Computing the Global Visibility Map Using Slice Geometry for Setup Planning

This paper introduces a new method that uses slice geometry to compute the global visibility map (GVM). Global visibility mapping is a fundamentally important process that extracts geometric information about an object, which can be used to solve hard problems, for example, setup and process planning in computer numerical control (CNC) machining. In this work, we present a method for creating the GVM from slice data of polyhedron models, and then show how it can help determine around which axis of rotation a part can be machined. There have been various methods of calculating the GVM to date, tracing back to the well-known seminal methods that use Gaussian mapping. Compared to the considerable amount of work in this field, the proposed method has an advantage of starting from feature-free models like stereolithography (STL) files and has adjustable resolution. Moreover, since it is built upon slicing the model, the method is embarrassingly parallelizable in nature, thus suitable for high-performance computing. Using the GVM obtained by this method, we generate an axis of rotation map to facilitate the setup planning for four-axis CNC milling machines as one implementation example.

DISCREPANCY ESTIMATES FOR ROTATION SEQUENCES AND OSCILLATION SEQUENCES

Two kinds of sequences, which are of interest in problems of uniform distribution and dynamical systems, are considered. The rotation sequences (or Kronecker sequences) (KS) are closely related to the orbits of the rotation map and the oscillation sequences (OS) are a discrete-time form of orbits of the simplest oscillators. The discrepancy of these sequences, which is a measure of deviation of the empirical distribution of a sequence from the ideal uniform distribution, is studied.

Recent Progress in the 3D Experimentation and Simulation of Nanoindents

This work studies the rotations of a (111) Cu single crystal due to the application of a conical nanoindent. With the aid of a joint high-resolution field emission SEM-EBSD set-up coupled with serial sectioning in a focused ion beam (FIB) system in the form of a cross-beam 3D crystal orientation microscope (3D EBSD) a 3D rotation map underneath the indent could be extracted. When analyzing the rotation directions in the cross section planes (11-2) perpendicular to the (111) surface plane below the indenter tip we observe multiple transition regimes with steep orientation gradients and changes in rotation direction. A phenomenological and a physically-based 3D elastic-viscoplastic crystal plasticity model are implemented in two finite element simulations adopting the geometry and boundary conditions of the experiment. While the phenomenological model predicts the general rotation trend it fails to describe the fine details of the rotation patterning with the frequent changes in sign observed in the experiment. The physically-based model, which is a dislocation density based constitutive model, succeeded to precisely predict the crystal rotation map compared with the experiment. Both simulations over-emphasize the magnitude of the rotation field near the indenter relative to that measured directly below the indenter tip. However, out of the two models the physically-based model reveals better crystal rotation angles