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Dynamic performance analysis and optimization of pulp-molding machine frames

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Abstract

The pulp-molding product is a new degradable and pollution-free packaging material replacing traditional packaging materials. Countries are strongly recommending that pulp-molding machines are mainly used to produce pulp-molding products. The stability, efficiency, and rapidity of its products’ molding and processing quality are largely controlled by the structural dynamic mechanics of the molding machine frame. Its equipment’s dynamic performance is measured by the 1st-order natural frequency. The pulp-molding machine frame was taken as an example for optimizing the design and investigating the dynamic performance in the work. Based on finite elements, the beam structure was divided into finite elements, and the global independent generalized displacement coordinates of equipment were extracted using multi-point constraint elements. The global independent generalized displacement coordinates and the Lagrange equation were used to establish the device’s elastic dynamic model. Besides, the correctness of the theoretical model was verified by the finite element method. Finally, the first natural frequency was taken as the optimization design goal, and the particle swarm optimization algorithm was utilized to optimize the section size of the beam in equipment. The results could optimize the molding machine’s design and analyze the dynamic performance at the pre-design stage.

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Abbreviations

M e :

Element mass matrix

K e :

Element stiffness matrix

L K b :

Stiffness matrix of the beam element in the local coordinate frame

K b :

Stiffness matrix of the beam element in the global coordinate frame

\({\varvec {K}}_{bi}^{g}\) :

Stiffness contribution matrix of the ith beam element to the machine

Δ ei :

Linear displacement of element node i

φ ei :

Angular displacement of element node i

E ke :

Kinetic energy of the beam element

f i :

The ith-order natural frequency in Hz

U :

Global independent displacement coordinates

M :

Overall mass matrix

K :

Overall stiffness matrix

L M b :

Mass matrix of the beam element in the local coordinate frame

M b :

Mass matrix of the beam element in the global coordinate frame

\({\varvec {M}}_{bi}^{g}\) :

Mass contribution matrix of the ith beam element to the machine

u e :

Element-nodal-displacement column vector

E k :

Kinetic energy of the machine

E pe :

Potential energy of the beam element

E p :

Potential energy of the machine

ω i :

The ith-order circular frequency in rad/s

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Acknowledgements

The authors acknowledge the Horizontal Topic: Finite Element Analysis and Design Optimization of Key Components of Paper-Plastic Equipment (grant no. 00520104).

Funding

The work was supported by Horizontal Topic: Finite Element Analysis and Design Optimization of Key Components of Paper-Plastic Equipment (grant no. 00520104).

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Authors and Affiliations

  1. School of Marine Engineering Equipment, Zhejiang Ocean University, Zhoushan, 316000, China

    Junbin Lou

  2. College of Information Science and Engineering, Jiaxing University, Jiaxing, Zhejiang, 314001, China

    Junbin Lou

  3. Maritime School, Zhejiang Ocean University, Zhoushan, 316000, China

    Yaping Gong

Authors
  1. Junbin Lou
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  2. Yaping Gong
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Contributions

Yaping Gong in charge of research ideas proposed constructive discussions; Junbin Lou analyzed and prepared the manuscript.

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Correspondence to Yaping Gong.

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Cite this article

Lou, J., Gong, Y. Dynamic performance analysis and optimization of pulp-molding machine frames. Int J Adv Manuf Technol 122, 209–217 (2022). https://doi.org/10.1007/s00170-022-09279-w

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  • DOI: https://doi.org/10.1007/s00170-022-09279-w

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