What is a Tolerance Chain? - Part One - Introduction

An engineer, contrary to most other human beings, knows that nothing in this world is exact. Everything has a certain tolerance, which is generally unknown. However, when an engineer designs a part by himself – he decides on those tolerances. But to what extent can variations be tolerated? The mechanical industry is filled with so many standard values of tolerances according to the part that is manufactured. And of course, pricing plays a major role here– too much accuracy and your part is going to cost hundreds of times more than expected- but too coarse tolerance can sometimes lead to a deadly hazard.

In any assembly, the parts are mated together, producing a supposedly working mechanism. However, as each parts has tolerances, the overall length of, say 4 parts connected together, can differ quite severely. This is exactly what is called the tolerance chain - the total tolerance value that is cumulative and the end result of all the dimensional tolerances. Moreover, sometimes when work pieces are fit together, physical properties of the materials are attributed to this tolerance value, as the materials can change their properties due to temperature increase, or other conditions. Also, any screw/nut that is present in the design has a tolerance (although those are usually very precise parts). The coating has certain thickness – it may vary from several microns to almost tenth of millimeter… Therefore when the end product is designed, the tolerance value is calculated with the end chain measurement conveyed to the design.

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No process is perfect and ideal work pieces cannot be delivered however hard and accurate the method is. When more than one fitting part is present, you have to provide a tolerance that is a cumulative value of all the tolerances of individual joints. Loose fitting parts affect many problems right from increased vibration to disjoining of parts. Relative movement of parts will cause considerable wear and tear between the mating parts and hence decrease its life/efficiency. Some joints are dependent on each other and a misalignment in one causes the same to other joints leading to breakdown of the entire assembly at times. The packages can be too small or too loose if the tolerance chain calculation is neglected.

There are various dimensional chains according to the number of dimensional irregularities involved. The 1 dimensional chain is calculated arithmetically through two methods: the Worst Case method and the Root Sum Squares method. Both will be covered in the next article.