Narrow Results

We explicitly express the spectral determinant of Friedrichs Dirichlet Laplacians on the 2-dimensional hyperbolic (Gaussian curvature -1) cones in terms of the cone angle and the geodesic radius of the boundary.

In order to reveal the influence of contact condition of spindle-holder to the dynamic characteristics of high speed spindle system, a milling spindle is taken as the research object, and the change rule of the spindle natural frequency is simulated based on the contact condition which is influenced by the drawbar force, interference and centrifugal force. The result shows that the contact clearance is decrease with the increase of drawbar force and interference, while rise with the increase of rotate speed; the natural frequency can be increased by both drawbar force and interference, however, it is decease with the increase of rotate speed.