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An approximate bending force prediction for 3-roller conical bending process

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Abstract

Roll bending process is an important metal forming process used to produce cylindrical and conical shells and sections for various applications. 3-roller conical bending is one such process. For this process it is important to evaluate the maximum force acting on the rollers during the rolling process for designing the rolling machine as well as for evaluating the coefficient of friction at roller-plate interface. It is observed that maximum force is acting on the roller during the static bending in roll bending process [Gandhi et al. 2008]. In the present study mathematical model for force prediction on the rollers have been developed. Effects of various material properties and geometrical parameters have been studied. It has been concluded that the proposed model can be effectively used to get the roller bending force for given geometrical parameters and material properties. It can also be used to get roller plate interface friction, if the experimental value of roll bending force is available.

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Abbreviations

B1, B2:

Bearings for top roller

B3,B4,B5,B6:

Bearings for bottom rollers

w:

width of the blank in mm

t:

thickness of the plate in mm

M:

bending moment in N-m

P:

Vertical load at the top roller and bending plate interface in N

a:

horizontal distance of the bottom roller centers in mm

x:

half the horizontal distance of the bottom roller centers in mm

Q:

Normal force exerted by the plate on the bottom roller at roller plate interface in N

θ:

Angle between frictional force and horizontal plane at the roller plate interface in radians

U:

Vertical distance travelled by the top roller for first stage of static bending in mm

E:

Young’s modulus in N/mm2

K:

strength coefficient in N/mm2

n:

strain hardening exponent

r1:

radius of bottom roller in mm

R:

radius of curvature of the bent plate in mm

y:

distance of fiber from neutral plane in mm

I:

Second moment of area (For plate it is equal to bt3/12) mm4

μ:

coefficient of friction at roller plate interface

ε:

strain

σ:

stress in N/mm2

υ :

Poisson’s ratio

yep :

distance of the fiber upto which elasticity E is constant in mm

χ:

curvature of the bend plate between bottom rollers mm−1

ε*:

strain at yield point

E*:

the ratio of modulus of elasticity to σs

te :

thickness of elastic layer in mm

ε0 :

strain of the strip mid-line

\( \overline \varepsilon \) :

effective strain

\( \overline \sigma \) :

effective stress

β:

bottom roller inclination

AF, AR :

Center distance between bottom rollers at front and rear end respectively

α:

top roller inclination in the present case it is zero

φ:

cone angle

RF, RR :

Bending radius at the front end and rear end respectively

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Authors and Affiliations

  1. Mechanical Engineering Department, S.V. National Institute of Technology, Surat, Gujarat, India

    M. K. Chudasama & H. K. Raval

Authors
  1. M. K. Chudasama
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  2. H. K. Raval
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Correspondence to M. K. Chudasama.

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Chudasama, M.K., Raval, H.K. An approximate bending force prediction for 3-roller conical bending process. Int J Mater Form 6, 303–314 (2013). https://doi.org/10.1007/s12289-011-1087-y

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  • DOI: https://doi.org/10.1007/s12289-011-1087-y

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