Grid generation as applied to optimize cutting operations of the five-axis milling machine

Authors:
S. S. Makhanov;S. A. Ivanenko
Affiliations:
Department of Information Technology, Sirindhorn International Institute of Technology, Thammasat University, Rangsit Center, Pathum Thani, 12121, Thailand;Computing Center of the Russian Academy of Science, Vavilov Str. 40, Moscow GSP-1, 117967, Russia
Venue:
Applied Numerical Mathematics - Special issue: Applied numerical computing: Grid generation and solution methods for advanced simulations
Year:
2003

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Abstract

Optimization of cutting operations is an active area of research in the CNC-based manufacturing. The limited capabilities of the CAD/CAM systems require development of a new software and new numerical methods verified by practical machining. First, we outline the recent methods of tool-path planning of industrial milling robots. Next, we present some introductory examples to demonstrate that the concept of adaptive curvilinear grid contains almost all the basic ingredients of tool-path planning, such as: adaptation to regions of large milling errors, conventional zigzag/spiral patterns and constraints related to the scallop height. Therefore, we formulate the problem of toolpath optimization in terms of interpolation of the required part surface in the curvilinear coordinate system associated with the cutter location points. In order to solve the problem numerically we introduce a variational grid generator based on minimization of the Dirichlet-type functional subjected to constraints related to the maximum allowed scallop between the consecutive tracks of the tool. The corresponding variational problem is then solved numerically by the quasi Newtonian scheme combined with a penalty-type iterative algorithm. We present an application of the algorithm to tool-path planning of the complex shaped parts and demonstrate the efficiency of the proposed scheme by methodological examples verified by real machining. Finally, we show that grid generation may constitute a basic component of a system of mathematical models for part optimization.