A GPU-Accelerated Fully Coupled Fluid-Solid-Thermal SPH Solver for Industrial Gearboxes: Application to Lubricant Flow and Heat Transfer in a Bevel-Helical Reducer

TL;DR

This work delivers a GPU-accelerated, fully coupled fluid–solid–thermal SPH framework implemented in SPHinXsys to simulate splash lubrication, churning losses, and heat transfer in industrial bevel–helical gearboxes. It combines governing equations for viscous flow with a weakly compressible SPH formulation, physics-driven relaxation, Riemann-based WSPH solvers, density re-initialization, boundary treatment, and thermal diffusion, plus a novel contact-factor metric for oil–gear interaction. Validation against Type C-PT FZG gearbox churning-loss data and a two-material slab conduction problem demonstrates accuracy in transient lubrication and heat transfer across interfaces. A comprehensive parametric study reveals that speed dominates churning losses and heating, while immersion depth and viscosity modulate effects by 10–20% and can reverse between low- and high-speed regimes; GPU acceleration yields a 7–9× speedup over CPU, enabling multi-million-particle simulations. The framework provides a practical, open-source tool for gearbox design and optimization, with future work to incorporate frictional heat generation and turbulence-enhanced heat transfer for higher-speed regimes.

Abstract

This study presents a GPU-accelerated, fully coupled fluid-solid-thermal Smoothed Particle Hydrodynamics (SPH) framework for high-fidelity analysis of splash-lubricated gearboxes. A series of thermo-fluid simulations of a bevel-helical gear reducer were conducted by varying shaft speed, oil immersion depth, and lubricant viscosity to evaluate their influence on splash dynamics, churning losses, and lubricant temperature rise. The results show that churning losses increase by nearly an order of magnitude as the speed rises from 150 to 600 rad/s, while the corresponding lubricant temperature rise becomes approximately three to four times smaller. Variations in immersion depth and viscosity adjust the heating rate only modestly-typically within 10-20%-with their influence reversing between low- and high-speed regimes. The GPU backend provides a 7-9 speedup over a high-performance desktop CPU, enabling multi-million-particle, full-gearbox thermo-fluid simulations without specialized hardware. These findings demonstrate the feasibility of high-fidelity thermal analysis of industrial gearboxes and provide quantitative insight into the coupled splash, churning, and heat-transfer mechanisms that govern gearbox thermal performance.

Figures (12)

• Figure 1: Validation gearbox setup and simulation results from SPHinXsys compared with experimental data. (a) Photograph of the experimental type C-PT FZG gearbox. (b) Churning losses at various oil sump temperatures of simulation vs. experimental
• Figure 2: Heat transfer in two slabs (a) The geometry and initial temperature settings of the slabs. (b) Temperature profile on the line of y = 0.25 at t = 2.0
• Figure 3: Geometry and internal structure of the Bevel–Helical Gear Reducer. (a) External view of the gearbox housing. (b) Internal configuration showing the three-shaft system and gear pairs with rotational directions.
• Figure 4: Mesh independence verification for churning loss torque and lubricant temperature arising. (a – c) Torque histories for Shafts 1–3 at particle spacings $d_p$ = 0.001, 0.0012, and 0.002 m. (d) Average lubricant temperature for the same resolutions.
• Figure 5: Churning-loss torque on Shafts 1–3 under two operating speeds. (a-c) Torque histories for Shaft 1-3 when Shaft 3 rotates at $\omega = 150$$\mathrm{rad/s}$. (b-f) Torque histories for Shaft 1-3 when Shaft 3 rotates at $\omega = 600$$\mathrm{rad/s}$. The horizontal axis is normalized by the number of revolutions completed by each shaft (10 revolutions of Shaft 3 correspond to 26.67 of Shaft 1 and 16.67 of Shaft 2).