Mechanistic modelling of 5-axis milling using an adaptive depth buffer
Mechanistic modelling of surface machining with a toroidal end mill is presented in this work for 5-axis machining. A graphical representation of tool movements (using tooth swept sectors or the swept surface of the tool) is rendered using a widely available rendering engine, whereby the in-process chip geometry and tool edge contact length are determined by an adaptive and local depth buffer. Owing to the chip geometry being highly dependent on the feedrate, a detailed derivation of the relative tool-workpiece velocity is presented based on the kinematics of a tilt-rotary table configuration. The mechanistic modelling is verified with experimental results and found to agree to within 7% of the peak-to-peak forces.
A System for Monitoring the Machining Operation by Referring to a Predicted Cutting Torque Pattern
Summary A system for predicting the cutting torque by using a geometric modelling system, and its application to verification of NC data and monitoring of the cutting process are described in the paper. The cutting process is simulated geometrically in a modelling system. Based on data obtained from the geometrical simulation and on technological data of the NC program, the cutting torque is estimated, by using an empirical equation, as a linear combination of the volume of the removed material and of the tool-workpiece contact surface area. The torque measured in the experiments was in good agreement with the preliminarily estimate. The system also proved to be applicable when machining a cast part with geometrical inaccuracies within a few millimeters.
Stability results for the solutions of some third and fourth order differential equations
SummaryThe paper investigates conditions under which solutions of the equations (1) and (2) of § 1.1 tend to zero as t → ∞.