Gear Sloshing Effect

The objective of this project is to perform gear sloshing simulation using Ansys Fluent for two different gearboxes with different clearance and two lubricants.

Sloshing is the phenomenon that happens within the closed container or when any object rotates or translates in the container that contains fluid. Gearbox sloshing is an important phenomenon to study whether proper lubrication is provided to all the teeth of the gear.

Geometry:

3D model of the gearbox is imported to SpaceClaim. Then, the fluid volume is extracted from the setup and is split using the midplane to obtain the 2D geometry upon which is simulations are performed.

Two gearboxes with different clearances are studied in the present project.

Mesh

All the triangles method is used for two gearboxes with an element size of 1mm and proximity was captured with 3 cells across the gap.

Physical Model

General	Transient Pressure-Based Gravity
Model	Turbulent (k-e model, Standard Wall Function) Multiphase (Volume of Fraction, Implicit)
Material	Fluid-Air Lubricant-Water & Oil
Monitors	Phases of Lubricants
Boundary Conditions	All the teeth are selected as left and right gears and are walls, with motion provided using UDF.

Now our main concern is to mark the region in which the lubricant resides when gears are not moving. For each of the gearbox geometry appropriate region is marked according to the coordinate system in which the geometry exists. Region marked for the lubricant for one of the gearbox geometry is as follows:

Appropriate phases are marked and zones are attached to their corresponding primary and secondary phases and the region for each of this phase is patched before running the simulation.

Before we run the simulation. Due to the movement of gears mesh needs to be resized correspondingly by using Dynamic Mesh option.

• At first, the dynamic Mesh Zones are created and the motion profile is provided to them using the uploaded UDF and their corresponding center of gravity location.

	Centre of Rotation
Left Gear	Right Gear
Model 1	(0,0)	(115,0)
Model 2	(-68.4485,0)	(48.5515,0)

• In the next step, mesh methods are provided by smoothing and remeshing properties

Mesh Methods	Options	Parameters
Smoothing	Diffusion
Remeshing	Local Cell Local Face	Minimum length Scale (m) Maximum length Scale(m) Minimum Skewness Maximum Skewness Size Remeshing Interval	0 0.0015 0.4 0.4 5

Time Step Calculation:

Given the angular velocity of the gears in the UDF is 200 radians/sec.

`(2 pi N)/60 = 200`

`N=1909.86` Number of rotations per minute

`N=31.831` Number of rotations per second

It implies each rotation takes 0.031416s

To obtain two full rotations and more, the following time step size and the number of time steps were taken.

	Time Step Size	Number of Time Steps
Case 1	1e-5	6300
Case 2	1e-4	630

Case 2, time step size was selected only for model 2 with oil as a lubricant and for the rest of the study, Case 1 data is used.

Moreover, for all the cases, the first-order upwind method is used in solution methods. And, the under-relaxation term for pressure and momentum are 0.3 and 0.7, respectively.

Results:

Model 1 (Water as Lubricant):

Model 1 (Oil as Lubricant):

Model 2 (Water as Lubricant):

Model 2 (Oil as Lubricant):

Discussion:

• The splashing of Oil is less than Water. Due to Oil having more viscosity than Water.
• Oil sticks to the teeth more than water. Thus oil is a good lubricant than water.
• Keeping in view limitation of Academic license, the sloshing was performed only for two rotations whereas to obtain industry-standard results, the study needs to be done for a higher number of rotations as well as considering the finer mesh.