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Prediction of dimensional errors in 3D complex shapes due to press elasticity

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Abstract

This paper presents an approach to predict dimensional errors in 3D complex shapes due to press geometry errors and elasticity. Using a press stiffness matrix formulation for the press deflections in forging operation, a quantitative relationship between forging die deviations and the press geometry errors and elastic deflections is developed, which is a function of the forging force, press stiffness and the spatial relationship between the forging dies and the press table. The stiffness matrix of a screw press is obtained using finite element analysis. To evaluate the effect of the press elasticity on dimensional errors of 3D components, a case study of forging for aerofoil shapes is carried out based on the results from physical modelling experiments. With the representative information of the tool shape and forging force data, numerical results of the forging die deviations as a source of dimensional errors for the aerofoil shape are obtained and evaluated. It is demonstrated that this approach is applicable to forging and other metal forming processes for complex shapes.

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Abbreviations

A :

Deformation area (mm2)

[C]:

Coordinate transformation matrix

E X ,E Y :

Offsets of forging force to the center of press table (mm)

f :

Friction factor

F X , F Y , F Z :

Force components applied on press ram (KN)

K :

Material flow stress constant (MPa)

[K]:

Stiffness matrix of press

[K]−1 :

Inverse of press stiffness matrix

l :

Billet dimension (mm)

M X , M Y , M Z :

Moment components applied on press ram (kNmm)

n 1 :

Material strain exponent

n 2 :

Material strain-rate exponents

{P}:

Forging force vector

r i :

Position vector of upper die surface (mm)

r 0 :

Position vector of press ram (mm)

Δr i :

Deviation vector of the upper die surface (mm)

x i , y i , z i :

Coordinates of points on the upper die surface (mm)

x 0 , y 0 , z 0 :

Coordinates of the press ram reference point (mm)

χ :

Scale factor for flow stress

δ :

Press linear deflection vector (μm)

ɛ :

Strain

\({\mathop \in \limits^\cdot }\) :

Strain-rate

{γ}:

Press deflection vector (mm)

\({\left\{ {\gamma ^{{eq}}_{0} } \right\}}\) :

Equivalent clearance vector of press guideway (mm)

λ :

Geometry scaling factor

θ :

Press angular deflection vector (μm/mm)

σ :

Material flow stress (MPa)

e, m :

Engineering and model materials

P, T :

Press and tool

R, T :

Press ram and table

X, Y, Z :

Three linear axis of the press

X′, Y′, Z′ :

Three rotational axis of the press

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Authors and Affiliations

  1. School of Mechanical and Manufacturing Engineering, Queen’s University Belfast, Belfast, BT9 5AH, UK

    H. Ou

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  1. H. Ou
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Correspondence to H. Ou.

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Ou, H. Prediction of dimensional errors in 3D complex shapes due to press elasticity. Int J Adv Manuf Technol 31, 61–70 (2006). https://doi.org/10.1007/s00170-005-0178-7

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  • DOI: https://doi.org/10.1007/s00170-005-0178-7

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