Optimize Gear Cooling with Volume of Fluid Simulations

How Toyota Improved Heat Flow in their Drive Units while Reducing Weight.

Phenomena: Oil Flow and Cooling in a Gear-Box

Potential Industry Applications:

  • Energy
  • Oil & Gas
  • Automotive
  • Manufacturing
  • Aerospace

Main Software: ANSYS Fluent

Analysis Type: CFD

Computing Power: HPC cluster network of 80 PC’s

Mesh: ~1.3 million cells (over mesh aka moving mesh)


  • Volume of Fluid (VOF)
  • Von Karman Analogy
  • Coupled to external airflow model


  • Bottom of casing was within safety limits
  • Top of casing was over safety limits
  • After redesign, temperature distribution was improved while reducing the drive unit’s total weight

How Toyota improved heat flow in their Gear Boxes

Oil in a gear box does more than just lubricate the system.  It also acts as a coolant, ensuring that the system doesn’t overheat or even ignite.

Gear boxes are common in many industries, including automobiles.  Accordingly, designers need a fast and economical way to optimize their cooling.  To simulate the cooling of a drive unit gear system, Toyota used ANSYS Fluent.

Mesh of gear volume. Note Image Courtesy of Ansys and not representative of Toyota’s design.

Why Gear Boxes Overheat

Heat in a gear system typically comes from friction. This friction arises primarily from the meshing of the gears and movement along bearings and shafts. This heat form the mechanism is transferred to the oil which in turn transfers heat to the enclosure before it is released to the surrounding environment.

“To assess the system you must not only make sure there is good lubrication wherever gears are touching. You must assess the cooling and churning losses of the oil. This will help to determine an optimal oil height around the gears,” explained Dr. Gilles Eggenspieler, Senior Fluid Product Line Manager at ANSYS.

To properly assess the drive unit, engineers have to not only assess the oil flow, but also the external air flow as well. Traditionally this would be a complicated simulation that required heavy computational power. Current methods allow the modeling of the oil flow and vehicle airflow to be done separately using data coupling. This allows for the simulation to be economically performed with fewer and more economic computing resources.

Simulating fluid oil in a Gear Box

Note Video Courtesy of Ansys and not representative of Toyota’s design.

Volume of fluid (VOF) simulation was used to study the surface interaction between the oil and air in the drive unit. This technique tracks the interface between the two immiscible fluids. “The surface can break up into droplets as surface tension is taken into consideration. As the liquid is tracked, the mesh will dynamically refine itself based on the location of the interface,” said Eggenspieler.  Once the interface region is known, the simulation can tell what areas to treat with oil characteristics and what areas should be treated as air.

“Around this interface, the mesh will be fine, typically a 2 to 3 cell gradient, which is needed to properly solve the simulation. Where there is no interface, the mesh will coarsen,” added Eggenspieler. This mesh refinement allows for the simulation to solve quickly. If instead the mesh were to be fine throughout the model, the simulation would take a lot of computing power to solve.

Example of a Zone of Re-meshing. Note Image Courtesy of Ansys and not representative of Toyota’s design.

In this simulation, gear geometry is modeled using a moving mesh. “To set up a moving mesh you must define a zone where re-meshing occurs. Ansys performs the surface movement first based on the set rotation speed. The system essentially looks at the simulation time step and multiplies that by the speed of displacement. The surface is then re-drawn and then re-meshed automatically,” explained Eggenspieler.

This means that the tooth geometry must be accurately modeled and meshed to ensure accurate fluid flow. Eggenspieler suggested, “If you start with a good mesh, everything will be okay. After all, the gear is pretty much symmetrical. For the initial mesh you must make sure you have an appropriate size function. As a general rule make the mesh size a tenth of the tooth height. However, every engineering firm will have their own rules here.”

However, this isn’t as easy as it sounds. Eggenspieler clarified, “It takes 2-3 trials to get the mesh that is optimized for accuracy and fast simulation. When you setup a mesh deformation and automatic refinement to track the oil/water interface, you only rarely get this optimum right the first time. Engineers must ensure they have the optimal simulation setup. First, this will save engineers a huge amount of time down the road and second, these best-practices can be re-used again and again for years.”

Once the fluid flow is determined, the Von Karman analogy can be used to determine the heat transfer coefficient of the oil. When this information is coupled with the airflow simulation, an accurate assessment of the drive unit heat propagation can be made.

To see an example of a gear system simulation (not representative of Toyota’s design) watch the video below:

Benefits of Volume of Fluid Simulations

The final simulation model took a network of about 80 PC’s to assess the 1.3 million cell mesh. The model showed that the bottom of the drive unit was cooling properly while the top was overheating. By re-positioning the drive unit’s cooling fins, Toyota was able to reduce the weight of the system while fixing the heating issues of the initial design.

But as good as simulations are, they are not absolute. They still have to be verified using lab tests. However, Eggenspieler pointed out, “We have really good accuracy between our simulations and lab tests. But at the end of the day people will still do lab tests. The point of simulation is: instead of testing 100 designs in the lab you might do only 3 or 4 now and do the rest of the testing virtually (i.e. simulation). Simulation can’t completely replace lab testing, but can be used for quick designs tests and performance assessments early in the design process – even before a first prototype is built. Using simulation, Toyota for example, were able to reduce the weight of their drive unit by 10% while improving the cooling.”

As for other VOF applications, there is a lot more you can simulate beyond gears. Other applications include boat movements, cavitation propellers, molten metal, waves, oil and gas, and more.

To learn more about ANSYS Fluent visit their website here. Or download their technical brief Simulation of Oil Lubrication and Losses in Gear Transmission System.

ANSYS has sponsored promotion of ANSYS Fluent on ENGINEERING.com. They have no editorial input to this post – all opinions are mine.  Shawn Wasserman

Written by

Shawn Wasserman

For over 10 years, Shawn Wasserman has informed, inspired and engaged the engineering community through online content. As a senior writer at WTWH media, he produces branded content to help engineers streamline their operations via new tools, technologies and software. While a senior editor at Engineering.com, Shawn wrote stories about CAE, simulation, PLM, CAD, IoT, AI and more. During his time as the blog manager at Ansys, Shawn produced content featuring stories, tips, tricks and interesting use cases for CAE technologies. Shawn holds a master’s degree in Bioengineering from the University of Guelph and an undergraduate degree in Chemical Engineering from the University of Waterloo.