Modeling of deformed swept volumes with SDE and its applications to NC simulation and verification

Representation of swept volumes has important applications in NC simulation and verification as well as robot-motion planning. Most research on .the representation of swept volumes has been limited to rigid objects. In this study, a sweep deferential equation (SDE) approach is presented for the representation of deformed swept volumes generated by flexible objects. The deformed swept volume analysis is integrated with machining physics to account for tool deformation/deflection for the NC simulation. End milling is modeled and analyzed and the tool deformations are calculated and integrated with the SDE program. A program is developed in C++ for the generation of deformed swept volumes. Using Boolean subtraction, the deformed swept volume of the tool is cut from the workpiece to simulate the machined part. It is shown that this representation approach constitutes an efficient and accurate NC simulation technique for collision detection, geometric verification as well as surface error prediction

Modeling of 3D swept volumes using sde/sede methods and its application to five-axis nc machining

This research falls in two important areas in solid modeling and manufacturing automation: (1) swept-volume modeling; (2) computer-based NC (Numerically controled) machining simulation and verification. The swept volume is defined as the volume swept by an object undergoing an arbitrary motion. Modeling of 3D swept volumes includes the boundary computation and representation of a swept volume generated by a general object undergoing general motion in three dimensional space. The Sweep Differential Equation (SDE) and Sweep Envelope Differential Equation (SEDE) methods are two of the important swept volume modeling methods employed in this dissertation. They exploit differential equations to obtain the boundary points of a swept volume generated by a moving object. The application of SDE/SEDE methods is addressed to computer-based NC simulation and verification. Comparison of the SDE/SEDE approach with other swept volume modeling methods is conducted too. It has been shown that the SDE and SEDE methods have great benefits in calculating and representing general swept volumes and the research has substantially advanced existing manufacturing technologies. The main contributions of the research are: (1) The SDE method has been extended to three dimensional space to represent cutter swept volumes generated by moving five-axis NC milling tools. A SDE sweep generator, which can represent and analyze three-dimensional swept volumes generated by flat-end and ball-end tools for a typical five-axis NC milling machine graphically, has been developed. In the SDE sweep generator, a machine control data based interpolation method is uniquely used to describe the interpolation motion equation of a five-axis NC milling tool. (2) The SEDE method is derived for a more efficient swept volume calculation. A SEDE-based algorithm for the numerical boundary computation of swept volume is described and combined with some novel smooth approximation formulas in order to calculate the swept volume generated by a general 7-parameter APT (Automatic Programming Tool) tool for a large class of sweeps that includes the motions encountered in five-axis NC milling processes. The SEDE approach for the most part reduces the computation to the determination of SEDE trajectories at the initial grazing points (the main part of the boundary of a swept volume) of the tool, and therefore appears to reduce computational cost as well as providing a natural connectivity for most points on the swept volume boundary. (3) An SEDE-based program has been integrated with Deneb Robotics\u27s Virtual NC commercial software. The SEDE module is used to replace Virtual NC\u27s convex hull sweep algorithm for a more accurate geometrical tool swept volume representation. By using the Boolean subtractor and verifier in Virtual NC, material removal of five-axis NC milling process is simulated and analyzed in an interactive machining environment. Furthermore, the SDE/SEDE approach has been integrated with a five-axis NC milling CAD/CAM system at NJIT to perform part design, tool path generation, Cutter Location (CL) and NC code simulation and verification, and actual machining on a FADAL VMC-20 five-axis NC milling machine. Several examples including machining of a turbine impeller are given to illustrate the effectiveness of this integration approach

Simulation of a finishing operation : milling of a turbine blade and influence of damping

Milling is used to create very complex geometries and thin parts, such as turbine blades. Irreversible geometric defects may appear during finishing operations when a high surface quality is expected. Relative vibrations between the tool and the workpiece must be as small as possible, while tool/workpiece interactions can be highly non-linear. A general virtual machining approach is presented and illustrated. It takes into account the relative motion and vibrations of the tool and the workpiece. Both deformations of the tool and the workpiece are taken into account. This allows predictive simulations in the time domain. As an example the effect of damping on the behavior during machining of one of the 56 blades of a turbine disk is analysed in order to illustrate the approach potential

NC Milling Error Assessment and Tool Path Correction

A system of algorithms is presented for material removal simulation, dimensional error assessment and automated correction of Þve-axis numerically controlled (NC) milling tool paths. The methods are based on a spatial partitioning technique which incorporates incremental proximity calculations between milled and design surfaces. Hence, in addition to real-time animated Þve-axis milling simulation, milling errors are measured and displayed simultaneously. Using intermediate error assessment results, a reduction of intersection volume algorithm is developed to eliminate gouges on the workpiece via tool path correction. Finally, the view dependency typical of previous spatial partitioning-based NC simulation methods is overcome by a contour display technique which generates parallel planar contours to represent the workpiece, thus enabling dynamic viewing transformations without reconstruction of the entire data structure

Virtual reality based creation of concept model designs for CAD systems

This work introduces a novel method to overcome most of the drawbacks in traditional methods for creating design models. The main innovation is the use of virtual tools to simulate the natural physical environment in which freeform. Design models are created by experienced designers. Namely, the model is created in a virtual environment by carving a work piece with tools that simulate NC milling cutters. Algorithms have been developed to support the approach, in which the design model is created in a Virtual Reality (VR) environment and selection and manipulation of tools can be performed in the virtual space. The desianer\u27s hand movements generate the tool trajectories and they are obtained by recording the position and orientation of a hand mounted motion tracker. Swept volumes of virtual tools are generated from the geometry of the tool and its trajectories. Then Boolean operations are performed on the swept volumes and the initial virtual stock (work piece) to create the design model. Algorithms have been developed as a part of this work to integrate the VR environment with a commercial CAD/CAM system in order to demonstrate the practical applications of the research results. The integrated system provides a much more efficient and easy-to-implement process of freeform model creation than employed in current CAD/CAM software. It could prove to be the prototype for the next-generation CAD/CAM system

Advanced Process Planning for Subtractive Rapid Prototyping

This paper presents process planning methods for Subtractive Rapid Prototyping, which deals with multiple setup operations and the related issues of stock material management. Subtractive Rapid Prototyping (SRP) borrows from additive rapid prototyping technologies by using 2½D layer based toolpath processing; however, it is limited by tool accessibility. To counter the accessibility problem, SRP systems (such as desktop milling machines) employ a rotary fourth axis to provide more complete surface coverage. However, layer-based removal processing from different rotary positions can be inefficient due to double-coverage of certain volumes. This paper presents a method that employs STL models of the in-process stock material generated from slices of the part along the rotation axis. The developed algorithms intend to improve the efficiency and reliability of these multiple layer-based removal steps for rapid manufacturing.Mechanical Engineerin