Grid Dependency Test- Bevel Gear
TITLE: Grid Dependency Test on a Bevel Gear.
SUMMARY: In this Project, we are going to know what exactly the term "GRID INDEPENDENCY" means. Meanwhile we will be Performing a grid dependency test for the Bevel gear simulation for mesh sizes of 6,5 and 4 mm Respectively. Various Parameters such as Von-Mises stress, Equivalent elastic strain and Total Deformation are our area of intrests to know for mentioned Simulation.
INTRODUCTION: 'Grid Dependency', 'Grid Independency' and 'Mesh Refinement' are all synonyms and infact they all mean the same. We know that the most fundamental method for checking the mesh quality is to refine a mesh unless and until we arrived at a point, where the critical result,lets say 'Equivalent Stress' does not change significantly with each refinement. It is called as Grid dependency test. Both refer to the independency of grid or mesh on the accuracy of the solution. By mesh convergence test (or grid independent test) the computational cost is reduced without compromising with accuracy of the solution.
While performing the Finite Element Analysis, we all are most concerned with the element mesh quality. We all may think how can one know whether the quality of mesh is good enough for Analysis? A high density mesh will obiously provide a highly accurate and more meaning full results. However if a mesh is too dense it will require a large amount of computing power, computer memory and even large amount of run time, espically for multiple iteration. So far the Grid Dependency is concerned if someone is looking for the best mesh which can give the smallest error, one must need to work on grid dependency as well. In order to perform the above mentioned Grid Dependency test we simulate a simulation and keeping the theorey in mind we shall be getting results at a point, where the critical results for Equivalent Stress does not change significantly. Here,the simulation is run on a Bevel Gear on three different elemental sizes which are - 6mm, 5mm, 4mm.
CASE 01 ( for mesh size 6mm)
In order to check the Grid Dependency test, Lets consider a Solid model Geometry of Bevel Gear. Our model was a solid,however we removed all unnecessary & unwanted region in order to ensure that computing resources are conserved & consumes less time during computing.
We Know That, So far Grid Dependency is concerned various parameters does not change significantly with each refinement. Which means even we change Mesh elemental size, certain parameters such as 'Equivalent Stresses', 'Elastic Strain' & 'Total Deformation' didn't undergoes significant changes. We apply a constant mesh facing size of 1.75mm in ever case for teeth of Bevel Gear, which are our area of intrests. Followed by varing Mesh Elemental sizes such as 6mm,5mm,4mm Respectively.
A coarse Messh can be seen on Bevel Gear except the teeths.
Then, we follow each steps which were required to fulfill the Boundary conditions in order to run simulation. For the sake of simplicity we named small & big gear. Now for general setup we assign type as frictional, behaviour to be Symmetric and Formulation as Agumented Lagrange. Meanwhile we also assign Moment for 100mm & rotaion for each 20 Deg. difference,after Simulating it we get our Desired analysis Results.
Equivalent (Von-Mises) stress:
When the Gear are in contact with each others, due to adhesion it is obvious that Maximum stress generated is suppose to be appear near teeth region. Our simulation addresses that that Bevel Gear undergoes a Maximum of 5.6135 MPa of Stress.
Equivalent elastic strain:
There is a Maximum of 3.0556e-5 mm/mm of Strain occupied while, 2.6588e-13 mm/mm of minimalistic.
Total Deformation:
Here, a Maximum of 6.5mm deformation occured, followed by 25mm of minimum Deformation.
Below is Provided with a Force Convergence Graph, which shows at 30 points how the force critetion converges.
CASE 02 ( for mesh size 5mm)
Similarly, by applying 1.75mm as a mesh local face sizing followed by 5mm of mesh Elemental size. After apply elemental size of 5mm it is visible that here the obtained mesh is coarse.
Equivalent (Von-Mises) stress:
Generated results shows that 5.7515 MPa of stress is generated during contact near teeth of the gears. The Equivalent stress intensity is Maximum when two gears are in contact.
Equivalent elastic strain:
It seems that generated total deformation is around 2.9646e-5 mm/mm & a minimum of 2.9128e-13 mm/mm
Total Deformation:
A maximum of 64.5 mm Deforrmation has taken placed,followed by 25 mm of least deformation.
Then, we can also observe the Force Convergence Graph based on our Simulated result on the basis of first 30 points.
CASE 03 (for mesh sizes of 4mm)
For case 03,Under Consideration for Mesh a local face sizing of 1.75mm is applied on the teeth of both the bevel gear. While in order to check the grid independency test, we have meshed the remaining part of bevel gear for an elemental size of 4mm.
Equivalent (Von-Mises) stress:
Meanwhile, the simulation is run as per all boundary condition simulated for above previous cases. The generated results on the Equivalent Stress is obtained. Its clearly visible that 4.3128 MPa of stress is generated during contact near teeth of the gears. The Equivalent stress intensity is Maximum during adhesion between two gears.
From above, Mentioned tabular data it is obvious that with time the Maximum & Minimum Equivalent Stress varies.
Equivalent elastic strain:
It seems that generated total deformation is around 2.5045e-5 mm/mm & a minimum of 3.7343e-13 mm/mm.
Total Deformation:
A maximum of 64.5 mm Deforrmation has taken placed,followed by 25 mm of least deformation.
Here,from above conducted results we have successfully carried out Force Convergence Graph for initial 30 Sec.
RESULT:
Here, we have compared all the generated results based on their Maximum values.
From above it is seen that,there is a slightly change in stress for 4mm mesh & strain,however the Total deformation remains contant. Also as we reduce the elemental size the mesh tends to change from coarse to fine gradually increases Nodes & Elements.
CONCLUSION:
From the provided literature on Grid Dependency it stated that changing mesh from coarse to fine the results improves and they did exactly. There are Significantly improvements in results for both equivalent Stress & Strain. Further reducing mesh there no large no. of values changing. If futher we try to reduce the mesh refinement it will only increase computing time,therefore 4mm mesh is optimal for Analysis.