Research On Computer-aided Manufacturing Technology Of T-spline Surfaces

In the field of computer-aided manufacturing (CAM), researchers in academy and industry have long been searching for a mathematical model that is able to represent complex workpiece as well as suitable for tool path generation processes. The polyhedron model and the tensor-product surfaces are two of the most famous representation methods. Nevertheless, both of them subject to defects in the complex workpiece modeling and tool path generation.The T-spline surface escaped from the limitation tensor-product structure. With the concept of local controlling domain, control vertices can be freely arranged. The number of control vertices on every row is not necessarily the same. Redundant vertices are removed and the total number of control vertices is greatly reduced. Because of its flexible topology and robust data structure, the T-spline surface has become the trend of free-form surfaces representation in the realm of CAD design, animation and CAE. Yet its application in manufacturing has not been fully explored.In this thesis, a computer-aided manufacturing solution using T-spline surface is presented. Taking advantage of the flexible topology of the T-spline pre-image, free-form surfaces in complex workpiece are well represented. Tool path is directly generated on the T-spline surface. The tedious process of file format exchange is no long needed. Through theoretical research and actual machining experiment, this work aims to deal with free-form surface machining, and to further extend the mutual development of new type surface in CAD/CAM area. Major contributions of this work include:1. Summarizing and comparative study of the different representation methods of free-form surface, the use of T-spline surface as the mathematical model in CAM system is proposed. A knot/vertex data structure is constructed and the concept of local controlling domain is developed. The evaluation of surface point and the vicinity geometric properties is improved. Based on these, tool path with user-defined parameters and error limitations can be directly generated on T-spline surface. The gap between free-form surface computer-aided design (CAD) and computer-aided manufacturing is bridged.2. The traditional Z-level roughing strategy often leads to uneven distributed cutting depth, tool vibration, and unsatisfying surface quality. In order to overcome these deficiencies, a morphing machining strategy (MMS) is proposed. Taking advantage of the flexible parametric pre-image of the T-spline, the complex shape of workpiece and stock are represented in a single T-spline surface, making it easy for surface deformation. An energy based T-spline surface deformation method is proposed. The tool path parameters such as the cutting depth and working allowance are set as the optimization constraints. Control vertices are moved and the original workpiece surface is gradually morphed to stock surface. A series of Interception surfaces are produced. Then, reverse the order of the surface series and generate tool path for each layer of the deformed surface. Finally, the workpiece is gradually carved out from the stock.3. The traditional space-filling curve (SFC) tool path will fail on non-rectangular parametric domain. Unfortunately, the parametric domain of the T-spline surface is a free shape with irregular boundaries and holes. In order to apply SFC tool path to T-spline surface, an improved space-filling curve (ISFC) finishing tool path planning strategy is proposed. Special treatments have been taken to generate grids, redistribute vertices and construct rational cells. Moreover, in order to deal with the undercut problem on tool path corners, the Hermite compensation curves are proposed. The tool is fed smoothly around the corners and uncut materials are carefully removed.4. Last but not least, a T-spline surface CAM prototype system is developed. The abovementioned surface point and local geometric properties evaluation methods, the MMS roughing strategy and the ISFC finishing tool path generation algorithm are realized in the system. The system can read in T-spline file and present surface display. It allows predefined and user-input tool path parameters for MMS to produce deformed surface layers. Within each layer, a non-retraction finishing tool path can be generated using the ISFC method. The system also supports tool path framework simulation. When the appropriate machine tool is configured, the tool path post process module is ready to output NC code for actual cutting.In order to further test the function of the prototype system, a series of typical mechanical parts and biomedical workpieces are used for tool path simulation and actual machining, including mouse, gearbox cover, artificial finger bone. Both roughing and finishing tool path are generated on each workpiece. Computer simulation and actual machining experiment are carried out. Results show the efficiency of the proposed tool path generation algorithm. It is also proven that the T-spline surface, with its flexible topology, is a suitable mathematical representation for complex models in CAM system.