the knife?  With this rotation, the error is .4 degrees.  Still, not too bad.  Zero rotation gives us a MINUS error of about the same magnitude, so that's a wash.

Figuring out the optimum rotation angle of the knife may seem like a mysterious process.  But it's not, and actually is easy to set up.  In the case of our 18"-long fixture, let's use a very large compass to draw a circle around the support mast for the pivot.  The circle will have an 18" radius.  Now, loosely install your knife in the holder and rotate the tip so it just intersects the 18" circle you just drew.  That's the angle you need, because the circle denotes a constant 18" distance from the pivot!  Tighten the holder down and start sharpening, with the assurance that the variation in your bevel angle along the length of your 8" knife is no more than .4 degrees.  Shorter knives will have less variation.  If you are sharpening 10-inchers or longer, maybe you should think about an even bigger fixture, maybe with a baseline of 20 inches or more.  Even so, it still will have a footprint less than 2 feet deep.

The downside of a setup that requires you to rotate the knife has some design complications you may not want to bother with.  For one, you probably need to have a knife holder than can rotate, too.  Then be easily locked into position without engaging in an excessively-complicated procedure.  And for longer blades you probably want some sort of support partway down the blade to keep the blade from flexing (or popping the knife out of the holder).  But to accommodate different blade lengths, the support has to be movable -- the knife rotation angle will change.  Or you will need to fabricate custom holders for each size of knife you have.  Mmm, more tradeoffs.  But that's the fun of design -- addressing problems like this in as elegant a manner as practical.  No, I didn't say "as possible" -- that's not engineering.  The art and fun of engineering is finding the balance between performance and practicality.