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.
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Abbreviations
- β :
-
Shape factor −
- 𝜖 d m :
-
Strain at damage −
- 𝜖 p l :
-
Strain at plastic deformation −
- ν :
-
Poisson’s ratio −
- ϕ :
-
Deflection angle of the belt rad
- ρ :
-
Density kg/m3
- σ 𝜃 :
-
Circumrefential bending stress MPa
- σ b :
-
Bending stress MPa
- σ c :
-
Compression stress MPa
- σ e q v :
-
Equivalent stress MPa
- σ r :
-
Radial bending stress MPa
- τ s :
-
Shearing stress MPa
- ξ :
-
Compression area factor −
- ξ :
-
Critical compression area factor −
- ξ e s t :
-
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 N ⋅ s/mm
- D :
-
Rigidity of the material N ⋅ mm
- d 1 − d 5 :
-
J-C model parameters −
- E :
-
Young’s modulus MPa
- F :
-
Perforation force N
- F A m a x :
-
Analytical peak perforation force N
- F E m a x :
-
Empirical peak perforation force N
- F P D i :
-
Estimated peak perforation force N
- F p l :
-
Perforation force at plastic deformation N
- F R m a x :
-
Rheological peak perforation force N
- g :
-
Thickness of the belt mm
- g P A :
-
Thickness of a polyamide core mm
- k :
-
Elastic constant N/mm
- m 𝜃 :
-
Circumferential bending torque N ⋅ mm
- m r :
-
Radial bending torque N ⋅ mm
- 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
- R e :
-
Yield point MPa
- R m :
-
Ultimate tensile strength MPa
- T :
-
Shearing force N
- v 0 :
-
Velocity of the punch mm/s
- w :
-
Deflection of the belt mm
- x :
-
Displacement of the piercing punch mm
- x d m :
-
Displacement at damage mm
- x p l :
-
Displacement at plastic deformation mm
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Wojtkowiak, D., Talaśka, K., Malujda, I. et al. Estimation of the perforation force for polymer composite conveyor belts taking into consideration the shape of the piercing punch. Int J Adv Manuf Technol 98, 2539–2561 (2018). https://doi.org/10.1007/s00170-018-2381-3
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DOI: https://doi.org/10.1007/s00170-018-2381-3