Composite adaptively sampled distance fields (cADF) are a new approach to shape representation that is well suited for shapes moving along a given path for NC milling. A caDF consists of a set of analytic or procedurally defined distance fields associated with both the original unmilled workpiece and with the volumes swept by milling tools as they move along their prescribed path. An octree bounding volume hierarchy is used to sample the distance functions and provides spatial localization of geometric operations thereby dramatically increasing the speed of the system. The resulting representation is fast to determine, provides high reconstruction accuracy, and requires relatively low memory. In NC milling as the tool moves along the tool path, the toll is in contact with the in-process workpiece over an engagement surface. In order to model the process mechanics and dynamics accurately, it is important to have a precise geometric properties of the engagement surface and/or removed volume. In this paper, we provide a brief introduction to cADFs and describe a new method for determining the engagement surface between a moving tool and workpiece, and calculate the geometric properties of the removed volume. This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved.  Composite adaptively sampled distance fields (cADF) are a new approach to shape representation that is well suited for shapes moving along a given path for NC milling. A cADF consists of a set of analytic or procedurally defined distance fields associated with both the original unmilled workpiece and with the volumes swept by milling tools as they move along their prescribed path. An octree bounding volume hierarchy is used to sample the distance functions and provides spatial localization of geometric operations thereby dramatically increasing the speed of the system with high accuracy and relatively low memory requirement. In NC milling as the tool moves along the tool path, the tool is in contact with the in-process workpiece over an engagement surface. In order to model the process mechanics and dynamics accurately, it is important to have a precise geometric properties of the engagement surface and/or removed volume. In this paper, we provide a brief introduction to cADFs and describe a new method for determining the angle and area of engagement surface between a moving tool and workpiece, and calculate the geometric properties of the removed volume for 3-axis milling. Our method can calculate these geometric features for quite complicated tool paths and general tools using much less memory and time compared to the state of the art methods without scarifying from accuracy. It can also be generalized to any type of 5-axis motions.
Another approach is to use distance fields to calculate the cutter workpiece engagements accurately, robustly and efficiently for 3-axis motions REF .
High Accuracy Computation of Geometric Properties of Cutter Workpiece Intersection using Distance Fields for NC Milling
Procedia CIRP
Mathematics