Challenge:

Perform an analysis to simulate the bending of a wire using 3 different types of materials for the wire.

Objective:

Perform an analysis to simulate the bending of wire in ANSYS. Use Copper Alloy (Non-Linear), Aluminium Alloy (Non-Linear) and Magnesium Alloy (Non-Linear) for the wire alone. Find out the Equivalent stress and Equivalent strain on the wire alone.

Step 1: Select Materials and Import Geometry

First, we load “Static Structural” on Ansys Workbench. We then “Edit” the Engineering Data to select the materials required for analysis.

In this case, we need to simulate the wire bending operation for three different wire materials- Copper Alloy NL, Aluminium Alloy NL and Magnesium Alloy NL. The material for the wheel and lever will remain the same in all cases, i.e., Structural Steel.

Copper Alloy NL properties

Density	8300 kg/m^3
Young’s Modulus	1.1E+11 Pa
Poisson’s Ratio	0.34
Bulk Modulus	1.1458E+11 Pa
Shear Modulus	4.1045E+10 Pa
Compressive Strength	2.5E+08 Pa
Yield Strength	2.8E+08 Pa
Tangent Modulus	1.15E+09 Pa

Aluminium Alloy NL Properties

Density	2770 kg/m^3
Young’s Modulus	7.1E+10 Pa
Poisson’s Ratio	0.33
Bulk Modulus	6.9088E+10 Pa
Shear Modulus	2.6692E+10 Pa
Yield Strength	2.8E+08 Pa
Tangent Modulus	5E+08 Pa

Magnesium Alloy NL Properties

Density	1800 kg/m^3
Young’s Modulus	4.5E+10 Pa
Poisson’s Ratio	0.35
Bulk Modulus	5E+10 Pa
Shear Modulus	1.6667E+10 Pa
Yield Strength	1.93E+08 Pa
Tangent Modulus	9.2E+08 Pa

Stainless Steel Properties

Density	7850 kg/m^3
Young’s Modulus	2E+11 Pa
Poisson’s Ratio	0.3
Bulk Modulus	1.6667E+11 Pa
Isotropic secant co-eff of thermal expansion	1.2E-5 C^-1
Compressive Strength	2.5E+08 Pa
Tensile Ultimate Strength	4.6E+08 Pa
Tensile Yield Strength	2.5E+08 Pa

The file containing the geometry is loaded on Ansys SpaceClaim. This is done to avoid the generation of errors while loading the model on Ansys Mechanical APDL. Once the geometry is verified, it is then updated and we proceed to edit the model on Ansys Mechanical. The geometry looks as follows:

The materials required for analysis are then assigned to the respective parts of the geometry.

Step 2: Defining the Contacts and Joints

To avoid confusion, the default contacts generated by the system are deleted and then defined manually. For wire-bending analysis, we need to define two primary contact pairs:

1. Wire to Lever Contact
2. Wheel to Wire Contact

The contact faces are carefully selected and a “Frictional” contact with friction co-efficient 0.2 is defined for both pairs.

Type of Contact	Frictional
Friction Coefficient	0.2
Formulation	Augmented Lagrange
Normal Stiffness Factor	0.1
Update stiffness	For Each Iteration
Interface Treatment	Add Offset, Ramped Effects

Since the lever is supposed to follow a revolute motion to bend the wire, we need to define the joint to which rotation can be given. Therefore, a “Revolute” joint with “Body to Ground” setting is defined for the lever.

Step 4: Meshing

For wire bending analysis, defining the mesh is of paramount importance. Once the global mesh is defined, the next step is to refine the mesh along critical areas which will be subjected to high stresses. These areas are shown below:

1. Face Sizing 2.2mm

2. Defining Sphere of Influence

For the second case, the mesh is refined by defining a local coordinate system and selecting elements as per ‘sphere of influence’. 7mm radius is defined for the sphere of influence and an element size of 0.8mm is selected. The patch conforming method is changed from \"Automatic\" to \"Tetrahedron\".

The final generated mesh looks as shown below (note the refined elements along the sphere of influence).

Step 5: Analysis Settings

We run the simulation for 8 steps. For ease of computation and analysis, we define the values separately for the 1^st step and then for the remaining steps.

Step 1

Steps 2 to 8

After defining timestep and other relevant values for analysis, we need to define joint loads. In this case, a fixed joint is assigned to the Wheel and angular displacement (Rotation) is applied on the lever. Before defining the angle values for rotation, we need to verify the coordinate axis for the lever and ensure that they are set right.

Step 6: Running the Simulation

Now that all the boundary conditions are properly defined, we select the required output and generate the solution.

Note: The solver failed to converge at a solution after a certain point. When the partial simulation was run, the slipping of the inner end of the wire (inside the wheel groove) became clear. I then fixed that end of the wire and proceeded with the simulation. The solution was successfully generated and the results obtained are shown below.

Case 1: Copper Alloy NL Wire

Equivalent Stress on Wire: 664.33 MPa (Max)

Equivalent Strain on Wire: 6.0713E-3 (Max)

Case 2: Al Alloy NL Wire

Equivalent Stress on Wire: 451.65 MPa (Max)

Equivalent Strain on Wire: 6.4112E-3 (Max)

Case 3: Magnesium Alloy NL Wire

Equivalent Stress on Wire: 489.7 MPa (Max)

Equivalent Strain on Wire: 1.0923E-2 (Max)

Comparing the Results

	Copper Alloy NL	Aluminium Alloy NL	Magnesium Alloy NL
Max Equivalent Stress on Wire (MPa)	664.33	451.65	489.7
Max Equivalent Strain on Wire (mm/mm)	6.07E-3	6.41E-3	1.09E-2

Conclusion

• As evident from the graph, during wire bending, the wire material experiences maximum stress during the initial bending phase. Following that, the stress decreases and remains almost constant for the rest of the process. The same pattern is observed with equivalent strain.

• The initial and final bend portions of the wire experience the most stress compared to other regions.

• Copper Alloy experiences maximum stress when compared with Aluminum and Magnesium alloy. Since the loads are the same in all cases, I infer that copper offers the highest resistance to bending and is the least favourable material for wire bending in our case.

• The highest strain is observed for Magnesium alloy. Magnesium alloy also has the lowest modulus of elasticity among the three and therefore, is the most favourable material for wire bending in our case.

Animations:

Copper Alloy Nl-

Equivalent Stress on Wire: https://youtu.be/05SP820NRvc

Equivalent Strain on Wire:https://youtu.be/rOlG8zkLTE8

Al Alloy NL-

Equivalent Stress on Wire:https://youtu.be/kd2LCQ3c0nU

Equivalent Strain on Wire:https://youtu.be/JPQ192NvriM

Magnesium Alloy NL-

Equivalent Stress on Wire:https://youtu.be/5UJOaMVuBPY

Equivalent Strain on Wire:https://youtu.be/aX6vZwi_R00