## A lesson in tolerance

 David Harding

David Harding, interim head of the Technical Division, wrote this column.

How good is good enough? Suppose you are baking a cake from a prize-winning recipe that calls for a cup of sugar. Will the cake still be superb if you put in an extra teaspoon of sugar or leave out a teaspoon? What if you are off in your measuring by a tablespoon? How about a quarter cup? Perhaps the recipe calls for two large eggs. Surely there will be a difference if you use one egg or three eggs, but what happens if you use medium eggs or extra-large eggs?

In technical jargon, we call the allowable variation from the planned quantity the tolerance.

If you want one part of a magnet to fit into another nicely, not too tight and not too loose, their sizes must agree. It is important to specify how far from the drawing dimension the parts can vary while still fitting acceptably. If you specify your tolerances too loosely, you run the risk of not being able to put the magnet together. If you specify the tolerances too tightly, you run the risk of paying far more than you need to because it generally takes more time and is more expensive to get the parts closer to the drawing dimensions. We use a system called geometric dimensioning and tolerancing in our drawings to concisely convey our requirements to the machine shops that make our parts.

The quality of the magnetic field in a conventional magnet depends predominantly on the precision with which the iron is shaped, forming a “gap” through which the particle beam travels. When we in Technical Division build a magnet with a 2-inch gap, we work with Accelerator Division scientists to decide how close we need to come to 2 inches to meet the magnetic field needs of the accelerator. Typically AD tells us that the accelerator will work well only if we can keep the variation in the gap to under two ten-thousandths of an inch, or about 1/20 the thickness of a piece of paper. That’s in a magnet that may weigh 20 tons or more. In your cake you would be asked to measure the sugar to 1/208 of a teaspoon.

We consider our tolerances carefully to achieve the accelerator goals while minimizing the costs. We balance the desire for perfection in the magnets with the reality of the imperfect beams.

We have also learned the value of checking parts as they come in to ensure that they do, indeed, meet our tolerances. Trying to save time by skipping that incoming inspection leads to greater delays when out-of-spec parts do not fit together during magnet assembly.

Tolerance is also an attitude that must be practiced at an appropriate level so that the pieces of the laboratory fit together. Setting limits on behavior can be harder than setting limits on sugar measurements or magnet steel dimensions. We tolerate differences of opinion but not offensive behavior. For a healthy lab we must maintain respect for each other.