Challenge on Gearbox Sloshing effect

Aim

The project aims at simulating the flow characteristics of lubricant substance in a 2D gear box to study the sloshing effect. The study is extended by using two different lubricants, namely, engine oil and n-heptane and by varying the immersion volume to study the effects on fluid flow.

1. Introduction

A gear is a mechanical component with cut teeth which meshes with a similar toothed component to transmit torque. Through the gear ratio, change in torque is achieved and a mechanical advantage is created. Gears find applications in several machines as transmission systems, also called a gear train and the most widely known application being the manual transmission in an automotive vehicle. The transmission system consists of meshing of different gears inside a casing. This assembly of gear is lubricated using suitable transmission oils. Lubricant oil is usually an organic compound used to reduce friction between the gear teeth and ultimately reduces the heat generated between the components.

2. Theory

2.1 Fluid sloshing effect

The movement of a fluid inside an object is termed as sloshing. This motion is caused due to the inertial waves which act inside the fluid rather than the surface caused by the restoring force developed. The sloshing of fluid exerts stress and hydrodynamic pressure on the walls of the object and can result in failure of the assembly.

In case of the gear box, the lubricant oil is subjected to motion due to the rotation of the gears. The restoring forces developed due to rotational motion of the fluid results in development of inertial waves. These inertial waves cause irregular fluid flow of the lubricant affecting its ability to lubricate the gear mesh throughout the range of motion. Also, the forces and hydrodynamic pressure exerted on the gears and casing due to the sloshing effect could cause wear and tear and reduce the fatigue life of the transmission system.

The property which influences the sloshing effect is the viscosity of the fluid. Higher the viscosity, lesser is the sloshing effect observed in the system.

2.2 Dynamic meshing

The dynamic mesh model is the continuously changing of the mesh grids or boundaries of the cell zones to model flows with prescribed or unprescribed motion over the given time interval. The motion is described using the 6DOF (degrees of freedom) solver and the new positions of the domain boundaries are calculated. This is used to update the mesh grids. In order to use dynamic mesh model, the case must define a starting volume mesh and assign motion to the specific face or cell zones using named selections.

To update the mesh grids, there are three different update methods:

a) Smoothing methods

This update method correlates the edges of the mesh grid with smoothing parameter, such as spring constant (Spring smoothing), adjustment of mesh vertex to geometric center of neighboring vertices (Laplacian smoothing), is used to determine the boundaries of grid at time t. For boundary layers to retain the height of the grids at the walls, the boundary layer smoothing method is used

b) Layering

This method includes addition or removal of layers of cells adjacent to a moving boundary. It is used for hexahedral or wedge mesh zones

c) Re-meshing

For tetrahedral and triangular mesh zones, the smoothing method applied may resulted in deformed mesh grid with poor mesh quality. Thus, local re-meshing is applied which divides the mesh grid with skewness above a certain user-defined limit into smaller mesh grid of improved quality. The CFD software such as ANSYS also allow the user to specify the minimum and maximum length of the mesh grid which are to be excluded from re-meshing to optimize processing expenditures.

Dynamic mesh models are applied in problems of automotive, aerospace, chemicals and environment industries. It can be used to study cases where the domain consists of components subjected to motion resulting in displacement and change in the characteristics after a given time interval. Some of the major applications include IC engine combustion simulation, wind turbines, spacecraft propellants etc.

2.3 UDF in ANSYS Fluent

UDF stands for User defined Functions. It is a program written in C programming language used to define boundary conditions, materials, source terms, initialize a solution, enchance post processing and so on. UDFs are used to enhance the functions of the software in addition to the standard features provided. UDFs must contain a header file or library which is compiled in ANSYS Fluent and read during setup.

The given study uses a UDF for defining the angular velocities of the gear edges.

#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]*/
}

In the above code, the library used is udf.h. It contains the definitions for DEFINE macros. For defining angular velocity to the gears, we use predefined macros DEFINE_CG_MOTION.

It includes six input arguments namely, UDF name, Dynamic Mesh Pointer, linear velocity, angular velocity, current time and time step. Inside the definition, the array index 0, 1 and 2 correspond to x-axis, y-axis and z-axis respectively.

3. Solving & Modeling approach

The first step involves volume extraction from the 3D gear box. Considering the processing limitations, the 3D volume is split and a 2D face is copied and used to generate mesh. Triangular method is applied in order to improve the mesh quality. The edges of the left and right gear are selected and the named selection is created.

The case is setup using UDF and the dynamic mesh is defined with smoothing and local re-meshing. The immersion level is defined using Adapt mesh wherein a region is created to encompass the immersed fluid. The turbulence model used is K-Ɛ realizable with enhanced wall treatment. The standard initialization is done and the case is run.

4. Pre-processing and setup

4.1 Geometry

The 3D model of the gear box is used to extract volume. From the extract volume the 2D face is selected.

Fig 1- 3D model of gear box

Fig 2- Sectional view of 3D model

Fig 3- Extracted fluid volume

Fig 4- 2D model of fluid volume (at the mid plane)

4.2 Mesh

The mesh method is applied to obtain triangular mesh grids as it has the highest quality for a 2D case. The element size is defined as 1 mm and the capture proximity function in sizing dialog box is checked to ensure refined mesh near the gear contact regions.

Fig 5 Mesh generated

The named selections are defined for left and right gears by selecting the edges.

Fig 6- Named selection

4.3 Setup

4.3.1 Models:

Mutliphase- Volume of Fluid-Implicit Formulation

Viscous – k-Ɛ Realizable with enhanced wall treatment

4.3.2 Materials

Air

Fig 7- Material properties of air

Engine oil

Fig 8- Material properties of engine oil

n-heptane (c7h16)

Fig 9- Material properties of n-heptane

4.3.3 Dynamic Mesh

Mesh methods:

Smoothing: Diffusion

Remeshing: Local cell

Fig 10- Parameters of local remeshing

Dynamic Mesh zones:

Rigid body type for the named selections- left gear and right gear. The motion is assigned using UDF and the center of gravity locations are mentioned for the both gears.

4.3.4 Initialization and time step

The standard initialization is used across all zones and the patch is created for the volume fraction of lubricant in the immersion region. The immersion region is defined using Adaption Controls where a cell register of region type is created

Fig 11- Cell register for immersion level

Time step is defined as 1e-04 and the simulation is run.

4.3.5 No. of time steps

Considering the angular velocity of ω = 200 rad/s, we calculate the number of rotations per second using

ω = 2πN / 60

N = 1911 rpm = 31.84 rotation/second

Using this, the time for one complete rotation can be calculated as 0.031 seconds.

Due to the processing limits, the simulation captures only 3 complete rotations for which simulation time is 3*0.031= 0.093 seconds. Thus, the number of time steps taken is 1000 (Simulation time/Time step size)

5. Results

5.1 Animation

5.1.1 Lubricant- Engine oil with 20% immersion level

5.1.2 Lubricant- Engine oil with 30% immersion level

5.1.3 Lubricant- n-heptane with 20% immersion level

5.1.4 Lubricant- n-heptane with 30% immersion level

5.2 Comparison of immersion volume

The increase in the immersion level from 20% to 30% of the total height results in more lubricant carried by the lower teeth of the gear. At the mesh region of the two gears, the intermixing of the lubricant with air is enhanced due to more sloshing of lubricant from the gears to top wall of the casing. This phenomenon is called as oil churning which results in the lubricant becoming spongy over time due to the oxidation of the oil. The increased sloshing also results in increased temperatures of lubricant oil. Due to this, the viscosity decreases and the lubricant properties of the oil are affected severely.

However, it can be observed that more is the immersion level, more amount of lubricant is displaced and better is the lubrication at the meshing of the gear. Hence, an optimal immersion level must be determined at the design stage to ensure effective lubrication with minimal sloshing effect.

5.3 Comparison of two different fuels

The two lubricants used in the given project are engine oil and n-heptane with viscosity being 1.06 kg/m-s and 0.000409 kg/m-s respectively. That is, the viscosity of n-heptane is very low compared to engine oil. From the animations, it can be observed that the sloshing effect is more in case of lower viscosity lubricant- n-heptane. Considering the wear and tear of the walls due to the sloshing effect, it can be inferred that low viscosity lubricant is not suitable. Another caveat of using a lower viscosity lubricant is the effect of temperature increase during operation of gear system. As the temperature rises, the viscosity is further reduced and this causes thinning of lubricant at the contact surfaces in the mesh region. This in turn exposes friction points between the gears and causes wear and tear. Thus, very low viscosity will result in reduction of the lubricity of the transmission system.

However, it can be observed that due to the sloshing, the lubricant is displaced towards the top wall of casing from the mesh region. The lubricant flow along the side walls and is re-circulated into the bottom slump. Since viscosity of the engine oil is high, the time taken for the lubricant to reach the slump is more than that of n-heptane. Due to this, less lubricant is available for displacement by the gear which in turn affects the lubrication of the contact region. In other words, the lower viscosity contributes in enhanced re-circulation of lubricant and improves lubricity of the transmission system.

6. Errors observed during simulation

a) Negative cell volume detected

The error means that the displacement of the mesh grid in one step has been significant resulting in collapse of the cells. To solve the error, check the following:

• Named selection of boundaries are continuous
• Mesh generated is of high quality
• Time step considered is small
• Local re-meshing parameters are set so that poor quality mesh is captured effectively

b) Floating point error

This error occurs when the solver compiles an arithmetic operation which has no solution or is a mathematical error. The error can be resolved by ensuring high quality mesh and limiting the time step in the solver

7. Conclusion

The following conclusions are made from successfully simulating the sloshing phenomena in gear box with two different lubricants and two different immersion levels:

a) Considering lubricity of the transmission system, lower viscosity and higher immersion levels are recommended. In the given study, n-heptane with 30% immersion level shows maximum lubricity.

b) Sloshing effect is detrimental to the system due to the wear and tear of the surface walls, oxidation of the lubricant oil. To reduce sloshing effect, lubricant oil of higher viscosity index and lower immersion level in the gear box are recommended. In the given study, engine oil with 20% immersion level shows minimal sloshing.

Thus, to design a gear box, a balance between the lubricity and the sloshing is to be established by selection of lubricant with appropriate viscosity.