The rotation-minimizing frame is the main research object for a spatial curve. Although the mathematical description is not complicated, it is not easy to directly make an exact minimizing-rotation frame for the Euler...The rotation-minimizing frame is the main research object for a spatial curve. Although the mathematical description is not complicated, it is not easy to directly make an exact minimizing-rotation frame for the Euler-Rodrigues frame. The condition for the non-normalized Euler-Rodrigues frame of the Pythagorean-Hodograph curve to become the rotation-minimizing frame is given in this article, which is an ordinary differential equation with rational form, the analytical solution that does not always exist. To avoid calculating the solution of ordinary differential equations, a global optimization algorithm for the conditions is proposed, that has a weight function in the objective function. The quintic Pythagorean-Hodograph curve is analyzed concretely with the method, and its objective function and constraint conditions of optimization are clarified. The example is analyzed by using this method with different weight functions and contrasting that approach with its exact value.展开更多
Well-designed tool orientation is crucial for the quality execution of five-axis machining with flat-end tools.Tool orientation can be specified in terms of tool inclination and tool tilt angles.For a given surface pa...Well-designed tool orientation is crucial for the quality execution of five-axis machining with flat-end tools.Tool orientation can be specified in terms of tool inclination and tool tilt angles.For a given surface path,these aspects need to be specified for each cutter contact point along the path,because poor tool orientation choice can cause large axial acceleration of the machine tool,leading to inferior quality of the machined surface.The rotation-minimizing frame aims to reduce unnecessary frame rotation during movement.This concept has been adopted to develop tool orientation methods that allow variation in the inclination angle,the tilt angle,and both the inclination and tilt angles.The intention is to reduce unnecessary rotation of the tool frame as the tool follows a specified path.Evaluation was conducted in the context of five-axis flat-end tool machining.Based on these methods,tool orientation was planned along surface paths of a torus,sphere,and dome.Changes in tool orientation were always smooth.From the perspective of reducing tool orientation changes and axial acceleration,it was demonstrated that simultaneous variation of the inclination and tilt angles based on rotation minimization provided the best results.展开更多
文摘The rotation-minimizing frame is the main research object for a spatial curve. Although the mathematical description is not complicated, it is not easy to directly make an exact minimizing-rotation frame for the Euler-Rodrigues frame. The condition for the non-normalized Euler-Rodrigues frame of the Pythagorean-Hodograph curve to become the rotation-minimizing frame is given in this article, which is an ordinary differential equation with rational form, the analytical solution that does not always exist. To avoid calculating the solution of ordinary differential equations, a global optimization algorithm for the conditions is proposed, that has a weight function in the objective function. The quintic Pythagorean-Hodograph curve is analyzed concretely with the method, and its objective function and constraint conditions of optimization are clarified. The example is analyzed by using this method with different weight functions and contrasting that approach with its exact value.
文摘Well-designed tool orientation is crucial for the quality execution of five-axis machining with flat-end tools.Tool orientation can be specified in terms of tool inclination and tool tilt angles.For a given surface path,these aspects need to be specified for each cutter contact point along the path,because poor tool orientation choice can cause large axial acceleration of the machine tool,leading to inferior quality of the machined surface.The rotation-minimizing frame aims to reduce unnecessary frame rotation during movement.This concept has been adopted to develop tool orientation methods that allow variation in the inclination angle,the tilt angle,and both the inclination and tilt angles.The intention is to reduce unnecessary rotation of the tool frame as the tool follows a specified path.Evaluation was conducted in the context of five-axis flat-end tool machining.Based on these methods,tool orientation was planned along surface paths of a torus,sphere,and dome.Changes in tool orientation were always smooth.From the perspective of reducing tool orientation changes and axial acceleration,it was demonstrated that simultaneous variation of the inclination and tilt angles based on rotation minimization provided the best results.
