Tool Path,Size And Shape Optimization In Five-axis Flank Milling Of Complex Surface

With the development of modern industry,some key parts in the fields of aerospace,national defense,transportation and energy,such as the impeller of the aeroengine,the induction wheel,the turbine blades,etc.,put forward higher requirement for machining efficiency and forming precision.Compared with point milling,flank milling is an efficient and high precision machining method.However,the current study focused on flank milling ruled surface with standard cylindrical or conical tool.However,many of the blade parts in the project are not ruled surfaces.Moreover,the simple profile of standard tool is difficult to flank milling the increasingly complex shape of non-ruled blade.Therefore,it is of great significance to extend the flank milling object to non-ruled surface.Flank milling of non-ruled surface is studied from the perspective of tool shape optimization in this dissertation.Four aspects are considered including the analytical expression of the envelope surface of a rotary cutter,the simultaneous optimization of tool size and tool path,shape optimization of hyperbolic tool,and shape optimization of generic rotary cutter.The main research work are listed as follows:(1)The thesis presents an analytical method for calculating the envelope surface of rotating tool with arbitrary generatrix.The three order B-spline curve is used to describe the arbitrary generatrix,and the parameter expression of the rotary cutter surface is obtained.Then,based on the envelope condition and body velocity in spatial kinematics,the analytical expression of the envelope surface of a genric rotating tool is established.In addition,the envelope surface under some special condition is analyzed.(2)A method for simultaneous optimization of tool path and tool size in a given constraint is presented.By using the analytic expression of the envelope surface,the discrete characteristic points of the envelope surface at each cutter location are obtained.Then,from the normal mapping relationship,the correspondence relation between “tool axis trajectory surface-envelope surface-design surface” is established,and the analytical formula of flank milling error is obtained on this basis.Moreover,this expression is a function of the control points of tool axis trajectory surface and tool size.Therefore,optimization of tool size and tool path is modeled as minimizing the sum of squared error under the constraints which limit the adjustment of the tool path and tool size to a range.The trust-region-reflective least squares method is used to obtain the optimal tool path and tool size.(3)The non-concave cylindrical,conical and drum cutter are not suitable for the flank milling of convex surface.To solve this problem,a new method is proposed for the flank milling of convex surfaces with concave hyperbolic tool.Based on the classification of points on the surface in differential geometry,the properties of the surface are studied,and draw the following conclusion: hyperbolic cutter is a negative Gauss curvature surface,which is suitable for flanking the surface with negative principal curvatures.Then,the generated line of the hyperbolic tool is defined by two generating radius and one generating angle,and thus formulate the parametric surface of the hyperbolic tool.Furthermore,by approximating the design surface with envelope surface of hyperbolic tool,the optimization model is established,which is under the constraints that defines the lower and upper bound of the two generating radius and the generating angle,to obtain the optimization shape of hyperbolic tool.Finally,two numerical example on rule surface and convex surface of the turbine blade are given to confirm the validity of the proposed approach.(4)The type of flank-millable surface is further extend,and the method of flank milling for non-ruled surface is also presented.The tool is regarded as the rotation surface,which is totally determined by its generatrix.When the three order B-spline curve is used to represent the generatrix,the problem of tool shape optimization is transformed into that of relocating the control point of its generatrix.Based on this idea,the control points of generatrix are optimized by the least squares criterion to achieve the approximation of the tool envelope to the design surface.And the effectiveness of the method is verified by non-ruled surface.Based on the analytical expression of the envelope surface of revolving cutter formed by rotating an arbitrary generatrix,the optimization model is used to modify the tool contour quantitatively such that the envlope surface approximate to the design surface as close as possible.And thus the flank-millable surface is extended to the non-ruled surface.The proposed methods enrich five-axis flank milling.