Process tolerance control in a 2D angular tolerance chart

The main tasks of tolerance charting include the identification of dimensional chains, the calculation of mean working dimensions, and the allocation of proper tolerances to the working dimensions for all machining cuts. When an angular featured component is involved, tolerance charting becomes very difficult because the axial dimensions are interrelated with the radial dimensions due to the angular feature. The purpose of this paper is to accomplish the above three tasks in a 2D tolerance chart, constructed for a component with an angular feature. With the algebraic method, the reverse chain matrix, which contains the reverse tolerance chains, is obtained first and the mean working dimensions are determined from the reverse chain matrix. The forward chain matrix for the forward tolerance chains is then obtained by inversing the reverse chain matrix. Thereafter, by using the forward chain matrix in a linear programming model, the tolerances are optimally allocated to the working dimensions. A numerical example is given in the paper.