A common difficulty in the simulation of complex fluid flow problems is that not every geometry can be well represented using a single, contiguous grid. This is especially true for the case of relative motion between components. Overset grids can be used to track relative motions with computational efficiency and recent advances in high performance computational fluid dynamics (CFD) software have enabled the coupled simulation of multiphase fluid flows and rigid body motions using overlapping overset grids.

Christine Klier PhD, Matthias Banholzer, Ludwig Berger, Kathleen Stock
CFD Schuck Ingenieurgesellschaft mbH.

A CFD method was developed and applied for the simulation of oil flow in a multiple rotating spur-gear system with emphasis on predicting the flow fields and pressure torques in the gearbox and between intermeshing gear regions. The multiphase flow in this problem was simulated using the Volume of Fluid (VOF) method and the results indicated that the applied CFD method offered a convenient and efficient way to study different oil filling levels in a gearbox with respect to their influence on oil flow and on the volume fraction of oil on gear flanks.

Introduction

Problems that arise when gear lubrication becomes insufficient are well known by every bicycle rider as well as car driver. Replacement of bearings, pistons, piston-rings, and gearwheels is not only time consuming but expensive and therefore gear lubrication is a significant concern for a wide range of industries that use power transmission. Prototype testing of gear-boxes does not always provide the necessary detailed information required for complex modern gears as they often carry greater loads with high rotational speeds. CFD model prediction is thus an effective tool for optimization of oil flow around the rotating components in a gear-box. The results from CFD simulations can help improve the efficiency of transmissions, reduce the friction between the gearwheels (pitting), minimize load-independent spin power losses, and assess oil splashing effects on gear housing.

The newly enhanced overset meshing capability that allows for multiple overlapping overset zones in CD-adapco’s STAR-CCM+, coupled with multiphase flow based on the VOF method, offers the necessary simulation environment for handling complex simulation problems such as rotating gear systems. This case study shows that this coupled approach can be successfully used to simulate oil flow in a rotating spur-gear system in a reasonable time with satisfactory results for evolving flow and pressure fields, and for oil distribution in the box and on gear flanks. Three various levels of oil and the influence of the rotational speed on lubrication were tested.

Method: Coupled Simulation of Multiphase Flow and Multiple Body Motion

The VOF method, which uses the Eulerian framework, was used to set up the multiphase flow simulation in this model. With this approach, the volume fraction continuity equation is solved for each Eulerian phase, while the immiscible fluid phases in the VOF model share velocity, pressure, and temperature fields which saves computational time compared to the Multiphase Segregated Model, another Eulerian approach available in the STAR-CCM+ simulation environment. Air entrapments and turbulence regimes, which are important in a gearbox with high rotational speeds, and oil splashing can be well represented by this approach.

For the simulation of multiple body motions, overset meshes (also known as Chimera grids) were used. The relative motion of one or more bodies, including arbitrary or tangential motions of objects in close proximity [1], can be simulated using this capability in STAR-CCM+. Each moving body is defined as a separate region and is represented by its own grid. The newest enhancement in the simulation platform allows for overset zones to also overlap with each other, an indispensable capability for the simulation of rotating intermeshing gears. While the solution is computed on all grids simultaneously [2], a background mesh serves as reference grid for all motions.

Gearbox and gearwheels were simulated including a symmetry plane boundary condition according to the mesh plane section shown in figure 1. The geometry was laid out as follows:
• Gear housing diameter (d) = 280 mm, length (l) = 200 mm
• Two gearwheels of each d = 130 mm, l = 58 mm.

The mesh (figure 1), consisting of polyhedral cells with five prism layer cells on wheel and housing surfaces, comprised of a total of about 5.4M cells. Furthermore, mesh refinement regions were defined to ensure adequate grid spacing in the overlapping zones. The smallest gap between the two rotating gearwheels was set to be around 1.5 mm. Due to high temperature operating conditions in many applications of gear lubrication, the decision was made to set fluid density and viscosity values based on oil at 100 °C. Three different initial oil level distributions were defined by the user field function functionality in STAR-CCM+. As shown in figure 2, for the low oil level, the first gear head was half covered by the oil sump while for the middle oil level, the teeth of second gear head already extended to the sump and for the high oil level, first gear head was completely covered by oil. One further detail of the set-up to be noted concerns the rotation rate of the gear system: to keep simulation time to a minimum, the rotation rate was set to a constant 2000 revolutions per minute (rpm). In practice, the rpm of gear systems frequently increases with time. To assess the importance of this effect, the influence of a linear ramp for the rotation rate was studied for the middle oil level and compared to the oil distribution in the box and on gear flanks for the case with constant revolution rates.

[1] Eppel, Deborah : “Epicyclic Gear Simulation with Overlapping Overset Mesh”, Dynamics, Issue 35, p 5, 2013.

[2] Schreck, Eberhard, Perić, Milovan and Snyder, Deryl (CD-Adapco): “Overset Grids Technology in STAR-CCM+®: Methodology and Applications”.