Week 2 Bevel Gear Challenge

GRID DEPENDENCY TEST FOR BEVEL GEAR SIMULATION USING ANSYS

OBJECTIVE

To perform a grid dependency test for the Bevel gear simulation for the following mesh sizes,

1. Case-1: Mesh size is 6 mm
2. Case-2: Mesh size is 5 mm
3. Case-3: Mesh size is 4 mm

To find and compare the results of Total Deformation, Von-Mises Stress and Equivalent Elastic Strain for all the cases.

1. THEORY

1.1 Bevel Gear:

Gears are defined as toothed wheels or multilobed cams, which transmit power and motion from one shaft to another by means of successive engagement of teeth. Gears are broadly classified into four groups, viz., spur, helical, bevel and worm gears.

Fig. 1.1 Bevel Gear.

Bevel gears, as shown in Fig.1.1, have the shape of a truncated cone. The size of the gear tooth, including the thickness and height, decreases towards the apex of the cone. Bevel gears are used to transmit power between two intersecting shafts. There are two common types of bevel gears straight and spiral.

1.2 Grid Dependency Test and its uses:

Numerical software packages solve problems by using a series of discrete points in the mesh or grid. Each point or node adds degrees of freedom (DOF) to the system. So, the more DOF’s in the model the better it will capture the structural behavior. Each DOF adds complexity and increases solve time. The engineer needs to balance the complexity of the model with solve time. It doesn’t take much for a finite element analysis to produce results. But, for results to be accurate, we must demonstrate that results converge to a solution and are independent of mesh size.

Numerical verification is composed of two main components. The first of these verifies that the discretized solution is reproducible and does not suffer from discretization errors. The so-called grid independence study validates that the solution obtained is invariant as the mesh is refined. As the mesh is refined with smaller elements the computed solution should converge to a unique solution.

A mesh convergence study verifies that the FEA model has converged to a solution. It also provides a justification for Mesh Independence and additional refinement is unnecessary. The results of an FEA model must be independent of mesh size. A convergence study ensures the FEA model captures the systems behavior, while reducing solve time.

2. ANALYSIS SETUP

2.1 Geometry:

a) Imported 3D model                                                                                                        b) 3D model edited in SpaceClaim

Fig.2.1 3D model of Bevel gear.

The given 3D model of Bevel gear is imported into ANSYS Workbench for static structural analysis. The Big gear has 24 teeth while the Small gear has 16 teeth. In order to make the given 3D model simple for analysis purpose the regions having minimal effect on the analysis results are removed using SpaceClaim is as shown in fig.2.1. b.

2.2 Material Properties:

Fig.2.2 Material property details.

The material used for analysis on Bevel gear is structural steel.

2.3 Contact Details:

2.3.1 Frictional contact details:

Fig.2.3.1 Frictional contact details of Bevel gear.

The type of contact between the faces of driver and driven gear teeth is defined as frictional contact with contact bodies being Small gear and target bodies being Big gear. Augmented Lagrange formulation is chosen because contact penetration is more controlled and can be used for any type of contact. Interface treatment is enabled as adjust to touch because the program ignores any initial gaps or penetration between the contact surfaces and creates an initial stress-free state.

2.3.2 Joint details:

a. Big gear                                                           

 b. Small gear

Fig.2.3.2 Joint details.

The Big and Small gears are specified with revolute type of joint having rotation about Z-axis with connection type being body-ground.

2.4 Meshing:

Fig.2.4 Meshing details of Bevel gear.

The Bevel gear model is meshed for different cases of element size i.e., 6 mm, 5 mm and 4 mm. The element size on the faces of the bevel gear teeth is set as 1.75 mm for all the cases of mesh size using face sizing option to better capture structural behavior, while reducing solve time. The analysis is carried out for each cases of mesh size individually.

Note:

1. The academic version of software has the problem size limit of 128k nodes or elements.
2. The analysis setup for only case-1 is demonstrated.

2.5 Boundary Conditions:

2.5.1 Analysis settings:

Fig.2.5.1 Analysis settings.

The total number of steps for analysis is specified as 6 with auto time stepping being ‘On’. The initial, minimum and maximum time step is specified as 0.1 s, 5e-2 s and 1 s respectively. In the solver controls, the large deflection is set to ‘On’.

2.5.2 Joint loads details:

a. Big gear

b. Small gear

Fig.2.5.2 Joint loads details.

The Big gear is the driver gear hence, moment (anti-clockwise) of 100 N-mm is specified for all the steps.

The small gear is the driven gear hence, rotation (clockwise) for 120⁰ is specified with an increment value of 20⁰ for each step.

3. RESULTS AND DISCUSSIONS

3.1 Total Deformation:

Case-1: Mesh size 6 mm

Case-2: Mesh size 5 mm

Case-3: Mesh size 4 mm

Fig.3.1 Total Deformation

From the deformation contour plot for all the cases, it is observed that the maximum deformation of 47.873 mm has occurred at the outer edges of the teeth of Bevel gear.

3.2 Equivalent (v-m) stress distribution:

Case-1: Mesh size 6 mm

Case-2: Mesh size 5 mm

Case-3: Mesh size 4 mm

Fig.3.2 Von-Mises stress distribution.

From the v-m stress contour plot for all the cases, it is observed that the maximum stress is developed at the interface of face and flank of the Bevel gear teeth.

3.3 Equivalent Elastic Strain:

Case-1: Mesh size 6 mm

Case-2: Mesh size 5 mm

Case-3: Mesh size 4 mm

Fig.3.4 Equivalent Elastic Strain.

From the Equivalent Elastic Strain contour plot for all the cases, it is observed that the maximum strain is developed at the interface of face and flank of the Bevel gear teeth.  

3.3. Comparison of Results:

The maximum and minimum values of Total Deformation, Equivalent (v-m) Stress and Equivalent Elastic Strain is tabulated as shown below.

From the table, it is observed that the maximum and minimum value of total deformation is 47.873 mm and 21.651 mm respectively for all the cases of Bevel gear.

It is observed that, the tabulated values of v-m Stress and Equivalent Elastic Strain for case-2 and case-3 are almost same. Hence, reducing mesh size further does not influence the result but only increases computational time.

From grid dependency test, the results of Bevel gear simulation for case-2 and case-3 are independent of mesh size. Hence, it validates that the solution obtained is invariant as the mesh is refined. It also provides a justification for Mesh Independence and additional refinement is unnecessary. 

4. Animation of Results:

4.1 Total Deformation:

Case-1: Mesh size 6 mm

Case-2: Mesh size 5 mm

Case-3: Mesh size 4 mm

4.2 Equivalent stress distribution:

Case-1: Mesh size 6 mm

Case-2: Mesh size 5 mm

Case-3: Mesh size 4 mm

4.3 Equivalent Elastic Strain:

Case-1: Mesh size 6 m

Case-2: Mesh size 5 mm

Case-3: Mesh size 4 mm

CONCLUSION

1. Static structural analysis and grid dependency test was carried out successfully on Bevel gear having following mesh sizes,

1. Case-1: Mesh size is 6 mm
2. Case-2: Mesh size is 5 mm
3. Case-3: Mesh size is 4 mm

2. From grid dependency test, the results of Bevel gear simulation for case-2 and case-3 are independent of mesh size. Hence, it validates that the solution obtained is invariant as the mesh is refined.

3. It also provides a justification for Mesh Independence and additional refinement is unnecessary.