Resource efficiency and environmental protection are becoming increasingly important in modern transmission development processes, especially minimizing the CO2 footprint. These factors are critical for complying with regulatory limits and remaining competitive in a challenging market. Gearbox manufacturers are constantly increasing the power density of their transmissions to meet these requirements. This requires careful analysis and reduction of excess material reserves to optimize efficiency. The aim is to design gearboxes that meet customers’ lifetime needs with quiet, vibration-free operation. These are the key characteristics of good NVH performance.

Development process

Transmission development is an iterative process that often involves multiple design and test cycles to achieve the desired performance characteristics. Modern simulation methods play a key role, as they enable engineers to create virtual prototypes and predict the behavior of transmission systems under different operating conditions. This significantly shortens the development time and also contributes to the cost efficiency of the development process. Proven tools such as the FVA-Workbench [1] improve the design process with fast and reliable simulations.

Analysis and optimization

In transmission development, an understanding of the influences acting on the gearbox and the resulting loads is essential. Accurate knowledge of the load distribution across the face width [2] resulting from the tooth meshes and optimization of the microgeometry play a decisive role.

Load-related deformations and misalignments in gearboxes can lead to considerable misalignments in the gear meshes and thus to uneven width contact. Uneven load distribution across the flank is not only detrimental to the service life, but also worsens the noise excitation [3]. To avoid this, gear corrections must be designed in such a way that deformations are compensated for, i.e. a flat and uniform pressure distribution without stress peaks is achieved. This leads to low stiffness fluctuations in the tooth mesh and thus to lower gear excitation in the form of rotational path errors. This requires detailed consideration of all gear deformations.

As with other manufacturing parameters, gear modifications are subject to inconsistency. An ideal design for the nominal load and geometry may prove to be suboptimal due to tolerances in the finished component. Angle modifications in particular are subject to considerable variance. For this reason, good nominal geometry and robust design are both of critical importance. The following provides an example of how the robustness of the design can be evaluated.

Calculation example

The following example uses detailed gearbox system analysis to demonstrate how the FVA-Workbench can automatically generate an initial flank modification design and then use map generation with varying flank modification to consider the influence of production tolerances. This makes it possible to determine an optimal and robust design for the respective application.

This example uses a model of a reducer gearbox from an electric vehicle (EV), see Figure 1. In addition to detailed modeling of the cylindrical stages and the shaft-bearing system, the gearbox casing, wheel bodies, and differential cage were also modeled as FE components to precisely consider all stiffnesses and cross influences that affect the gear mesh and the load distribution across the face width. As the gearbox was tested on a test bench, the model also includes mounting brackets on the gearbox housing.

Figure 1: Two-stage reducer gearbox design without flank modifications

In the FVA-Workbench, scripts can be used to perform customized mass calculations. The easy-to-use scripting language makes it possible to automatically calculate extensive analyses. This can be used to define all parameters of a model, run calculations, and then export the results, for example to Excel.

If extensive calculation studies are frequently required during development, it is advisable to parallelize mass calculations in order to reduce computing time. A server solution such as the FVA SimulationHub is best suited for this. The server solution enables calculation jobs to be calculated on any number of instances on the server. The time saved with the SimulationHub is linearly scalable, i.e. two instances halve the computing time.

Automated design of basic flank modifications

A preconfigured script is used for an initial basic design of the flank modifications for all cylindrical gear stages in the gearbox in the FVA-Workbench. It first calculates the gearbox without modifications, and then analyzes the contact and the load distribution across the face width. It calculates the recommended modifications in the second step, such as the tip relief according to Sigg [4] and a helix angle modification for a centered contact pattern. These are integrated into the model and then a simulation is performed, which makes it possible to directly compare the gear mesh and the gear excitation with and without modifications, as shown in Figure 2.

Figure 2: The results of the automated basic flank modification design on the contact pressure distribution of the gear mesh and the transmission error, both without (left) and with (right) modifications.

This automated preliminary design already results in a centered tooth contact with reduced stresses and no stress peaks at the contact edges, which leads to significantly lower fluctuations.

Different gear tooth stiffnesses influence the transmission deviation, which means that it is not possible to directly compare the fluctuations of different gear designs and other gearboxes. Alternatively, the fluctuation of the tooth loads and the resulting excitation level can also be calculated, which makes it possible to perform a qualitative and quantitative comparison of different cylindrical gear stages and gearboxes.

Parameter study on the influence of manufacturing tolerances

In an additional study, the performance characteristics of the transmission error are determined for different torques T and variations of the four flank modifications: profile crowning Cα,
profile slope CHα, lead crowning Cβ, and lead slope CHβ (see Figure 3 and Figure 4). This makes it possible to determine whether the nominal design of the flank modifications also produces consistently low gear mesh excitations over the production-related tolerance range.

Figure 3: Transmission error at 300 Nm torque for four varied flank modification design parameters

The minimum and maximum transmission error are determined from the tolerance range results and the standard deviation is calculated as a measure of the robustness of the design.

This example shows that the design of the nominal flank modification leads to very little transmission error at 300 Nm torque. However, most of the results show significantly higher transmission deviation when manufacturing tolerances are considered, even though the tolerances of the four input parameters are symmetrical to the nominal design. At 100 Nm torque, the transmission error of the nominal design is significantly higher and is much closer to the mean value for all results. These effects cannot be predicted without detailed analysis of the tolerance. Significantly higher safety factors must also be used in these cases, which makes the design larger, heavier, and more expensive.

Figure 4: Transmission deviation of all variations in the tolerance range over the torque, frequency distribution for 100 and 300 Nm.

Conclusion

The FVA-Workbench can be used for simple, fast, and detailed calculation of complex transmission systems. All relevant details of the system in which the stiffness and behavior could potentially have an influence on the gear mesh are considered. The contact pattern can be optimized with targeted flank modifications, resulting in reduced stresses, longer service life, and low vibration – in other words, excellent NVH performance.

Flank modifications can nominally create an outstanding design under load. However, if the influence of manufacturing tolerances is not considered, there is a significant risk of producing inferior gearboxes. These may have to be reworked or rejected as scrap, which can lead to increased production costs, customer dissatisfaction, and reduced competitiveness.

With the FVA-Workbench the design process can largely be automated, allowing the user to focus on the important task of evaluating the results. This makes it possible to develop a robust gearbox in a short time and minimize the risk of problems during production. This not only saves time during development, but also lowers costs and material usage, thus lowering the CO2 footprint of the gearbox.

References

[1] FVA-Workbench "Module descriptions" available online at: FVA-Workbench - fva-service.de

[2] T. Placzek, "Load Distribution and Flank Modification in Spur and Helical Gear Stages," Technical University of Munich Institute of Machine Elements (FZG), Munich, 1988

[3] D. Mandt and H. Geiser, " Excitation behavior with flank corrections," FVA 338 I+II Heft 634, Frankfurt, 2001

[4] H. Sigg, "Profile and Longitudinal Corrections on Involute Gears," presented at the Semi-Annual Meeting of the AGMA (American Gear Manufacturers Association) 109.16, Chicago, October 1965

Author

Dipl.-Ing. Dennis Tazir
Gear Specialist, FVA GmbH

Dennis Tazir is a software developer and simulation expert with a background in transmission design and analysis. He has been working at FVA GmbH as a software developer since February 2020. Prior to that, he worked at Opel for over seven years as a senior simulation engineer for transmission design, having previously held similar roles at the TECOSIM Group for Opel. He began his career as a research assistant at the Fraunhofer Institute for Structural Durability and System Reliability LBF, where he worked for over four years. He holds a degree in mechanical engineering from the Technical University of Darmstadt (1999-2006).