# Experimental Analysis of Transformer Core Vibration and Noise under Inter-Harmonic Excitation
## 3 Results and Discussion
### Inter-Harmonic Frequency Influence on Core Noise  
In the noise characteristic research, similar to the vibration characteristic experimental scheme, the inter-harmonic content in the excitation is 5% of the fundamental wave, that is, \(m\) = 0.05. The inter-harmonic frequencies contained in the excitation are respectively taken as: 2, 5, 10, 15, 20, and 40 Hz. Under different inter-harmonic frequency conditions, gradually increase the voltage amplitude from 0 to 50 V, use a sound level meter to record at different measurement points, and use supporting software to perform spectrum analysis on the measured values. The change of the transformer noise level with the increase of the excitation fundamental wave amplitude is shown in Figure 10 when the inter-harmonic content is 5%.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Inter-Harmonic Content**} & \multirow{2}{*}{**Frequency (Hz)**} & \multicolumn{3}{c}{**Peak-to-Peak Vibration Displacement (nm)**} \\ \cline{3-5}  & & **Measuring Point 1** & **Measuring Point 2** & **Measuring Point 3** \\ \hline \multirow{3}{*}{1\%} & 5 & 177.8 & 157.3 & 179.6 \\  & 20 & 175.2 & 162.0 & 174.5 \\  & 40 & 168.8 & 165.5 & 172.2 \\ \hline \multirow{3}{*}{3\%} & 5 & 283.6 & 242.1 & 276.3 \\  & 20 & 198.4 & 177.4 & 205.0 \\  & 40 & 165.3 & 170.2 & 167.9 \\ \hline \multirow{3}{*}{5\%} & 5 & 320.6 & 281.5 & 323.4 \\  & 20 & 236.7 & 200.1 & 235.7 \\ \cline{1-1}  & 40 & 198.1 & 180.3 & 193.8 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Peak-to-peak vibration displacement with voltage amplitude of 41.18 V.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Inter-Harmonic Content**} & \multirow{2}{*}{**Frequency (Hz)**} & \multicolumn{3}{c}{**Peak-to-Peak Vibration Displacement (nm)**} \\ \cline{3-5}  & & **Measuring Point 1** & **Measuring Point 2** & **Measuring Point 3** \\ \hline \multirow{3}{*}{1\%} & 5 & 179.2 & 158.6 & 178.2 \\  & 20 & 177.7 & 159.9 & 173.3 \\  & 40 & 170.3 & 164.3 & 176.6 \\ \hline \multirow{3}{*}{3\%} & 5 & 324.5 & 290.6 & 328.7 \\  & 20 & 227.1 & 190.2 & 221.1 \\  & 40 & 200.3 & 173.1 & 206.3 \\ \hline \multirow{3}{*}{5\%} & 5 & 390.6 & 315.5 & 383.3 \\  & 20 & 264.4 & 246.1 & 260.1 \\ \cline{1-1}  & 40 & 231.0 & 202.7 & 225.5 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Peak-to-peak vibration displacement with voltage amplitude of 44.12 V.  
The overall change trend of the noise sound pressure level of the transformer core model is similar to the conclusion obtained from the vibration experiment. When the voltage amplitude is less than 25 V, the noise is basically environmental noise, and the influence of inter-harmonics is small. However, as the voltage amplitude increases, the influence of inter-harmonics on the noise of the transformer becomes more serious. The lower the inter-harmonic frequency, the greater the amplitude of the core noise level and the faster its growth rate. Especially for inter-harmonics with a frequency less than 20 Hz, the noise increases by 2 dB to 3 dB for every 3 V increase in voltage, and the growth rate is significantly greater than the inter-harmonics with a frequency greater than 20 Hz. When the voltage amplitude is 50 V, the noise level with 2 Hz inter-harmonic excitation is 9 dB higher than that without inter-harmonic excitation.