single-au.php

IJAT Vol.15 No.5 pp. 631-640
doi: 10.20965/ijat.2021.p0631
(2021)

Technical Paper:

# Vibration Mode and Motion Trajectory Simulations of an Articulated Robot by a Dynamic Model Considering Joint Bearing Stiffness

## Ryuta Sato*,†, Yuya Ito**, Shigeto Mizuura**, and Keiichi Shirase*

*Department of Mechanical Engineering, Kobe University
1-1 Rokko-dai, Nada-ku, Kobe 657-8501, Japan

Corresponding author

**DAIHEN Corporation, Kobe, Japan

March 24, 2021
Accepted:
May 18, 2021
Published:
September 5, 2021
Keywords:
articulated robot, mathematical model, joint bearing stiffness, vibration mode, circular trajectory
Abstract

Articulated robots are widely used in industries because they can perform manufacturing tasks with complicated movements. Higher speed and accuracy of motions are always required to improve the quality and productivity of products. The vibration characteristics of the robots are an important factor to achieve higher speed and accuracy motions. Robots are increasingly being used for machining. The vibration characteristics must also be considered when designing proper cutting conditions for the machining. To design control and cutting strategies for higher speed and accuracy motions or higher productivity of the machining process, it is effective to investigate the vibration characteristics of the robot and develop a mathematical model which can represents the vibration characteristics. The aim of this study is to investigate the vibration characteristics of an architectural robot and develop a mathematical model which can represent the dynamic behavior of the robot. To achieve this, vibration mode of an industrial architectural robot is analyzed based on measured frequency characteristics. According to the results of the modal analysis, it was clarified that the axial and angular stiffness of bearings of each joint of the robot has a significant impact on the vibration characteristics. Therefore, in this study, a mathematical model of the robot is developed considering the joint bearing stiffness. The mathematical model that also considers the kinematics of the robot, stiffness of reduction gears, control system for motors, and disturbance, such as friction and gravity, is introduced into the model. The control system is precisely modeled based on actual control algorithm in accordance with the implemented source codes. Although mass and inertia of the links are obtained from the 3D-CAD model, stiffness and damping parameters of the bearings and reduction gears are identified by matching the measured and simulated frequency responses. It has been confirmed that the model can adequately represents the vibration mode of the actual robot. Circular motion tests were performed to verify the model. Motion trajectories of the end effector were measured and simulated. As a result, it has been confirmed that the developed model is effective to analyze the dynamic behaviors.

R. Sato, Y. Ito, S. Mizuura, and K. Shirase, “Vibration Mode and Motion Trajectory Simulations of an Articulated Robot by a Dynamic Model Considering Joint Bearing Stiffness,” Int. J. Automation Technol., Vol.15 No.5, pp. 631-640, 2021.
Data files:
References
1. [1] “Industrial Robotics – Insights into the Sector’s Future Growth Dynamics,” McKinsey & Company, 2019.
2. [2] D. Kostic, B. Jager, and R. Hensen, “Modeling and Identification for High-Performance Robot Control: An RRR-Robotic Arm Case Study,” IEEE Trans. on Control Systems Technology, Vol.12, No.6, pp. 904-919, 2004.
3. [3] A. Verl, A. Valente, S. Melkote, C. Brecher, E. Ozturk, and L. T. Tunk, “Robots in Machining,” CIRP Annals – Manufacturing Technology, Vol.68, pp. 799-822, 2019.
4. [4] D. Milutinovic, M. Glavonjic, N. Slavkovic, Z. Dimic, S. Zivanovic, B. Kokotovic, and L. Tanovic, “Reconfigurable Robotic Machining System Controlled and Programmed in a Machine Tool Manner,” Int. J. of Advanced Manufacturing Technology, Vol.53, pp. 1217-1229, 2011.
5. [5] N. Slavkovic, D. Milutinovic, and M. Glavonjic, “A Method for Off-line Compensation of Cutting Force-induced Errors in Robotic Machining by Tool Path Modification,” Int. J. of Advanced Manufacturing Technology, Vol.70, pp. 2083-2096, 2015.
6. [6] A. Hayashi, H. Tanaka, M. Ueki, H. Yamaoka, N. Fujiki, and Y. Morimoto, “Forward Kinematics Model for Evaluation of Machining Performance of Robot Type Machine Tool,” Int. J. Automation Technol., Vol.15, No.2, pp. 215-223, 2021.
7. [7] M. F. Zaeh and O. Roesch, “Forward Kinematics Model for Evaluation of Machining Performance of Robot Type Machine Tool,” Int. J. Automation Technol., Vol.9, No.2, pp. 129-133, 2015.
8. [8] L. B. Silva, H. Yoshioka, H. Shinno, and J. Zhu, “Tool Orientation Angle Optimization for a Multi-Axis Robotic Milling System,” Int. J. Automation Technol., Vol.13, No.5, pp. 574-582, 2019.
9. [9] Y. Altintas and E. Budak, “Analytical Prediction of Stability Lobes in Milling,” CIRP Annals – Manufacturing Technology, Vol.44, pp. 357-362, 1995.
10. [10] G. Quintana and J. Ciurana, “Chatter in Machining Process: a Review,” Int. J. of Machine Tools and Manufacture, Vol.51, pp. 363-376, 2011.
11. [11] H. Mayeda, “Dynamic Models of Robot Arm and Its Identification,” J. of the Robotics Society of Japan, Vol.7, No.2, pp. 95-100, 1989 (in Japanease).
12. [12] O. Zirn, “Machine Tool Analysis – Modelling, Simulation and Control of Machine Tool Manipulators,” A Habilitation Thesis, ETH Zurich, 2008.
13. [13] S. Cubero, “Industrial Robotics – Theory, Modelling and Control,” PLV Pro Literatur Verlag Robert Mayer-Scholz, 2007.
14. [14] L. Ding, H. Wu, Y. Yao, and Y. Yang, “Dynamic Model Identification for 6-DOF Industrial Robots,” J. of Robotics, Vol.2015, Article ID 471478, 2015.
15. [15] T. Yasuo, Y. Omaki, T. Nampo, and H. Mayeda, “Identification and Model Based Control of a 6 D.O.F. Industrial Manipulator,” Proc. of IFAC Robot Control, pp. 111-117, 1997.
16. [16] M. M. Olsen and H. G. Petersen, “A New Method for Estimating Parameters of a Dynamic Robot Model,” IEEE Trans. on Robotics and Automation, Vol.17, No.1, pp. 95-100, 2001.
17. [17] J. J. Craig, P. Hsu, and S. S. Sastry, “Adaptive Control of Mechanical Manipulators,” The Int. J. of Robotics Research, Vol.6, No.2, pp. 16-28, 1987.
18. [18] N. D. Vuong and M. H. Ang Jr., “Dynamic Model Identification for Industrial Robots,” Acta Polytechnica Hungarica, Vol.6, No.5, pp. 51-68, 2009.
19. [19] L. Ding, X. Li, Q. Li, and Y. Chao, “Nonlinear Friction and Dynamical Identification for a Robot Manipulator with Improved Cuckoo Search Algorithm,” J. of Robotics, Vol.2018, Article ID 8219123, 2018.
20. [20] M. C. Good, L. M. Sweet, and K. L. Strobel, “Dynamic Models for Control System Design of Integrated Robot and Drive Systems,” ASME J. of Dynamic Systems, Measurement, and Control, Vol.107, pp. 53-59, 1985.
21. [21] H. N. Huynh, G. Kouroussis, and O. Verlinden, “Modal Updating of a 6-axis Robot for Milling Application,” Proc. of the 25th Int. Congress on Sound and Vibration, 2018.
22. [22] H. N. Huynh, H. Assadi, E. Riviere-Lorphevre, O. Verlinden, and K. Ahmadi, “Modelling the Dynamics of Industrial Robots for Milling Operations,” Robotics and Computer-Integrated Manufacturing, Vol.61, Article 101852, 2020.
23. [23] M. Bottin, S. Cocuzza, N. Comand, and A. Doria, “Modeling and Identification of an Industrial Robotwith a Selective Modal Approach,” Applied Science, Vol.10, Article 4619, 2020.
24. [24] R. Sato, G. Tashiro, and K. Shirase, “Analysis of the Coupled Vibration between Feed Drive Systems and Machine Tool Structure,” Int. J. Automation Technol., Vol.9, No.6, pp. 689-697, 2015.
25. [25] N. W. Spong, S. Hutchinson, and M. Vidyasagar, “Robot Modeling and Control,” John Wiley and Sons, Inc., 2005.
26. [26] R. Sato, “Feed Drive Simulator,” Int. J. Automation Technol., Vol.5, No.6, pp. 875-882, 2011.
27. [27] J. H. Holland, “Adaptation in Natural and Artificial Systems,” The University of Michigan Press, 1975.
28. [28] ISO 230-4, “Test Code for Machine Tools – Part 4: Circular Tests for Numerically Controlled Machine Tools,” 2005.

*This site is desgined based on HTML5 and CSS3 for modern browsers, e.g. Chrome, Firefox, Safari, Edge, Opera.

Last updated on Jul. 19, 2024