In this paper, optimum positioning of cylindrical cutter for five-axis flank milling of non-developable ruled surface is addressed from the perspective of surface approximation. Based on the developed interchangeability principle, global optimization of the five-axis tool path is modeled as approximation of the tool envelope surface to the data points on the design surface following the minimum zone criterion recommended by ANSI and ISO standards for tolerance evaluation. By using the signed point-to-surface distance function, tool path plannings for semi-finish and finish millings are formulated as two constrained optimization problems in a unified framework. Based on the second order Taylor approximation of the distance function, a sequential approximation algorithm along with a hierarchical algorithmic structure is developed for the optimization. Numerical examples are presented to confirm the validity of the proposed approach.
DING Han1 & ZHU LiMin2 1 State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China
This paper analyzes the stability of milling with variable pitch cutter and tool runout cases characterized by multiple delays,and proposes a new variable-step numerical integration method for efficient and accurate stability prediction. The variable-step technique is emphasized here to expand the numerical integration method,especially for the low radial immersion cases with multiple delays. First,the calculation accuracy of the numerical integration method is discussed and the variable-step algorithm is developed for milling stability prediction for single-delay and multiple-delay cases,respectively. The milling stability with variable pitch cutter is analyzed and the result is compared with those predicted with the frequency domain method and the improved full-discretization method. The influence of the runout effect on the stability boundary is investigated by the presented method. The numerical simulation shows that the cutter runout effect increases the stability boundary,and the increasing stability limit is verified by the milling chatter experimental results in the previous research. The numerical and experiment results verify the validity of the proposed method.
Traditional five-axis tool path planning methods mostly focus on differential geometric characteristics between the cutter and the workpiece surface to increase the material removal rate(i.e.,by minimizing path length,improving curvature matching,maximizing local cutting width,etc.) . However,material removal rate is not only related to geometric conditions such as the local cutting width,but also constrained by feeding speed as well as the motion capacity of the five-axis machine. This research integrates machine tool kinematics and cutter-workpiece contact kinematics to present a general kinematical model for five-axis machining process. Major steps of the proposed method include:(1) to establish the forward kinematical relationship between the motion of the machine tool axes and the cutter contact point;(2) to establish a tool path optimization model for high material removal rate based on both differential geometrical property and the contact kinematics between the cutter and workpiece;(3) to convert cutter orientation and cutting direction optimization problem into a concave quadratic planning(QP) model. Tool path will finally be generated from the underlying optimal cutting direction field. Through solving the time-optimal trajectory generation problem and machining experiment,we demonstrate the validity and effectiveness of the proposed method.
In industry,the defective point data often make most surface reconstruction methods suffer from inherent problems that some specific aided information is difficult to obtain. To solve the problem,a novel implicit reconstruction method without any such information is proposed. This approach extends morphological operations into 3D space and provides an improved procedure to construct off-set gradient functions for indirect approximation. By this method,the dual relative functions guarantee a minimal crust surrounding the point data. They can generate a smooth and watertight resulting surface,filling holes and merging overlapping samples reasonably. Compared with other existing methods,the proposed method is better suited to handle defective point clouds in a convenient and efficient manner. The feasibility and effectiveness of the method are demonstrated through a series of practical examples.
