Gear whine is a major source of unwanted noise in automotive applications. It is tonal in nature, which makes it more apparent to the human ear than other stochastic noise mechanisms. Prediction of gear whine behavior in automatic transmissions is a particularly complex problem, where the conventional FEA approach precludes the rapid assessment of “what if?” scenarios due to the slow pace of model building and solution times. This paper will present an alternative approach, which is a fully parametric functionality-based model, including the effects of and interactions between all components in the transmission. It will be shown how the transmission error in all gear pairs can be predicted, and how this can be used to excite the transmission model dynamically to predict the vibration response in any part of the system, including the housing.

### 1: Introduction

### 2: Modeling

#### 2.1: Bearings

#### 2.2: Non-uniform Components

#### 2.3: Gears

#### 2.4: System Model

### 3: Analysis

#### 3.1: Static Analysis

The non-linear analysis can be completed in a couple of minutes. The results show the full six degree of freedom deflection of the system, the rotational speeds of and forces acting on all components, gear and bearing misalignments. Additional results, such as the expected damage that each component will suffer, are also calculated.

#### 3.2: Planetary Transmission Error Analysis

A key point is that the analyses are solved simultaneously. For example, it is not possible to solve the shaft-bearing system to predict the mesh misalignment and then use this misalignment to predict the transmission error at the gear mesh. This is because the details of the tooth contact are not only influenced by the misalignment, but the misalignment is influenced by the tooth contact.

### 4: Parametric Investigation

#### 4.1: Investigation 1

A single load case, first gear, 40Nm on the input shaft, was analyzed. The influence of bearing outer race displacement on the predicted gear mesh misalignment and transmission error of the first gear pair is shown in main effect plots [14] in Figure 8. It is clear from these graphs that the largest influence on the mesh misalignment and transmission error is from the left bearing, and a movement in the Y direction has the greatest effect.

This is a simple example and shows how the modeling approach can be used to give a rapid understanding of the effects of tolerances. In a more complete study it would be necessary to investigate the effects of all bearings on all gear meshes. This type of comprehensive study could easily be completed in less than four hours.

#### 4.2: Investigation 2

It is clear that the pre-load of this bearing has a significant effect on the misalignment. For each candidate a modal analysis was completed [12] and the model excited with the predicted transmission error. The housing vibration was predicted at a position expected to be a significant source of airborne noise, see Figure 9. The housing vibrations for the six variants are shown in Figure 10.

It is clear that the variation in the preload has a significant effect on the housing vibration. This is mainly due to the change in bearing and system stiffness modifying the natural frequencies of the gearbox and changing the transfer paths from gear mesh to housing.

### 5: Conclusion

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