Twist drills, a study based on openSCAD

[homebrewed]

Due to some questions I had about sharpening drills using the Vevor M13A drill sharpening tool I recently purchased, I decided to do some modelling using openSCAD. Its linear_extrude() function includes a "twist" parameter that can be used to generate helical forms -- like the flutes in a drill. OpenSCAD has boolean operators that can subtract one shape from another, which is exactly what's needed to create the flutes, and then a "grinding wheel" type surface to produce the cutting lips.

The biggest question in my mind was how a drill's cutting lips are drawn as straight, despite the fact that the cutter face is a section of a (twisted) cylinder. I wasn't sure if all the drawings I found on the web were factually correct or not.

It took a bit of work to figure out the geometry so I could properly specify the helix' twist factor -- the linear_extrude just expects the number of degrees the extruded form is rotated, over the specified length of the extrusion. So a bit of math was needed to do the conversions. Another pair of variables that ultimately I was unable to find were also related to the flutes -- the diameter of the helix, and its distance from the drill's center. I basically played around with some values until I got some results that looked about right. I own and used Machinery's Handbook volume 26 to get as much info as I could, but it was surprisingly light in the very specific information I was looking for.

Anyway, after doing a lot of experiments I have some conclusions regarding my original concern. It appears that the form of the cutting lips can range from a very non-straight shape to a fairly-straight shape, but it can't ever be absolutely straight. Increasing the diameter of the disk that forms the helix helps to straighten-out the curve of the cutting lips, but at the expense of reducing the overall width of the lips. The problem is that this reduces the drill's rigidity in the radial direction so it might have a greater tendency to snap under a large load. Like many real-world situations, there's a tradeoff involved.

Here's a photo showing one of my "studies" done with one selection of helix radius and diameter. It looks a lot like the physical drills I have.



The "grind" used to accomplish this wasn't done by modelling fixtures that rotate the drill lips across the grinding wheel. It was done by reproducing the result of a linear traverse of the drill across the (flat) plane of a grinding wheel. Like the lip of a cup-style grinding wheel. The grinding radius created by a rotating-style grinding tool can also be reproduced with openSCAD but I haven't quite gotten my head around the geometric considerations yet. It would be the difference between a pair of cylinders rather than flat planes. With all the correct angles, of course.....

 

[m1kemex]

Some time ago I applied myself to make a drill sharpener and realized, like you did, that drill geometry is more complex than it seems. I'm sure that the real geometry of the face is some special curve, like an involute. However, I don't remember all the details now.

 

[markba633csi]

Wow, more to it than I thought. It's definitely "high-falutin" math involved

 

[homebrewed]

Some time ago I applied myself to make a drill sharpener and realized, like you did, that drill geometry is more complex than it seems. I'm sure that the real geometry of the face is some special curve, like an involute. However, I don't remember all the details now.

The tip of a drill is formed by the intersections of three different shapes. The first is the cylindrical body. The second is the helix. Actually, two helices. These three elements can be seen in this rendering:


I used openSCAD's linear_extrude() function to create the helices. Its Boolean difference() function created the grooves in the drill body.

To simulate the grinding operation I created two cubic forms and tilted them +/- 31 degrees, the complement of the included angle divided by 2 (31 = 90 - (118/2)). They also were used in the difference() function. So the "sharpened" drill body (with no grooves) looks like this:


The intersection of the cylinder and cubes creates two elliptical surfaces. So there are a couple of derived shapes there. The blunt knife edge across the top will eventually form the central chisel portion of the drill.

The intersection of the helical grooves and drill body creates a more complex shape because the "grind" intersects different portions of the helix along the Z axis. It looks like this is what forms that fairly-straight cutting lip:


In this rendering the view is looking straight down at the tip of the drill. I'm only drawing the helix, not the drill body.

Finally, just to round-out the pretty pictures, here's a rendering of the simulated drill bit after just one of the lips has been "ground":


The straightest portion of the lip (shown in gray) is the cutting edge. This is for a right-handed drill bit. I initially had the helices going the wrong direction and that produced some _really_ strange drill bit shapes.

Once the different components have been created it's fairly straightforward to play around with them to see how they interact with each other and affect the final result. The simulation only requires 27 lines of openSCAD code (and that includes 4 comment lines).

 

[homebrewed]

I belatedly realized that the straight portion of the cutting lips also depends on the choice of helix angle. I suspected there's a "sweet spot" where the angle of the grind, in combination with the helix pitch, combine to produce an exactly straight line. I noticed that my choice of helix angle was pretty close to the grind angle -- 29 degrees vs. 31 degrees -- so I changed the helix angle to match the grind angle. Voila -- the cutting lip now is very close indeed to a straight line:



This also suggests that a drill designed to use 118 degrees won't produce that perfectly shaped cutting lip when reground to 135 degrees -- the helix angle would have to be 22.5 degrees instead of 31. It was easy enough to change my code to simulate this situation, and I was partly correct -- but it's more complicated than I thought. Simply changing the helix angle to 22.5 degrees didn't work, either -- in fact, the shape of the lip was WORSE. I suspect that the radius of curvature of the flutes (the same as the radius of the linearly-extruded disk) also is a factor. I may just have gotten lucky in my initial choices.

I'm sure I can play around with all the parameters to get something that does look good for 135 degrees, but it would be nice to have some analytical basis for all the variables involved.

I thought I had a "drop the mike" moment in the wings but it wasn't to be

 

[m1kemex]

Well, forget for a moment how it looks and just focus on what a drill bit does: it moves linearly along its axis while turning at the same time. Therefore, the main problem of a drill bit is differential motion: the closer to the center of the bit, the closer the linear speed of the cutting edge is to zero.

Linear speed is important because it affects clearance or the depth the edge can dig into the material without rubbing. At the center there is a lot of forward motion and almost no rotational motion, so it ceases to behave like a cutter and it just acts as a punch / chisel.

The real geometry of the edge is an integration of the proper clearance angle for each diameter along the length of the edge. Commercial drill bit grinding is an approximation to this shape, not identical.

P. S. This complexity emanates from a more general geometrical principle: all circles are unique. For example, even though you can generate a circle of any diameter using the same formula, the sections of two circles of different diameters don't fit / contact / intersect each other except in a single point. Each "curvature" is unique, despite being conceptually the same. Like I said, I don't know what to call a curve that is the product of two planes diverging from each other.

 

[yota]

try sharpening a countersink. talk about complex.

 

[homebrewed]

try sharpening a countersink. talk about complex.

I have been (slowly) working on a fixture to make my own multi-fluted countersinks and reamers using a rotary table mounted on a home-made sine table. It has 3 degrees of freedom, because the RT body can be rotated as well.

A countersink requires all 3 degrees of freedom in order to achieve the relief angles needed -- the conical shape introduces some "interesting" problems in that regard. The same issues would apply when sharpening one.

 

[yota]

which is why I always see a bunch of dull countersinks whenever I go to look at machining tools for sale. I've ended up with a bunch buying tool bundles. first few, I thought, great, I'll just sharpen them. ha ha.

 

[Jake M]

I belatedly realized that the straight portion of the cutting lips also depends on the choice of helix angle.

This is also going to depend on the "shape" of the flutes. (I know the flutes are nothing and the shape is what remains of the drill, but bear with me...)

I'm not sure from the pictures, but it "looks" like you've modeled those as round? If so, that'll make a difference. The final "shape" of the flute is the result of a round (let's say grinding wheel) plowing through the flute at some angle that may or may not be on centerline of the drill, and may or may not be parallel to the helix angle, while the drill is rotating on it's fixturing, giving some 'shape" that's not there, and a "radius like" grind on the outer circumference of the wheel that may be imparting it's own shape, or some angled cross section of that shape... It's a weird shape, and it's not uniform among all drills, although most "not specialized drills" are very similar. But universally, there will be "some" angle at which the side of the flute contains a straight line. Typically that will coincide with the drill point angle that the drill was born with

If one were to change the point angle of a given drill bit, it WILL have some "shape" to it. Typically not enough to notice unless you're looking for it, although sometimes it can be significant. I've never seen it make a "good" or "bad" drill bit by doing so, but that is a real thing you're stumbling on.

Incicentally... I think that's 85 percent of the trouble with a Drill Doctor. That's my weapon, I'm bought into the system since long before other options were affordable. :-( It indexes off of the flutes. The helix angle is not a given, although there's a more common one. Any other drill will throw off the drill doctor's indexing. The helix shape is not a given, which is not a deal breaker EXCEPT, that if the side of the flute where the cutting lip is were taken as a given (because it kind of is), the OPPOSITE side of the flute does not necessarily have any given shape or distance. That throws off the drill doctor's indexing. And some drill bits have a relief on most of the lands, (the outside diameter between the flutes), which again messes with the drill doctor's indexing. Which means you've got to teach yourself to recognize a bad grind, and know how to "eyeball" a fix by clocking ahead or behind of where the built in indexers landed.

I'm very curious, how does the Vevor indexing work? Does it (as I believe) index from the cutting lip? How doe the "dial" interact with that indexing? I'd love to know, but it's hard to cough up a new drill grinder when I have one that works perfectly well*, and yet I'm still more prone to hand grinding anyhow, when I'm home... Is that something that's "practical" to get pictures of, or is that a little peephole that's gonna be meanigless to me anyhow?

*The drill doctor does work perfectly well AFTER the learning curve. I'm 25 years in, and in the beginning, it was a steep learning curve, during which I learned to hand grind. If I needed a new grinder tomorrow, I'd probably get another drill doctor. If I needed a drill grinder 25 years ago, AND there was another affordable option?........ Not really sure, because now I've got a bias....