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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2019, Vol. 53 Issue (6): 1110-1118    DOI: 10.3785/j.issn.1008-973X.2019.06.010
Mechanical and Energy Engineering     
Investigation on general stiffness of automatic horizontal dual-machine cooperative drilling and riveting system
Jun-xia JIANG(),Chen DONG,Chen BIAN,Hui-yue DONG
School of Mechanical Engineering, Zhejiang University, Hangzhou 310027, China
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Abstract  

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.

Key words： automatic drilling and riveting      multi-axis machine tool      general stiffness      Jacques matrix      small elastic deformation theory     
Received: 26 October 2018      Published: 22 May 2019
CLC:  V 262.4  
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Jun-xia JIANG
Chen DONG
Chen BIAN
Hui-yue DONG
Cite this article:

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.

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http://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2019.06.010     OR     http://www.zjujournals.com/eng/Y2019/V53/I6/1110


卧式双机联合自动钻铆系统综合刚度研究

为分析卧式双机联合自动钻铆系统中多轴机床的刚度特性分布规律，定量分析该机床末端弹性变形. 建立多轴机床的运动学模型，确定运动关节、柔性运动轴和末端执行器为其末端变形主要来源；针对柔性运动轴与末端执行器的力学特性，采用有限元法得到其对应坐标系内的刚度矩阵；针对运动关节，采用试验法得到关节空间内的刚度矩阵；通过雅克比矩阵法建立运动关节的增强型末端刚度矩阵，通过点传递法建立柔性运动轴的末端刚度矩阵；基于弹性小变形理论，综合各个变形来源的末端刚度矩阵建立多轴机床的综合末端刚度模型；通过实际测试，该刚度模型与实验结果误差小于10%，证明了该综合刚度模型的准确性.


关键词： 自动钻铆,  多轴机床,  综合刚度,  雅克比矩阵,  弹性小变形理论 
Fig.1 Layout of automatic horizontal dual-machine cooperative drilling and riveting system
Fig.2 Distribution of flexible links in multi-axis machine tool with inner riveting head
Fig.3 Kinematic 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.1 D-H parameters of multi-axis machine tool
Fig.4 Theory and structure of riveting head
Fig.5 Stress deformation cloud diagram of Z-axis link
Fig.6 Stress deformation cloud diagram of A-axis link
Fig.7 Joint stiffness identification test site
Fig.8 Measuring 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.2 Displacement and generalized force of all joints
Fig.9 Force transfer model of flexible link
Fig.10 Multi-axis machine end deformation measurement test
Fig.11 End 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.3 Comparison of experimental and calculated end deformation
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