# Measurement of the Speed of Induction Motors Based on Vibration with a Smartphone
## 1 Introduction
The noise signal is then processed by an algorithm based on MATLAB, which can establish the speed of the motor by identifying the frequency of the rotor shaft. Other studies focused on the acquisition and analysis of motor currents for fault diagnosis purposes [20], and are also used to estimate the rotor speed [21; 22; 23]. The current of the stator is sampled and analysed to detect harmonic components that depend on the rotor speed. Such estimation techniques avoid the use of electromechanical sensors, which are usually expensive, fragile, and often difficult to install, but they still require some extra devices to capture and analyse these currents, which are not always accessible or easy to measure. The interaction between the set of alternating currents that circulate through the windings and the electromagnetic fields that occur in an induction motor yields to the production of an electromagnetic torque on the motor shaft. However, that same interaction between electromagnetic fields and currents, combined with some physical anisotropy of the materials and some small mechanical manufacturing imperfections, also leads to the manifestation of undesirable radial and axial forces between the stator and the rotor of the motor. These undesired parasitic forces produce mechanical vibrations that are transmitted and spread throughout the entire motor housing and the whole attached mechanical structure. The amplitude of the vibrations at a point of the motor depends on both the strength of the forces and the mechanical response of the motor casing and its structure [7]. Vibrations analysis has been used for a long time and extensively as an operational technique for motor condition monitoring [24; 25]. But motor vibration incorporates a significant component that is excited by the mechanical rotation of the shaft. Consequently, vibration signal analysis has also been exploited to develop methods for measuring the motor speed [26]. The interest in this measurement principle continues today, as this technique provides good precision compared to other methods [7; 27]. In [7], an experimental comparison between the estimation of the speed of an induction motor by means of the vibration signal and by the motor current signal was carried out. The work concluded that the speed of a motor fed with an inverter could be measured with an error lower than 0.05% using the vibration signal while applying different methods based on current analysis; the error always ranged between 0.4% and 0.6%. The most popular sensor for measuring rotational speed based on vibration is the accelerometer due to its precision [25; 26]. The accelerometer measures the acceleration forces by means of a piezoelectric transducer, which transforms the mechanical strength into an electrical signal. Low-cost, easy-to-install, and accurate sensor alternatives are also explored. In [28], the performance of a magnetoresistive sensor is compared with a conventional accelerometer, concluding that although the first is a nonintrusive contactless method providing good results, in high magnetic field conditions, there is a risk of a disruption in vibration measurements. The possibility of using an electrostatic sensor to measure vibrations is analysed in [25]. Even though it is a low-cost candidate sensor, the results show that it captures unwanted noise because the electrode of the sensor is exposed to the air, which disrupts the vibration signal. As can be seen, there is still a need to investigate other possible sensors that allow motor vibrations to be measured with a nonintrusive, accurate, and low-cost method. This is where smartphones can play a relevant role. Today, mobile technology continues to evolve rapidly thanks to the integration of faster multicore chips, memories with increasing sizes, and a growing number of refined sensors, each time more sophisticated.