Week 2 Bevel Gear Challenge

Grid Independency test

Mesh or grid independence study is carried to determine this optimum point where a fairly accurate solution for the problem is found at the expense of least computational resources. In other words, given a level of accuracy for the solution, the mesh used is good enough to achieve that accuracy at the expense of minimum possible computational power. Using an optimum mesh, the accuracy of the results are good enough to capture all the necessary flow features, their gradients and so forth.

In other words, a coarse grid will not capture all the flow features (not a solution of required accuracy) and a finer mesh will give a solution of a little higher accuracy than required but at the expense of computational power and time. This and this alone is the reason for performing a mesh independence study. Grid-independent means calculation results change so little along with a denser or looser grid that the truncation error can be ignored in numerical simulation. If the results tend towards identical, the grid can be considered as grid-independent. Grid independent is associated with the accuracy or even rationality of numerical results.

Grid convergence is the term used to describe the improvement of results by using successively smaller cell sizes for the calculations. A calculation should approach the correct answer as the mesh becomes finer, hence the term grid convergence.

The grid resolution and time step have a very great effect on the results of unsteady numerical simulation in a certain range. When considering grid-independent issue, in principle a very dense grid can avoid this problem but the calculation resource may be wasted unnecessarily. In practice, we usually increase the grid resolution according to a certain ratio, for example 1/3, and then compare the results of two neighbourhood results. If the results tend towards identical, the grid can be considered as grid-independent. Such strategy can utilize computational resource most efficiently as well as obtain reasonable results.

Objective:

Objective of the work is to simulate Static structural analysis of Bevel gear simulation using different mesh size like 4mm, 5mm, 6mm and carry out a Grid independency test to find out Equivalent stress, Total deformation and Stress intensity for the given mesh sizes. After getting all the result need to analyse and compare the results of the three cases and conclude which is the best suitable mesh size.

Experimental Procedure:

To carry out Static structural analysis and Grid Independency test on Ansys workbench, several steps has been followed.

1. Engineering Data (Material Selection): This is the first step, where we have to select the material on which the analysis would be carried out. For the Case-1, Cast Iron (Ductile) has been chosen.

Material Properties of Structural Steel

Frictional Contacts on Gear teeth

2. Import Geometry: After assigning the base material of the geometry, the model has been imported in Ansys using Ansys Space claim, where unwanted middle portion of the gears have been cut out to reduce the Solving time and it would help to reduce Computational Calculation & solving time.

2. Model: This step is the major step of Analysis. After importing the model, need to click on “Edit” to open the “Model Window” where we can assign several constraint and Boundary condition.

Step-1(Geometry): Under geometry click on the imported model and assign the material individually.

Step-2 (Connections): Under Connection have to insert “Contacts”, where have to assign “Frictional Contacts” and assign the Contact faces of the gears. After Contacts has been given, need to assign “Joints “as a type “Revolute joint” for the both Gears.

4. Mesh: Global mesh sizes 4mm, 5mm & 6mm were taken. Face sizing has been inserted to assign different element size on gear teeth and size as 1.75 mm has been chosen and Smoothening has been kept Low for meshing the model.

4. Static Structural:

Step-1 (Analysis Setting): Under Analysis setting several parameters have been modified according to the problem. No. of Steps kept as 6, Time Stepping kept as Program and all Solver Controls have been kept as Programmed Controlled.

Step-2 Need to Assign the Joints for the individual gears. DOF has been kept as on Z axis and Magnitude has been given in Tabulated Data, where in one gear it has been kept as Degree of rotation (30 Degree increment) and on the other gear Moment has been given in the Tabulated data as 100 N-mm on each.

6. Solution: To get the result as per the objective of the work have to insert Equivalent Stress, Total Deformation and Equivalent Elastic Strain.
7. Solve: To obtain the result click on Solve.

Result & Discussion:

Case-1 (Mesh Size: 5mm)

1. Equivalent Stress: Maximum Stress: 3.2089 Mpa. And Minimum Stress: 8.6242e^-08

2. Equivalent Elastic Strain: Maximum Stress Intensity: 2.3012e-5 Mpa and Minimum Stress Intensity 1.1869e-12 Mpa

3. Total Deformation: The maximum deformation result got 47.882mm and Minimum deformation: 21.651 mm.

Grid Independency Input & Output Parameters:

Grid Independency Result for Diffrent Mesh size of 4mm, 5mm & 6mm:

Discussion on Grid Independency Result:

Grid Independency test has been carried out on the Bevel gear by taking different mesh sizes of 4mm, 5mm and 6 mm. I t has been observed that result has been varuied depending on the mesh size setting. More finer mesh size gives more accurate result compared to the coarser mesh setting of higher element size. Where finer mesh setting of lower element size has the maximumum no of nodes and due to the maximum no of element, which computes the geometry more accurately compared to the coarser settings and percent change also been reduced quite an extent.

So, it can be concluded that the optimum mesh setting as 4mm has been considered for non contact region. More finer setting can be consider further but the value in result would not varried on that extent.