ISSN: 2180-1053 Vol. 3 No. 1 January-June 2011 31
3.2 finite element modelling of thin-wall workpiece
The structural of the thin-wall workpiece is modelled with the three- dimensional twenty-node parabolic hexahedron solid element as
shown in Figure 5. Parabolic hexahedron solid element is preferred since the thickness of the wall is very thin and the change in structural
properties of the wall due to material removed is very important for
accurate prediction of the wall delections [16, 17]. For the three- dimensional element, each node has three degrees of freedom, i.e,
three displacements δ
x
, δ
y
and δ
z
and the displacements within each element are interpolated by the nodal values [18].
δ δ δ
FIGURE 5: Parabolic hexahedron solid element.
FIGURE 5: Parabolic hexahedron solid element.
Figure 6 shows the thin-wall component model for delection calculations. The initial wall thickness t
i
is reduced to t
c
at the transient zone where the cuter lutes enter and exit the material
in the milling process. The displacements of the whole structure component are obtained by assembling and solving the inite
element equations for each element together as follows:
[ ]
{ } { }
1 1
x x
x
wp wp
wp wp
n n
n n
wp
F K
= δ
[ ]
{ }
δ
{ }
β β
β β
β β
β
[ ]
{ } { }
= δ
6
[ ]
{ }
δ
{ }
β β
β β
β β
β where
[ ] { }
{ }
=
δ
where
[ ]
x
wp wp
n n
wp
K is the
{ }
δ
workpiece and
{ }
F
β β
β β
β β
β
is the stifness matrix of the workpiece,
[ ] { }
{ }
=
δ
[ ]
workpiece,
{ }
1
x
wp
n
δ
is the
{ }
ting force acting on
β β
β β
β β
β
is the nodal displacement of the workpiece and
[ ]
{ } { }
=
δ
[ ]
is the stiffness
{ }
δ
iece and
{ }
1
x
wp
n
F is th
rkpiece calculated in Secti
β β
β β
β β
β is the vector
of the cuting force acting on the transient surface of the workpiece calculated in Section 3.1. The nodal displacement for the structural
component can be solved by deining the displacement boundary conditions for the model.
ISSN: 2180-1053 Vol. 3 No. 1 January-June 2011 Journal of Mechanical Engineering and Technology
32
Figure 6: Modelling the thin-wall component.
β β
β β
β β
β
Figure 6: Modelling the thin-wall component.
3.3 statistical analysis
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