An algebraic approach for dimensional chain identification in process planning

In general, there are two purposes in identifying dimensional chains for a part's process plan: determining the nominal dimensions and allocating proper tolerances to these dimensions for manufacturing operations. This paper proposes an algebraic approach for dimensional chain identification based on the tolerance charting technique. Before the new approach is presented, the digraphic method is outlined in order to introduce the concept of the reverse dimensional chain and to express the relationship between the reverse and the forward dimensional chains. However, the algebraic approach presented in this paper does not require the generation of any graphs or trees. It identifies the reverse dimensions by use of the original tolerance chart. The forward dimensional chains are obtained from the reverse dimensional chains by use of the relationship between the reverse and the forward dimensional chains. The reverse dimensional chains can be used to determine the nominal dimensions directly while the forward dimensional chains are necessary to allocate the tolerances for manufacturing.