Ming Leu (mleu@mst.edu, 573-341-4482), Xiaobo Peng, Weihan Zhang

This project is aimed at developing computer simulation software for verification of NC machining code. The geometry of a milling cutter is defined using models of general APT tools. For the NC simulation, the swept volume of the cutter is generated based on the sweep differential equation approach, and Boolean operation is performed between the swept volume and the workpiece to update the geometry of the workpiece in real time. The algorithms are very efficient and our software is more advanced than commercial NC machining verification programs in that it can simulate the effect of cutter deformation based on a mechanistic model.

Web link for this project: http://web.mst.edu/~vrpl/projects.htm

1. “A Verification System of 5-Axis NC Machining with General APT Tools,�? M. C. Leu, L.Wang, and D. Blackmore, Annals of the CIRP, Vol. 46, No. 1, 1997, pp. 419-424.

Abstract: This paper presents a new swept volume generator for computer based NC verification using the SEDE (sweep-envelope differential equation) method and its application. It calculates the boundary points of a swept volume generated by a 7- parameter APT tool with 5-axis motion in NC machining. The SEDE sweep generator coverts the problem of swept volume representation into the sweeping of initial grazing points along their motion trajectories. It reduces computational complexity and provides an easy connectivity for surface fitting of the boundary points. This sweep generator has been integrated with a commercial CAD/CAM system. An example is given to illustrate the capability of the integrated system and the process of simulating material removal for NC machining verification.

2. “The Sweep-Envelope Differential Equation Algorithm and Its Application to NC Machining Verification,�? D. Blackmore, M. C. Leu, and L. Wang, Journal of Computer Aided Design, Vol. 29, No. 9, 1997, pp. 629-637.

Abstract: A new method, called the Sweep-Envelope Differential Equation, for characterizing swept volume boundaries is introduced. This method is used as the theoretical foundation of an algorithm for computing swept volumes using the trajectories of the sweep-envelope differential equation which start at the initial grazing points of the moving object. The major advantages of this algorithm are: (1) the grazing points need essentially only be computed at the initial position of the object - the remaining grazing points are generated by the flow of the sweep-envelope equation - so the computation complexity is drastically reduced; and (2) it provides automatic connectivity for computed boundary points that facilitates integration with standard algorithms and CAD software for visual realization and Boolean operations. Examples are presented that illustrate successful integration of our prototype program (based on the algorithm) with commercial NC verification software.

3. “Error Analysis for Four-Axis Side Milling of Undevelopable Ruled Surface,�? B.Yang, M. C. Leu and J. Zhou, Journal of Control Engineering Practice, Vol. 6, No. 4, April 1998, pp. 347-356.

Abstract: Based on the geometric features of the Undevelopable Rules Surface (URS) and conical and cylindrical milling cutters, this paper analyzes the interference errors which take place when a part with URS is machined using 4- axis side milling. Formulas to calculate the interference errors are derived and methods to reduce the errors are proposed. Experimentation on a turbine impeller whose blades are URS shows that the derived formulas and the proposed error control methods are effective. Thus our analysis provides a promising solution for the practical problem occurred in the machining of parts with URS.

4. “Simulation of NC Machining with Cutter Deflection by Modeling Deformed Swept Volumes,�? M. C. Leu, F. Lu, and D. Blackmore, Annals of the CIRP, Vol. 47, No. 1, 1998, pp. 441-446.

Abstract: Most research on NC machining verification does not consider cutter deflection caused by cutter-workpiece interaction during machining. Described in this paper is a deformed swept-volume analysis integrated with machining mechanics to account for cutter deflection in NC machining simulation. This analysis uses an extended Sweep Differential Equation approach to represent the swept volumes of flexible moving objects. An end milling mechanics model is used to compute the cutter deflection, which is incorporated in generating the deformed swept volume of the cutter by a software program developed in C++. The simulation of the machining process and machined part is achieved by geometrically subtracting the cutter swept volume from the workpiece. Besides NC program verification, the simulation results are also shown useful to prediction of machining surface error and modification of machining parameters for error reduction.

5. “Freeform Object Design and Simultaneous Manufacturing,�? Wei Zhang, Weihan Zhang, Heng Lin and M. C. Leu, Proceedings of the Society of Photo-optical Instrumentation Engineers, 2003, pp. 265-273.

Abstract: Today’s product design, especially the consuming product design, focuses more and more on individuality, originality, and time to market. One way to meet these challenges is using the interactive and reactionary product design methods and rapid prototyping/rapid tooling techniques. This paper presents a novel Freeform Object Design and Simultaneous Manufacturing (FODSM) method that combines a natural interaction feature in the design phase and a simultaneous manufacturing feature in the prototyping phase. The natural interactive three-dimensional design environment is achieved by adopting virtual reality technology. The geometry of the designed object is defined through the process of “virtual sculpting�? during which the designer can touch and visualize the designed object and can hear the generated manufacturing noise. During the designing process, the computer records the sculpting trajectories and automatically translates them into NC code so as to simultaneously machine the designed part. The paper introduces the principle and key techniques of the new method.