Taper angles

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I have a small woodworking router plane that has a vertical round rod
carrying the blade on the lower end. The clamping mechanism does not
provide enough force to securely hold the rod under all circumstances. The
clamp is simply a rod with a hole through it for the blade rod, pulled tight
to the router body by a thumb nut with a ¼"-28 tpi thread .
I am thinking that a V groove to hold the rod may do it. The question
arises what angle for the V. In steel, self holding tapers are generally
around 3-4°, self releasing are of the order of 15° or more. Does anyone
know where the transition point is, or better still, point to a diagram of
separation force versus taper angle? I figure I can tolerate a pretty tight
taper as there will only be a small area of tangential contact and the rod
will readily skew in the V and release.
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The blade is of high-carbon steel, about like a drill bit. If you want to hold it in a position, think of a collet-like solution first.
If you can get 1/8" pipe thread taps and dies, it's easy to make a tapered threaded section, and a conical-threaded nut to draw the collet closed. You get the screw mechanical advantage and the large steel/steel contact area, plus the tightest part of the fit can be close to the point of force application.
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____________________________________ Here is an image

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The Stanley router plane uses square shanked blades clamped into a 90 degree V.
I didn't realise there was any other way to do it...
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Oh, I see; I was thinking of older granny-tooth gizmos, big cast iron parts. For this, maybe a wipe of cement and a pinch of few-hundred- grit SiC powder, to raise the friction?
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There are other ways to do it. The Stanley router plane uses blades that are round shanked with a V groove. They fit in a round hole, and are held by a knurled head screw which bears in the V groove. The V groove keeps the blade from twisting. (Stanley made more than one router plane...)
As to the original question, regarding the transition point between self-holding and self-releasing tapers, it is easy to calculate. In practice, however, you can be way off the calculations. It depends on surface finish and lubrication. I have a horizontal mill with a NMTB40 taper spindle, which by the calculations should be self- releasing. It isn't. The spindle and tool holders are in very good shape, but it always takes a couple of hits on the drawbar to free the tool holders.
But there is another thing to consider here. The shallower the angle, the better the walls will grip the cutter. But the shallower the angle, the greater will be the precision of fit required. Make it too shallow, and the cutter will quickly go from "just entering the groove" to "bottoming out". A little bit of wear, or a slight difference in cutter sizes, and it won't work. You don't have much takeup to play with. Rather than worrying about what angle takes you from self-holding to self-releasing, I'd pick an angle that will allow some leeway for size and wear.
John Martin
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The transition point is exactly at the arctangent of the coefficient of friction. In other words, the if the angle is greater than that, it's self-releasing, below that it'll be self-locking. Time to get the tables out...
Look up how it's determined and see how the angle relates to the value.
Stan
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7 deg is about the limit for locking on taper angles. (Thats 14 included) Moldmaker info Gil
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____________________ Many thanks for the help guys. I have elected to go for the increase in friction route for now and see how it goes. Soft solder on the inside of the clamp hole where the pressure is applied with a medium silicon carbide grit pressed into it. I had to remake the clamp from steel as the original was stainless. John.

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