0
Research Papers

Elastodynamic Model-Based Vibration Characteristics Prediction of a Three Prismatic–Revolute–Spherical Parallel Kinematic Machine

[+] Author and Article Information
Jun Zhang

School of Mechanical Engineering,
Anhui University of Technology,
Ma'anshan 243032, China;
State Key Laboratory for Manufacturing
Systems Engineering,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: zhang_jun@tju.edu.cn

Yan Q. Zhao

School of Mechanical Engineering,
Anhui University of Technology,
Ma'anshan 243032, China
e-mail: zhaoyanqin_91@163.com

Marco Ceccarelli

Department of Civil and Mechanical Engineering,
University of Cassino and South Latium,
Cassino 03040, Italy
e-mail: ceccarelli@unicas.it

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received May 2, 2015; final manuscript received January 10, 2016; published online February 18, 2016. Assoc. Editor: Heikki Handroos.

J. Dyn. Sys., Meas., Control 138(4), 041009 (Feb 18, 2016) (14 pages) Paper No: DS-15-1199; doi: 10.1115/1.4032657 History: Received May 02, 2015; Revised January 10, 2016

Parallel kinematic machines (PKMs) have been proposed as an alternative solution for high-speed machining (HSM) tool for several years. However, their dynamic characteristics are still considered an issue for practice application. Considering the three prismatic–revolute–spherical (3-PRS) PKM design as a typical compliant parallel device, this paper applies substructure synthesis strategy to establish an analytical elastodynamic model for the device. The proposed model considers the effects of component compliances and kinematic pair contraints so that it can predict the dynamic characteristics of the 3-PRS PKM. Based on eigenvalue decomposition of the characteristic equations, the natural frequencies and corresponding vibration modes at a typical configuration are analyzed and verified by numerical simulations. With an algorithm of workspace partitions combining with eigenvalue decompositions, the distributions of lower-order natural frequencies throughout the workspace are computed to reveal a strong dependency of dynamic characteristics on mechanism's configurations. In addition, the effects of the radii of the platform and the base along with the cross section of the limb on lower-order natural frequencies are analyzed to provide useful information during the early design stage. At last, frequency response analysis for the tool center point (TCP) is worked out based on the elastodynamic model to provide primary guideline for cutting chatter avoidance.

FIGURES IN THIS ARTICLE
<>
Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.

References

Hennes, N. , and Staimer, D. , 2004, “ Application of PKM in Aerospace Manufacturing—High Performance Machining Centers ECOSPEED, ECOSPEED-F and ECOLINER,” 4th Chemnitz Parallel Kinematics Seminar, Chemnitz, Germany, Apr. 20–21, pp. 557–577.
Tsai, M. S. , Shiau, T. N. , Tsai, Y. J. , and Chang, T. H. , 2003, “ Direct Kinematic Analysis of a 3-PRS Parallel Mechanism,” Mech. Mach. Theory, 38(1), pp. 71–83. [CrossRef]
Li, Y. M. , and Xu, Q. S. , 2007, “ Kinematic Analysis of a 3-PRS Parallel Manipulator,” Rob. Comput. Integr. Manuf., 23(4), pp. 395–408. [CrossRef]
Li, Y. M. , and Xu, Q. S. , 2004, “ Kinematics and Stiffness Analysis for a General 3-PRS Spatial Parallel Mechanism,” ROMANSY, Montreal, Canada, June 14–18, pp. 26–29.
Pond, G. T. , and Carretero, J. A. , 2004, “ Kinematic Analysis and Workspace Determination of the Inclined PRS Parallel Manipulator,” 15th CISM—IFToMM Symposium on Robot Design, Dynamics and Control, Saint-Hubert, QC, pp. 1–6.
Geoffrey, P. , and Carretero, G. A. , 2006, “ Formulating Jacobian Matrices for Dexterity Analysis of Parallel Mechanism,” Mech. Mach. Theory, 41(12), pp. 1505–1519. [CrossRef]
Li, Q. C. , Chen, Z. , Chen, Q. H. , Wu, C. Y. , and Hu, X. D. , 2011, “ Parasitic Motion Comparison of 3-PRS Parallel Mechanism With Different Limb Arrangements,” Rob. Comput. Integr. Manuf., 27(2), pp. 389–396. [CrossRef]
Nigus, H. , 2014, “ Semi-Analytical Approach for Stiffness Estimation of 3-DOF PKM,” Modern Mech. Eng., 4(2), pp. 108–118. [CrossRef]
Huang, T. , Zhao, X. Y. , and Whitehouse, D. J. , 2002, “ Stiffness Estimation of a Tripod-Based Parallel Kinematic Machine,” IEEE Trans. Rob. Autom., 18(1), pp. 50–58. [CrossRef]
Li, Y. G. , Song, Y. M. , Feng, Z. Y. , and Zhang, C. , 2007, “ Inverse Dynamics of 3-PRS Parallel Mechanism by Newton-Euler Formulation,” Acta Aeronaut. Astronaut. Sin., 28(5), pp. 1210–1215.
Xi, F. F. , Angelico, O. , and Sinatra, R. , 2005, “ Tripod Dynamics and Its Inertia Effect,” ASME J. Mech. Des., 127(1), pp. 144–149. [CrossRef]
Wiens, G. J. , Shamblin, S. A. , and Oh, Y. H. , 2002, “ Characterization of PKM Dynamics in Terms of System Identification,” J. Multi-Body Dyn., 216(1), pp. 59–72.
Wu, P. D. , Xiong, H. G. , and Kong, J. Y. , 2012, “ Dynamic Analysis of 6-SPS Parallel Mechanism,” Int. J. Mech. Mater. Des., 8(2), pp. 121–128. [CrossRef]
Ji, Z. , 1993, “ Study of the Effect of Leg Inertia in Stewart Platforms,” IEEE Conference on Robotics and Automation, Atlanta, GA, May 2–6, pp. 121–126.
Xi, F. F. , Sinatra, R. , and Han, W. Z. , 2001, “ Effect of Leg Inertia on Dynamics of Sliding-Leg Hexapods,” ASME J. Dyn. Syst., Meas. Control, 123(2), pp. 265–271. [CrossRef]
Ceccarelli, M. , and Carbone, G. , 2002, “ A Stiffness Analysis for CaPaMan,” Mech. Mach. Theory, 37(5), pp. 427–439. [CrossRef]
Carbone, G. , and Ceccarelli, M. , 2004, “ A Stiffness Analysis for a Hybrid Parallel-Serial Manipulator,” Robotica, 22(5), pp. 567–576. [CrossRef]
Khemili, I. , and Romdhane, L. , 2008, “ Dynamic Analysis of a Flexible Slider-Crank Mechanism With Clearance,” Eur. J. Mech. A/Solids, 27(5), pp. 882–898. [CrossRef]
Zhu, C. X. , Wang, J. , Chen, Z. W. , and Liu, B. , 2014, “ Dynamic Characteristic Parameter Identification Analysis of a Parallel Manipulator With Flexible Links,” J. Mech. Sci. Technol., 28(12), pp. 4833–4840. [CrossRef]
Zhang, X. P. , Millks, J. K. , and Cleghorn, W. L. , 2007, “ Dynamic Modeling and Experimental Validation of a 3-PRR Parallel Manipulator With Flexible Intermediate Links,” J. Intell. Rob. Syst., 50(4), pp. 323–340. [CrossRef]
Zavrazhina, T. V. , 2008, “ Influence of Elastic Compliance of Links on the Dynamics and Accuracy of a Manipulating Robot With Rotational and Translational Joints,” Mech. Solids, 43(6), pp. 850–862. [CrossRef]
Kang, B. , and Millks, J. K. , 2003, “ Dynamic Modeling of Structurally Flexible Planar Parallel Manipulator,” Robotica, 20(3) pp. 329–339.
Pira, G. , Cleghorn, W. L. , and Mills, J. K. , 2005, “ Dynamic Finite-Element Analysis of a Planar High-Speed, High-Precision Parallel Manipulator With Flexible Links,” Mech. Mach. Theory, 40(7), pp. 849–862. [CrossRef]
Bonnemains, T. , Chanal, H. , Bouzgarrou, B. C. , and Ray, P. , 2009, “ Stiffness Computation and Identification of Parallel Kinematic Machine Tools,” ASME J. Manuf. Sci. Eng., 131(4), p. 041013. [CrossRef]
Bonnemains, T. , Chanal, H. , Bouzgarrou, B. C. , and Ray, P. , 2013, “ Dynamic Model of an Overconstrained PKM With Compliances: The Tripteor X7,” Rob. Comput. Integr. Manuf., 29(1), pp. 180–191. [CrossRef]
Law, M. , Ihlenfeldt, S. , Wabner, M. , Altintas, Y. , and Neygbauer, R. , 2013, “ Position-Dependent Dynamics and Stability of Serial-Parallel Kinematic Machines,” CIRP Ann. Manuf. Technol., 62(1), pp. 375–378. [CrossRef]
Hong, D. , Kim, S. , Choi, W. C. , and Song, J. B. , 2003, “ Analysis of Machining Stability for a Parallel Machine Tool,” Mech. Based Des. Struct. Mach., 31(4), pp. 509–528. [CrossRef]
Zhao, Y.-Q. , Zhang, J. , Ruan, L.-Y. , Luo, H.-W. , and Yu, X.-L. , 2016, “ A Modified Elasto-Dynamic Model Based Stastic Stiffness Evaluation for a 3-PRS PKM,” Proc. Inst. Mech. Eng., Part C, 230(3), p. 586233. [CrossRef]
Zhang, J. , Dai, J. S. , and Huang, T. , 2015, “ Character Equation-Based Dynamic Analysis of a Three-Revolute Prismatic Spherical Parallel Kinematic Machine,” ASME J. Comput. Nonlinear Dyn., 10(2), p. 021017. [CrossRef]
Li, Y. G. , Liu, H. T. , Zhao, X. M. , Huang, T. , and Chetwynd, D. G. , 2010, “ Design of a 3-DOF PKM Module for Large Structural Component Machining,” Mech. Mach. Theory, 45(6), pp. 941–954. [CrossRef]
Law, M. , Phani, A. S. , and Altintas, Y. , 2013, “ Position-Dependent Multibody Dynamic Modeling of Machine Tools Based on Improved Reduced Models,” ASME J. Manuf. Sci. Eng., 135(2), p. 021008. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Structure of a 3-PRS PKM module

Grahic Jump Location
Fig. 2

A kinematic diagram of the 3-PRS PKM module in Fig. 1

Grahic Jump Location
Fig. 3

Assembly of an individual PRS limb subsystem

Grahic Jump Location
Fig. 4

Force diagram of limb body

Grahic Jump Location
Fig. 5

Definition of spatial beam element

Grahic Jump Location
Fig. 7

Free-body diagram of the platform

Grahic Jump Location
Fig. 6

Spherical joint model

Grahic Jump Location
Fig. 8

Displacement relationship between the platform and the limb body

Grahic Jump Location
Fig. 9

Procedure for frequency mapping of the system

Grahic Jump Location
Fig. 14

The FRF distributions when θy = −30 deg to 30 deg: (a) in xt direction and (b) in yt direction

Grahic Jump Location
Fig. 10

Natural frequencies distributions over the working plane of pz = 675 mm: (a) the first-order, (b) the second-order, (c) the third-order, (d) the fourth-order, (e) the fifth-order, and (f) the sixth-order

Grahic Jump Location
Fig. 12

Variations of natural frequencies with respect to the limb body cross sections: (a) the first-order, (b) the second-order, (c) the third-order, (d) the fourth-order, (e) the fifth-order, and (f) the sixth-order

Grahic Jump Location
Fig. 13

The FRF distributions when θx = −30 deg to 30 deg: (a) in xt direction and (b) in yt direction

Grahic Jump Location
Fig. 11

Variations of natural frequencies with respect to rp and rb: (a) the first-order, (b) the second-order, (c) the third-order, (d) the fourth-order, (e) the fifth-order, and (f) the sixth-order

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In