A least squares algorithm for fitting data points to a circular arc cam. (May 2017) - Lin, Shan; Jusko, Otto; Härtig, Frank; Seewig, Jörg
Highlights: A mathematical description of circular arc cam is presented. A global fitting algorithm for four circular arc cam is proposed. By incorporating parameter constraints, the fitted cam profile is closed and smooth. Both of the GUM and Monte Carlo simulations are applied to evaluate the uncertainties of estimated fitting parameters. The proposed algorithm is more reliable compared to the conventional approach. Abstract: Precise evaluation of form error is important for quality control in the manufacture of camshafts. For circular arc cams, a conventional method is to fit each arc segment of the cam individually. In such a case, at the connecting points of two fitted segments, there may be discontinuity or non-smoothness. In this paper, a global cam fitting algorithm based on the nonlinear least squares method is proposed. A circular arc cam is represented by the mathematic function in terms of form, rotation and position parameters. By imposing parameter constraints, a closed and smooth profile can be obtained as the result of fitting. In order to evaluate the performance of the proposed algorithm, the uncertainties of the fitted parameters are estimated by the GUM uncertainty framework and Monte Carlo simulations. Compared to the conventional cam fit, the uncertainties obtained by the proposed algorithm are lower. Additionally, the factors which significantly affect the fitting results are specified.