Faculty of Engineering and Natural Sciences
Solid Sweeping: Properties, Computations and Applications
& Improving Productivity in Free-form Surface Machining
Department of Mechanical Engineering,
University of Connecticut,
Sweeping a set of points along a trajectory is one of the fundamental operations in geometric and solid modeling. In general, sweeps are considered to be essential in geometric modeling, NC machining, motion planning, collision detection, mechanical design, ergonomics, robot workspace analysis and other applications. The mathematical envelopes of families of both rigid and non-rigid moving shapes play a fundamental role in these applications. However, many properties of sweeps as well as their ‘‘informational completeness’’ are not well understood, which is the primary reason why computational support for solid sweeping remains scarce. A generic point membership classification (PMC) for sweeping solids of arbitrary complexity moving according to one parameter affine motions has been proposed, and this is defined in terms of inverted trajectory tests against the original geometric representation of the generator object. Importantly, this PMC test provides complete geometric information about the set swept by 3D objects in general motions. From a practical point of view, this approach provides the first steps towards a generic technique to compute multi-parameter sweeps, which arise in relatively more complex problems compared to one-parameter sweeps, such as offset surface computations, Minkowski sums, packaging problems, planning the sequence of assembling products, finding the insertion and removal paths of objects and etc. The results of this research will briefly advance the state of the art in geometric modeling, computer aided manufacturing, path planning, collision detection, and etc. by providing new algorithms. These new algorithms will help predicting, quantifying, and correcting potential malfunctions in kinematic pairs, overcutting or undercutting in machining, testing tool paths for CNC machining induced by geometric singularities.
Free-form machining is one of the commonly used manufacturing processes for several industries such as automobile, aerospace, die and mold industries. In 3D complicated free-form surfaces, it is critical, but often difficult, to select applicable cutting conditions to achieve high productivity while maintaining high quality of parts. It is essential to optimize the feedrate in order to improve the machining efficiency of the ball-end milling. Conservative constant feedrate values have been mostly used up to now since there was a lock of physical models and optimization tools for the machining processes. The common approach used in feedrate scheduling is based on the geometric and volumetric analysis, but they do not concern the physics of the free-form machining process. The new approach is based on the mechanics of the cutting process. The feedrate values are set to values which keep either average or instantaneous machining forces to prescribed values. In this study, feedrate scheduling strategies are compared theoretically and experimentally for 3D ball-end milling of free-form surfaces. It is shown that the machining time can be decreased significantly along the tool path with the new force based feedrate scheduling.
Huseyin Erdim is currently a Ph.D. candidate in Mechanical Engineering at University of Connecticut, CT. Prior to that, he received M.Sc. and B.S. in Mechanical Engineering from Koc University, Istanbul in 2005 and Middle East Technical University, Ankara in 2003 respectively. He worked on improving productivity in free-form surface machining based on the physics of the cutting process during Master's. This work brought him The Outstanding Young Researcher Award from Japan Society of Mechanical Engineers. His current work in Ph.D. focuses on understanding the fundamentals and computational properties of sweeps together with their applications. His graduate studies have led to 7 journal publications (2 of them are invited). His primary research interests include geometric and solid modeling, geometric reasoning, NC machining, and more generally, theoretical and computational tools for systematic mechanical design, manufacturing and analysis.
March 25, 2009, 13:40,