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Estimation of the perforation force for polymer composite conveyor belts taking into consideration the shape of the piercing punch

  • Dominik Wojtkowiak
  • Krzysztof Talaśka
  • Ireneusz Malujda
  • Grzegorz Domek
Open Access
ORIGINAL ARTICLE
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Abstract

Due to the improvement of the mechanical properties of polymer composite belts used in vacuum belt conveyors, its perforation process causes a lot of technical issues for manufacturers worldwide. The objective of this paper is to analyze the belt punching process with two cutting edges and present the influence of the piercing punch shape on the perforation force. Based on the analysis, the analytical stress model was derived and validated by using both empirical and FEM tests. The application of the proposed model was proved by presenting the methodology used to estimate the perforation force for the flat piercing punch based on the mechanical properties of the belt obtained from simple strength tests (uniaxial tension, compression, and shear), with an error between 4 and 15%. In this report, the analysis of the piercing punch profiles was made and eight different piercing punch profiles were tested. Presented results confirmed that the spherical bowl punch may be considered as a most effective tool for belt punching, because it reduced the perforation force by 60% and the precision of the created holes was the best among the tested punch profiles for all three groups of polymer composite belts. By combining the obtained results, in the form of shape factors β, with the perforation force approximation model, it is possible to calculate peak force value for the specified tool profile and belt type and use this data in the design process of the punching dies.

Keywords

Spherical bowl piercing punch Punching Belt perforation Vacuum conveyor belts FEM analysis Polymer composites 

Nomenclature

β

Shape factor   −

𝜖dm

Strain at damage   −

𝜖pl

Strain at plastic deformation   −

ν

Poisson’s ratio   −

ϕ

Deflection angle of the belt   rad

ρ

Density   kg/m3

σ𝜃

Circumrefential bending stress   MPa

σb

Bending stress   MPa

σc

Compression stress   MPa

σeqv

Equivalent stress   MPa

σr

Radial bending stress   MPa

τs

Shearing stress   MPa

ξ

Compression area factor   −

ξ

Critical compression area factor   −

ξest

Estimated compression area factor   −

A

Punch-belt contact area   mm2

a

Compression distance of the scrap   mm

\(A^{\prime }\)

Scrap compression area   mm2

b

Damping constant   Ns/mm

D

Rigidity of the material   Nmm

d1d5

J-C model parameters   −

E

Young’s modulus   MPa

F

Perforation force   N

FAmax

Analytical peak perforation force   N

FEmax

Empirical peak perforation force   N

FPDi

Estimated peak perforation force   N

Fpl

Perforation force at plastic deformation   N

FRmax

Rheological peak perforation force   N

g

Thickness of the belt   mm

gPA

Thickness of a polyamide core   mm

k

Elastic constant   N/mm

m𝜃

Circumferential bending torque   Nmm

mr

Radial bending torque   Nmm

μ

Friction coefficient   –

p

Pressure applied by moving punch   MPa

R

Radius of the piercing punch   mm

r

Radius of the lost contact area   mm

Re

Yield point   MPa

Rm

Ultimate tensile strength   MPa

T

Shearing force   N

v0

Velocity of the punch   mm/s

w

Deflection of the belt   mm

x

Displacement of the piercing punch   mm

xdm

Displacement at damage   mm

xpl

Displacement at plastic deformation   mm

Notes

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Copyright information

© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Dominik Wojtkowiak
    • 1
  • Krzysztof Talaśka
    • 1
  • Ireneusz Malujda
    • 1
  • Grzegorz Domek
    • 2
  1. 1.Faculty of Machines and Transport, Basics of Machine DesignPoznan University of TechnologyPoznańPoland
  2. 2.Faculty of Mathematics, Physics, Technical SciencesKazimierz Wielki University in BydgoszczBydgoszczPoland

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