Kinematics Driven Geometric Modeling for Virtual Design and Manufacturing

这项拨款为开发用于设计和制造运动自由曲面的综合计算机辅助设计/计算机辅助制造系统提供资金。运动自由曲面具有综合的几何和运动控制结构，体现了计算机数控（CNC）加工过程所需的刀具运动的几何形状。将开发基于有理Bezier和b样条（NURBS）的多参数自由运动的综合和分析算法。由多参数NURBS运动产生的运动自由曲面将用于常用的刀具几何形状，如线切割电火花加工（EDM）工艺的线条，五轴磨削工艺的平面和五轴铣削工艺的圆柱体。将开发具有多分辨率渲染能力的多感官虚拟环境，用于设计、逼近和精细调整运动自由曲面。分析和最小化由离散化引起的加工误差的方法将用于生成和优化刀具运动。将开发一种具有视觉、听觉和触觉反馈功能的五轴虚拟铣床，不仅可以模拟刀具运动的位置，还可以模拟刀具运动的速度和加速度。本课题的研究成果将在一台实际的五轴数控铣床上进行验证。这个项目代表了NURBS几何从纯几何域到运动学域的扩展。它为解决虚拟设计和制造管道各个阶段的几何和运动学问题提供了一个集成的框架。通过在设计阶段早期结合运动学问题，该项目如果成功，将产生一种新的方法和软件工具，用于设计没有几何可加工性问题的雕塑形状，如过切和欠切。该项目的成果还将为汽车和航空航天工业的模具、模具和其他雕刻形状的并行设计和制造提供基础。

This grant provides funding for the development of an integrated computer-aided design/computer-aided manufaturing system for design and manufacture of kinematic freeform surfaces. The kinematic freeform surfaces have integrated geometric and kinematic control structures that embody the geometry of tool motions required for Computer Numerically Controlled (CNC) machining processes. Algorithms for synthesizing and analyzing rational Bezier and B-spline (or NURBS) based multi-parameter freeform motions will be developed. Kinematic freeform surfaces generated by the multi-parameter NURBS motions will be developed for commonly used cutting-tool geometries such as lines for wire-cut Electric Discharge Machining (EDM) processes, planes for 5-axis grinding processes, and cylinders for 5-axis milling processes. Multisensory virtual environments with multi-resolution rendering capabilities will be developed for design, approximation, and fine-tuning of kinematic freeform surfaces. Methods for analyzing and minimizing the machining errors due to discretization will be developed for generation and optimization of tool motions. A 5-axis virtual milling machine with visual, aural, and haptic feedback capabilities will be developed to simulate not only the position but also the velocity and acceleration of tool motions. The research results of this project will be validated on a real 5-axis CNC milling machine. This project represents an extension of NURBS geometry from the purely geometric domain to the kinematic domain. It offers an integrated framework for addressing geometric and kinematic problems in various stages of the virtual design and manufacturing pipeline. By incorporating kinematic issues early in the design stage, the project, if successful, would yield a new methodology and a software tool for designing sculptured shapes that are free of geometric machinability problems such as under- and over-cut. The project results will also provide a basis for concurrent design and manufacturing of dies, molds and other sculptured shapes for automobile and aerospace industries.