Locating error analysis for workpieces with general fixture layouts and parameterized tolerances

In manufacturing engineering, locating error analysis for workpieces is a common issue in predicting the quality of machined features, computer-aided fixture design and tolerance allocation. This article presents a locating error analysis approach for workpiece with general fixture layouts and parameterized tolerances. Initially, a fixture is transformed into six locating points in the space. A linearized model is then derived to convey the relationship between the errors of locating points and the locating errors, by using the implicit differentiation and the first-order Taylor expansion. Then, the tolerances for the features of plane, cylinder and free-form surface are parameterized using 4 × 4 homogeneous transformation matrices. Finally, two formulas are derived to calculate the errors in the locating points in surface-to-surface mating and hole-to-pin mating. Two workpieces are presented to demonstrate and validate the proposed method. The relative errors between the results calculated by the proposed method and the results calculated by 3DCS are less than 3%.