Shelving Units: The Engineering Case for Quantifying Quality

Tolerance stack-up is an engineering concept defined as an accumulation of dimensional variations in a part or assembly made up of multiple parts. No part can be made perfect, and many mechanical drawings include dimensions with specified tolerances such as 15.000" +/- 0.005" to convey an acceptable range within which the dimension meets specifications.

The usually accepted tolerance range for most professional woodworkers is +/- 1/64" or  +/- 0.016". This degree of accuracy is not hard to obtain given experience and good equipment. The problem lies in a design that combines multiple parts in such a way that the dimensional variations add or subtract. The accumulation of dimensional variation can become significant if many parts are used to make up a single assembly as in the shelf unit side frames pictured here. Viewed in another way, if four sequentially assembled parts are off by only 1/64", the final accumulated dimension represented by their assembly will be off by 1/16". And that is significant. The same holds true for angular dimensions and perpendicularity.

I am not able to measure the shelf unit side frame diagonals during the glue-up process because the many clamps required interfere with the measurements. I rely on taking measurements with an accurate square in each of the internal frame openings and adjust clamping pressure where required to get good readings. The side frame diagonals are within 1/16" of each other or better when the clamps are removed.

Diagonal measurements within 1/16" or better are generally good enough to consider larger assemblies acceptably square. My designs often rely on ultra-accuracy to insure the overall object assembly comes together well. The Alice Table comes to mind as a good example.

Tolerance stack-ups are analyzed in terms of either a worst case scenario where an assumption is made that all dimensions will end up at one of the outer extremes of the specified tolerance, or statistically where a probable average of variation is assumed. I will often consider my woodworking technique and shop equipment good enough where I assume a probability of small average variation.

I should maybe consider playing it safer the next time I evaluate a particularly complex design by using a rough worst case analysis. It might save an unpleasant surprise. The computer screen might tell me I can build something, but reality might dictate otherwise. So far though, the shelf unit side frames are gluing up well.