Tenon Size vs. Holding Power

Part 1

There has been considerable discussion about what size tenon should be used when mounting a workpiece in the jaws of a scroll chuck. Some turners say to use the largest tenon the workpiece will allow by opening the jaws almost fully. Others maintain that the greatest “holding power” is obtained when the jaws are closed down to a diameter only slightly greater than the minimum so that more surface area of the jaws comes into contact with the wood.

These two views are not the same. Is one right and the other wrong, or do other factors come into play that favor one or the other in different situations? Factors like whether the workpiece is a tall vase or a shallow bowl or platter? And does the shape of the jaws make a difference?

It appears that there is no simple answer. Larger tenons work better most of the time but a smaller tenon may be preferred in at least one case. So how can you know when to choose one rather than the other? This article explains the principles involved so you can make a more-informed evaluation of the requirements of a particular workpiece and size the tenon accordingly.

Torque and Leverage

“Holding power” is a rather vague term that refers to the ability of a chuck to hold a piece of wood on the lathe. A better understanding can be achieved if it is broken down into two components that work together to hold the piece. I refer to these as the “torque” component and the “leverage” component.

Obviously, the chuck must supply a twisting force (torque) to the piece in order to make it spin against the cutting edge of the tool. Sometimes, when things go wrong, the piece may actually stop rotating while the chuck is still going at full speed. This can be caused by taking a cut that is too heavy, getting a catch, or by using a tenon whose diameter is too small.  

It is equally obvious that the wood pushes the cutting tool down against the tool rest. And therefore, because of the action-reaction principle, the tool pushes upward against the wood. The result is a levering action almost identical to what would exist if you grasped the end of the piece and pulled it straight up. The tenon will be pushed into the chuck at the top and will be pulled out at the bottom.

Because the piece is rotating, an alternating force acts on the tenon at each jaw that first tends to push it deeper into the chuck and then quickly changes direction and tends to pull it out. If the grip of the jaws is insufficient, the pushing-then-pulling forces can cause the piece to loosen and possibly come out of the chuck.

For a chuck to hold a piece securely, both the torque and leverage components must be sufficiently strong. And it is no surprise that a larger-diameter tenon (with matching chuck jaws) produces greater strength in both components.  

At this point it may seem that you should always use the largest-diameter tenon that the workpiece and chuck combination will allow, with the chuck jaws open to near maximum capacity. For the most part this is the case, but there is at least one exception.

Basic Principles

Torque.  Torque is a twisting force. A torque applied to an object tends to make it rotate. A simple example is a wrench applied to a nut. The longer the handle on the wrench, the greater the twisting force you can apply.  

Another example is a string wrapped around a disk mounted on an axle. A weight hung on the string produces a torque that causes the disk to rotate.  

In these examples, the moment arm is the length of the handle of the wrench (very nearly) and the radius of the disk (exactly). More precisely, it is the shortest distance between the line of action of the force and the pivot point. The amount of torque produced is the force multiplied by the moment arm. The greater the moment arm, the greater will be the torque produced by a given force.  

For a tenon gripped by the jaws of a scroll chuck, the moment arm is the radius of the tenon because the torque-producing force is applied tangentially (sideways) to the circumference of the tenon.  This means that for a given force, a larger tenon will produce a larger torque.

Leverage.

A lever consists basically of two arms and a pivot point called the fulcrum. If one of the arms is longer than the other, a mechanical advantage is obtained so that a small force applied farther from the fulcrum is able to balance a larger force located closer to the fulcrum.

The same principles apply if the arms are at right angles to each other, and this forms the basis of a nail-pulling device we called a “wrecking bar” back in the hills of East Tennessee.  You soon learn that it is easier to pull a stubborn nail by putting a block under the crook to shorten the arm that goes to the nail. This principle carries over to a tenon in the jaws of a chuck. You get more leverage (not desired) with a smaller tenon, which makes the piece more likely to come out of the chuck.

Machined Diameter

A set of chuck jaws is made by first machining a disk to the diameter and profile of the jaws and then cutting the disk into four sections. Some material is lost in the process of cutting the jaws from the disk. When the jaws are mounted on the chuck and the chuck fully closed, the diameter of the gripping surface will be slightly less than the original machined diameter and the gripping surface will not make a perfect circle.

To size a tenon so the gripping surface makes perfect contact with the wood all the way around the circle, the tenon diameter needs to be just slightly greater than the smallest diameter the jaws will grip. If the jaws are opened wider to accommodate a larger tenon, contact will be lost near the center of each jaw.

Generally speaking, larger tenons are better for torque transfer from the chuck to the tenon and also for withstanding the leverage exerted by the upward force the cutting tool exerts on the wood. But opening the jaws wider than the machined diameter causes a partial loss of contact between the jaws and the tenon.  

So the question arises:  Is it better to use a smaller tenon equal to the machined diameter of the jaws, or is it better to open the jaws almost fully even though some contact is lost?  

Jaw Dig-in with Large Tenons

When the jaws grip a tenon larger than their machined diameter, the radius of curvature of the jaws does not match that of the tenon. The result is that the ends (or sides) of the jaws tend to dig into the wood.

If the wood is sound and if the jaws are not over-tightened to the point where the wood is crushed, the digging in will actually add to the ability of the chuck to transfer torque to the workpiece.

The digging in does not occur when the jaws are expanded into a recess as opposed to gripping a tenon because the radius of curvature of the jaws is less than that of the recess. It follows that you do not get the added benefit to torque transfer that the digging in provides with a tenon.

A Property of Frictional Force

Having more of the jaw in contact with the wood does not necessarily result in a greater frictional force. An experiment in basic physics shows that the frictional force is, for the most part, independent of the area of contact between the two surfaces. The same force is required to pull a rectangular block across a flat, hard, non-sticky surface when the block is stood on edge as when it is resting on one of its larger flat faces.  

This means that using a tenon the same diameter as the machined diameter of the jaws may not be an advantage. In theory, the frictional force will be the same for a larger tenon where the contact area is less. If a larger tenon is used with the same frictional force, a greater torque will be produced because the moment arm is greater.  

The physics experiment does not apply to a larger tenon where the jaws dig in at the sides of the jaws. In that case, the force will be much greater than for a smaller tenon where no dig-in occurs. However, it almost certainly does apply to the serrated Oneway jaws (described below) where dig-in does not occur.

No dig-in is possible when the jaws are expanded into a recess. It follows that the friction force will be the same for a large recess and a small one. In this case, for the torque component, the larger recess is preferred because the greater moment arm gives a greater torque capability.

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