Exploring Interpolation Algorithm of Smooth Feedrate Scheduling for Sensitive Points of NURBS Curve
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摘要: NURBS插补相对于传统直线和圆弧插补具有极大优势,但其存在敏感点区域插补速度波动剧烈而引起超出机床加工运动能力范围的问题。为了提高NURBS曲线插补运动学性能,改善其加速度和加加速度轨迹突变问题,提出一种NURBS曲线几何特性的敏感点区域速度平滑的插补算法。其通过搜索G1或G2不连续的断点和具有大曲率的关键点,在这些敏感点处分别利用FIR级联滤波器进行S型加速度的平滑速度规划,而后采用断点处速度近似调整的方法,来对其运动学特性进一步改善。仿真和实验结果表明,该算法在敏感点处平滑速度规划和运动学性能良好。Abstract: Compared with conventional linear and circular interpolation, non-uniform rational B-spline (NURBS) interpolation has a greater advantage. However, it has the intense interpolation feedrate fluctuation problem that causes the excessive machining motion capability of a machine tool. In order to improve the kinematic performance of the NURBS interpolation and modify the saltation of acceleration and the jerk of motion, this paper proposes a smooth feedrate scheduling interpolation algorithm for the sensitive points of the NURBS curves based on their geometric characteristics. Through searching for the breakpoints, which are G1 or G2 discontinuity, and the critical points that have great curvature, the feedrate profile for these points are smoothed with the S-shaped acceleration by using the finite impulse response (FIR) cascade filter. Furthermore, this paper proposes an approximation method for fixing the feedrate of breakpoints to make their acceleration and jerk satisfy the desired requirements. Thus, this method can enhance the performance of NURBS interpolation. The simulation and experimental results verify that the algorithm proposed in the paper can smooth the feedrate and has a satisfactory kinematic performance in the sensitive points.
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Key words:
- NURBS /
- algorithm /
- machine tool /
- feedrate /
- acceleration
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[1] Suh S H, Kang S K, Chung D H, et al. Theory and design of CNC systems[M]. London:Springer, 2008 [2] Shpitalni M, Koren Y, Lo C C. Realtime curve interpolators[J]. Computer-Aided Design, 1994,26(11):832-838 [3] Yeh S S, Hsu P L. The speed-controlled interpolator for machining parametric curves[J]. Computer-Aided Design, 1999,31(5):349-357 [4] Farouki R T, Tsai Y F. Exact Taylor series coefficients for variable-feedrate CNC curve interpolators[J]. Computer-Aided Design, 2001,33(2):155-165 [5] Yeh S S, Hsu P L. Adaptive-feedrate interpolation for parametric curves with a confined chord error[J]. Computer-Aided Design, 2002,34(3):229-237 [6] Liu X B, Ahmad F, Yamazaki K, et al. Adaptive interpolation scheme for NURBS curves with the integration of machining dynamics[J]. International Journal of Machine Tools and Manufacture, 2005,45(4-5):433-444 [7] Xu R Z, Xie L, Li C X, et al. Adaptive parametric interpolation Scheme with limited acceleration and jerk values for NC machining[J]. The International Journal of Advanced Manufacturing Technology, 2008,36(3-4):343-354 [8] Lee A C, Lin M T, Pan Y R, et al. The feedrate scheduling of NURBS interpolator for CNC machine tools[J]. Computer-Aided Design, 2011,43(6):612-628 [9] 富宏亚,李茂月,刘源,等.基于曲率特性的柔性加减速NURBS插补器[J].计算机集成制造系统,2012,18(9):1921-1929 Fu H Y, Li M Y, Liu Y, et al. NURBS interpolator with flexible acceleration and deceleration based on curvature properties[J]. Computer Integrated Manufacturing Systems, 2012,18(9):1921-1929(in Chinese) [10] 尹涓,罗福源,游有鹏.NURBS曲线曲率极值点快速分析与定位算法研究[J].机械科学与技术,2015,34(10):1560-1567 Yin J, Luo F Y, You Y P. Study on algorithm of fast analysis and location curvature extremes for NURBS curves[J]. Mechanical Science and Technology for Aerospace Engineering, 2015,34(10):1560-1567(in Chinese) [11] 林峰,张正红,陈胜.基于进给速度敏感点识别的NURBS曲线平滑插补算法研究[J].中国机械工程,2012,23(9):1060-1064 Lin F, Zhang Z H, Chen S. Research on smooth NURBS interpolation algorithm based on feedrate sensitive point identification[J]. China Mechanical Engineering, 2012,23(9):1060-1064(in Chinese) [12] Chen C S, Lee A C. Design of acceleration/deceleration profiles in motion control based on digital FIR filters[J]. International Journal of Machine Tools and Manufacture, 1998,38(7):799-825 [13] 于东,胡韶华,盖荣丽,等.基于滤波技术的数控系统加减速研究[J].中国机械工程,2008,19(7):804-807 Yu D, Hu S H, Gai R L, et al. Research on accelerartion and deleration for CNC machine tools based on filtering[J]. China Mechanical Engineering, 2008,19(7):804-807(in Chinese) [14] 张晓辉,于东,胡毅,等.基于滤波技术的NURBS曲线插补算法研究[J].中国机械工程,2009,20(14):1695-1699 Zhang X H, Yu D, Hu Y, et al. Research on NURBS curve interpolation algorithm based on filtering[J]. China Mechanical Engineering, 2009,20(14):1695-1699(in Chinese) [15] Piegl L, Tiller W. The NURBS book[M]. 2nd ed. Berlin Heidelberg New York:Springer, 1997
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