Numerical Simulation on Gearbox Sloshing effect by varying the Clearance between two gears

Numerical Simulation on Gearbox Sloshing effect by varying the Clearance between two gears:

Objective: Here we need to analyze the flow pattern of the fluid for two different clearances of the same geometry. Geometries are with general clearance and increased clearance. Here we given two fluids, using water and oil need to do the simulation. In total four cases have to be simulated. We are including Volume of Fraction, and it\'s animation files have to be compared for all the four cases.

What is Sloshing effect:

• In fluid dynamics, slosh refers to the movement of liquid inside another object (which is, typically, also undergoing motion).
• Strictly speaking, the liquid must have a free surface to constitute a slosh dynamics problem, where the dynamics of the liquid can interact with the container to alter the system dynamics significantly.
• A lot of research has been done and today also organizations like NASA, ISRO, and some other Motor field Industries are very much interested in the projects related to the sloshing.
• Sloshing also an important factor considered while doing performance checking of cars, Space-craft vehicles, and On-road transport (Tankers) vehicles, etc.
• Selecting the lubricant in the gearbox, ball bearings, and oil tanks, etc will depend on the sloshing effect.

Case1: (A)

Gears type: Less-clearance

Lubricant: Water

Geometry:

• The above figure is the actual geometry and gears, a solid body including the fluid region.
• We need to remove the gears (solid bodies) from the domain.
• Here we have to do the simulation using a fluid. we need to extract the fluid region out of it.

• A fluid volume has been extracted here. But this will not help us to see the simulation results.
• For that, firstly select the plane tool and create three planes by using the axis-direction.
• Now, by using the Split body tool has to cut the body by selecting the plane in which direction we have to cut the plane.
• After cutting the body as a section plane in XY-direction, an actual fluid domain will appear. But that is 3D-geometry which we don\'t want.
• We are interested in doing the simulation in 2D.
• For that, select the face of geometry in XY-direction. Then an actual 2D plane will be selected which we want to run the simulation on. Copy that geometry when the only face is selected and paste it in as a new design in the Space claim and save it.
• This is the actual 2D geometry we desired to run the simulation.

• While giving the motion for both the gears, be cautious that increased clearance gear is different has a different center of gravity compared to other gear.
• We can also experience this difference where we are creating a region (cell adaption) for the lubricant fluid.

Meshing:

Element Size: 1mm

Number of Elements: 15875

Number of Nodes: 28327

Method: All Triangles Method

• For the meshing, an element size of 1mm is taken.
• All Triangles Method has been adopted.
• Also adopted the Capture Proximity, to capture the physics at the clearance or where two gears are merges which is very less in area.

Setup: (Serial)

General:

1. Solver - Pressure-Based
2. Time - Transient
3. Gravity - Yes (X = 0m/s, Y = -9.81m/s)

Models:

1. Multiphase - Volume of Fluid (Formulation - Implicit)
2. Viscous - K-Epsilon (Realizable, Enhanced Wall Treatment)

Mesh Models:

1. Dynamic Mesh - Yes

• Mesh Methods: Smoothing, Layering, Remeshing

2. Dynamic Mesh Zones: (Motion of gears)

• left_gear - left_motion
• right_gear - right_motion

3. Centre of gravity location

• For left_gear --> x= 0m, y= 0m
• For right_gear --> x= 0.115m, y= 0m

4. Adapt --> Cell Registers --> region. (Input Co-ordinates)

• Input Co-ordinates (m)

a) X-Min = -0.05612

b) X-Max = 0.17112

c) Y-Min = -0.0675

d) Y-Max = -0.0375

5. In Remeshing, setup helps us to give the appropriate mesh scale while the dynamic mesh is given in \'Mesh Scale Info\'. We need to give minimum, maximum and Maximum cell skewness values has to be given.

User-Defined:

• Functions --> Compiled --> Add (for adding the UDF file)
• Given C-code has been taken as the UDF.

#include \"udf.h\"

DEFINE_CG_MOTION(right_motion, dt, vel, omega, time, dtime)
{
	vel[0] = 0.0;
	vel[1] = 0.0;
	vel[2] = 0.0;

	omega[0] = 0.0;
	omega[1] = 0.0;
	omega[2] = 2.0e2; /* [rad/s]*/
}
DEFINE_CG_MOTION(left_motion, dt, vel, omega, time, dtime)
{
	vel[0] = 0.0;
	vel[1] = 0.0;
	vel[2] = 0.0;

	omega[0] = 0.0;
	omega[1] = 0.0;
	omega[2] = -2.0e2; /* [rad/s]*/
}

Materials:

1. Fluid

• Fluid - Air (Density = 1.225 kg/m3, Viscocity = 1.7894e-05 kg/m-s)
• Fluid - Water (Density = 998.2 kg/m3, Viscocity = 0.001003 kg/m-s)

Boundary Conditions:

• Keep them as they are. Don\'t need to change them.

Phases: (Physics - List/Show all phases)

1. Air - Preliminary phase
2. Water - Secondary phase

Methods:

1. Scheme - SIMPLE
2. Initialization - Hybrid
3. Patch

• Phase - water
• Variable - Volume of Fraction
• Registers to patch - region_0
• Value - 0

4. Run Calculation

• Time step size = 0.0001
• No. of Time steps = 1250

Results:

1. Graphs - Volume fraction (Water) - Contour (Note: Be sure that you change the phase from air to water. )
2. Animation - Volume fraction (Water) - animation

Solution:

Animation:

Link: https://www.youtube.com/watch?v=4a12ntkIgZk

Volume Fraction Contour:

• This the last or end frame of the time step in the simulation.
• By completing one rotation fluid is captured in each and every tooth of the gears.
• After some rotations, the fluid is getting settled slowly at the bottom of the sump.

Case1: (B)

Gears type: Less-clearance

Lubricant: Oil

Geometry:

• No change in geometry.
• Can run the simulation on the same geometry.

Meshing:

• We can continue with the mesh generated in the previous case.
• No changes needed in meshing.

Setup: (Serial)

Materials:

1. Fluid

• Fluid - Air (Density = 1.225 kg/m3, Viscocity = 1.7894e-05 kg/m-s)
• Fluid - Oil (Density = 871 kg/m3, Viscocity = 0.0406889 kg/m-s)

Phases: (Physics - List/Show all phases)

1. Air - Preliminary phase
2. Oil - Secondary phase

Methods:

1. Scheme - SIMPLE
2. Initialization - Hybrid
3. Patch

• Phase - Oil
• Variable - Volume of Fraction
• Registers to patch - region_0
• Value - 0

These were the only changes done for the case1 (B) simulation in the Setup.

Solution:

Animation:

Link: https://www.youtube.com/watch?v=wV2UARQGeM8

Volume Fraction Contour:

• This is the last or end frame of the time step in the simulation.
• By completing one rotation fluid is captured in each and every tooth of the gears.
• After giving the same time step values also, the fluid didn\'t get settled completely compared to the case1 (A).
• This is because the viscosity of the oil is more than the water.
• And there is not much diffusivity is there in the container because of the viscosity. Oil rarely mixes with the air compared to the water which is a great factor.
• By this, we can say that there will be very fewer air bubbles that can form.

Case2: (A)

Gears type: Increased-clearance

Lubricant: Water

Geometry:

• Everything is the same in the geometry like dimensions, number of tooths of gears, and container dimensions, etc.
• The only change is we observed is the center of gravity of the gears have been changed because while designing the axis is changed compared to the previous geometry which is less in clearance.
• The center of gravity is mentioned in the Setup.

Meshing:

Element Size: 1mm

Number of Elements: 16868

Number of Nodes: 30235

Method: All Triangles Method

• For the meshing, an element size of 1mm is taken.
• All Triangles Method has been adopted.
• Also adopted the Capture Proximity, to capture the physics at the clearance or where two gears are merges which is very less in area.

Setup: (Serial)

General:

1. Solver - Pressure-Based
2. Time - Transient
3. Gravity - Yes (X = 0m/s, Y = -9.81m/s)

Models:

1. Multiphase - Volume of Fluid (Formulation - Implicit)
2. Viscous - K-Epsilon (Realizable, Enhanced Wall Treatment)

Mesh Models:

1. Dynamic Mesh - Yes

• Mesh Methods: Smoothing, Layering, Remeshing

2. Dynamic Mesh Zones: (Motion of gears)

• left_gear - left_motion
• right_gear - right_motion

3. Centre of gravity location

• For left_gear --> x= -0.0684485m, y= 0m
• For right_gear --> x= 0.04855m, y= 0m

4. Adapt --> Cell Registers --> region. (Input Co-ordinates)

• Input Co-ordinates (m)

a) X-Min = -0.1612

b) X-Max = 0.28112

c) Y-Min = -0.0775

d) Y-Max = -0.0345

5. In Remeshing, setup helps us to give the appropriate mesh scale while the dynamic mesh is given in \'Mesh Scale Info\'. We need to give minimum, maximum and Maximum cell skewness values has to be given.

User-Defined:

• The same UDF file has been used for this case also.

Materials:

1. Fluid

• Fluid - Air (Density = 1.225 kg/m3, Viscocity = 1.7894e-05 kg/m-s)
• Fluid - Water (Density = 998.2 kg/m3, Viscocity = 0.001003 kg/m-s)

Boundary Conditions:

• Keep them as they are. Don\'t need to change them.

Phases: (Physics - List/Show all phases)

1. Air - Preliminary phase
2. Water - Secondary phase

Methods:

1. Scheme - SIMPLE
2. Initialization - Hybrid
3. Patch

• Phase - water
• Variable - Volume of Fraction
• Registers to patch - region_0
• Value - 0

4. Run Calculation

• Time step size = 0.0001
• No. of Time steps = 1250

Results:

1. Graphs - Volume fraction (Water) - Contour (Note: Be sure that you change the phase from air to water. )
2. Animation - Volume fraction (Water) - animation

Solution:

Animation:

Link: https://www.youtube.com/watch?v=8DNLt-ojQNk

Volume Fraction Contour:

• This the last or end frame of the time step in the simulation.
• By completing one rotation fluid is captured in each and every tooth of the gears.
• There is some effect of increased clearance on the lubricant if we observed. The rotation fluid is more compared to the previous case.

Case2: (B)

Gears type: Increased-clearance

Lubricant: Oil

Geometry:

• No change in geometry.
• Can run the simulation on the same geometry.

Meshing:

• We can continue with the mesh generated in the previous case.
• No changes needed in meshing.

Setup: (Serial)

Materials:

1. Fluid

• Fluid - Air (Density = 1.225 kg/m3, Viscocity = 1.7894e-05 kg/m-s)
• Fluid - Oil (Density = 871 kg/m3, Viscocity = 0.0406889 kg/m-s)

Phases: (Physics - List/Show all phases)

1. Air - Preliminary phase
2. Oil - Secondary phase

Methods:

1. Scheme - SIMPLE
2. Initialization - Hybrid
3. Patch

• Phase - Oil
• Variable - Volume of Fraction
• Registers to patch - region_0
• Value - 0

These were the only changes done for the case2 (B) simulation in the Setup.

Solution:

Animation:

Link: https://www.youtube.com/watch?v=fyh--hTzaZw

Volume Fraction Contour:

• This is the last or end frame of the time step in the simulation.
• By completing one rotation fluid is captured in each and every tooth of the gears.
• After giving the same time step values also, the fluid didn\'t get settled completely compared to the case2 (A).

Conclusion:

1. As mentioned in the object, all two cases have been simulated.
2. In any of the cases, the viscosity of the liquid plays an important role. As the viscosity of the oil is more than the water. The Splashing phenomenon is more in the water. Oil sticks to the teeth very well.
3. Coming to the diffusion point of view, when the rotation of gears starts air gets diffuse quickly into the water and in oil, it is taking a considerable amount of time.
4. This is because of oxygen Molecules presenting in both the air and water but not in the oil.
5. Water is a kind of material that, can quickly convert into droplets and air bubbles when it hits the walls and the gear bodies. But oil is not like that, it neatly sticks to the teeth of the gear.
6. The life of the gear is seen by its fatigue strength. It can be increased when we use oil as a lubricant.
7. When using the dynamic mesh, there will be a lot of deformation of elements when the gears comes in to contact come to contact. This difficulty is reduced or prevented by using the Maximum Cell Skewness size value as 0.5.