Construction of closed-form equations and graphical representation for optimal tolerance allocation

The Lagrange multiplier method (LM) is currently used to allocate tolerance for optimum manufacturing cost. This is a tedious iterative process and sometimes it allocates a component's tolerance outside its process tolerance limits. The present work develops a graphical representation which can help the process engineer to visualize the minimum and maximum values for assembly tolerances. The graphical representation developed can also help the process engineer to determine the exact total manufacturing cost of the assembly and help to fix the tolerance, which would not fall outside the limits prescribed. A simple C program is developed to construct the closed-form equations (CFE), and a single EXCEL graphical representation is derived for assembly tolerance, allocated tolerance, and total manufacturing cost. The developed algorithm has been demonstrated on a two- to five-component linear assembly, to help the process/manufacturing engineer's visualization before determining the tolerance specification on component dimensions. The test results show a maximum percentage deviation of 0.09% of assembly tolerance and 0.33% of total manufacturing cost between the LM and the newly developed CFE method.