Week 4- Rolling operation

Overview:

Structural analysis was performed to study the behaviour of a workpiece made of copper under the effect of rolling by evaluating the Equivalent stress, deformation in a certain direction and plastic strain.

Geometry:

A rectangular workpiece of size 100*9*10 mm was made to move in between the roller of diameter 50 mm. The front end of the workpiece is tapered to provide the smooth initial movement.

General Setup:

Both the rollers are defined with structural steel as the material and copper NL was assigned for the workpiece.

Contacts:

The connection between the roller and workpiece is modelled as a frictional contact with a frictional coefficient of 0.2. Augment Lagrange formulation with the defined normal stiffness factor of 0.1 that updates every iteration was used to carefully model the interpenetration of elements. This setup is used for both the rollers.

Joints:

Rollers are provided with cylindrical joint connected to the ground due to which the motion in X and Y direction can be constrained. Since the displacement of the roller in the Z-direction is not constrained, a planar joint was defined on the side face of the roller. This ensures that there will not be any minute displacement in the Z-direction. Hence there exist only the rotation of the roller.

Analysis Setting:

The analysis was carried out in 14 steps and to account for large deformations, large deflection was enabled. To provide a stabilizing force for converging against instability due to non-linearities, stabilizing energy is switched on with an energy dissipation ratio of 0.1 which is recommended for bending or extrusion application. The workpiece is provided with the displacement condition that varies almost linearly throughout the time step. It is defined in such a way that the workpiece will be displaced 90mm at the end of the final time step.

Rotational boundary condition was defined for both the cylindrical joints in which the rotation angle varies almost nearly from 0 to 210⁰. Also, it is ensured that both the rollers will be rotating in the opposite direction.

Results:

Equivalent stress of the complete setup and Plastic strain of the workpiece is determined, and the values obtained are tabulated. Plastic strain accounts for the permanent deformation in the given material or workpiece. The figure below shows the variation of equivalent stress on the setup and the plastic strain.

Parameters	Maximum	Average	Minimum
Plastic Strain	1.5337 mm/mm	0.91243 mm/mm	2.2045e-002 mm/mm
Equivalent Stress	2746.4 MPa	456.42 MPa	4.8283e-003 MPa

It could be observed from the figure below the deformation in z direction is 5.83 mm in both direction

The deformation figure below confirms the total displacement of the workpiece is 90mm.