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.