Some thoughts on internal chucking (long)
David Eaves
>Hello there,
There have been a few posts recently about the problem of internal dovetail chucking having a tendacy of spliting the recess out. Fortunatly, out of 17 bowls I've done so far I've only split one out. I thought I knew why at the time it had happened. However, inspired by the other posts and a desire not to do it again I thought I would conisder what is happening. Both force wise and consider some real numbers and strengths. I'm new to this game and don't have the years of experience others have, so feel free to add comments or disagree with my reasoning.
Simplified plan view of turning a bowl
This drawing shows the cutting forces simplified. In reality the force will be a 3 dimensional direction due to the resistance to cutting. That will be the dominant direction in the event of a catch too. The general idea is still the same, the recess will be effectively pivoting around the side nearest the tool, and the material from that point onwards will be resisting spliting in tension. (In compression it won't want to split)
From my materials knowledge and the way the force is applied I believe the resistance to split out will be proportional to the area, of the "foot" width and not the distance. I had a good idea what the relationshoip was so I worked the maths out.
Relative strengths for different "Foot" widths
This diagram shows the key dimensions.
In these diagrams d is the chuck diameter, this was assumed to be 2" (50mm)
The distance x I have called the "foot" width. This is the width from the edge of the chuck to the edge of the bowl. In the diagram on the left it is x and on the right it has increased to 2x.
By working out what area is available to resist splitting, the strength relative to a starting diameter can be determined. In the calculations I started with 0.5" (12.5mm) as the minimum, and worked it out up to 1.5" (75mm).
This graph shows the results.
The diameter is plotted along the horizontal scale, and the strength at 0.5" is taken as 1. The vertical scale then gives the strength relative to this. For example, if x is doubled the relative strength increases by a factor of 2.4.
Key Observations
You can use this chart to work out the relative increase in strength. The relationship is not entirely linear, in all cases the strength increase is greater than the increase in foot width (this effect would be more pronouced if smaller dimensions were considered too)
Additional Notes
I've also thought about the depth of the recess. It goes without saying if it is more shallow there will be less strength. But what if you go deeper and there is a void. Is this a problem?
In the above left diagram, the illustation shows the void created by a dovetail deeper than the chuck depth. If you consider a force from cutting pushing backtowards the headstock, the red arrows show what happens. This pushing has the efefct of wanting to push the chuck into the wood, this will have a tendancy to make it want to split open, and/or move around. Therefore I think it is best if the chuck contacts the base as closely as possible. This failure is what I believe caused my bowl to jump out. I had cut a recess deeper by mistake than the recommended depth for my jaws.
Finally, the above right diagram just shows that if you use that profile, the red shaded section does not contribute to suporting the bowl.
Assumptions
There are a number of simplifications, in the model. For a start as wood is not homogeneous and the stresses generated will not be uniform (which will cause other effects). Also the grain aligment will affect how it stays in. This model assumes normal bowl alignment. If the internal recess was into end grain it would be highly unstable and likely to split out. In that case a compression grip would be much safer and stronger.
Okay, I hope this is helpful. Please let me kow if you think this is useful or not.
David