Research On The Basic Kinematics-Geometry Theory And Tool Positioning Strategy For 5-axis NC Machining

In this dissertation, complex 5-axis NC machining process is studied based on kinematics-geometry theory. Especially local optimization and global optimization for tool positioning strategy are presented.For describing the complex motion of tool relative to designed surface, curve frame and pole congruence on designed surface are adopted to set up the base model of 5-axis NC machining. In the model, machining process is the process of truncation of pole by tool continuously and the length of remained pole is machining error. So the relationship among tool surface, tool envelope surface and designed surface are expressed explicitly. Further, two important kinematics-geometry characteristic are dicusssed: Minimum condition of pole is equal to envelope condition; The envelope condition can be discussed on the axis trajectory surface. The relationship between geometry invariant of envelope surface and tool kinematics-geometry parameters is given by three groups of differential formula. The base model and relative work can be fit for general cutter, general designed surface and many machining methods. It forms the theoretical basis of this dissertation.Based on the model of 5-axis NC machining the local tool positioning method is discussed in detail. The Basic Curvature Formula is derivated to describe the intrinsic relationship among tool surface, tool envelope surface and designed surface. The formula shows that the induced curvature between tool envelope surface and designed surface can be expressed with the induced curvature between tool surface and designed surface. Local tool positioning method is just based on the formula. The concept of band osculation is presented by analyzing surface contact types. Based on Basic Curvature Formula the basic proposition of band osculation machining method is proved: Band osculation between tool envelope surface and designed surface is equivalence to line osculation between tool surface and designed surface. The important meaning is that we can optimize tool positions by only considering single tool position instead of considering tool envelope surface, so the tool positioning process can be simplified. Further, offset characteristic of band osculation machining is proved. An important conclusion that osculation tool position is independent of tool path can be drawn. Based on the offset characteristic of band osculation machining, tool positioning method, conditions, error evaluation, tool positioning method with restriction and optimization of tool path are discussedin detail. The theory above all offers a platform for band osculation machining method in engineer application. Based on the platform cylindrical cutter, conical cutter and torus cutter are used to machining some designed surfaces. In addition, if the condition is not satisfied another local tool positioning method is presented. The two tool positioning methods are all called local tool positioning method.Correspondent to local tool positioning method, global tool positioning method is presented. The target of this method is minimizing the error range between tool envelope surface and designed surface. Under the small error supposition two important propositions are proved. (1) The form error of tool surface family and normal quantity of the position error transfer to their envelope surface by equal quantity; (2) Offset transformation can't change the error range. Based on the theory global tool positioning are simplified greatly, for cylindrical cutter, if the tool axis trajectory surface approach the offset surface we can get the optimized tool positions; for conical cutter, the conical cutter surface can be look on as the error surface of cylindrical cutter, so if the conical approach the cylindrical surface we can get the optimized tool positions; for general milling cutter, based on initial tool axis trajectory surface we can get the mapping surface of designed surface, then let the tool axis trajectory surface approach this surface, optimized tool positions can be achieved. During the realization of this method, local tool positioning method and three point offset (TPO) method are adopted to get the initial tool positions. After that, a least square model is founded to minimize the error range based on error between tool envelope surface and designed surface.In this dissertation I try my best to study the 5-axis NC machining from theoretical point. Based on comprehension to error rule between tool envelope process and designed surface a uniform frame for tool positioning of end milling and flank milling is founded. Under this frame all kinds of tool positioning method are studied. At last, screw propeller, spatial cam and impeller are machined to verify the effectiveness and validity of local tool positioning method and global tool positioning method.