تولید مسیر ابزار بهینه سازی شده مبتنی بر برنامه ریزی پویا برای فرزکاری پهلو پنج محور در سطح قانون

This paper presents a computation scheme that generates optimized tool path for five-axis flank milling of ruled surface. Tool path planning is transformed into a matching problem between two point sets in 3D space, sampled from the boundary curves of the machined surface. Each connection in the matching corresponds to a possible tool position. Dynamic programming techniques are applied to obtain the optimal combination of tool positions with the objective function as machining error. The error estimation considers both the deviation induced by the cutter at discrete positions and the one between them. The path planning problem is thus solved in a systematic manner by formulizing it as a mathematical programming task. In addition, the scheme incorporates several optimization parameters that allow generating new patterns of tool motion. Implementation results obtained from simulation and experiment indicate that our method produces better machining quality. This work provides a concise but effective approach for machining error control in five-axis flank milling.

Five-axis CNC machining has become popular in industry since the early 1990s, finding applications in manufacture of aerospace, automobile, air-conditioning, and mold parts. With two additional degrees of freedom, it provides advantages [1] and [2] over three-axis machining like higher productivity and better quality. Machining preparatory work such as change of jigs and fixtures is reduced and thus the total manufacturing time is shortened. In addition, the tool-cutting end can be a good match with the shape of the machined surface. There are two different milling methods in five-axis machining. In point milling (or end milling), the cutting edges near the end of a tool performs the action of material removal [3]. On the contrary, the cylindrical part of a tool does the main cutting in flank milling [4]. Tool path planning is a critical issue in any machining operation. To generate the tool path that achieves the specified surface roughness is a major concern in point milling. Elimination of tool interference is another challenge in use of five-axis machining. The tool must be properly posed in 3D space using the two rotational degrees of freedom so as not to cause any unexpected collisions in the machining environment [5] and [6]. The situation in flank milling is more complicated. To completely avoid tool interference is difficult, if not impossible, in most cases except for machining of simple shapes such as cylindrical, conical, and developable surfaces [7]. In practice, the surface quality after machining is considered acceptable on condition that the amount of tool interference can be limited within a given tolerance. The following literature survey only reviews the studies related to five-axis flank milling, as the focus of this research is on the tool path generation of that milling method. Liu [8] proposed a heuristic algorithm that offsets the points corresponding to the parameter values 0.25 and 0.75 of a ruling with a distance of the tool radius. The line connected by the offset points determines the tool orientation. The tool path generated in this manner produces serious tool interferences near the middle of the machined surface. Bohez et al. [9] determined the tool orientation by offsetting the end points of surface rulings. The offset direction is chosen as the average of the surface normal at these points. They claim that this approach can significantly reduce the amount of tool interference. Lartigue et al. [10] modeled the tool swept volume using the envelope surface. The machined geometry is thus estimated. They also proposed an evaluation method of the machining error that can be applied to compare the quality of different tool paths. Tsay et al. [11] and [12] studied the influence of the yaw and tilt angles on the amount of tool interference in five-axis flank milling from the machining error estimation of various examples. The result works as look-up tables integrated in a tool path generation algorithm for B-spline ruled surface. Bedi et al. [13] studied the relationship between the tool orientation at a cutter location and the amount of undercut/overcut in flank milling of a ruled surface. They assumed that a cylindrical cutter initially makes a contact with a boundary curve of the surface with the tool orientation as the surface ruling at the contact point. Based on this work, they [14] proposed a nonlinear optimization scheme for minimizing the tool interference at discrete positions by locally adjusting the tool position and orientation around the contact ruling. Chu and Chen [7] proposed approximation of a ruled surface using consecutive developable surfaces. The tool path free of local interference is generated by guiding the tool along the rulings of the developable surfaces. However, the machining error cannot be precisely controlled in their method. The above literature review shows several limitations in previous studies. First, optimization methods have been applied to locally adjust the tool orientation at discrete locations, but they are all based on a greedy approach. An implicit assumption is thus made: the global optimum equals to the sum of local optimums. Unfortunately, this statement is generally not true. In addition, the previous methods neglect the possibility of skipping some rulings (or contact points along the boundary curves) in the tool path. The path computed in this manner is not guaranteed to produce better result in terms of the machining error. To overcome these problems, we propose a novel idea for tool path generation in five-axis flank milling of ruled surface. A geometric problem (tool path generation) is converted into a mathematical programming task. Specifically, determination of the tool motion transforms into a global matching problem between two curves. The machining error becomes the objective function to be minimized in a global optimization process. Moreover, the boundary curves of the ruled surface are extended in different degrees for generating the tool contact points. The solution space of tool path is enlarged, thus producing a better result than that without the extension. A series of machining tests are conducted to validate our idea. The measure result demonstrates that the tool path generated by the proposed method gives a minimal machining error. This work provides a concise but effective approach to improving machining error control in five-axis flank milling.

Previous studies investigated the influence of the tool orientation on the machining error for five-axis flank milling of ruled surface. The result helps improve the machining quality in different ways like serving as heuristics, look-up tables, or integrating with local optimization methods in the tool path generation. However, most approaches suffer from inherent limitations that restrict their effectiveness of reducing the error. Thus, this work proposes a new concept in which the problem of tool path generation is transformed into a task of curve matching. One matching line that connects the two boundary curves of the ruled surface determines a cutter location and the tool axis at the location. A tool path consists of a series of such connection lines. The machining deviation is produced by the tool at each line as well as the tool motion between consecutive lines. The total machining error is estimated as their sum. Dynamic programming techniques are applied to compute the optimal tool path with the machining error as the objective function. Implementation results obtained from simulation and experiment indicate that our method produces better machining quality. In practice, this work provides a systematic and effective approach to generating tool path of high quality in five-axis flank milling. It also serves as a good control mechanism of the machining error. The transformation of tool path generation to a global optimization task gives novelty to CAM/NC research. Such a new concept leads to several potential topics in future work. First, the current method is limited in single pass tool path. It can be extended into flank milling of multiple passes. The machined surface will be decomposed into consecutive strips. The decomposition process becomes another optimization problem in addition to the tool path generation within each strip, which has been solved by this work. In addition, this research only allows the forward curve matching, i.e., the tool must move forward. We plan to explore the possibility of combining both tool forward and backforward motions. This is readily accomplished by removing the forward constraint in the curve matching. Once the corresponding network is obtained, the subsequent computation procedures remain the same. The machining error might be further reduced by doing so.