Week 4- Rolling operation

SIMULATION OF ROLLING OPERATION USING ANSYS WORKBENCH

OBJECTIVE

To simulate the rolling operation on a workpiece made of copper by increasing the length of the workpiece by 60 mm and decreasing its size on both sides by 8 mm. Run the simulation for 14 steps by ensuring that the edge of the workpiece is displaced by 90mm.

To find out the following results:

1. Equivalent stress for the whole setup.
2. Equivalent Plastic strain for the workpiece.
3. Directional Deformation in the Z axis for the workpiece.
4. Prove that the workpiece has displaced by 90mm.

1. THEORY

1.1 Rolling:

Rolling is the process of reducing the thickness or changing the cross section of a long strip by compressive forces applied through a set of rolls. In addition to flat rolling, shape rolling is used to make products with various cross sections. Products made by rolling include: (a) plate, sheet, foil, rod, seamless pipe, and tubing; (b) shape-rolled products, such as I-beams and structural shapes; and (c) bars of various cross section. Other rolling operations include ring rolling and thread rolling.

Rolling may be carried out at room temperature (cold rolling) or at elevated temperatures (hot rolling). The process involves several material and process variables, including roll diameter (relative to material thickness), reduction per pass, speed, lubrication, and temperature. Spreading, bending and flattening are important considerations for controlling the dimensional accuracy of the rolled stock.

1.2 The Flat Rolling Process:

Fig.1.2 Schematic illustration of, (a) the flat-rolling process. (b) Friction forces acting on strip surfaces. (c) Roll force, F, and torque, T, acting on the rolls.

A schematic illustration of the flat-rolling process is shown in Fig. 1.2a. A metal strip of thickness h₀ enters the roll gap and is reduced to thickness h_f by a pair of rotating rolls, each powered individually by electric motors. The surface speed of the rolls is Vr. The velocity of the strip increases from its entry value of V₀ as it moves through the roll gap; the velocity of the strip is highest at the exit from the roll gap and is denoted as V_f. The metal accelerates in the roll gap in the same manner as an incompressible fluid flowing through a converging channel. Because the surface speed of the rigid roll is constant, there is relative sliding between the roll and the strip along the arc of contact in the roll gap, L. At one point along the contact length (called the neutral point or no-slip point) the velocity of the strip is the same as that of the roll. To the left of this point, the roll moves faster than the strip; to the right of this point, the strip moves faster than the roll. Consequently, the frictional forces which oppose motion between two sliding bodies act on the strip as shown in Fig. 1.1b.

The rolls pull the material into the roll gap through a net frictional force on the material. Thus, the net frictional force must be to the right in Fig. 1.1b. This also means that the frictional force to the left of the neutral point must be higher than the friction force to the right. Although friction is necessary for rolling materials, energy is dissipated in overcoming friction. Thus, increasing friction also increases rolling forces and power requirements. Furthermore, high friction could damage the surface of the rolled product. Thus, a compromise is made in practice: Low and controlled friction is induced in rolling through the use of effective lubricants.

The maximum possible draft is defined as the difference between the initial and final strip thicknesses, or (h_o – h_f). It can be shown that this quantity is a function of the roll radius, R, and the coefficient of friction, between the strip and the roll by the following relationship:

`h_o-h_f=μ^2 R`

Thus, as expected, the higher the friction and the larger the roll radius, the greater the maximum possible draft becomes.

In rolling plates and sheets with high width-to-thickness ratios, the width of the strip remains effectively constant during rolling. However, with smaller ratios (such as a strip with a square cross section), its width increases significantly as it passes through the rolls. This increase in width is called spreading. It can be shown that spreading increases with (a) decreasing width-to-thickness ratio of the entering strip (because of reduction in the width constraint), (b) increasing friction, and (c) decreasing ratio of the roll radius to the strip thickness. The last two effects are due to the increased longitudinal constraint of the material flow in the roll gap. Spreading can be prevented also by using additional rolls (with vertical axes) in contact with the edges of the rolled product in the roll gap (edger mills), thus providing a physical constraint to spreading.

2. ANALYSIS SETUP

2.1 Geometry:

a. Imported model.                              b. Length increased to 60 mm.            c. Width decreased on both side by 8 mm.

Fig.2.1 3D model of copper rolling operation.

The given 3D model of copper rolling assembly is imported into SpaceClaim. The length of the workpiece is increased to 60 mm and the width is decreased on both sides by 8 mm.

2.2 Material Properties:

Fig.2.2 Material property details of workpiece (Copper Alloy NL).

The material assigned for workpiece is Copper Alloy NL and for rollers is Structural Steel.

2.3 Connection Details:

2.3.1 Contact details:

a. Contact between workpiece and wheel 1.

b. Contact between workpiece and wheel 2.

Fig.2.3.1 Contact details of copper rolling operation.

Contact between, (a) Workpiece (contact body) and wheel 1 (target body), (b) Workpiece (contact body) and wheel 2 (target body) are assigned as frictional contact with coefficient of friction = 0.2. The formulation type of contact is set as Augmented Lagrange and normal stiffness value is inputted as 0.1 factor with update stiffness set to as ‘each iteration’.

2.3.2 Joint Details:

                                                                              (a)

                                                                              (b)

Fig.2.3.2 Joint details of, (a) wheel 1, (b) wheel 2.

The revolute type of joint is selected for both wheels with connection type being body-ground, since only rotation is specified to the wheels.

2.4 Meshing:

a. Body sizing of workpiece.                                                                              b. Meshed model.

Fig.2.4 Meshing details of copper rolling model.

The element size of workpiece is set as 2 mm using body sizing option. The total number of nodes and elements generated are 9321 and 1629 respectively.

Note: The academic version of software has the problem size limit of 128k nodes or elements.

2.5 Boundary Conditions:

2.5.1 Analysis settings:

Fig.2.5.1 Analysis settings.

In the analysis settings the number of steps considered is 14. In solver controls, large deflection is set to ‘On’. Under the nonlinear controls, the stabilization is set as constant with energy dissipation ratio being 0.1.

2.5.2 Boundary condition for copper rolling operation:

a. Displacement applied to workpiece in negative Y-direction.

b. Joint load applied to both the wheels along Z-axis.

Fig.2.5.2 Boundary conditions for copper rolling operation.

The displacement applied to workpiece is such that the it should displace by 90 mm. In order to pull in the workpiece for rolling operation, one of the wheels has to rotate in clockwise and the other wheel has to rotate in anti-clockwise direction. The rotation angle is specified from 0⁰ to 195⁰.

3. RESULTS AND DISCUSSIONS

3.1 Equivalent stress for the whole setup:

The maximum v-m stress developed in the whole setup of rolling operation is 3155.4 MPa. The workpiece is plastically deformed by reducing its thickness and increasing its width.

3.2 Equivalent Plastic strain for the workpiece:

The maximum strain developed in the workpiece is 1.7422.

3.3 Directional Deformation in the Z axis for the workpiece:

It is observed that the workpiece has deformed 6.019 mm along positive and negative direction of Z-axis.

3.4 Directional Deformation in the Y-axis for the workpiece to show that it has displaced by 90mm:

From the plot, it is observed that, initially at time 0 s the workpiece was at 0.6 mm in negative Y-axis but at the end of the rolling operation i.e., at time 14 s, the workpiece is displaced to 90.013 mm in negative Y-axis. Hence, it is proved that the workpiece has displaced by 90 mm.

4. ANIMATION OF RESULTS:

4.1 Equivalent stress for the whole setup:

4.2 Equivalent Plastic strain for the workpiece:

4.3 Directional Deformation in the Z-axis for the workpiece:

4.4 Directional Deformation in the Y-axis for the workpiece:

CONCLUSION

1. The given model was opened in spaceclaim and the length of workpiece was increased by 60 mm and its width was decreased by 8 mm on both sides.
2. The simulation of the rolling operation on a workpiece made of copper was made to run for 14 steps successfully.
3. The Equivalent stress for the whole setup is 3155.4 MPa.
4. The Equivalent Plastic strain for the workpiece is 1.7422.
5. The Directional Deformation in the Z-axis for the workpiece is 6.019 mm.
6. The Directional Deformation in the Y-axis for the edge of workpiece is 90.013 mm. Hence, it is proved that the workpiece has displaced by 90mm.