飞机装配时的孔位精度直接影响其最终装配质量,而待制孔零件易发生变形和整体偏移,因此一般通过基准孔信息对待制孔位进行补偿。提出一种基于Kriging插值的孔位修正方法,通过基准孔建立孔位理论坐标与实际偏差值的Kriging模型,进而预测待制孔的孔位偏差,并给出每个位置的预测标准误差,以指导基准孔的增添和布置。最后通过有限元和数值实验分别验证了零件在极限变形和整体平移旋转情况下该方法的有效性,实现了孔位估计误差小于0.3 mm。
Hole position accuracy in aircraft assembly directly affects the final assembly quality, while parts to be holed are prone to deformation and overall offset. Therefore, the hole position is generally compensated by reference hole information. In this paper, a method of hole position correction based on the Kriging interpolation is proposed. The Kriging model of theoretical coordinates and the actual deviation of hole position are established through reference hole, and then the deviation of hole to be made is predicted. The prediction root mean square error of each position is given to guide the addition and layout of the reference hole. Finally, the effectiveness of the method under the condition of ultimate deformation or overall translation and rotation is verified by the finite element method and numerical experiments. The hole position estimation error is less than 0.3 mm.
[1] ZHAN Q, WANG X. Hand-eye calibration and positioning for a robot drilling system[J]. The International Journal of Advanced Manufacturing Technology, 2012, 61(5-8):691-701.
[2] TANG N, LI Y, LIU P, et al. Bi-directional obtaining and offline compensation method of locating error for airplane panel[J]. Systems Engineering and Electronics, 2012, 34(3):631-636.
[3] 严伟苗. 大型飞机壁板装配变形控制与校正技术研究[D]. 杭州:浙江大学, 2015. YAN W M. Study on technologies for controlling and correcting large aircraft panel assembly deformation[D]. Hangzhou:Zhejiang University, 2015(in Chinese).
[4] ZHU W, MEI B, YAN G, et al. Measurement error analysis and accuracy enhancement of 2D vision system for robotic drilling[J]. Robotics and Computer-Integrated Manufacturing, 2014, 30(2):160-171.
[5] TIAN W, ZENG Y, ZHOU W, et al. Calibration of robotic drilling systems with a moving rail[J]. Chinese Journal of Aeronautics, 2014, 27(6):1598-1604.
[6] BRISTOW J W, IRVING P E. Safety factors in civil aircraft design requirements[J]. Engineering Failure Analysis, 2007, 14(3):459-470.
[7] 涂国娇. 环形轨自动化制孔系统孔位修正方法研究[D]. 杭州:浙江大学, 2015. XU G J. Study on correcting method of hole position for a flexible track automatic drilling system[D]. Hangzhou:Zhejiang University, 2015(in Chinese).
[8] 唐伟. 一类蒙皮/长桁壁板结构预连接工艺优化方法研究[D]. 杭州:浙江大学, 2017. TANG W. Study on optimization methods of pre-joining processes for a class of skin-stringer panel structures[D]. Hangzhou:Zhejiang University, 2017(in Chinese).
[9] 刘光孟, 汪云甲, 张海荣, 等. 空间分析中几种插值方法的比较研究[J]. 地理信息世界, 2011, 9(3):41-45. LIU G M, WANG Y J, ZHANG H R, et al. Comparative study of several interpolation methods on spatial analysis[J]. Geomatics World, 2011, 9(3):41-45(in Chinese).
[10] ZHU W, QU W, CAO L, et al. An off-line programming system for robotic drilling in aerospace manufacturing[J]. The International Journal of Advanced Manufacturing Technology, 2013, 68(9-12):2535-2545.
[11] 周叔阳, 韩志仁, 郭喜锋, 等. 模拟退火算法在预连接孔排布中的应用研究[J]. 机械科学与技术, 2019, 38(6):959-962. ZHOU S Y, HAN Z R, GUO X F, et al. Application research of simulated annealing algorithm in pre-connected hole arrangement[J]. Mechanical Science and Technology for Aerospace Engineering, 2019, 38(6):959-962. (in Chinese).
[12] 董辉跃, 周华飞, 尹富成. 机器人自动制孔中绝对定位误差的分析与补偿[J]. 航空学报, 2015, 36(7):2475-2484. DONG H Y, ZHOU H F, YIN F C. Analysis and compensation for absolute positioning error of robot in automatic drilling[J]. Acta Aeronautica et Astronautica Sinica, 2015, 36(7):2475-2484(in Chinese).
[13] 王龙飞, 张丽艳, 叶南. 一种适用于曲面结构的机人制孔误差在线补偿技术[J]. 航空学报, 2019, 40(11):422871. WANG L F, ZHANG L Y, YE N. An on-line compensation technology for robotic drilling error suitable for curved structure[J]. Acta Aeronautica et Astronautica Sinica, 2019, 40(11):422871(in Chinese).
[14] 王青, 郑守国, 李江雄, 等. 基于孔边距约束和Shepard插值的孔位修正方法[J]. 航空学报, 2015, 36(12):4025-4034. WANG Q, ZHENG S G, LI J X, et al. A correction method for hole positions based on hole margin constraints and Shepard interpolation[J]. Acta Aeronautica et Astronautica Sinica. 2015, 36(12):4025-4034(in Chinese).
[15] CRESSIE N. The origins of kriging[J]. Mathematical geology, 1990, 22(3):239-252.
[16] 张继文, 刘莉, 李昌硕, 等. 仿人机器人全方位步行参数的代理模型优化[J]. 机器人, 2016, 38(1):56-63. ZHANG J W, LIU L, LI C S, et al. Surrogate model based optimization for omni-directional walking parameters of humanoids[J]. Robot, 2016, 38(1):56-63(in Chinese).
[17] SANTNER T J, WILLIAMS B J, NOTZ W, et al. The design and analysis of computer experiments[M]. New York:Springer, 2003.
[18] JONES D R, SCHONLAU M, WELCH W J. Efficient global optimization of expensive black-box functions[J]. Journal of Global Optimization, 1998, 13(4):455-492.
[19] ROUSTANT O, GINSBOURGER D, DEVILLE Y. DiceKriging, DiceOptim:Two R packages for the analysis of computer experiments by Kriging-based metamodeling and optimization[J]. Journal of Statistical Software, 2012, 51(1):54.
[20] 曾怀恩, 黄声享. 基于Kriging方法的空间数据插值研究[J]. 测绘工程, 2007, 16(5):5-8, 13. ZENG H E, HUANG S X. Research on spatial data interpolation based on Kriging interpolation[J]. Engineering of Surveying and Mapping, 2007, 16(5):5-8, 13(in Chinese).