# Analysis of Dimensional Tolerances on Hydraulic and Acoustic Properties of a New Type of Prototypal
## 5 Acoustic Measurements of Prototype Pumps
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{_f (Hz)_} & \multicolumn{8}{c}{**Microphone Numbers**} & \multicolumn{8}{c}{**Thirds**} & \multicolumn{3}{c}{**Octaves**} \\ \cline{2-13}  & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **Lmj** & **Smj** & **KAj** & **LAj** & **Lmj** & **LAj** \\ \cline{2-13}  & **-1.48** & **-0.15** & **-0.20** & **0.33** & **0.16** & **-0.10** & **0.26** & **0.42** & & & & & & \\ \hline
25 & 84.1 & 81.8 & 62.5 & 46.8 & 65.4 & 83.8 & 82.4 & 78.1 & 80.1 & 15.4 & \(-\)44.7 & 35.4 & & & \\
31.5 & 62.3 & 60.0 & 54.9 & 40.0 & 56.8 & 63.7 & 60.3 & 62.0 & 60.1 & 8.0 & \(-\)39.3 & 20.8 & 80.2 & 40.9 \\
40 & 58.9 & 49.4 & 58.5 & 55.7 & 52.9 & 51.8 & 46.4 & 53.7 & 54.7 & 4.3 & \(-\)34.6 & 20.1 & & & \\
50 & 70.8 & 67.8 & 74.2 & 74.9 & 73.0 & 66.0 & 65.3 & 62.2 & 71.1 & 5.0 & \(-\)30.2 & 40.9 & & & \\
63 & 71.7 & 76.4 & 76.1 & 75.2 & 71.9 & 66.0 & 78.4 & 59.6 & 74.4 & 6.8 & \(-\)26.2 & 48.2 & 77.1 & 50.9 \\
80 & 75.4 & 73.0 & 67.1 & 69.8 & 64.9 & 63.8 & 68.7 & 69.0 & 70.1 & 3.8 & \(-\)22.5 & 47.6 & & & \\
100 & 69.9 & 64.8 & 60.9 & 61.9 & 65.4 & 65.1 & 60.8 & 62.8 & 64.6 & 2.7 & \(-\)19.1 & 45.5 & & \\
125 & 74.6 & 73.3 & 75.1 & 66.6 & 71.0 & 66.2 & 68.5 & 70.0 & 71.5 & 3.3 & \(-\)16.1 & 55.4 & 75.0 & 58.9 \\
160 & 69.8 & 69.1 & 70.5 & 69.5 & 68.6 & 74.1 & 71.9 & 75.1 & 71.8 & 2.8 & \(-\)13.4 & 58.4 & & & \\
200 & 81.8 & 71.1 & 76.8 & 74.0 & 69.4 & 78.2 & 76.5 & 74.0 & 76.3 & 3.8 & \(-\)10.9 & 65.4 & & & \\
250 & 83.0 & 72.6 & 79.8 & 76.3 & 73.0 & 80.2 & 79.5 & 75.9 & 78.4 & 3.5 & \(-\)8.6 & 69.8 & 81.2 & 72.6 \\
315 & 77.1 & 68.8 & 73.4 & 70.6 & 75.0 & 72.6 & 74.0 & 65.7 & 73.0 & 3.5 & \(-\)6.6 & 66.4 & & & \\
400 & 83.4 & 80.6 & 80.2 & 69.9 & 69.7 & 79.6 & 73.2 & 74.2 & 78.2 & 5.2 & \(-\)48.7 & 37.4 & & & \\
500 & 84.2 & 81.3 & 80.5 & 71.4 & 70.8 & 80.6 & 74.4 & 75.1 & 79.0 & 4.9 & \(-\)3.2 & 75.8 & 81.9 & 78.7 \\
630 & 65.4 & 67.1 & 69.4 & 71.3 & 73.8 & 68.2 & 70.4 & 71. The value of the A-weighted sound level was determined on the basis of the measured sound pressure level \(L_{Ai}\) in the j-th band and after the correction \(K_{A}^{j}\) resulting from the characteristics of the weighted curve using the following formula:  
\[L_{A}^{j}=L_{p}^{j}+K_{A}^{j} \tag{4}\]  
\(L_{p}^{j}\)--sound pressure level in the j-th frequency band,  
\(L_{A}^{j}\)--A-weighted sound level in the j-th frequency band, and  
\(K_{A}^{j}\)--correction according to the A characteristic for the j-th frequency band. Figure 14 presents the value of the acoustic pressure level \(L_{m}\), corrected acoustic pressure level \(L_{A}\), acoustic power level \(L_{p,A}\) in the function of the discharge pressure \(p_{t}\) at a constant rotational speed of a pump shaft \(n\) = 1500 rpm. Figures 15 and 16 present a tertian and an octave spectrum of the gear pump after tooth root undercutting for the nominal discharge pressure and nominal rotational speed. The measurement of the a\({}_{\text{RMS}}\) vibration acceleration was located on the rear cover of the gear pump in the axis of the driving wheel shaft. The choice of the measurement point resulted from the previous tests with the use of the acoustic probe. The distribution of sound intensity on the surface of the pump body, determined by the energy method, showed a local increase in sound vibrations. This fact proves the transmission of sound-generating vibrations mainly from the pump drive. Figure 14: The noise of the gear pump after tooth root undercutting for the nominal rpm [15; 17]. Figure 16: The octave spectrum of an experimental unit for the nominal pressure and rotational speed [15; 17]. Figure 15: The tertian spectrum of an experimental unit for the nominal pressure and rotational speed [15; 17]. Comparing the acoustic characteristics of the prototype pumps with the basic units, it turned out that the solution with a polyevolvent outline is characterized by 3 to 5-dB lower noise emission to the environment. The beneficial effect of noise reduction was observed in the range from 0 to 20 MPa.