In the aircraft digital assembly process, the position and attitude of the aircraft components is usually controlled by the coordinates of the measuring points fixed on the components. The aircraft component would be adjusted from its initial attitude to the target one according to the attitude and position relationship between the actual coordinates of the measuring points located on aircraft component and the theoretical coordinates. In actual working conditions, the actual length between the measuring points would be deviated from the theoretical length, or even out of tolerance, which could cause a large internal force to the system during the attitude adjusting and positioning, and affect the accuracy of the attitude adjustment for an aircraft component. To improve the overall accuracy of the aircraft component's attitude adjustment, and reduce the system's internal force in the attitude adjustment process, a method for optimizing measuring points is presented in this work. The deviation calculation between measuring points fixed on aircraft components and the theoretical coordinates is presented in details, and the optimized measuring points are finally determined by constructing the optimization criterion of the measuring points. Furthermore, the optimized measuring points are matched to the theoretical coordinates, so that the error of the construction points are within the design tolerance, and the sum of the squares of the distances between the construction points and the target points are minimized. The results show that there are more measuring points whose position accuracy met the design requirement. After optimization and algorithm construction of measured points, the numbers of effective measuring points could be increased by 30% and the internal force of the system during the attitude adjustment and positioning of the aircraft components is reduced by 4.4% of that without optimization and configuration.
[1] ZHAO G, ZHANG C Y, JING X S, et al. Station-transfer measurement accuracy improvement of laser tracker based on photogrammetry[J]. Measurement, 2016, 94:717-725.
[2] ACERO R, SANTOLARIA J, PUEO M, et al. Verification of a laser tracker with an indexed metrology platform[J]. The International Journal of Advanced Manufacturing Technology, 2016, 84(1-4):595-606.
[3] 李辉, 刘巍, 张洋, 等. 激光跟踪仪多基站转站精度模型与误差补偿[J]. 光学精密工程, 2019, 27(4):771-782. LI H, LIU W, ZHANG Y, et al. Model establishment and error compensation of laser tracker station-tansfer[J]. Optics and Precision Engineering, 2019, 27(4):771-782(in Chinese).
[4] ARUN K S, HUANG T S, BLOSTEIN S D. Least-squares fitting of two 3-D point sets[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1987, 9(5):698-700.
[5] UMEYAMA S. Least-squares estimation of transformation parameters between two point patterns[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1991, 13(4):376-380.
[6] HORN B K P, HILDEN H M, NEGAHDARIPOUR S. Closed-form solution of absolute orientation using orthonormal matrices[J]. Journal of the Optical Society of America A, 1988(5):1127-1135.
[7] HORN B K P. Closed-form solution of absolute orientation using unit quaternions[J]. Journal of the Optical Society of America A, 1987(4):629-642.
[8] 罗芳, 邹方, 周万勇. 飞机大部件对接中的位姿计算方法[J]. 航空制造技术, 2011(3):91-94. LUO F, ZOU F, ZHOU W Y. Posture calculating algorithm in large aircraft component butt[J]. Aeronautical Manufacturing Technology, 2011(3):91-94(in Chinese).
[9] WANG Z Y, JEPSON A. A new closed-form solution for absolute orientation[C]//IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1994.
[10] WALKER M W, SHAO L. Volz-estimating 3-D location parameters using dual number quaternions[J]. CVGIP:Image Understanding, 1991, 54(3):358-367.
[11] 张宪朝. 基于变形补偿的中机身壁板调姿拟合算法[J]. 科技经济导刊, 2016(22):9-11. ZHANG X C. Fitting algorithm of attitude adjustment of middle fuselage panel based on deformation compensation[J]. Technology and Economic Guide, 2016(22):9-11(in Chinese).
[12] 朱绪胜, 郑联语. 基于关键装配特性的大型零部件最佳装配位姿多目标优化算法[J]. 航空学报, 2012, 33(9):1726-1736. ZHU X S, ZHENG L Y. Multiple-objective optimization algorithm based on key assembly characteristics to posture best fit for large component assembly[J]. Acta Aeronautica et Astronautica Sinica, 2012, 33(9):1726-1736(in Chinese).
[13] 雷沛, 郑联语. 面向飞机大部件调姿的PPPS机构球铰点中心位置闭环标定方法[J]. 航空学报, 2016, 37(10):3186-3196. LEI P, ZHENG L Y. Closed-loop calibration method of PPPS mechanism ball joint center position for posture adjustment of large aircraft components[J]. Acta Aeronautica et Astronautica Sinica, 2016, 37(10):3186-3196(in Chinese).
[14] 王青, 余小光, 乔明杰, 等. 基于序列二次规划算法的定位器坐标快速标定方法[J]. 浙江大学学报:工学版, 2017, 51(2):319-327. WANG Q, YU X G, QIAO M J, et al. Rapid calibration based on SQP algorithm for coordinate frame of localizers[J]. Journal of Zhejiang University:Engineering Science, 2017, 51(2):319-327(in Chinese).
[15] DEVENDEVILLE L, DUMONT S, GOUBET O, et al. Algorithms for constrained best-fit alignment[J]. Journal of Informatics and Mathematical Sciences, 2013, 5(2):77-100.
[16] 王巍, 周天一, 王诚鑫. 基于激光跟踪仪测量系统的翼身对接技术研究[J]. 装备制造技术, 2018(10):203-206. WANG W, ZHOU T Y, WANG C X. Research on wing body docking technology based on laser tracker measurement system[J]. Equipment Manufacturing Technology, 2018(10):203-206(in Chinese).
[17] 朱永国, 黄翔, 李泷杲, 等. 飞机装配高精度测量控制网精度分析与构建准则[J]. 中国机械工程, 2014, 25(20):2699-2704. ZHU Y G, HUANG X, LI L G, et al. Precision analysis and layout rules of surveying control network for aircraft assembly[J]. China Mechanical Engineering, 2014, 25(20):2699-2704(in Chinese).
[18] TRASLOSHEROS A, SEBASTIAN J M, TORRIJOS J, et al. An inexpensive method for kinematic calibration of a parallel robot by using one hand-held camera as main sensor[J]. Sensors, 2013, 13(8):9941-9965.
[19] MEI B, ZHU W D, YUAN K Z, et al. Robot base frame calibration with a 2D vision system for mobile robotic drilling[J]. The International Journal of Advanced Manufacturing Technology, 2015, 80:1903-1917.
[20] 王志浩, 陈文亮, 王慧, 等. 飞机自动钻铆并联调姿托架标定方法[J]. 计算机集成制造系统, 2018, 24(12):2964-2973. WANG Z H, CHEN W L, WANG H, et al. Calibration method of aircraft automatic drilling and riveting parallel posture adjustment bracket[J]. Computer Integrated Manufacturing Systems, 2018, 24(12):2964-2973(in Chinese).
[21] 李玉昆, 李永泉, 佘亚中, 等. 3-UPS/S并联稳定平台满载工况误差分析与运动学标定[J]. 中国机械工程, 2017, 28(8):958-965. LI Y K, LI Y Q, SHE Y Z, et al. Error analysis and kinematics calibration of 3-UPS/S parallel stabilizing platform in full load conditions[J]. China Mechanical Engineering, 2017, 28(8):958-965(in Chinese).
[22] NI Y B, ZHANG B, GUO W X, et al. Kinematic calibration of parallel manipulator with full-circle rotation[J]. Industrial Robot, 2016, 43(3):296-307.
[23] BI Y B, YAN W M, KE Y L. Numerical study on predicting and correcting assembly deformation of a large fuselage panel during digital assembly[J]. Assembly Automation, 2014, 34(2):204-216.
[24] FANG Q, CHEN W D, ZHAO A A, et al. Control system designing for correcting wing-fuselage assembly deformation of a large aircraft[J]. Assembly Automation, 2017, 37(1):22-33.
CJA