Modeling of electromagnetic power output in a vibration-induced micro-generator with a silicon-based helical micro-spring

This paper develops an electromagnetic power output model in a vibration-induced micro-generator with a silicon helical micro-spring to predict the electricity output. The generator consists of a movable ferro-platinum permanent magnet membrane on the micro-spring, a winding copper induction coil and two glass spacers. This model considers the coupling issues of mechanical kinematics and electromagnetism that convert mechanical energy to electric energy through vibration. Analytical formulas are developed to predict analyze the values in the spring constant of the helical micro-spring, a three-dimensional magnetic field of electromagnetic induction and the parasitical damping coefficient. Good agreement between the analysis and experiment: 82.6% precision for power output, 6.2% difference for current output and 9.6% deviation for voltage output are demonstrated at 60 Hz vibration frequency with a 0.03 mm vibration amplitude. From a series of analytical results, it is known that a 4.2 times power output can be achieved by controlling the oscillator with an appropriate vibration amplitude and the best-designed load resistance.