From Gear Mesh to System: Advanced Prediction of Transmission Error
Eliminating common assumptions of single gear mesh calculations by considering the full system for higher-fidelity gear transmission error prediction and gearbox NVH analysis
The demand for lower emissions and greater electrification is intensifying in the realm of transmission applications, especially within the automotive industry. At the same time, there is a push to enhance performance and quality. This evolving landscape necessitates sophisticated structural design strategies,
focusing on lightweighting, durability, and the optimization of noise, vibration, and harshness (NVH). Fortunately, engineers now have access to ever-advancing tools that facilitate a CAE-led design approach, offering valuable insights at each stage of development with the appropriate level of detail. This approach minimizes design iterations and reduces the reliance on physical testing, ultimately saving both time and costs.
In a multi-fidelity modelling process, simpler and faster models are invaluable for early design exploration, such as assessing the impact of different tooth geometries on robustness. As development progresses, higher-fidelity models become crucial. Though they demand more detailed design inputs and are computationally intensive, their true value lies in the later stages of development, where they validate a select few, more refined design choices.
This paper delves into the analysis of gearbox transmission error and the resultant vibrations within a representative electric vehicle (EV) powertrain model. Transmission error (TE) quantifies the displacement of the gear mesh induced by the combination of varying tooth contact force, mesh stiffness, and flexibility of the system. Two levels of fidelity of TE analysis are considered in this paper: single mesh loaded tooth contact analysis (LTCA) and gearbox transmission error (GBTE) analysis. In addition, these approaches are combined in turn with two distinct tooth contact models—a Basic uncoupled 2D finite element model, and an Advanced coupled 3D finite element model. This gives us four different combinations to compare and contrast.
GBTE analysis, see Figure 1, is a quasi-static phased system analysis that evaluates the gearbox at multiple rotational angles. It performs an LTCA at each angle, accurately phasing all gear meshes. By considering system coupling and the phasing of all gears, GBTE analysis captures the complex interactions within the system, such as those occurring in planetary gearsets. It facilitates the calculation of the overall gearbox transmission error.

This analysis adopts less restrictive assumptions than single mesh calculations, allowing for variations in misalignment and torque through the gear meshes and system deflections during the meshing cycle. It considers changes in stiffness experienced by the gear mesh as the system rotates and recognizes that forces in one gear mesh can affect forces in others. Additionally, this approach allows the gear mesh to transfer moments in the misalignment direction, in addition to forces along the line of action, providing a fuller picture of the gear excitations, resulting in predictions of linear TE and tilt TE.