In the paper we propose an approximation model of the measured point cloud for machined cylindrical surfaces. The developed model is different from the traditional view because it relies on the contact of mating surfaces. The model allows to determine the parameters of cylindrical surfaces such as the coordinates of the center and the radius. To evaluate the geometrical parameters of the model the objective function is formulated, which characterizes the nature of the interface and a number of limitations. The approximation problem is solved by use of nonlinear optimization methods. The model takes into account the surfaces contact, which influences in deformation of its irregularities. The irregularities it is form deviations and surface roughness. The application of the model on the example of the shaft coupling with the inner ring of the bearing. There is given an estimate of geometric parameters for interfacing compared to method of least squares, which is widely used for coordinate measurements. As a result of research it was obtained that the proposed method can predict more accurately the parameters, which describe the location of the cylindrical surfaces made during assembly.
Riemannian Newton optimization methods for the symmetric tensor approximation problem
