Mathematical modeling of piezo motor operation modes

At present, micro electromechanical systems appear to be progressively applicable in engineering. The problem of reducing weight-and-dimensional characteristics of the spacecraft (SC) system is of great importance in the space field. One of the solutions is replacement of electromechanical motors in different SC units by piezo motors. It is necessary to take into account the condition of consistency of PZT stack actuators (the sources of mechanical energy) with the load when calculating and designing the piezo motors of high energy transfer coefficient. In this case, the most relevant is mathematical modeling of a product design with correct consideration of the specific drive load in an actual industrial field.
Mathematical modeling by the finite element method in combination with 3D numerical simulation is most accurate and appropriate. However, this method is laborious and timeconsuming. In practice, designers and constructors prefer to use simple linear one-dimensional mathematical models, which provide an accurate information about materials and product design. In linear one-dimensional models of oscillatory systems for the range of frequencies applied in piezo motors, it is necessary to consider the acoustic and mechanical principles of energy conversion and transfer from the source to the load. In this paper, a one-dimensional mathematical model of the piezo motor with consideration of mechanical and acoustic energy transfer is developed. This model allows calculating the frequency–response characteristics of mechanical acoustic oscillating system according to which the materials of elements and design of the drive are chosen