Simulative evaluation of heat transfer and surface temperature distribution of an industrial gear unit

Transparente 3D-Darstellung eines Getriebes mit Zahnrädern und Ölfilm im Inneren des Gehäuses. — Digital twin of an industrial gearbox X3K.e using DIVE [1].

SEW-EURODRIVE employs a multi-physics simulation approach to optimize thermal behavior in gear units. Internal oil flow and heat transfer are modeled using Smoothed Particle Hydrodynamics (SPH) via software DIVE [1], enabling accurate representation of complex, transient fluid dynamics, see Fig. 1. For external convective cooling, particularly under forced convection, Finite Volume Method (FVM) simulations are performed in ANSYS Fluent [2]. Coupled heat transfer coefficients from both domains are mapped onto a Finite Element Model (FEM) in ANSYS Mechanical to resolve surface temperature distributions. Experimental validation, including thermographic imaging, confirms model fidelity. This integrated CFD-FEM workflow enables predictive thermal design, reducing physical prototyping and extending lubricant service life.

Validation of Surface Temperature Distribution – experimental setup:

To validate thermal simulation models, a three-stage industrial gearbox of the X.e-series was experimentally investigated under steady-state operating conditions at an input speed of 1500 rpm. Surface temperatures were acquired using contact sensors and infrared thermography (see. Fig. 2), both without and with an auxiliary fan mounted on the input shaft. The implementation of forced convection resulted in a measurable reduction of surface temperatures. The obtained data provide a robust basis for the calibration of thermal models and the design of optimized cooling strategies in industrial drivetrain systems.

Fig. 2: Test run of industrial gearbox X3K.e without fan/surface temperature distribution

Validation of Surface Temperature Distribution – Results without external cooling:

Fig. 3.: Oil distribution during operation

This first study investigates heat transfer in a gearbox operating without an active cooling system. The simulation assumes a realistic oil level, ensuring all bearings are in contact with oil at standstill. At a rotational speed of 1500 rpm, transient flow simulations reveal that a quasi-steady-state condition is reached after about one second. In the high-speed region of the first stage, oil is vigorously splashed onto the inner housing walls, indicating efficient heat transfer, see Fig. 3. In contrast, the low-speed shaft region lacks oil contact, suggesting limited heat transfer driven only by conduction and oil mist.

Initial evaluation of local heat transfer coefficients (HTC) is based on temperature gradients. High HTC values are observed in the oil sump and high-speed bearing zones, while other areas show minimal heat exchange due to limited oil movement. However, this method underestimates HTC values, especially in regions with splashed oil, due to its sensitivity to particle density and size.

Fig. 4.: Inner HTC distribution using Nusselt number correlations

To improve accuracy, a Nusselt number-based approach is introduced, linking HTC directly to local wall velocity. This method yields more realistic values in high-speed regions but underestimates HTC in low Reynolds number zones, see Fig. 4. Two hybrid solutions are proposed:

using the maximum HTC values from both methods with a minimum threshold (e.g., 60 W/m²K) for oil mist regions
applying a Gaussian function to adjust HTC values in low-speed areas.

The computed HTC distributions are subsequently imported into ANSYS Mechanical, where they are mapped onto an independent structural mesh using spatial coordinates. Outer HTC values are calculated via analytical correlations and adjusted to match total no-load power losses, compensating for the only roughly known external heat transfer distribution on the test rig.

A comparison between the simulated surface temperature distribution and thermal imaging from experimental test runs reveals a high degree of correlation for both methods. The Gaussian-modified HTC approach slightly enhances the accuracy in regions with steep temperature gradients. This method results in a mean deviation of approximately 0.5% for the first hybrid approach and around 2% (less than 1.5 K) for the second, demonstrating its robustness and suitability for capturing realistic thermal behavior in oil-lubricated gear systems operating without active cooling.

Fig. 5.: Surface temperature distribution using the Gaussian-modified HTC approach

Validation of Surface Temperature Distribution – Results with external cooling:

To determine the internal HTC, oil distribution is simulated under adapted boundary conditions. The external HTC is influenced by increased air velocity due to fan cooling, which is typically unknown. Therefore, an additional simulation using ANSYS Fluent, based on the finite volume method, is required. Two approaches are used:

simulate air velocity and convert it to HTC using empirical correlations
directly calculate HTC using thermal boundary conditions, see Fig. 6.

Although more computationally intensive, the second method is used, because it offers better integration of the results in ANSYS Mechanical.

Accurate CAD modeling and defining a “Frozen Rotor” interface are essential for simulating the rotating fan and surrounding airspace. A stationary simulation using the SST turbulence model significantly reduces computational effort. Despite local discrepancies, the averaged simulated and measured air velocities show good agreement.

Fig. 6: Air velocity distribution / HTC distribution

The resulting surface temperature distribution from the simulation in ANSYS Mechanical closely matches experimental data, especially when using the direct HTC calculation. Deviations occur mainly in high-gradient areas, but overall agreement is satisfactory, see Fig. 7. Both methods yield similar results, with an average deviation of about 3%.

Fig. 7: Surface temperature distribution using external cooling

The proposed simulation methods, whether or not a fan is used, accurately predict the surface temperature distribution of the gearbox, validating their effectiveness for thermal analysis in industrial applications.

Conclusion

This study presents and validates a method to determine the surface temperature distribution of an industrial gear unit. The internal heat transfer coefficient (HTC) is calculated using DIVE software based on SPH, with Nusselt correlations applied in high-velocity regions. External HTC is derived from Nusselt correlations for natural convection and radiation, or via ANSYS FLUENT when a fan is used. Surface temperatures are computed in ANSYS Mechanical using internal/external HTC and bearing power losses. Simulated results align well with measurements, especially without fan cooling. The approach demonstrates the potential of numerical simulations to reduce physical testing and support sustainable gear unit development. Detailed information will be presented on International Conference on Gears 2025, Munich.