Abstract
Paper presents a proposal of mathematical algo-rithm used in order to modelling and testing of vibrating mechatronic systems. A shaft is the mechanical subsystem of the considered system. A ring piezoelectric transducer is bonded on the shaft’s surface. Knowledge of the dynamic characteristics of the designed systems is essential for the proper operation and should be taken into consideration during the design phase as well as verified during operation of the system. This is why authors decided to present a method that can be very useful for analysis of such kind of systems. In order to calculate the characteristic of mechatronic system a mechanical subsystem was analysed in the first step. The dynamic flexibility of mechanical subsystem was calculated using the exact and approximate methods. It is impossible to use the exact method in order to analyse mechatronic systems this is why the approximate Galerkin method was used to analyse the system with piezoelectric actuator. An exactness of the approximate method was verified. In the presented work a torsional vibrating mechatronic system with piezoelectric transducer used as the vibration actuator is presented. The considered piezoelectric actuator is the sectional, cylindrical transducer supplied by the external harmonic electric voltage. Obtained results – characteristics of mechanical subsystem and mechatronic system are juxtaposed on charts. DOI: http://dx.doi.org/10.5755/j01.mech.20.1.6597
Highlights
A proposal of mathematical algorithm using in order to modelling and testing of torsional vibrating mechatronic system is presented in this work
It is impossible to use the exact method of separation of variables in order to analyse mechatronic systems, this is why only the approximate method was used in this case
Knowledge of the dynamic characteristics of the designed systems is essential for the proper operation and should be taken into consideration during the design phase as well as verified during operation of the system [5]
Summary
A proposal of mathematical algorithm using in order to modelling and testing of torsional vibrating mechatronic system is presented in this work. The system is excited by the torque generated by the transducer so Eq (14) can be simplified and written down as: In this case characteristic Yp that describe relations between externally applied electric voltage and angle of rotation of the mechanical subsystem. In presented case the characteristic was calculated when length of the transducer Lp = L 3 This characteristic describes relation between value and frequency of electric voltage that supplies the piezoelectric actuator and an angle of rotation of the shaft, measured in rad/V.
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