Simulation of Gearbox Sloshing Effect
Introduction
In gearbox for the smooth running of gears and to increase the lifetime of gears, lubrication is required. The lubricant reduces the friction at the contact between the mating gears which increases the lifetime of gears. So for this, the lubricant should be properly provided to all the teeth of the gears. To understand the flow of lubricant in the gearbox a CFD simulation is required.
In this report, gearbox sloshing effect is simulated for two different lubricants(namely water and oil) and for two different clearances of gears.
Numerical Model
(1) Geometry:
The below figure shows the 2D geometry of gearbox with a small clearance between gears.
The below figure shows the 2D geometry of gearbox with increased clearance between gears.
(2)Mesh:
For the small clearance gearbox case, the mesh is made of triangles as shown in the below figure.
The mesh parameters for the small clearance gearbox case are shown in below table:
|
Element Type |
Triangles |
|
Element size |
0.5 mm |
|
Cell Count |
83983 |
The mesh quality for the small clearance gearbox case is shown in the below figure. The quality of the mesh is good which is above 65% and can proceed for further steps.
For the increased clearance gearbox case, the mesh is made of triangles as shown in the below figure.
The mesh parameters for the small clearance gearbox case are shown in below table:
|
Element Type |
Triangles |
|
Element size |
0.5 mm |
|
Cell Count |
89858 |
The mesh quality for the increased clearance gearbox case is shown in the below figure. The quality of the mesh is good which is above 65% and can proceed for further steps.
(3) Setup:
The gearbox sloshing effect simulations are performed for four cases which are:
(i) Small clearance gearbox with water as the lubricant
(ii) Small clearance gearbox with oil as the lubricant
(iii) Increased clearance gearbox with water as the lubricant
(iv) Increased clearance gearbox with oil as the lubricant
The properties of fluids used are shown in below table:
|
property |
Value |
|
Density |
Water: 998.2 kg/m3 Oil: 871 kg/m3 Air: 1.225 kg/m3 |
|
Viscosity |
Water: 0.001003 kg/m-s Oil: 0.04006889 kg/m-s Air: 1.7894e-05 kg/m-s |
The gravity is enabled whose value is given as 9.81 m/s2
Small clearance gearbox cases:
30710 cells are marked for the adaption of water or oil and the coordinates used for marking of the cells are,
|
X - min |
-56.12 mm |
|
X - max |
171.12 mm |
|
Y - min |
-67.5 mm |
|
Y - max |
-37.5 mm |
The coordinates of the CG of (a)left gear - (0,0,0) mm ; (b) right gear - (115,0,0) mm.
Increased clearance gearbox cases:
31378 cells are marked for the adaption of water or oil and the coordinates used for marking of the cells are,
|
X - min |
-123.95 mm |
|
X - max |
104.05 mm |
|
Y - min |
-68.5 mm |
|
Y - max |
-40.15 mm |
The coordinates of the CG of (a)left gear - (-68.4485,0,0) mm ; (b) right gear - (48.5515,0,0) mm.
Dynamic meshing is used for creating the rotation of gears. The remeshing parameters used for dynamic meshing are shown in below table:
|
Min. length scale |
1e-05 m |
|
Max. length scale |
0.0025 m |
|
Max. skewness |
0.5 |
|
size remeshing interval |
2 |
The input for rotation of gears is given using a user-defined function (UDF) which is shown below
#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]*/
}
The equations solved are the continuity and momentum equations (RANS equations). The turbulence model used in the simulations is realizable two equation k − ε turbulence model with enhanced wall treatment which is widely used for industrial applications because of its robustness. The computations are performed using ANSYS FLUENT with unsteady, double precision and a pressure based solver is used. The SIMPLE algorithm is selected for the velocity-pressure coupling. The second-order upwind scheme is used for the space discretization for higher accuracy and first-order implicit is used for time discretization. The VOF multiphase model with 2 phases is used with Implicit formulation and the sharpening interface modeling.
The time step chosen for the simulations is 5e-5 s
Results:
Case(1): Small clearance gearbox with water as the lubricant
The geometry used for this simulation is a small clearance gearbox and water is used as the lubricant.
The below image shows the residuals for the case(1) and the simulation is performed for 2100 time steps i.e., 0.105 s.
The gearbox sloshing effect for case(1) can be visualised in the below video where the volume fraction of water contour is used where red colour indicates only water and blue colour indicates only air.
Case(2): Small clearance gearbox with oil as the lubricant
The geometry used for this simulation is a small clearance gearbox and oil is used as the lubricant.
The below image shows the residuals for the case(2) and the simulation is performed for 2100 time steps i.e., 0.105 s.
The gearbox sloshing effect for case(2) can be visualised in the below video where the volume fraction of oil contour is used where red colour indicates only oil and blue colour indicates only air.
Case(3): Increased clearance gearbox with water as the lubricant
The geometry used for this simulation is an increased clearance gearbox and water is used as the lubricant.
The below image shows the residuals for the case(3) and the simulation is performed for 2100 time steps i.e., 0.105 s.
The gearbox sloshing effect for case(3) can be visualised in the below video where the volume fraction of water contour is used where red colour indicates only water and blue colour indicates only air.
Case(4): Increased clearance gearbox with oil as the lubricant
The geometry used for this simulation is an increased clearance gearbox and oil is used as the lubricant.
The below image shows the residuals for the case(4) and the simulation is performed for 2100 time steps i.e., 0.105 s.
The gearbox sloshing effect for case(4) can be visualised in the below video where the volume fraction of oil contour is used where red colour indicates only oil and blue colour indicates only air.
Conclusions
The simulation of gearbox sloshing effect with different clearances and different lubricants is performed and visualised.