Skip to main content
SpringerLink
Log in

A Geometric Error Modeling Method and Trajectory Optimization Applied in Laser Welding System

  • Regular Paper
  • Published:
International Journal of Precision Engineering and Manufacturing Aims and scope Submit manuscript

Abstract

In this paper, a geometric error modeling method is carried out on six-axis motion platform (SMP) in laser welding system (LWS), and an optimized algorithm is proposed for the alignment in LWS based on the error model. First, the topological structure of the given SMP is analyzed, and related homogeneous transformation matrices which are used for standing the orientation of SMP are established. By these matrices, the geometric error model is developed mathematically. Then, the error model is used for predicting the alignment deviations. A corresponding series of experiments for calculating the optical power loss in alignment are employed, and the comparison between simulation and experiments results indicate the validation of the error model. Furthermore, an optimized algorithm is applied to search the optimum aligning trajectory. Compared to conventional method, this algorithm has a broader range in searching extreme value, which can reduce the computational volume and improve the efficiency. It is also beneficial for improving the success rate of escaping from the local minimum spot and finding the optimum alignment spot. The error model is helpful to analyze the error propagation process and improve the alignment efficiency in LWS, which can be applied to other similar multi-axis precise system.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

Abbreviations

SMP:

Six-axis motion platform

MMS:

Multi-axis motion system

MMP:

Multi-axis motion platform

OD:

Optical device

LWS:

Laser welding system

B :

Typical body

X, Y, Z, U, V, W :

Axis in MMS

x, y, z, α, γ, β :

Geometric error

T :

Intersubject transformation matrix

E :

Error matrix of homogeneous transformation

T s :

Intersubject coordinate offset matrix

E s :

Motion transformation matrix

T s k :

Kinematic error matrix

E s k :

Static error matrix

LD:

Laser diode

SMF:

Single-mode optical fiber

PL:

Power loss

EMM:

Error modeling method

EMSM:

Error modeling searching method

References

  1. Yang, H. M., Chen, C. T., Ro, R., et al. (2010). Investigation of the efficient coupling between a highly elliptical Gaussian profile output from a laser diode and a single mode fiber using a hyperbolic-shaped microlens. Optics & Laser Technology, 42(6), 918–926.

    Article  Google Scholar 

  2. Jedrzejczyk, D., Asbahr, P., Pulka, M., et al. (2014). High-power single-mode fiber coupling of a laterally tapered single-frequency diode laser. IEEE Photonics Technology Letters, 26(8), 845–847.

    Article  Google Scholar 

  3. Zheng, Y., Li, B., & Duan, J. (2015). Automatic waveguide-fiber alignment algorithm based on polynomial fitting. In 2015 international conference on photonics, optics and laser technology (PHOTOPTICS) (pp. 77–80).

  4. Koganti, P. B., & Udwadia, F. E. (2017). Dynamics and precision control of uncertain tumbling multibody systems. Journal of Guidance, Control and Dynamics, 40(5), 1176–1190.

    Article  Google Scholar 

  5. Tang, H., Duan, J. A., Lan, S., et al. (2015). A new geometric error modeling approach for multi-axis system based on stream of variation theory. International Journal of Machine Tools and Manufacture, 92, 41–51.

    Article  Google Scholar 

  6. Chen, G., Li, T., Chu, M., et al. (2014). Review on kinematics calibration technology of serial robots. International Journal of Precision Engineering & Manufacturing, 15(8), 1759–1774.

    Article  Google Scholar 

  7. Kim, C. K., Lai, M. C., Zhang, Z. C., et al. (2017). Modeling and numerical simulation of afterburning of thermobaric explosives in a closed chamber. International Journal of Precision Engineering & Manufacturing, 18, 979.

    Article  Google Scholar 

  8. Liu, T., Qian, L., Xu, Y., et al. (2016). Kinematic error modeling and analysis of the loading device based on multi-body theory and stream of variation theory. In 2016 IEEE international conference on information and automation (ICIA), IEEE.

  9. Andolfatto, L., Lavernhe, S., & Mayer, J. R. R. (2011). Evaluation of servo, geometric and dynamic error sources on five-axis high-speed machine tool. International Journal of Machine Tools and Manufacture, 51(10–11), 787–796.

    Article  Google Scholar 

  10. Li, X., Zhao, H., Zhao, X., et al. (2017). Contouring compensation control based on high accuracy contour error estimation for multi-axis motion systems. International Journal of Advanced Manufacturing Technology, 93, 1–11.

    Article  Google Scholar 

  11. Tang, H., Duan, J. A., & Lu, S. (2017). Stream-of-variation (SOV) theory applied in geometric error modeling for six-axis motion platform. IEEE Transactions on Systems Man & Cybernetics Systems, 99, 1–9.

    Article  Google Scholar 

  12. Ibaraki, S., Goto, S., Tsuboi, K., et al. (2018). Kinematic modeling and error sensitivity analysis for on-machine five-axis laser scanning measurement under machine geometric errors and workpiece setup errors. The International Journal of Advanced Manufacturing Technology, 96, 4051–4062.

    Article  Google Scholar 

  13. Creamer, J., Sammons, P. M., Bristow, D. A., et al. (2017). Table-based volumetric error compensation of large five-axis machine tools. Journal of Manufacturing Science and Engineering. https://doi.org/10.1115/1.4034399.

    Google Scholar 

  14. Zhao, D., Bi, Y., & Ke, Y. (2017). An efficient error compensation method for coordinated CNC five-axis machine tools. International Journal of Machine Tools and Manufacture, 123, 105–115.

    Article  Google Scholar 

  15. Xin, L. (2010). Kinematic error modeling for tailored blank laser welding machine based on the improved MBS. Journal of Mechanical Engineering, 46(2), 61.

    Article  Google Scholar 

  16. Chen, J. X., Lin, S. W., & Zhou, X. L. (2016). A comprehensive error analysis method for the geometric error of multi-axis machine tool. International Journal of Machine Tools and Manufacture, 106, 56–66.

    Article  Google Scholar 

  17. Cheng, Q., Zhao, H., Zhang, G., et al. (2014). An analytical approach for crucial geometric errors identification of multi-axis machine tool based on global sensitivity analysis. The International Journal of Advanced Manufacturing Technology, 75, 107–121.

    Article  Google Scholar 

  18. Lee, R. S. (2012). Applying bidirectional kinematics to assembly error analysis for five-axis machine tools with general orthogonal configuration. The International Journal of Advanced Manufacturing Technology, 62(9–12), 1261–1272.

    Article  Google Scholar 

  19. Chun, J., Wu, Y., Dai, Y., et al. (2005). Study on automatic alignment technique in fiber active devices packaging. China Mechanical Engineering, 16(24), 2163–2167.

    Google Scholar 

  20. Zhao, J. L., Liu, Y., Guo, Z., et al. (2015). Error analysis on CNC gear hobbing machine spindle transmission chain based on SOV theory. International conference on advanced engineering materials and technology,. https://doi.org/10.2991/icaemt-15.2015.42.

    Google Scholar 

  21. Jee, S. (2012). Real-time inertia compensation for multi-axis CNC machine tools. International Journal of Precision Engineering & Manufacturing, 13(9), 1655–1659.

    Article  Google Scholar 

  22. Qazani, M. R. C., Pedrammehr, S., & Nategh, M. J. (2018). An investigation on the motion error of machine tools’ hexapod table. International Journal of Precision Engineering & Manufacturing, 19(4), 463–471.

    Article  Google Scholar 

  23. Aguado, S., Samper, D., Santolaria, J., et al. (2012). Towards an effective identification strategy in volumetric error compensation of machine tools. Measurement Science & Technology, 23(6), 065003.

    Article  Google Scholar 

  24. Zhang, E. Z., Zhao, J., Ji, S. J., et al. (2015). Comprehensive error modeling and compensation for precision polishing platform based on orthogonal experiment and interpolation algorithm. Guangxue Jingmi Gongcheng/Optic and Precision Engineering, 23(12), 3422–3429.

    Google Scholar 

  25. Kilikevičius, A., & Kasparaitis, A. (2017). Dynamic research of multi-body mechanical systems of angle measurement. International Journal of Precision Engineering & Manufacturing, 18(8), 1065–1073.

    Article  Google Scholar 

  26. Zeng, W., & Rao, Y. (2019). Modeling of assembly deviation with considering the actual working conditions. International Journal of Precision Engineering & Manufacturing, 20(5), 791–803.

    Article  Google Scholar 

  27. Du, S., Yao, X., Huang, D., et al. (2015). Three-dimensional variation propagation modeling for multistage turning process of rotary workpieces. Computers & Industrial Engineering, 82, 41–53.

    Article  Google Scholar 

  28. Suruga Seiki Corporation. Suruga Fiber Alignment Information: Alignment System. http://eng.surugaseiki.com/alignment.

Download references

Acknowledgements

This research is supported by the Natural Science Foundation of China (Grant No. 51705149), and the Natural Science Foundation of Hunan Province, China (Grant No. 2018JJ3168).

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, Hunan University of Science and Technology, Xiangtan, 411201, Hunan, China

    Hao Tang, Zilin Zhang, Changping Li & Tae Jo Ko

  2. School of Mechanical Engineering, Yeungnam University, Gyeongsan, 712-749, Korea

    Tae Jo Ko

Authors
  1. Hao Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zilin Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Changping Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Tae Jo Ko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hao Tang.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tang, H., Zhang, Z., Li, C. et al. A Geometric Error Modeling Method and Trajectory Optimization Applied in Laser Welding System. Int. J. Precis. Eng. Manuf. 20, 1423–1433 (2019). https://doi.org/10.1007/s12541-019-00151-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12541-019-00151-8

Keywords

Search

Navigation