# Measurement of the Speed of Induction Motors Based on Vibration with a Smartphone
## 5 Conclusions  
This paper presents a new, simple, and nonintrusive method for inservice and field motor speed measurement, based on a smartphone as the acquisition and recording device of the vibration signal, and a MATLAB algorithm to determine the motor speed. The proposed method to measure the motor speed relies on the assessment of the frequency spectrum of the vibration data of the motor. In the experimental section, a sampling frequency as reduced as 200 Hz was sufficient for acquiring the necessary frequency components to determine the speed of a four-pole induction motor. This new method does not require the installation of any external accelerometer or other type of sensor, since the vibration signal is acquired by the accelerometers integrated into a common smartphone by means of a free application. Still, the proposed approach is a contact method. A magnet and a self-adhesive magnet are required to fix the smartphone to the induction motor chassis. These elements were chosen as a low-cost solution in the marketplace. The use of the accelerometer integrated into a smartphone allows avoiding the necessity of extra  
Figure 12: Spectra of the axial components of the vibration signal corresponding to a motor speed of \(\Omega_{tt}=1581\) r/min (\(\omega_{m}=26.35\) Hz) for axis x (**top**), y (**middle**), and z (**bottom**). \begin{table}
\begin{tabular}{c c c} \hline \hline Vibration & Peak Value of the Amplitude of the Axial & Frequency Corresponding to the Peak Value of the \\ Component & Vibration Signal Spectra, & Amplitude of the Axial Vibration Signal Spectra, \\ Axis & \(|F_{REF}(\omega_{F,REF})|=\text{MAX}\{|F_{REF}(\omega)|\}\) & \(\omega_{F,REF}:|F_{REF}(\omega_{F,REF})|=\text{MAX}\{|F_{REF}(\omega)|\}\) \\ \hline \multirow{2}{*}{\(X\)} & \(\text{MAX}\{|\,F_{X}(\omega)|\}=1\)\(F_{X}(\omega_{F,X}=26.3184\) Hz\()|=84.3203\) & \multirow{2}{*}{\(\omega_{F,X}=26.3184\) Hz} \\  & p.u. & & \\ \hline \multirow{2}{*}{\(Y\)} & \(\text{MAX}\{|\,F_{Y}(\omega)|\}=1\)\(F_{Y}(\omega_{F,Y}=26.3184\) Hz\()|=55.0815\) & \multirow{2}{*}{\(\omega_{F,Y}=26.3184\) Hz} \\  & p.u. & & \\ \hline \multirow{2}{*}{\(Z\)} & \(\text{MAX}\{|\,F_{Z}(\omega)|\}=1\)\(F_{Z}(\omega_{F,Z}=73.8770\) Hz\()|=69.0521\) & \multirow{2}{*}{\(\omega_{F,Z}=73.8770\) Hz} \\  & p.u. & & \\ \hline \multirow{2}{*}{Vibration  Component} & Peak Value of the Amplitude of the RMS & Frequency Corresponding to the Peak Value of the \\  & Vibration Signal Spectra, & Amplitude of the RMS Vibration Signal Spectra, \\  & \(|F\left(\omega_{F,RMS}\right)|=\text{MAX}\{|\,F(\omega)|\}\) & \(\omega_{F,RMS}:|F(\omega_{F,RMS})|=\text{MAX}\{|\,F(\omega)|\}\) \\ \hline \multirow{2}{*}{\(RMS\)} & \(\text{MAX}\{|\,F(\omega)|\}=1\)\(F(\omega_{F,RMS}=73.8770\) Hz\()|=93.2191\) & \multirow{2}{*}{\(\omega_{F,RMS}=73.8770\) Hz} \\  & p.u. & & \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Peak values of the amplitude of the axial (upper part) an RMS (lower part) vibration signal spectra and corresponding frequencies. space, extra wiring, regular maintenance, or accessibility of the rotor shaft. In addition, the proposed procedure does not require stopping the machine, unless strictly required for personal protection or security reasons. The method was tested in the laboratory, feeding the motor with different power supplies (mains and inverter) and mechanical loads (no mechanical load and DC generator). An extensive set of tests was carried out in the laboratory, including different length (duration) of vibration samples and different positions/orientations of the smartphone on the tested motor, including the supporting frame. Given that the proposed method is based on the identification of the frequency corresponding to the rotation of the mechanical shaft of the motor (without using features unique to induction motors), everything seems to indicate that it could also be used to measure the speed of any kind of rotating shaft device, although that feature was not tested in this work.