# On the Correlation of Symbols' Vibrational Behavior and Manufacturing Processes
## 3 Experimental Measurement Setup  
Nineteen 8-inch cymphals made of MS63, B8, and B20 are studied in this work. A group of five B8 blanks, noted as B8-1, B8-2, B8-3, B8-4, and B8-5, and a group of four blank B20 symbols, noted as B20-41, B20-42, B20-43, and B20-44, are included. A group of five B20 semi-finished hammered symbols are also studied, noted as B20-51, B20-52, B20-53, B20-54, and B20-55. Additionally, five finished/commercial cymbals--an MS63, a B8 (noted as B8-0), and three B20s (noted as B20-1, B20-2, and B20-3)--are introduced in this study. The symbols are presented and described in Table 1. It is noticed that the finished/commercial cymbals are of similar curvature and mass, while the MS63 cymbal stands out as having the greatest mass and curvature of them all. For the cymbal groups, the mass values in Table 1 correspond to the mean value for each group. Since the proposed methodology may be applied to any type of cymbal at any manufacturing state, the brand names of the manufacturers have been blurred. A miniature impact hammer (Model 086E80, PCB, Depew, NY, USA) [27] and a miniature accelerometer (Model TLD352A56, PCB, Depew, NY, USA) [28] were used to excite each cymbal and detect the response. Since acceleration is the required kinematic quantity, the FRF is expressed in terms of accelerance. The auto- and cross-spectra of the signals are used for the calculation of the estimator \(H_{2}\left(\left(\mathrm{m}/\mathrm{s}^{2}\right)/\mathrm{N}\right)\), which is described by  
\[H_{2}(\omega)=\frac{G_{aa}(\omega)}{G_{Fa}(\omega)} \tag{6}\] \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Alloy** & **Quantity** & **Index** & \begin{tabular}{c} **Diameter** \\ **(in)** \\ \end{tabular} & **Mass (g)** & \multicolumn{2}{c}{**Manufacturing Stage**} & \multicolumn{2}{c}{**Cymbal**} \\ \hline  & & & & **Blank** & \
\begin{tabular}{c} **Semi-** \\ **Finished** \\ \end{tabular} &
\begin{tabular}{c} **Finished/** \\ **Commercial** \\ \end{tabular} & **Front View** & **Side View** \\ \hline MS63 & \(1\) & MS63 & \(8\) & \(380\) & & & & \\ B8 & \(1\) & B8-0 & \(8\) & \(195\) & & & \\ B8 & \(5\) & B8-1,2,3,4,5 & \(8\) & \(222\) & \(\checkmark\) & & & \\ B20 & \(1\) & B20-1 & \(8\) & \(151\) & & & \(\checkmark\) & \\ B20 & \(1\) & B20-2 & \(8\) & \(150\) & & & \\ B20 & \(1\) & B20-3 & \(8\) & \(157\) & & & \\ B20 & \(4\) & \(41\),42,43,44 & \(8\) & \(241\) & & & \\ B20 & \(5\) & B20- & \(8\) & \(247\) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Characteristics of the 8-inch cymbals studied. where \(G_{aa}(\omega)\) is the auto-spectrum of the acceleration and \(G_{Fa}(\omega)\) is the cross-spectrum of the force and the acceleration [29]. The signals were recorded and further processed by a real-time multi-analyzer (Model OR34, OROS, Montbonnot-Saint-Martin, France). According to [PERSON] et al. 's analysis [26], the sampling frequency is set to 8.192 kHz, providing 6401 FFT lines with 0.5 Hz frequency resolution up to 3.2 kHz. The roving excitation method was used on a grid of 144 measurement points on each symbol. This number of points preserves the stability of calculations, as explained in detail in the following section (Section 4.1). Each point is excited 5 times for averaging. The grid consists of 16 radii, each with 9 points spaced 1 cm apart, as shown in Figure 1. The accelerometer was attached to the symbol using wax and positioned at a point where a drummer typically strikes with a drumstick. A torque gauge (Model BTG, Tohnichi, Tokyo, Japan) was used to ensure repeatable screw tightening. To preserve the stability criterion of the CFDAC calculations, the number of measurement points is initially determined (144 in our case, as explained in detail in Section 4.1). An axis-symmetric grid of the 144 uniformly distributed points is developed on the symbol under study, as presented in Figure 1. The roving excitation method is applied to the grid of the measurement points on each symbol.