基于纬线法的鼓形刀具刀位误差分布计算
收稿日期: 2014-11-05
修回日期: 2014-12-07
网络出版日期: 2014-12-18
基金资助
高等学校博士学科点专项科研基金(20111102110021);国家自然科学基金(51105026);国家科技重大专项(2013ZX04011031)
Calculation of tool position error distribution of barrel cutter based on latitude approach
Received date: 2014-11-05
Revised date: 2014-12-07
Online published: 2014-12-18
Supported by
Specialized Research Fund for the Doctoral Program of Higher Education (20111102110021); National Natural Science Foundation of China (51105026); National Science and Technology Major Project (2013ZX04011031)
刀具误差分布是描述刀具表面与设计曲面之间相对位置关系的重要表达方式,在刀具姿态调整与行宽优化中具有重要应用价值。为提高鼓形刀具刀位误差分布的计算效率与精度,提出了一种基于纬线法的新算法,即纬线圆圆心定位法。该方法通过刀具表面一系列纬线圆的圆心来计算刀具表面与设计曲面之间的最短距离,进而求解其刀位误差分布曲线。针对纬线圆圆弧包络法、纬线圆圆弧离散法和纬线圆圆心定位法,讲解了3种计算方法的基本原理,并详细地分析了影响3种方法计算效率与精度的主要因素。然后,对比分析了纬线圆数量对3种方法计算效率与精度的不同影响。最终,利用某叶片零件加工表面进行了实验验证。结果证明,3种算法皆可满足行宽计算误差不大于5%的要求。但是,3种算法中,纬线圆圆弧离散法所需计算时间最长,纬线圆圆弧包络法其次,所需计算时间减少约50%,纬线圆圆心定位法的计算效率最高,所需计算时间减少约80%。在计算精度方面,纬线圆圆弧离散法与纬线圆圆心定位法精度较好且准确度相差不大,但是比纬线圆圆弧包络法精度提升不足5%。
孟凡军 , 陈志同 , 宁涛 , 徐汝锋 . 基于纬线法的鼓形刀具刀位误差分布计算[J]. 航空学报, 2015 , 36(12) : 4014 -4024 . DOI: 10.7527/S1000-6893.2014.0338
The tool position error distribution plays an important role in the strip-width calculation and the description of the spatial relationship between the cutter surface and designed surface. In order to improve the efficiency and precision about the tool position error distribution calculation of barrel cutter, a latitude circle center location algorithm based on the latitude separation approach is presented in this paper. The shortest distances between cutter surface and designed surface are calculated according to the center of a series of latitude circles in the new algorithm, then the tool position error distribution curve can be obtained. There are three different means dealing with latitude circles, namely latitude circle arc envelope algorithm, latitude circle arc discretization algorithm, and latitude circle center location algorithm. Firstly, the fundamental principles of three algorithms are introduced respectively while the main factors on the calculation efficiency and precision are analyzed. Secondly, the different influences of latitude circle number on the calculation efficiency and precision are compared in three algorithms. Finally, a given example verifies the validity of the concepts and algorithms in this paper. The results show that the strip-width calculation errors of the three algorithms are less than 5%. The latitude circle discretization algorithm is the most time-consuming, and the calculation time of latitude circle envelope algorithm is reduced by 50% while the calculation time of latitude circle center location algorithm is reduced by 80%. The latitude circle center location algorithm and latitude circle discretization algorithm are similar in terms of the calculation precision, but the improvement of calculation precision is less than 5% compared to the latitude circle envelope algorithm.
[1] Li L, Chen B, Liu F, et al. Complexity analysis and calculation for sculptured surface in multi-axis CNC machining based on surface subdivision[J]. International Journal of Advanced Manufacturing Technology, 2014, 71(5-8):1433-1444.
[2] Gray P, Bedi S, Ismail F. Rolling ball method for 5-axis surface machining[J]. Computer-Aided Design, 2003, 35(4):347-357.
[3] Zhou F F, Lu H Z, Yuan J L, et al. Review on multi-point method for roundness error separation[J]. Advanced Materials Research, 2013, 797(2013):555-560.
[4] Senatore J, Monies F, Redonnet J M, et al. Improved positioning for side milling of ruled surfaces:Analysis of the rotation axis's influence on machining error[J]. International Journal of Machine Tools and Manufacture, 2007, 47(6):934-945.
[5] Jin M, Zhang L, Chen Z T. End-points error controlling method for torus tool position optimization in five-axis NC machining[J]. Journal of Beijing University of Aeronautics and Astronautics, 2006, 32(9):1125-1128(in Chinese).金曼,张俐,陈志同.圆环面刀具五坐标加工端点误差控制刀位优化[J].北京航空航天大学学报, 2006, 32(9):1125-1128.
[6] Chen Z T, Yue Y, Xu R F. A middle-point-error-control method in strip-width maximization-machining[J]. Journal of Mechanical Engineering, 2011, 47(1):117-123(in Chinese).陈志同,乐毅,徐汝锋.中点误差控制宽行加工算法[J].机械工程学报, 2011, 47(1):117-123.
[7] Gray P J, Bedi S, Ismail F. Arc-intersect method for 3 frac(1, 2) frac(1, 2)-axis tool paths on a 5-axis machine[J]. International Journal of Machine Tools and Manufacture, 2007, 47(1):182-190.
[8] He Y, Chen Z T, Wu X Z. Iso-parametric tool path overlapping method for sculptured surfaces in wide strip machining[J]. Acta Aeronautica et Astronautica Sinica, 2014, 35(4):1142-1148(in Chinese).贺英,陈志同,吴献珍.复杂曲面宽行加工等参数线刀轨精确搭接方法[J].航空学报, 2014, 35(4):1142-1148.
[9] Zhu Y, Ning T, Chen Z T. Kinematic analysis of cylindrical coordinate CNC machine in integral impeller machining[J]. Acta Aeronautica et Astronautica Sinica, 2014, 35(8):2364-2374(in Chinese).朱燏,宁涛,陈志同.圆柱坐标数控机床加工整体叶轮的运动学分析[J].航空学报, 2014, 35(8):2364-2374.
[10] Yan J Y, Chen Z T, He Y. A quick calculation method of tool position error based on envelope theory[J]. Acta Aeronautica et Astronautica Sinica, 2011, 32(11):2131-2139(in Chinese).颜家勇,陈志同,贺英.基于包络理论的刀位误差快速求解算法[J].航空学报, 2011, 32(11):2131-2139.
[11] Feng Y. Development of an NC programming system based on the strip-width maximization machining algorithm and research on its key technology[D]. Beijing:Beihang University, 2012(in Chinese).冯瑶.宽行加工编程系统开发及关键技术研究[D].北京:北京航空航天大学, 2012.
[12] Xu R F, Chen Z T. Study on methods for calculating tool position error distribution during 5-axis machining of sculptured surfaces[J]. Advanced Materials Research, 2011, 314(8):1517-1522.
[13] Zhu L M, Zhang X M, Ding H. Analytical expression of the swept surface of a rotary cutter using the envelope theory of sphere congruence[J]. Journal of Manufacturing Science and Engineering, 2009, 131(4):041017.
[14] Zhu L M, Ding H, Xiao Y L. Simultaneous optimization of tool path and shape for five-axis flank milling[J]. Computer-Aided Design, 2012, 44(12):1229-1234.
[15] He Y, Chen Z T. Optimising tool positioning for achieving multi-point contact based on symmetrical error distribution curve in sculptured surface machining[J]. International Journal of Advanced Manufacturing Technology, 2014, 73(5-8):707-714.
[16] Li Z Q, Chen Z T, Xiao J. Latitude distribution algorithm of cutter position optimization on drum-like cutter for strip-maximization[J]. Journal of Beijing University of Aeronautics and Astronautics, 2007, 33(6):731-735(in Chinese).李正强,陈志同,肖俊.鼓形刀宽行刀位优化纬线分割算法[J].北京航空航天大学学报, 2007, 33(6):731-735.
[17] Wang D, Chen W Y, Li T, et al. Five-axis flank milling of sculptured surface with barrel cutters[J]. Key Engineering Materials, 2009, 407(2009):292-297.
[18] Li T, Chen W Y, Xu R F, et al. Flank milling for blisk with a barrel ball milling cutter[J]. Key Engineering Materials, 2009, 407(2009):202-206.
[19] Meng F J, Chen Z T, Xu R F, et al. Optimal barrel cutter selection for the CNC machining of blisk[J]. Computer-Aided Design, 2014, 53(8):36-45.
[20] Wang R Q, Chen W Y, Xiao J, et al. Tool positioning strategy for free form surface flank grinding with drum wheel[J]. China Mechanical Engineering, 2006, 17(16):1719-1722(in Chinese).王瑞秋,陈五一,肖俊,等.鼓形砂轮周磨自由曲面刀位算法[J].中国机械工程, 2006, 17(16):1719-1722.
[21] Choi B K, Jerard R B. Sculptured surface machining theory and application[M]. Netherlands:Kluwer Academic Publishers, 1998:128.
[22] Xu R F. Research on tool position error calculation and tool path planning methods in 5-axis machining of sculptured surfaces[D]. Beijing:Beihang University, 2010(in Chinese).徐汝锋.宽行加工刀位误差求解与刀轨规划技术研究[D].北京:北京航空航天大学, 2010.
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