Gearwheel sensitivity analysis

Identification of the noise source

Identification of the noise source

IGW POWER drives solutions for gears, gearbox assemblies and prismatic parts. Although most known for its efficient and reliable products for the rail industry, the company also supplies a diverse amount of applications and markets from construction machinery to medical devices.

Challenge

Besides the overall reliability and durability, the noise characteristics are one of the key topics for the gear and gearbox design. This parameter is expected to be as low as possible since it strongly affects the operability of the final product and its environment.

The current state of the art in gear noise analysis is the finite element method approach. For the initial stages of the design, it is important to quickly identify parameters of the design crucial for its noise characteristics. However, the cost of such an activity cannot be excessive from the perspective of time and resources. This is why the fast Uptimai Preliminary analysis tool was used for the first sensitivity analysis of the gearwheel.

The goal of this preliminary study was to evaluate the sensitivity of noise-related phenomena to 6 geometrical parameters of the gearwheel. Using the method of Uptimai, only 19 computations were required to reach this goal, which can be later used as a baseline for follow-up design steps.

Fig. 1. Example of the analysed gearwheel type

Solution

This type of very fast analysis was also used because there was no fully automatic connection between the wheel geometry model of the wheel, the meshing software and the MSC Nastran that provided the amplitude-frequency characteristics of the gearwheel noise. This increased the cost of each simulation and therefore only very few were available to be made. The main focus of the study was on the maximum noise level (equivalent radiated power, ERP), frequency of this ERP peak, and the probability of resonating frequencies to occur.

Fig. 2. Example of the extracted amplitude-frequency characteristics

During this process, it is the Uptimai algorithm that decides which input parameter combinations have to be computed in the next step. These input data are provided in small batches, where every new iteration is proposed based on the results of the previous ones. This adaptivity gives the analysis the key advantage in accuracy and cost over traditional methods of statistical analysis.

Fig. 3. Sensitivity analysis of the equivalent radiated power and its frequency

As a result, the Uptimai sensitivity analysis was presented in the post-processing environment, showing the effect of wheel geometry parameters on the overall variance of results. For three of four observed output variables, parameters defining the gearwheel rib thickness (especially A1) are among those most influential. E.g. for the frequency with the highest ERP level (output 2), the effect of other parameters was found to be negligible.

Fig. 4. Sensitivity analysis of output related to resonating frequencies

However, the distance of holes in the rib from the axis and their number affects the maximum of ERP as well. The number of holes in the rib, R9, becomes partially important when finding if the last observed ERP peak frequency is in the resonance with the previous one, the number of holes is the key input parameter. (see Fig.1 for reference).

The only parameter neglected for all outputs is the hole diameter D_6. Other input parameters related to holes in the rib are probably relatively much more significant than this one and D_6 is just “hidden in their shadow”.

This, and other findings as well, can be gathered within the following analysis steps. A simple model will be created from additionally computed samples, allowing to find the effect of interactions between input parameters. Then, the creation of the full statistical model reveals the complete set of insights into the design.