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Inertia matching analysis of a 5-DOF hybrid optical machining manipulator

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Abstract

Inertia matching means the ratio of the mechanical load inertia is converted to each actuator shaft to motor inertia, which is guaranteed within a reasonable range. At present, inertia matching is widely applied to tandem manipulators and CNC machine tools. However, the researches on the inertia matching of large load inertia optical machining manipulators have not been paid sufficient attention. We took the 5-DOF hybrid optical machining manipulator as the research object, established inverse dynamics model based on virtual work principle, and expressed the algebraic relationship between the joint-reflected inertia (JRI) coefficient and the ratio of load inertia. We also determined the inertia matching range of the machining manipulator by analyzing the mechanical system’s resonance frequency, energy matching efficiency and other factors qualitatively and quantitatively, as well as combining the load inertia ratio with dynamic precision characteristics. Finally, according to the derivation results, we analyzed the inertia matching rules of the 5-DOF hybrid optical machining manipulator with different structural parameters in certain machining tasks. In addition, the JRI coefficient and inertia matching principle proposed in this paper can be widely applied to other machining manipulators’ selection of driving equipment under different machining targets, and can also be used to evaluate the selection results.

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Abbreviations

R :

Rotation matrix

J :

Jacobian matrix of U{unP}S branch-chains axial velocity

l i, l 0 :

Length of U{unP}S branch-chains, UP branch-chain

e i, e 0 :

Unit vector of U{unP}S branch-chains, UP branch-chain

v A :

Velocity of the center point A of moving platform

ω A :

Angular velocity of UP branch-chain

ω i :

Angular velocity of the ith U{unP}S branch-chain

J ωi, J ωA :

Jacobian matrix of angular velocity of U{unP}S branch-chains, UP branch-chain

J vi :

Jacobian matrix of velocity of U{unP}S branch-chains

\({{\boldsymbol{J}}_{{v^A}}}\) :

Jacobian matrix of velocity of U{unP} branch-chain

J 0 :

Jacobian matrix of U{unP} branch-chain axial velocity

v ci :

The center of mass velocity of U{unP}S branch-chains

\({{\boldsymbol{v}}_{{c^A}}}\) :

The center of mass velocity of UP branch-chain

h :

Distance from centroid C to point A

h i :

Distance from centroid Ci of Si to point Ai

\(h_i^{\prime}\) :

Distance from centroid Ci of Si1 to point Bi

ω mi :

Angular velocity of the motor rotors etc.

J ωmi :

Jacobian matrix of absolute angular velocity of the motor rotors etc. of U{unP}S branch-chains

p i :

Lead of ball screw of U{unP}S branch-chains

\({{\boldsymbol{I}}_{{i^0}}}\) :

Inertia tensor of Si of U{unP}S branch-chains

\({\boldsymbol{I}}_{{i^0}}^{\prime}\) :

Inertia tensor of Si1 of U{unP}S branch-chain

\({{\boldsymbol{I}}_{{c^0}}}\) :

Inertial tensor of S with respect to the centroid C

I mi :

Rotary inertia of the servo motor rotors

m :

Mass of S of UP branch-chain

m i :

Mass of Si of U{unP}S branch-chains

m i :

Mass of Si1 of U{unP}S branch-chains

p :

Screw pitch of the spiral trajectory

D :

Machining diameter of the spiral trajectory

M :

Inertial matrix

J L :

Load inertia converted to each actuator shaft

J M :

Motor inertia

k s :

Torsion stiffness

c s :

Damped coefficient

φ :

Load inertia ratio

ζ φ :

Energy matching efficiency

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Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant No. 91648105) and the Priority Academic Program Development of Jiangsu Higher Education Institutions.

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Authors and Affiliations

  1. School of Mechatronic Engineering, China University of Mining and Technology, Xuzhou, China

    Yixuan Kong, Gang Cheng & Feng Guo

  2. Shandong Zhongheng Photoelectric Technology Co., Ltd, Zaozhuang, China

    Gang Cheng & Wei Gu

  3. National Machine Tool Product Quality Supervision and Inspection Center, Tengzhou, China

    Laibin Zhang

Authors
  1. Yixuan Kong
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  2. Gang Cheng
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  3. Feng Guo
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  4. Wei Gu
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  5. Laibin Zhang
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Corresponding author

Correspondence to Gang Cheng.

Additional information

Recommended by Associate Editor Hak Yi

Yixuan Kong received her B.S. in 2017 and is currently a postgraduate student in Mechatronic Engineering of China University of Mining and Technology in China. Her research interests are in mechanism theory and parallel manipulators.

Gang Cheng received his M.S. in 2003 from the Chinese Academy of Sciences and the Dr. Sc. Tech. in 2008 from China University of Mining and Technology in China, where he is currently a Professor. His research interests include mechanism theory and reliability of electromechanical equipment.

Feng Guo received a bachelor’s degree from China University of Mining and Technology in 2016 and is currently studying for a Ph.D. from China University of Mining and Technology. His current research interests include parallel manipulators and control of robots.

Wei Gu received his M.S. from China University of Mining and Technology. He currently works in Shandong Zhongheng Photoelectric Technology Co., Ltd. His research interests are robotics and control theory.

Laibin Zhang is currently working at the National Machine Tool Product Quality Supervision and Inspection Center. His research interest is to optimize the performance of machining robots and research on control strategies.

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Kong, Y., Cheng, G., Guo, F. et al. Inertia matching analysis of a 5-DOF hybrid optical machining manipulator. J Mech Sci Technol 33, 4991–5002 (2019). https://doi.org/10.1007/s12206-019-0938-1

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  • DOI: https://doi.org/10.1007/s12206-019-0938-1

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