# Optimization of the Housing Shape Design for
## 2 Noise and Vibration Measurement of the Gearbox
### Order Analysis
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Equipment** & **Model** & **Specification** \\ \hline \multirow{4}{*}{Data acquisition} & \multirow{4}{*}{B\&K 3560-B-130} & 5 channel signal analyzer \\  & & Frequency range: 0–25.6 kHz \\  & & Input voltage range: 10 V (peak) \\ \cline{2-3}  & \multirow{2}{*}{DEWE 43A} & 16 channel signal analyzer \\  & & (8 analog inputs and 8 digital/counter inputs) \\ \hline \multirow{4}{*}{Torque meter} & \multirow{2}{*}{HBM T22/1 KNM} & Nominal torque: 1 kNm \\  & & Nominal speed: 20,000 rpm \\  & & Output signal: \(\pm\)5 V and 10 \(\pm\) 8 mA \\ \hline \multirow{4}{*}{Tachometer} & \multirow{4}{*}{B\&K MM-0024} & Combined infra-red transmitter/receiver \\  & & Maximum distance: 800 mm \\  & & Operating speed range: 20,000 rpm \\ \cline{2-3}  & \multirow{4}{*}{ONO SOKKI MP-981} & Magnetic detector \\  & & Frequency range: 1–20 Hz \\  & & Operating speed range: 20,000 rpm \\ \hline \multirow{4}{*}{Microphone} & \multirow{4}{*}{B\&K 4190-L-001} & Sensitivity: 50 mV/Pa \\  & & Dynamic range: 15–148 dB \\  & & Frequency range: 3.15–20,000 Hz \\ \hline \multirow{2}{*}{Accelerometer} & \multirow{2}{*}{PCB 352C68} & Sensitivity: 10.2 mV/(m/s\({}^{2}\)) \\  & & Frequency range: 0.5–10,000 Hz \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Specification of test equipment for order analysis. the test gearbox was 2650 rpm, the driving range was set to approximately 1.5 times to drive up to 4000 rpm. The frequency range for the frequency analysis was set to 4000 Hz to consider the fourth harmonic component for the GMF of the stage 1 gear pair. In the frequency analysis results of the sound pressure level and acceleration level, as shown in Figure 5, the frequencies at which the high noise and vibration levels appear were changed depending on the rotational speed. Therefore, the main noise of the gearbox was owing to the rotating components, such as the gears, bearings, and shafts, and the main noise was generated from the gears through comparison with GMFs. High noise around 3000 Hz did not appear in the vibration data, therefore this noise is not radiated noise caused by the structural vibration of the gearbox. Considering the constant frequency component without respect to the rotational speed and because the sideband component appears in a V-shape according to the rotational speed, this noise is considered to be the switching noise and its side band components of the inverter. In Figure 6, the frequency analysis was performed with FFT results of noise and vibration when the rotational speed was fixed at the rated speed of 2650 rpm. Two of the three main noises indicating  
Figure 4: Results of the noise and vibration measurement. (**a**): Sound pressure level; (**b**): Acceleration level. Figure 5: Order analysis of the noise and vibration with gear mesh frequency (GMF). (**a**): Sound pressure level; (**b**): Acceleration level. a noise above 60 dB (A) were the gear mesh components; the other noise was a value not present in the vibration data, indicating an inverter switching noise. The high noise values in the low-frequency range (300-400 Hz) are the resonance effect due to the natural frequency around 400 Hz when compared with the frequency response function results of the gearbox, as shown in Figure 7.  
From the measured noise data, only the GMF components were extracted, and the contribution to the total noise was analyzed according to the rotational speed of the input shaft. The GMF components were extracted up to the fourth harmonic component for the first and second stages of the gear train measured up to 4000 Hz. In Figure 8, the overall noise occurred from approximately 64 dB (A) to 82 dB (A) depending on the rotational speed of the input shaft. In the first stage of the gear train, the first and second harmonic components contributed to the noise at a level within 10 dB (A) compared to the total noise level.