X for Multiplication

This month we look at X which is the Multiplication Factor used in certain safety related calculations.

Many of these factors which affect our personal safety whilst we are woodturning are not influenced by a simple mathematical relationship but by a more complicated formula.

An example of this is the calculation for the energy in a rotating workpiece on the lathe. This energy is proportional to the square of the lathe speed. Therefore if we double the lathe speed we actually increase the forces tending to tear the wooden workpiece apart by a factor of 4.

If we treble the speed then these forces rise to 9 times the forces at the original speed.

If you increase the rotational speed of any workpiece sufficiently it will ultimately fail as the forces tending to pull the workpiece apart overcome the binding strength of the workpiece.

Therefore whilst it is often desirable to increase the lathe speed to improve the finish achieved on a turning we are also significantly increasing the stresses on the workpiece with the attending corresponding risk of failure.

A similar situation arises when workpieces of differing diameters are considered. Doubling the workpiece diameter will quadruple the forces acting on the workpiece at the same speed.

LEARNING POINTS

Continually increasing the rotational speed of a workpiece will ultimately result in the failure of the workpiece.

Doubling the rotational speed of a workpiece will quadruple some of the forces acting on it.

Doubling the diameter of a workpiece will quadruple some of the forces acting on it.