# Measurement of the Speed of Induction Motors Based on Vibration with a Smartphone
## 2 Materials and Methods  
The complex vibration signal of a motor contains, among others, a component (of great amplitude) at the mechanical frequency of rotation of the rotor, which can be acquired and used to estimate the speed of rotation of the shaft. The mechanical frequency of rotation of the rotor can be obtained by applying to the frequency spectrum of the vibration signal a peak detection algorithm. In this work, a new low-cost and nonintrusive method is proposed for the field measurement of the speed of induction motors. The method is based on the spectral analysis of motor vibration, but unlike other conventional techniques, the proposed method does not require the installation of any external accelerometer. The new proposal consists of acquiring the vibration signal by means of the accelerometers integrated in a common smartphone. The vibration signal is then processed by a MATLAB-based algorithm, which calculates the motor speed by recognising the mechanical frequency of the rotor shaft from the spectrum of the vibration signal. To the authors' knowledge, this is the first time that a smartphone is proposed as a practical means of motor speed measurement by motor vibration signature analysis. The new method proposes to use the accelerometers embedded in a common smartphone as sensors to capture the vibration signal produced by an induction motor during its operation. A free application [37] was used to create a csv file with the time record of the axial components of the motor vibration signal, \(f_{REF}(t)\), for each reference axis, \(REF=[X,Y,Z]\). Finally, an algorithm based on MATLAB computes the rotation speed by finding the mechanical frequency of the rotor shaft from the harmonic spectrum of the vibration signal. Figure 1a shows the educational test bench of the induction motor and the configuration of the different tests carried out in this work. As shown, the core of the test platform is the induction motor, whose vibrations are captured and registered by a common smartphone. A magnet and a self-adhesive magnet are required to fix the smartphone to the induction motor chassis, as shown in Figure 1b. Two different power supplies were used: the grid supply and a frequency converter. The motor shaft can be left free, without mechanical load, or can be coupled to a DC  
Figure 1: (**a**) Schematic of the different tests performed; (**b**) Scheme to show how the smartphone is attached to the induction motor during the tests by means of a self-adhesive magnet. generator that supplies a variable resistance, allowing the load torque of the motor to be adjusted. During the tests, the rotation speed of the motor shaft was measured using a portable optical tachometer because it is a well-established and conventional contactless method. In all tests, the speed of the motor, \(\Omega_{m}\), was measured twice using two different portable optical tachometers. The mean value of the measurements of the two speeds was considered as the real value of the rotor speed. In addition, a smartphone was used to capture and record the motor vibration signal. Appendix A includes extra information about the tachometers, the smartphone, the free application used for recording, the attachment of magnets, and the test bench used in this work. All tests followed the next procedure. Once the test configuration was set (grid or inverter as supply source and the type of mechanical load), the rotor speed was measured using two portable optical tachometers. Once the value of the rotor speed was measured, a smartphone was attached to the induction motor through a magnet, and the samples of the axial components of the motor vibration, \(f_{X}(t),f_{Y}(t)\), and \(f_{Z}(t)\), were recorded with the help of the free application. Subsequently, the recorded csv file obtained by the free application with the information about vibrations was processed with a routine programmed in MATLAB designed to obtain the frequency spectra of the axial vibration signals, \(F_{X}(\cdot\cdot\omega)\), \(F_{Y}(\cdot\omega)\), and \(F_{Z}(\cdot\omega)\).