# Measurement of the Speed of Induction Motors Based on Vibration with a Smartphone
## 1 Introduction  
Electric motors are a fundamental part of the industrial and commercial equipment in society. They are used in a wide variety of industrial applications, as well as at the domestic consumer level in many household appliances. Induction motors are used in a multitude of electric drive applications due to their simplicity, robustness, and low price [1]. It is estimated that three-phase cage induction motors power about 90% of industrial drives [2, 3]. In recent decades, due to the continuous increase in the cost of electricity and the concern for sustainable development, different ways have been investigated to reduce the world's electricity consumption, since induction motors account for about 68% of the global industrial energy consumption [4]. Recent works have estimated that the energy consumption of electric motors could be reduced by about 4% to 5% by simply using the best available motors [5, 6]. Among the different techniques available to estimate the efficiency of an industrial induction motor, the rotational speed measurement is a simple and widely used one [7, 8]. Appropriate measurement of the rotational speed of induction motors is a key factor inmonitoring the state of the motor system. Traditionally, sensors such as encoders and resolvers are used for continuous speed monitoring. They should be coupled to the motor shaft or installed in close proximity of the rotating element [9] to measure the speed. This type of sensor requires extra wiring, extra space, and regular maintenance [10]. Due to all these reasons, the use of these sensors involves additional costs [11]. However, if the speed of an industrial induction motor needs to be monitored or supervised a few times a day (i.e., every hour) or for a few days, portable tachometers, mostly optical, are commonly used [12]. This approach presents an acceptable combination of measurement precision and low cost. This type of measurement requires having a reflective adhesive sticker in the motor shaft. Unfortunately, sometimes for safety reasons [13], and other times because the motor is inside a casing, the shaft of the motor is not accessible [14; 15]. In these cases, to put the reflective sticker on the shaft, it is necessary to stop the machine, which can result in additional costs for the industry. For all these reasons, in recent years, researchers have been focused on developing new ways of measuring the motor speed by means of different types of sensors (image, sound, and vibrations, among others), not specifically designed for speed measurement. The development of more accessible image sensors, cameras, and image processing techniques has brought new image-based methods as an alternative to conventional techniques. For example, a system for measuring induction motors speed using a low-cost image device is presented in [16]. The method requires a camera, and it is necessary to make a mark in the motor shaft. In [17], the speed of a motor is estimated using a tachometer based on a webcam. The authors proposed a method to estimate the relative load of three-phase induction motors for application in electrical energy audits. Methods based on images are nonintrusive, but the rotor shaft must be visible so that the camera can capture its movement. Similarly, thanks to advances in low-cost sound sensors, sound-based methods to measure the rotational speed are a novel alternative. An algorithm that processes a sound signal emitted by an IM to estimate the speed, the torque, and the efficiency was introduced in [18]. The system was developed using an Arduino board and an analog microphone. The method is nonintrusive, but extra specific hardware is required, and it does not perform properly when induction motors are fed with frequency converters. In [19], a new low-cost and nonintrusive procedure is proposed for the field measurement of the speed of induction motors, which is based on the analysis of the spectrum of the audible noise emitted by the motors. A smartphone is used to acquire the motor noise.