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1、附錄 附錄 A:英文資料 :英文資料Real-time generation and control of cutter pathfor 5-axis CNC machiningAbstract:This paper presents a new approach to real-time generation and control of the cutter path for 5-axis machining application
2、s. The cutter path generation method comprises real-time algorithms for cutter-contact path interpolation, cutter offsetting, and coordinate conversion. In addition, a global feedback loop is closed by the interpolator s
3、o as to augment the CNCcontrolled accuracy in practical cutter path generation. An error compensation algorithm and a feedrate adaptation algorithm for the control loop are developed, respectively.Keywords:5-axis machin
4、ing; Cutter path generation; interpolator; Error CNCcompensation; Feedrate adaptation1.Introduction5-axis computer numerical controlled ( ) machine tools are widely used in machining CNCdies, molds, turbine blades, a
5、nd aerospace parts. These parts usually have complex geometry and are represented by parametric or free-form surfaces. As compared to 3-axis machining, the 5-axis machining offers many advantages such as higher productiv
6、ity and better machining quality. In 5-axis machining, the orientation of the tool can be determined by the two additional degrees of freedom so as to obtain efficient cutter paths. To achieve high efficiency and interfe
7、rence-free cutter path planning, many algorithms for determination of the cutter path direction and interval and detection and avoidance of the cutter interference have been developed. Based on these algorithms that are
8、implemented in a computer-aided manufacturing ( ) system, the cutter paths that comprise cutter location and orientation CAMtrajectories are determined and represented by a series of linear or spline motion commands.To
9、conduct on-line 5-axis machining, the motion commands generated by the CAM system are loaded to the machine that adopts a real-time interpolator. The interpolator CNC CNCcan convert the cutter path to motion trajectorie
10、s of the five separate axes in order to coordinate their motion in 5-axis machining. Many interpolators for different types of curves have been developed. Among them the linear and the spline interpolators are the most p
11、opular in parametric surface machining. It was reported by Yang and Kong that linear interpolator can monitor the practical cutter path so as to compensate for the path deviation error or CCto reduce it through on-line
12、adaptation of the velocity (this means to slow down the CCmachining as the path error is too large). CCIn this paper, we first discuss the existing approach to cutter path generation and control and the corresponding pr
13、oblems. Then, a new approach is proposed. Simulation examples are provided to support the adequacy of the proposed approach. Finally, concluding remarks are given.2. Tool path description and machine tool motionThe cutte
14、r tools commonly used in 5-axis machining are endmill cutters. The cutter’s end can be flat, spherical, or filleted. Fig.1 shows a typical filleted endmill cutter with a tool radius of and a corner radius of . Notice th
15、at the cutter for =0 refers to a flat endmill and the t r c r c rcutter for =refers to a spherical endmill. denotes the cutter contact ( ) point that is c r t r C CCthe intersection of the cutter and the sculptured s
16、urface, S.N is the unit normal vector to the surface on and denote the path direction and the path interval (or . C T ( ) B T N ? ? CCscallop) direction, respectively. and are the cutter location ( ) point and the tool
17、 N O CLorientation vector, respectively. Traditionally, the cutter orientation ( ) is set to a fixed angle Ooff the surface principle normal ( ) during machining. However, the angle formed between Nand can be altered s
18、o as to avoid cutter interference. Geometrically, this angle can be N Ofurther decomposed into an inclination angle ( ) and a tilt angle ( ) so that the endmill is ? ?rotated about with along B and then with along . B
19、ased on the surface and cutter C ? ? Npath geometry (and ), the data are defined. Through some , , , C N T ? ? CL ( , ) L Omathematical manipulation, we can have the cutter offsetting algorithm as follows.(1) ( )( cos
20、 cos sin cos sin ) c t c c L C r N r r T N B r O ? ? ? ? ? ? ? ? ? ? ? ?(2 ) sin cos cos sin sin O T N B ? ? ? ? ? ? ? ? ?Based on the above algorithm, the cutter location and orientation trajectories are determined and
21、represented by linear or spline motion commands.Because to utilize linear motion commands requires a significantly large file and CLresults in velocity fluctuation along the cutter path, we utilize parametric spline fun
22、ctions to represent the cutter path here. In practice, we need three spline functions for the cutter location ( ) and two spline functions for the tool orientation ( ).Notice that the three ? ? , , L xt yt zt ? Ocompone
23、nts of can be reduced to two Euler angles. In this paper, the Euler angles, and, O t ?are defined so that the tool axis is originally in the z-direction, then rotates with along t ? t ?x-axis, and finally rotates witha
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