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Model Parameter Identification of a Machining Robot Using Joint Frequency Response Functions

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Abstract

The utilization of machining robots using industrial six degree-of-freedom (DOF) robot manipulators in the general cutting process is hindered by their cutting instability caused by a significantly lower dynamic stiffness than that of conventional machine tools. The dynamic stiffness of the machining robot is particularly low in low order eigenmodes of approximately 30 Hz or less compared to conventional machine tools. And it is also low in higher order eigenmodes, resulting in reduced cutting stability over the entire machining speed range. In this paper, we propose a frequency response function (FRF) estimation model using an 18 DOF multibody dynamics (MBD) model, which accounts for the key eigenmodes influencing low and high-speed milling, for the purpose of advancing stability improvement methods in robotic machining. First, a method for joint rotational FRF measurement in the joint frame for orthogonal three-directional excitations in the fixed frame is proposed. This not only enables quantitative evaluation of the influence of each joint on the structural dynamic behavior, but also enables model parameter identification with improved accuracy by considering the dynamic behavior of each joint. Subsequently, we employ particle swarm optimization (PSO) to identify the numerous parameters associated with the MBD model, which encompasses an implicit form of equation of motion. Finally, the proposed method is validated by comparing the estimated and measured FRFs.

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Abbreviations

DOF:

Degree of freedom

FRF:

Frequency response function

TCP:

Tool center point

MBD:

Multibody dynamics

PSO:

Particle swarm optimization

\(\omega\) :

Angular speed

\(\dot{\omega }\) :

Angular acceleration in the link frame

\(\ddot{x}\) :

Linear acceleration in the x direction of the link frame

\(\ddot{y}\) :

Linear acceleration in the y direction of the link frame

\(\ddot{z}\) :

Linear acceleration in the z direction of the link frame

\(D\) :

Distance between two corresponding accelerometers

\(R\) :

A rotation matrix

\(H\) :

TCP FRF matrix

\({H}_{q}^{x}\) :

Joint FRF matrix by excitations in the fixed frame

\({H}_{q}^{\tau }\) :

Joint FRF matrix by excitations in the joint frame

\(J\) :

Jacobian matrix

\({J}_{v}\) :

Linear motion Jacobian matrix

\({J}_{\omega }\) :

Angular motion Jacobian matrix

\(q\) :

Generalized coordinates

\(F\) :

An excitation force in the fixed frame

\(\tau\) :

An excitation torque in the joint frame

DCIF:

Dynamic compliance influence factor

\({M}_{q}\) :

Mass matrix of the machining robot

\({C}_{q}\) :

Damping matrix of the machining robot

\({K}_{q}\) :

Stiffness matrix of the machining robot

\(m\) :

Mass

\(I\) :

Mass moment of inertia

\(u\) :

A unit vector of a joint in the fixed frame

\(r\) :

A position vector between a joint and an inertia in the fixed frame

\(w\) :

A weight function

\(f\) :

A cost function

\(P\) :

A penalty function

\(g\) :

An inequality function

\(\lambda\) :

Lagrange multiplier

FRAC:

Frequency response assurance criterion

a:

An accelerometer mounting location

b:

An accelerometer mounting location

c:

An accelerometer mounting location

d:

An accelerometer mounting location

x:

X direction in the joint frame

y:

Y direction in the joint frame

z:

Z direction in the joint frame

X:

X direction in the fixed frame

Y:

Y direction in the fixed frame

Z:

Z direction in the fixed frame

cm:

Center of mass

References

  1. Pham, A.-D., & Ahn, H.-J. (2021). Rigid precision reducers for machining industrial robots. International Journal of Precision Engineering and Manufacturing, 22, 1469–1486.

    Article  Google Scholar 

  2. Guo, Y., Dong, H., & Ke, Y. (2015). Stiffness-oriented posture optimization in robotic machining applications. Robotics and Computer-Integrated Manufacturing, 35, 69–76.

    Article  Google Scholar 

  3. Lee, J. H., Kim, S. H., & Min, B.-K. (2022). Posture optimization in robotic drilling using a deformation energy model. Robotics and Computer-Integrated Manufacturing, 78, 102395.

    Article  Google Scholar 

  4. Kim, M., Park, H.-W., & Lee, S.-K. (2022). Investigation of machining stability considering thermal and rotation effect: Effectiveness of impact excitation for a rotating spindle. International Journal of Precision Engineering and Manufacturing, 23, 1143–1162.

    Article  Google Scholar 

  5. Pan, Z., Zhang, H., Zhu, Z., & Wang, J. (2006). Chatter analysis of robotic machining process. Journal of materials processing technology, 173(3), 301–309.

    Article  Google Scholar 

  6. Cordes, M., Hintze, W., & Altintas, Y. (2019). Chatter stability in robotic milling. Robotics and Computer-Integrated Manufacturing, 55, 11–18.

    Article  Google Scholar 

  7. Celikag, H., Ozturk, E., & Sims, N. D. (2021). Can mode coupling chatter happen in milling? International Journal of Machine Tools and Manufacture, 165, 103738.

    Article  Google Scholar 

  8. Altintas, Y., Stepan, G., Budak, E., Schmitz, T., & Kilic, Z. M. (2020). Chatter stability of machining operations. Journal of Manufacturing Science and Engineering, 142(11), 52.

    Article  Google Scholar 

  9. Wei, X., Miao, E., & Ye, H. (2022). Analytical prediction of three dimensional chatter stability considering multiple parameters in milling. International Journal of Precision Engineering and Manufacturing, 23, 711–720.

    Article  Google Scholar 

  10. Mousavi, S., Gagnol, V., Bouzgarrou, B. C., & Ray, P. (2017). Dynamic modeling and stability prediction in robotic machining. The International Journal of Advanced Manufacturing Technology, 88, 3053–3065.

    Article  Google Scholar 

  11. Huynh, H. N., Assadi, H., Dambly, V., Rivière-Lorphèvre, E., & Verlinden, O. (2021). Direct method for updating flexible multibody systems applied to a milling robot. Robotics and Computer-Integrated Manufacturing, 68, 102049.

    Article  Google Scholar 

  12. Bottin, M., Cocuzza, S., Comand, N., & Doria, A. (2020). Modeling and identification of an industrial robot with a selective modal approach. Applied Sciences, 10(13), 4619.

    Article  Google Scholar 

  13. Wang, R., Li, F., Niu, J., & Sun, Y. (2022). Prediction of pose-dependent modal properties and stability limits in robotic ball-end milling. Robotics and Computer-Integrated Manufacturing, 75, 102307.

    Article  Google Scholar 

  14. Nguyen, V., & Melkote, S. (2021). Hybrid statistical modelling of the frequency response function of industrial robots. Robotics and Computer-Integrated Manufacturing, 70, 102134.

    Article  Google Scholar 

  15. Chen, H., & Ahmadi, K. (2022). Estimating pose-dependent FRF in machining robots using multibody dynamics and Gaussian Process Regression. Robotics and Computer-Integrated Manufacturing, 77, 102354.

    Article  Google Scholar 

  16. Elliott, A., Pavić, G., & Moorhouse, A. T. (2008). Measurement of force and moment mobilities using a finite difference technique. Journal of the Acoustical Society of America, 123(5), 3312.

    Article  Google Scholar 

  17. Craig, J. J. (2006). Introduction to robotics. Pearson Education.

  18. Ma, Y., Tian, Y., & Liu, X. (2023). Rapid predictions for lower-order dynamics of machine tools based on the rigid multipoint constraints. International Journal of Precision Engineering and Manufacturing, 2, 1–16.

    Google Scholar 

  19. Dumas, C., Caro, S., Garnier, S., & Furet, B. (2011). Joint stiffness identification of six-revolute industrial serial robots. Robotics and Computer-Integrated Manufacturing, 27(4), 881–888.

    Article  Google Scholar 

  20. Huynh, H. N., Rivière-Lorphèvre, E., & Verlinden, O. (2018, June). Multibody modelling of a flexible 6-axis robot dedicated to robotic machining. 5th joint international conference on multibody system Dynamics (pp. 1–18).

  21. Huynh, H. N., Verlinden, O., & Rivière-Lorphèvre, E. (2017). Robotic machining simulation using a simplified multibody model. Annals of DAAAM & Proceedings, 28.

  22. Nefske, D. J., & Sung, S. H. (1996, February). Correlation of a coarse-mesh finite element model using structural system identification and a frequency response assurance criterion. In Proceedings-SPIE the International Society for Optical Engineering (pp. 597–602). SPIE International Society for Optical.

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Acknowledgements

This research was funded by the Ministry of Trade, Industry and Energy of Korea (Grant numbers 20018076 and 20012834).

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Authors and Affiliations

  1. DN Solutions, 40, Jeongdong-ro 162 beon-gil, Seongsan-gu, Changwon, Gyeongsangnam-Do, 51537, Republic of Korea

    Changwon Oh

  2. School of Mechanical Engineering, Yonsei University, Seoul, 03722, Republic of Korea

    Ju-Hyeong Lee, Tae In Ha & Byung-Kwon Min

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  1. Changwon Oh
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Correspondence to Byung-Kwon Min.

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Oh, C., Lee, JH., Ha, T.I. et al. Model Parameter Identification of a Machining Robot Using Joint Frequency Response Functions. Int. J. Precis. Eng. Manuf. 24, 1647–1659 (2023). https://doi.org/10.1007/s12541-023-00890-9

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