## Introduction

In the ideal world, every part is dimensioned exactly as designed. However, in reality any machined component can only be manufactured to a certain tolerance. Several parts combined will lead to a tolerance chain– the combined tolerance of all parts– causing dimensional fluctuations between different assemblies. As it was noted in Tolerance Chain Overview article, there are two common methods to calculate the tolerance chain: Worst Case method and Root Sum Square method.

## The Worst Case Method

This method is also known as minimum-maximum method. It is incorporated during the design stage itself. It works on the principle that when the work piece is designed, the dimensions are designated in such a manner that there is a tolerance value that is a ‘+’ or ‘-‘ from the accurate value. This method is used when the numbers of pieces are less and assemblies of work pieces are involved. The actual accumulated dimension is the mean value of all the partial dimensions and arithmetic sum of all the individual tolerances. So, if you have 4 parts tolerance plus/minus 0.1mm., your total assembly tolerance will be plus/minus 0.4mm

## Root Sum Square Method

The Root Sum Squre is a statistical method where the 6 sigma technique is employed. The entire bunch of produced components is put to a rigorous test. A component is selected and is measured for the specific dimensions. The deviation from a nominal dimension is written for several smaples of all the components, and a certain probability curve is drawn. This method is less strict, as it takes into account that the possibility of ALL the components manufactured to the extreme tolerance boundaries is highly improbable.

## Other Methods

Other viable statistical methods to calculate tolerance chain include optimization of number of products and combination of two or more processes – but there are pretty complex. Separate methods (Monte Carlo, RMS methods) are available to calculate the tolerance chainsp Designated software and applications have also been introduced that make the tedious calculation simpler and the outputs decipherable.

## Conclusion

In design, an engineer must avoid too many linear chains as it leads to many irregular surfaces and fit. The numbers of linear tolerance chains play an important role since the overall length and magnitude of the tolerance is decided by the same. Many external agents influence the dimensional inaccuracy starting from the method of manufacturing to some factors that cannot be controlled manually like the atmospheric dust, temperature etc. Irregularities occur in the 2 Dimensional and 3 Dimensional grids. Understanding how the tolerance chain affects various functionalities of the work pieces will give a clear insight to the designation of the same and allow better design.