The quantitative analysis of the end elastic deformation was realized in order to analyze the distribution of stiffness performance of the multi-axis machine tool in automatic horizontal dual-machine cooperative drilling and riveting system. The kinematic model of the multi-axis machine tool was established. Machine joints, end effector and flexible links were determined to be the main sources of the end deformation in the multi-axis machine tool. Stiffness matrixes of flexible links and end effector in their respective coordinate systems were obtained by the finite element method based on their mechanical properties. The stiffness matrix of machine joints in the joint space was obtained by the test method. The enhanced end stiffness matrix of machine joints was established by the Jacobian matrix method, and the end stiffness matrixes of flexible links were established by the point transformation method. Based on the small elastic deformation theory, the end stiffness matrixes of all end deformation sources were integrated to establish the general end stiffness model of the multi-axis machine tool. Through the actual test, the error between the general end stiffness model and the experimental results was less than 10%, which proves the accuracy of the general stiffness model.
Jun-xia JIANG,Chen DONG,Chen BIAN,Hui-yue DONG. Investigation on general stiffness of automatic horizontal dual-machine cooperative drilling and riveting system. Journal of ZheJiang University (Engineering Science), 2019, 53(6): 1110-1118.
Fig.1Layout of automatic horizontal dual-machine cooperative drilling and riveting system
Fig.2Distribution of flexible links in multi-axis machine tool with inner riveting head
Fig.3Kinematic model of multi-axis machine tool
连杆
θi/(°)
αi?1/(°)
ai?1/mm
di/mm
关节范围
1
0
0
0
dX
0~4 500 mm
2
90
?90
0
dY
0~2 500 mm
3
90
?90
0
dZ
?800 ?La ~ ? La mm
4
θA
?90
0
0
?30°~30°
5
θB
?90
0
0
?15°~15°
Tab.1D-H parameters of multi-axis machine tool
Fig.4Theory and structure of riveting head
Fig.5Stress deformation cloud diagram of Z-axis link
Fig.6Stress deformation cloud diagram of A-axis link
Fig.7Joint stiffness identification test site
Fig.8Measuring principle of rotating joint
关节
Dji/mm
τji/N
关节
Dji/rad
τji/(N·m)
X轴
0.01
9 697.5
A轴
0.015
572.7
Y轴
0.015
9 699.8
B轴
0.007
300.4
Z轴
0.03
1 796.5
?
?
?
Tab.2Displacement and generalized force of all joints
Fig.9Force transfer model of flexible link
Fig.10Multi-axis machine end deformation measurement test
Fig.11End deformation experimental device
位姿
Fe / N
Dc / mm
De / mm
η / %
X轴
Y轴
Z轴
A轴
B轴
1 000
900
?300
0
0
10 000
0.129
0.139
7.19
2 000
400
?500
0
0
10 000
0.120
0.127
5.51
3 000
1 400
?500
10
10
10 000
0.159
0.175
9.14
3 000
1 400
?100
0
0
10 000
0.140
0.155
9.68
1 000
900
?100
10
0
15 000
0.194
0.206
5.82
2 000
1 400
?500
10
10
15 000
0.223
0.241
7.47
3 000
400
?300
0
0
20 000
0.205
0.221
7.24
1 000
900
?100
10
0
20 000
0.237
0.253
6.32
Tab.3Comparison of experimental and calculated end deformation
[1]
杜兆才, 姚艳彬, 王健 机器人钻铆系统研究现状及发展趋势[J]. 航空制造技术, 2015, (4): 26- 31 DU Zhao-cai, YAO Yan-bin, WANG Jian Research status and development trends of robot drilling and riveting system[J]. Aeronautical Manufacturing Technology, 2015, (4): 26- 31
LUM N, LUO Q E7000 ARJ-manual flexible tooling for horizontal riveting system[J]. SAE International Journal of Aerospace, 2014, 7 (2): 241- 245
doi: 10.4271/2014-01-2250
[5]
王珉, 陈文亮, 郝鹏飞, 等 飞机数字化自动钻铆系统及其关键技术[J]. 航空制造技术, 2013, (Z1): 80- 83 WANG Min, CHEN Wen-liang, HAO Peng-fei, et al Lightweight automatic drilling system and key technology for aircraft[J]. Aeronautical Manufacturing Technology, 2013, (Z1): 80- 83
[6]
喻龙, 章易镰, 王宇晗, 等 飞机自动钻铆技术研究现状及其关键技术[J]. 航空制造技术, 2017, (9): 16- 25 YU Long. ZHANG Yi-lian, WANG Yu-han, et al. Research status of aircraft automatic drilling and riveting system and its key technology[J]. Aeronautical Manufacturing Technology, 2017, (9): 16- 25
[7]
赵辉. 基于UMAC的自动钻铆机控制系统研究与开发[D]. 南京: 南京航空航天大学, 2014: 3–13. ZHAO Hui. Research automatic control system of drilling and riveting machine based on UMAC[D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2014: 3–13.
[8]
KIM B H, YI B J, OH S R, et al Non-dimensionalized performance indices based optimal grasping for multi-fingered hands[J]. Mechatronics, 2004, 14: 255- 280
doi: 10.1016/S0957-4158(03)00039-4
[9]
SALGADO M A, LACALLE L N L D, LAMIKIZ A, et al Evaluation of the stiffness chain on the deflection of end-mills under cutting forces[J]. International Journal of Machine Tools and Manufacture, 2005, 45 (6): 727- 739
[10]
闫蓉, 陈威, 彭芳瑜, 等 多轴加工系统闭链刚度场建模与刚度性能分析[J]. 机械工程学报, 2012, 48 (1): 177- 184 YAN Rong, CHEN Wei, PENG Fang-yu, et al Closed-loop stiffness modeling and stiffness index analysis for multi-axis machining system[J]. Journal of Mechanical Engineering, 2012, 48 (1): 177- 184
[11]
GAO X, LI B, HONG J, et al Stiffness modeling of ma-chine tools based on machining space analysis[J]. The International Journal of Advanced Manufacturing Technology, 2016, 86 (5-8): 1- 14
[12]
吴石, 李荣义, 刘献礼, 等 复杂曲面模具加工系统综合刚度场建模与分析[J]. 机械工程学报, 2016, 52 (23): 189- 198 WU Shi, LI Rong-yi, LIU Xian-li, et al The Modeling and analysis about comprehensive stiffness field of complex curved surface mould processing system[J]. Journal of Mechanical Engineering, 2016, 52 (23): 189- 198
[13]
张启祥. 飞机壁板自动钻铆机送钉系统技术研究[D]. 杭州: 浙江大学, 2018: 7–13. ZHANG Qi-xiang. Research of the rivet feeding system technology of aircraft panel drilling and riveting ma-chine[D]. Hangzhou: Zhejiang University, 2018: 7–13.
[14]
吴少帅. 飞机壁板自动钻铆过程变形分析[D]. 杭州: 浙江大学, 2017: 53–59. WU Shao-shuai. Research on deformation analysis of automatic drilling and riveting technology of aircraft sheet [D]. Hangzhou: Zhejiang University, 2017: 53–59.
