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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.

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References

Figures

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Fig. 1

Structure of a 3-PRS PKM module

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Fig. 2

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

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Fig. 3

Assembly of an individual PRS limb subsystem

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Fig. 4

Force diagram of limb body

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Fig. 5

Definition of spatial beam element

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Fig. 6

Spherical joint model

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Fig. 7

Free-body diagram of the platform

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Fig. 8

Displacement relationship between the platform and the limb body

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Fig. 9

Procedure for frequency mapping of the system

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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

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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

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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

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Fig. 13

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

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Fig. 14

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

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