Vibrator model for design of vibration machines

One of the directions of development of mechanical engineering is the design and production of vibratory machines for compacting bulk media, ranging from low-frequency road vibratory rollers and vibratory plates for road ramming and asphalt paving and ending with foundries and high-frequency compactors for creating new materials. An actual problem in the design of this type of vibrating machine is the choice of vibration parameters of the working tool, the values of which should depend on the parameters of the material being processed, and, as a consequence, the choice of a device that meets these requirements. There are no universal devices on the market, however it is possible to create a universal model and design suitable for designing vibratory machines for various purposes. The paper considers a model of a universal vibrator, the operating principle of which is based on bending transverse vibrations of plates. Unlike half-wave rod-type transducers, this design, with the same overall dimensions and power consumption, has a large dynamic range of oscillations of the working tool in a wide frequency range, the shape of the working surface of which can be set arbitrarily. The design and structure can be changed within the basic set of elements by choosing, for example, the zero values of the corresponding parameters. A distributed model is obtained based on the equations of mathematical physics, which is reduced to an integral form by determining the impulse response (Green's function) of a round plate and then the entire sensor. A parametric study is carried out, the possibility of changing the frequency response of the vibrator is shown. The developed mathematical model is applicable for both low-frequency and high-frequency applications, since it is linear and performed using dimensionless complexes of the similarity theory. The model considers the elastic hysteresis of structural elements, thereby providing reliable values of the amplitude of the resonant vibrations of the working tool. The validation of the model has shown a high accuracy in determining the resonant frequencies.