Multiple-frequency synchronization of the four exciters in a far super-resonant vibrating system with an isolation frame

Generally, the synchronization studies on two or multiple exciters are preconditioned by being a single frequency, while the multiple-frequency synchronization problems in a vibrating system, including double-frequency and triple-frequency, are less considered, which are also very significant in engineering. This paper attempts to solve this issue by considering a dynamical model with an isolation frame, driven by the four exciters. The synchronization for the four exciters and its stability under the double-frequency and triple-frequency conditions are studied in detail. Firstly, the mathematical modeling of the system is established, and the corresponding motion differential equations are derived. Using the asymptotic method and the average method, yields the theoretical condition of implementing multiple-frequency synchronization, and the theoretical condition for stability of the system complies with the Routh–Hurwitz criterion. The dynamic characteristics of the system, including stable phase differences, stability abilities, responses of the system, and relative motion relationship, are qualitatively discussed by numeric. Finally, simulations are performed by applying a Runge–Kutta program to validate the theoretical and numerical qualitative results. It is shown that, by reasonably matching the key parameters of the system, the stronger, stable, and valuable motion states of vibrating machines, including vibration amplitudes, frequencies, and motion trajectory, can be realized, which are exactly the desires in engineering.

Research of the influence of acoustic load on a piezoelectric emitter to control the cavitation erosion of materials

The paper analyzes the possibilities of research the cavitation erosion of materials that are subjected to cavitation effect. The study is carried out by a system for controlling the magnitude of the acoustic load on the piezoelectric emitter of the ultrasonic vibrating system. The analysis of the processes of interaction between the ultrasonic emitter and the processed environment was carried out on the basis of a research of the model, which was created on the basis of a system of electromechanical analogies. The analysis made it possible to reveal the dependence of the electrical impedance of the ultrasonic vibrating system on the magnitude of the acoustic load. The revealed dependencies made it possible to propose and develop a control system. It is able to provide a study of the properties that are located near the emitting surface of the ultrasonic emitter of materials influenced to cavitation ultrasonic, including under abnormal conditions (high temperatures and pressures).

The Effect of a Rubber Sheet on the Dynamic Response of a Machine Foundation Located over a Small Thickness of Soil Layer

Placing a machine footing over a small thickness of soil layer, which is located over a bedrock, could encounter many challenges due to the bed’s notable stiffness in comparison to the soil. The advantages of using rubbers to protect facilities (structures, machine foundations, nearby footings and equipment, etc.) from vibration and control its consequences are well known nowadays. In this study, the benefits of employing a small thickness of rubber sheet (2 mm) on the dynamic response of a machine foundation which is located over four thicknesses of soil (210, 420, 630, and 840 mm) has been investigated. The soil layer is located over an artificial bedrock that is consisted of a thick concrete layer. The tests have been conducted in a vast test pit of size 2500×2500 mm and a depth of 840 mm by using a semi large-scale machine foundation model with a square concrete foundation of width 400×400×100 mm. It was observed that, by increasing the soil layer thickness, the resonant frequency and amplitude of the vibrating system decreases. Moreover, by employing a rubber sheet beneath the machine footing, the resonant frequency of the vibrating system significantly decreases especially for a small thickness of the soil layer. Although, using a rubber sheet could slightly increase the resonant amplitude, but the benefit of the resonant frequency-changing capability of the rubber sheet is too impressive by taking the resonant frequency of the system far enough from the unchangeable working frequency of the machine and preventing the resonant phenomenon to happen.

Theoretical Study on Synchronization of the Counter-Rotating Exciter in the Compound Vibrating Field

Aiming at the impact of the complex vibration environment generated by the integrated vibration equipment on the vibration testing equipment, this paper proposes a new method to solve the vibratory synchronization problem in the compound vibration environment. A new concept of the compound vibrating field is proposed, and a new simple vibrating system with a single counter-rotating exciter in a compound vibrating field is established. The motion differential equation of the system is established by the integral mean method with small parameters, and then the periodic coefficient differential equation is obtained through linearization. Based on the relevant theory of the second-order differential equation with periodic coefficient, the synchronization criterion and stability criterion of the vibrating system are derived. According to the theoretical criteria, the coupling characteristics of the exciter and the vibrating field are numerically simulated and analyzed, which supports the theoretical results. The proposed compound vibrating field provides a new way for studying vibratory synchronization.

Stability Characteristics of a Vibrating System with Double Rigid Frames Driven by Four Co-Rotating Coupling Vibrators

In this paper, a dynamic model is adopted to investigate the stability and response characteristics of a vibrating system driven by four vibrators placed on two different rigid frames (RFs). Using the equations of motion of the system derived, the conditions for synchronization and stable operation of the system are studied by the average method and Hamilton’s rules, respectively. Based on the theoretical results obtained, some factors are further studied concerning the stable phase differences (SPDs), the coefficients for ensuring stability, and the vibration amplitudes of the two RFs in different resonant regions. These serve to reveal the stability and response characteristics of the system that determine the ultimate function of the vibrating machine. Finally, numerical simulations are carried out to examine the validity of the theoretical methods and numerical qualitative results. Based on the results from the theory and simulation analyses, it is suggested that the working region of the system should be selected in the sub-resonant region corresponding to the natural frequency (NF) of the main vibrating system in the [Formula: see text]- and [Formula: see text]-directions. In this case, the ideal relative circular motion for two RFs with a well isolation effect can be achieved, and the energy is saved.