INVESTIGATION OF THE NORMAL VIBRATION MODES STABILITY IN SOME ESSENTIALLY NONLINEAR SYSTEMS

In the paper stability of nonlinear normal modes is analyzed by two approaches. One of them is the method of Ince algebraization, when a new independent variable associated with the unperturbed solution is introduced in the problem. In this case equations in variations are transformed to equations with singular points. The problem of determination of solutions corresponding to boundaries of the stability/ instability regions is reduced here to the problem of determination of functions that have singularity at the mentioned points. Such solutions can be obtained in the form of power series, which coefficients are satisfying a system of homogeneous linear algebraic equations. The condition ensuring the existence non-trivial solutions for such systems determines the boundaries between the stability / instability regions in the system parameter space. An advantage of the Ince algebraization is that we do not use the time-presentation of the solution when studying its stability. Other approach to investigating steady state stability is associated with the classical Lyapunov definition of stability. The analytical-numerical test proposed in the paper can be applied to a stability problem when the problem has no analytical solution. It also allows to obtain boundaries between the stability / instability regions in the system parameter space. In the present paper the first approach is used to analyze stability of normal vibration modes in the system of connected oscillators on the essentially nonlinear elastic support, and the second one is used to analyze stability of a horizontal vibration mode in the so-called stochastic absorber.

Anti-sway method for reducing vibrations on a tower crane structure

We develop a solution to the problem of the behavior of a tower crane considered as a deformable system, and therefore subject to vibrations, whereas the controlled movement of a payload is implemented. The motion of the payload is calculated taking into account the normal vibration modes of the tower crane and the swaying of the payload. A “command smoothing” method relative to an open-loop system is used for reducing the sway of the payload, through smoothing the original command by the crane operator. This leads, as a consequence, to a reduction in the vibrations of the crane structure. An iterative calculation of the sway angle and the corresponding applied velocity profiles as input to the crane motors is applied. The tower crane is considered as a high nonlinear underactuated system; it is modeled considering the possible deformation of the structure. The results relating to the normal deformations of the crane are obtained, highlighting how these vibrations are strongly attenuated when an anti-sway system for the payload is implemented. Therefore, it is shown how this control leads to the best results in terms of performance for both the payload movement (shortest possible profile for the rotation movement and damping of the load oscillation) and the structure of the tower crane. Applying the method described in this paper, the structure of the tower crane does not undergo the strong horizontal and vertical oscillations that occur when the elastic structure is not considered in the crane model.

Crack Size Identification for Bearings Using an Adaptive Digital Twin

In this research, the aim is to investigate an adaptive digital twin algorithm for fault diagnosis and crack size identification in bearings. The main contribution of this research is to design an adaptive digital twin (ADT). The design of the ADT technique is based on two principles: normal signal modeling and estimation of signals. A combination of mathematical and data-driven techniques will be used to model the normal vibration signal. Therefore, in the first step, the normal vibration signal is modeled to increase the reliability of the modeling algorithm in the ADT. Then, to help challenge the complexity and uncertainty, the data-driven method will solve the problems of the mathematically based algorithm. Thus, first, Gaussian process regression is selected, and then, in two steps, we improve its resistance and accuracy by a Laguerre filter and fuzzy logic algorithm. After modeling the vibration signal, the second step is to design the data estimation for ADT. These signals are estimated by an adaptive observer. Therefore, a proportional-integral observer is then combined with the proposed technique for signal modeling. Then, in two stages, its robustness and reliability are strengthened using the Lyapunov-based algorithm and adaptive technique, respectively. After designing the ADT, the residual signals that are the difference between original and estimated signals are obtained. After that, the residual signals are resampled, and the root means square (RMS) signals are extracted from the residual signals. A support vector machine (SVM) is recommended for fault classification and crack size identification. The strength of the proposed technique is tested using the Case Western Reserve University Bearing Dataset (CWRUBD) under diverse torque loads, various motor speeds, and different crack sizes. In terms of fault diagnosis, the average detection accuracy in the proposed scheme is 95.75%. In terms of crack size identification for the roller, inner, and outer faults, the proposed scheme has average detection accuracies of 97.33%, 98.33%, and 98.33%, respectively.

Vibratory Conveying by Harmonic Longitudinal and Polyharmonic Normal Vibrations of Inclined Conveying Track

Vibratory conveying of a material point by harmonic longitudinal and polyharmonic normal vibrations of an inclined conveying surface is considered. The dependence of dimensionless conveying velocity – a ratio of velocity to the product of frequency and amplitude of longitudinal vibration – on several dimensionless parameters is investigated in the moving modes without hopping. Maximal conveying velocity is achieved at the certain values of normal vibration amplitudes and phase difference angle between the longitudinal and normal vibrations, which are called optimal. Their values are dependent on two dimensionless parameters: the inclination angle parameter – a ratio of an inclination angle tangent to a frictional coefficient, the intensive vibration coefficient – a ratio of the longitudinal amplitude of vibration to the amplitude of the first harmonic of normal vibration and frictional coefficient. In a condition of the intensive longitudinal vibration, when its amplitude significantly greater than amplitudes of normal vibration, dimensionless velocity is almost independent of the intensive vibration parameter and it depends only on inclination angle parameter, i.e. on inclination angle and frictional coefficient. The optimal values of harmonics' amplitudes of polyharmonic normal vibration are determined in dependence of inclination angle parameter with the number of harmonics from 2 to 7. The graphs of considered dependencies are presented and the most important values of parameters are presented in the table. Conclusions are made to determine the optimal vibration parameters and the problems of further research are indicated. The considered vibrations can be used in different vibratory conveying devices with electromagnetic drives.

Modeling and Load Capacity Analysis of Reciprocating Hybrid Linear Guideway With Annular Groove and Sloped Recesses

In this work, we research a reciprocating hybrid linear guideway and study its load capacity. This hybrid guideway's bearing surface is designed with an annular groove and two sloped shallow recesses. The analysis is based on modeling by mass-conserving cavitation algorithm (p − θ cavitation algorithm), where a modified smoothing switch function is raised for better convergence. Focusing on the normal direction to reciprocation, the load-guideway system is simplified as a single-degree-of-freedom linear time-varying system and solved by Newmark-β method. Due to the hybrid guideway's time-varying dynamic characteristics, there is a normal vibration in reciprocation. By analyzing two typical load cases in detail, the results indicate that the hybrid guideway has greater load capacity than the hydrostatic guideway, and the normal vibration is small enough for most engineering situations.

Research on the mechanism of drag reduction by wall vibration through Lattice Boltzmann method

In this paper, the hydrodynamics of streamwise and normal vibration wall are studied using the Lattice Boltzmann method. Firstly, based on the two-dimensional flow geometry model, which is made up of flat wall and water fluid, the characters of the fluid near the streamwise and normal vibration wall are simulated under the condition of mutative vibration parameters. By rigorous data treating, some notable results such as the velocity distribution, density distribution curves of the flow field, and the frictional force of the solid-liquid interface are gained. Secondly, the reason of the change of frictional resistance at the solid-liquid interface by wall vibration are studied. And the results are evidence that well drag reduction effect can be obtained by applying appropriate flow vibration parameters to the solid wall. In addition, the reduction in fluid density near the solid-liquid wall is another significant cause behind the frictional drag decrease.