Variation Analysis for Rigid Workpiece Locating Considering Quadratic Effects Using the Method of Moments

Locators are used to constrain and position workpieces. The proper arrangement of locators, i.e., the locating scheme, is essential for both functionality and quality. In this paper, we propose a quadratic method to calculate the positional and rotational variations of a rigid workpiece using the Method of Moments. First, the workpiece geometry is quadratically approximated (hence allowing the inclusion of the linear and quadratic geometry data) to form the nonlinear constraint equations of the locators through a homogenous coordinate transformation. For a deterministic analysis, these highly nonlinear constraint equations can be solved using the Newton-Raphson method. To calculate the workpiece variations due to the locating source variations, the workpiece positional and rotational errors are first quadratically approximated around the locator positions using the Taylor expansion and then calculated using the Method of Moments. The advantage of the Method of Moment for a variation analysis is its efficiency as compared to the time-consuming Monte Carlo simulations. Examples are presented to benchmark the proposed method with prior research. By using the proposed method, the quadratic geometry effect and the interactions between locating source errors can be captured and hence the analysis results are more accurate, especially when error sources are large.