Amplitude Of Forced Vibration Research Articles

Vertical vibration model for the roll system of a six-high rolling mill based on the Timoshenko beam theory

During the production of cold-rolled strips, the high-speed operation of rolling mills generates vibrations that significantly impact the production efficiency, the strip quality, and the rolling mill service life. Therefore, investigating the vibration characteristics of rolling mills is of paramount importance. Previous studies predominantly treated the rolls as point masses, overlooking variations in the vibrations along the lengths of the rolls. In this study, the working, intermediate, and backup rolls were regarded as continuous elastic bodies, and they were simplified as Timoshenko beams. The modal superposition method was used to solve the vertical vibration equations for the rolls of a six-high rolling mill; thus, the natural frequencies and modal shapes for the rolls were obtained for both free and forced vibrations. A finite-element model validation confirmed that the accuracy of the novel Timoshenko beam six-high rolling mill vibration model introduced in this paper is significantly higher than that of the traditional Euler beam model when the roller length-to-diameter ratio is relatively small. Further analysis based on this model indicates that the forced vibration of the rolls is primarily influenced by fluctuations in rolling force. The amplitude of forced vibration is affected by factors such as the friction coefficient in the deformation zone, rolling speed, and cumulative rolling distance of the work rolls. These findings provide a precise representation of the characteristics of forced vibrations in rolling mills and offer valuable theoretical insight to ensure stable rolling mill operation.

Optimization of the Control Algorithm for an Active Bearing Support

This article presents a spindle system with an active bearing support for which the author proposed a control system based on a PID controller. This type of solution improves the mechanical properties of this spindle by changing the stiffness, which results in a wider range of permissible rotational speeds, lower power losses and an increased resistance to vibrations of the entire system. This work describes the mechanism of changing the bearing preload. During tests on a real test stand, the correct functioning of the preload control system was checked for various dynamic conditions. In this work, the author describes the controller used to work in a feedback system, explains how the settings for this controller were selected and their optimization. The assessment of the correct operation of the controller is based on minimizing the amplitude of forced vibrations for the front spindle end by actively controlling the preload of the bearings. This publication is intended to present one of the ways to solve the important problem of limiting the maximum values of the vibration amplitude in the spindle system for its wide range of operating conditions. It also shows how important its optimal settings are in control systems.

Design optimization of a single-mass impact damper

This research article presents a numerical approach to establish an optimal design methodology for a single-mass impact damper (SMID), which is a passive energy dissipation device with robust performance. Due to the nonlinear characteristics of SMID and a lack of analytical models, designing a single-mass impact damper with optimal combination of the parameters has been challenging. Furthermore, an uncontrolled mass of the SMID on a vibrating structure may lead to chaotic vibration responses. This study identifies a range of design parameters of the SMID to ensure non-chaotic responses and validates the optimal design combinations using an experimental prototype. The results show that a single-mass impact damper designed with the optimal combination of design parameters can provide better vibration damping and relatively steady response. This study also compares the performance of an optimized single-mass impact damper with an optimized tuned mass damper and finds that the single-mass impact damper can work more effectively than the tuned mass damper in damping free vibrations of a single-degree-of-freedom primary structure. Although the SMID cannot suppress forced vibration amplitude as effectively as a tuned mass damper (TMD) at resonance, it has the advantages of lower cost and easier installation than the TMD. Overall, this study provides a basis for the optimal design of a single-mass impact damper and resolves the issues related to design methodology and chaotic vibration response with a single-mass impact damper.

Thermoelastic nonlinear vibration and dynamical response of geometrically imperfect carbon nanotube-reinforced composite plates on elastic foundations including tangential edge constraints

The combined influences of initial geometrical imperfection, elasticity of in-plane constraints of edges, elastic foundations and elevated temperature on the nonlinear vibration and dynamical response of carbon nanotube-reinforced composite rectangular plates are investigated in this paper. Carbon nanotubes (CNTs) are reinforced into matrix according to functionally graded distributions. The properties of CNTs and matrix are assumed to be temperature dependent and effective properties of nanocomposite are determined using an extended rule of mixture. Governing equations in terms of deflection and stress function are established within the framework of thin plate theory including von Kármán nonlinearity, geometric imperfection and interactive pressure from elastic foundation. Analytical solutions are assumed for simply supported plates and Galerkin method is applied to result in nonlinear time differential equation. This nonlinear equation is solved using fourth-order Runge–Kutta scheme. Parametric studies are executed to examine numerous influences on the natural frequency, nonlinear to linear frequency ratio and nonlinear dynamical response of CNT-reinforced composite plates. The results reveal that increase in imperfection size results in increase and decrease in natural frequencies and the amplitude of forced vibration, respectively. In contrast, it is found that the elevated temperature reduces the natural frequencies and enhances the amplitude of forced vibration.

Virtual vibration absorber for active forced vibration reduction

Forced vibrations caused by unbalance can negatively impact the surface finish of high-precision grinding. This paper presents a model-free virtual vibration absorber control law, which effectively reduces vibration levels by emulating a physical vibration absorber. The control law's tuning parameters can be adjusted in real-time to track the spindle frequency, ensuring the excitation frequency always matches the anti-resonance created by the virtual vibration absorber. The control law is first experimentally validated on a flexure and then applied to a high-precision vertical grinding machine achieving a reduction of the forced vibration amplitude due to spindle unbalance by up to 85%.

A NUMERICAL ANALYSIS OF FORCED STEADY-STATE VIBRATIONS OF AN ELECTRO-VISCOELASTIC SYSTEM IN CASE OF A JOINT IMPACT OF ELECTRICAL AND MECHANICAL LOADS

In the current paper an estimation of a mechanical response of a structure on joint mechanical (force and kinematic) and electrical (voltage and current) impacts taking into account different options of their combinations was carried out. A mechanical response was esteemed basing on solution to the problem of natural vibrations for piecewise-homogeneous electro-viscoelastic bodies. A cantilever plate with piezoelectric element attached to its surface was chosen as an object under study. The plate was made of viscoelastic material the mechanical properties of which are described using complex dynamic moduli. A piezoelectric ceramic material was chosen as the one for piezoelectric elements. An amplitude of forced steady-state vibrations of a component of displacement vector that is perpendicular to the surface of the plate was chosen as a quantity that characterize a mechanical response. Variational equation of motion of the object under consideration is formulated based on relations of linear elasticity, linear viscoelasticity and Maxwell’s equations for a conducting media in a quasistatic approximation. Ranges of changing of values of excitation impacts for vibration modes taken into account were chosen on the basis of values of natural vibrations frequencies obtained from the solution to natural vibration problem for electro-viscoelastic bodies. Numerical implementation of the stated problem was performed in finite element software package ANSYS. Some characteristic peculiarities of a mechanical response depending on a type and magnitude of external impact were obtained as the result of the carried out numerical experiments. There was demonstrated that in case of joint impact of two loading factors there reveals an additional capability of control a mechanical response of an electro-viscoelastic system.

The change material mechanical properties based on elastic-viscous material model

The manuscript proposes to use the elastic-viscous material model to simulate the process of changing the mechanical state of the material during operation time. The proposed model established a link between the mechanical properties of the material and the structure's operation. Material mechanical parameters are represented by two parameters: elastic modulus and viscous drag coefficient. The structure's performance evaluation parameter is represented by two kinetic parameters during vibration, namely natural frequency and forced vibration amplitude. The novel aspect of this study is the inclusion of a viscous drag coefficient in the mechanical properties of materials to compensate for the shortcomings of previous evaluation models that are not consistent with reality. This research allows for a more in-depth examination of the material's mechanical properties as well as its ability to change over the course of the structure's life. The study improved some kinetic characteristics related to the material's operation by increasing the number of parameters of the viscosity coefficient in the mechanical properties of the material.

A Novel Single Tube Semi-Active Tuned Liquid Gas Damper for Suppressing Horizontal Vibrations of Tower-like Structures

The purpose of this paper is to present a novel single tube semi-active tuned liquid gas damper (SA-TLGD) for suppressing horizontal vibrations of tower-like structures and to study its damping effectiveness. The main difference to the well-known state-of-the-art tuned liquid column damper (TLCD) is the special geometric shape of the developed SA-TLGD. Contrary to the TLCD, the presented SA-TLGD only consists of a single horizontal tube that is partially filled with water. A large deformable elastic membrane with neglectable stiffness is used as the interface between the liquid and the air. Both ends of the horizontal tube are sealed and the resulting gas spring is used as the restoring force and frequency tuning parameter, respectively. The developed SA-TLGD is a semi-active vibration damping device, where its natural frequency and magnitude of energy dissipation can be re-adjusted during operation. Due to the lack of any vertical tube parts, this new type of vibration absorber requires significantly less installation space compared to the classical TLCDs. The equations of motion of the SA-TLGD and the coupled main system are derived by the application of conservation of momentum. The procedure of optimal tuning of the SA-TLGD is presented, and computational numerical studies are performed to demonstrate the damper effectiveness. It is shown that the application of the developed SA-TLGD provides a large reduction in the maximum horizontal forced vibration amplitudes of tower like-structures and that its semi-active functionality enables the possibility of re-adjustment any time during the operation life of the structure.

An identification method for excitation location and its application in faults location

In this paper, an excitation location method is proposed, which uses the amplitude ratios of the left and right shaft ends (SEAR), to identify the excitaiton location (EL), inspired by the relationships of forced vibration amplitude with the excitation amplitude, the excitation frequency, and the amplitude frequency characteristics between the excitation location and the measurement points (MP). An experimental study for a rotor system is carried out to verify the identification method for excitation location. Furthermore, as one of its application fields, the application framework of the excitaiton location identification method in fault location is proposed and a cracked multistage blade-disk-shaft system is taken as an example to demonstrate the application process by simulation data. The proposed method only needs to establish the axial transmission model of vibration, and only needs to measure the vibration response of the left and right shaft ends. Therefore, it is easy realize in vibration modeling and has strong feasibility in vibration response measuring.

Effect of Elements of the Cutting Conditions on the Amplitude of Vibration during End Milling

The choice of cutting mode elements in end milling has a significant effect on machining performance. However, an increase in these parameters leads to an increase in cutting force and vibration amplitude. Therefore, the designation of the elements of the cutting mode must be carried out taking into account the dynamic phenomena accompanying milling. The article shows the influence of the depth of cut on the amplitudes of forced vibrations. The choice of the optimal values of the cutting mode during end milling is proposed to ensure the minimum vibration amplitude.

Ice-shedding-induced vibration of conductors with active vibration control

A method is proposed for attenuating the vibration of suspended conductors. The idea involves the application of vibration control that contributes to reducing substantially the conductor rebound height following ice shedding. The theoretical background of the method is developed, and its application to vibration following ice shedding is tested by numerical simulations. A simplified model of a conductor with vibration damper is constructed, which simulates the dynamic behaviour of the conductor with damper at the location where the damper is attached. The model takes into account the nonlinear elastic material behaviour of the conductor together with the effects of a vibration damper with active control. Such vibration control may successfully attenuate even high-amplitude vibration that follows ice shedding. Simulation results provide to what extent the vibration amplitude is reduced due to the application of active control. After further improving the method, it may also be adaptable to decrease the amplitude of forced vibrations which are induced by wind and characterized by high amplitude.

Chatter in milling with robots with structural nonlinearity

Stiffness and damping nonlinearities are often negligible in machine tool vibrations, but they are shown to be prominent in industrial robots that are used for milling, mainly due to the several nonlinear phenomenon that occur in the robot’s revolute joints. In this paper, a 2DOF nonlinear vibratory model is presented to study regenerative chatter in robotic milling. The presented model includes cubic stiffness and damping terms to account for the robot’s structural nonlinearities. The machining forces are represented by a combination of periodic forces and delayed vibration terms; the former is generated by the feed motion of the tool and the later by chip regeneration. Furthermore, the machining force model is non-smooth due to (a) periodic entrance and exit of the cutting edges to and from the cutting region, and (b) loss-of-contact at high-amplitude oscillations. The dynamics in the presented model is therefore described by a set of nonlinear Delay Differential Equations with periodic coefficients and non-smooth forces. Numerical continuation with smoothing techniques is used to determine the combinations of spindle speed and axial depth of cut at which the forced periodic vibrations go through secondary Hopf or period doubling bifurcations, causing chatter in the milling process. A KUKA robotic arm with milling end-effector is used as a case study. The presented analysis shows that feedrate, which has no effect on chatter in machine tools with linear dynamics, alters the stability of vibrations in milling systems with nonlinear structural dynamics. Nonlinear systems’ stiffness and damping depend on vibration amplitude. Since feedrate directly influences the amplitude of forced vibrations, the nonlinear system’s damping and stiffness and consequently its chatter stability changes by feedrate.

Static and dynamic characteristics of a compound sphere using Initial Stress Reference Independence

We study the influence of residual stress on the static and dynamic characteristics of a spherical structure. We consider a shrink-fitted compound sphere, where residual stress is developed due to the interference between outer and inner spherical layers. We calculate this residual stress and model the residually stressed material with suitable hyperelastic strain energy satisfying Initial Stress Reference Independence (ISRI). Under the action of inhomogeneous residual stress, the compound sphere behaves as an anisotropic, functionally graded composite sphere, which is reflected by the model. We apply this model to obtain stress distributions and inflation characteristics of the compound sphere. Our results demonstrate the hypothesis that residual stress moderates the stress concentration and reduces the stress gradient in biological/engineering structures. We obtain critical stretch and pressure for spherically symmetric deformations. An increase in interference/residual stress increases the critical stretch/pressure and improves the structural stability. We then apply an analytical approach to calculate the natural frequency of the compound sphere for small amplitude radial vibration. We observe that an increase in residual stress increases the natural frequency and widens the range of stable free vibration. We numerically investigate the free and forced vibration of the compound sphere. Forced vibration amplitude reduces as interference/residual stress increases, which is reflected in the frequency–amplitude plots. The frequency response shows a small hardening non-linearity. We investigate the subharmonic and superharmonic responses for small and large amplitude vibration.

Optimization of Cutting Conditions with an End Mill According to the Criterion of the Smallest Amplitude of Vibration

The article discusses the issues of chatter damping during milling. The relationship between the amplitude of forced vibrations and the cutting speed has been established. The choice of the optimal values ​​of the cutting condition during end milling is proposed to ensure the minimum vibration amplitude.

Controlling the Vibration Amplitude of a System with a Piezoelectric Element by Applying an Electric Voltage to it

The article is devoted to the study of the mechanical response of an electro-viscoelastic structure if an electric voltage with given characteristics supplied to a piezoelectric element attached to the surface of the structure. A cantilever plate made of a viscoelastic material is considered as a structure under study. The amplitude of displacements of the free end of the plate in resonance modes occurring at forced steady-state vibrations is considered as the mechanical response. Excitation of vibrations is realized by a harmonic movement applied to the clamped end of the plate. The control of the mechanical response within the framework of this work is supposed to be performed by supplying an electric signal to the piezoelectric element. This signal changes harmonically and has the form of a potential difference which changes according to a harmonic law. The magnitude of the vibration amplitude of the structure is determined numerically by the finite element method implemented in the ANSYS software package. The viscoelastic properties of the plate material are described according to the relations of hereditary theory of viscoelasticity in terms of complex dynamic moduli. Within the framework of this work, the relations between the mechanical response of the structure and the magnitude and polarity of the electric voltage applied to the piezoelectric element were obtained. It is shown that by a proper selection of the characteristics of the electric voltage, it is possible to control the magnitude of the amplitude of forced steady-state vibrations.

Metallic and porous Ti nanorod arrays for visible-IR light absorption and dendrite-free stable lithium-metal batteries

It is still a challenging task to prepare highly porous nanorod arrays of metals formed on substrates for optical and energy storage applications. Herein, we demonstrate the design and synthesis of black color, metallic and highly porous Ti nanorod arrays as novel current collectors for dendrite-free and highly stable Li-metal anodes. The high porosity of metallic nanorod arrays provides numerous heterogeneous nucleation sites and huge contact area and large space for the accommodation of Li metal. The conductive metallic Ti nanorod arrays enhance electrode integration. Effectively, it eliminates formation Li dendrites and demonstrates superior cycling stability over 300 cycles. Additionally, the unique porous structures of the nanorod arrays can decrease the amplitude of forced vibration in narrow space leading to light absorption. Interestingly, the metal is black instead of metallic color. The black metallic nanorod arrays can absorb more than 96% of both visible and infra-red lights. This black color metallic porous nanorod arrays may find additional applications in aerospace, energy, biomedical, defence, and chemical industries.

Forced Vibrations of Planetary Gears with Elements of the Increased Flexibility

The paper continues the research of dynamics of planetary gears with elements of the increased flexibility. The ba-sis for the analytical model and input equations is the system of nine differential equations of dynamics of the plane-tary mechanism received earlier. In the generalized forces the engine moment, the moment caused by torsion of an elastic shaft of a sun gearwheel, and elastic forces in meshing of gearwheels and on satellites axes are considered. The planetary carrier’s speed is assumed to be constant. The rigidity of the axle of the satellite in the tangential di-rection considerably exceeds the rigidity of the axle in the radial direction, therefore, the displacement in the tangen-tial direction is absent. The moment of the engine changes under the harmonious law. In this case forced vibrations of a sun gearwheel and the satellite can be considered separately from forced vibrations of the satellite in the radial di-rection owing to flexibility of the satellite axle. Amplitude-frequency characteristics of these oscillations are con-structed. Characteristics of vibration processes are expressed through mass-dimensional, kinematic and strength parameters of the planetary gear taking into account flexibility of its elements. Influence of the relative height of the flexible axle section, gear ratio of the mechanism and module of gearing on the amplitude of forced vibrations and the position of the resonance area is investigated. Conclusions are drawn on limits of variation of these parameters and their influences on the structure of planetary gears.

Моделювання впливу параметрів збурень на роботу двоканального п’єзоелектричного гравіметра

The work is devoted to the problem solving of study of the influence of both perturbing accelerations parameters and the inherent parameters of a dual-channel piezoelectric gravimeter on its operation, by means of a computer. For this purpose, a mathematical model of a dual-channel piezoelectric gravimeter was used. In consequence of the carried out mathematical model modeling, the results of modeling on a computer are obtained and presented. The influence of the external disturbance parameters on a new dual-channel piezoelectric gravimeter operation was modeled. As external disturbances, the following was considered: influence of both frequencies and amplitudes of forced vibrations of the base (along longitudinal and transverse axes), on which a dual-channel piezoelectric gravimeter is located, as well as the disturbing vibration accelerations for the most unfavorable resonance cases: w = w0, w = 2w0, w = 3w0, 2w = w0, 3w = w0, where w0 — is the natural vibration frequency of a dual-channel piezoelectric gravimeter, w - is the disturbances frequency. In consequence of the carried-out modeling, the graphs of the output signal change were obtained for various values of the disturbance frequency of vibration accelerations, the damping coefficient and various values of the disturbing vibration accelerations amplitudes. In view of each result and graph that have obtained, the analyzes as to the steady-state forced vibrations magnitude of a two-channel piezoelectric gravimeter as well as the conclusion concerning presence or absence of resonance were made. Using the results of previous studies of the authors, the comparison of the analytical solution of the equations of a dual-channel piezoelectric gravimeter motion, when exposed to the external disturbances was carried out with the results of digital modeling. The analysis of the modeling results has shown that the mean root square deviation of the solutions does not exceed 0.009 mm and this analysis has confirmed the adequacy of the mathematical model of a two-channel piezoelectric gravimeter, in other words, the obtained mathematical model of a dual-channel piezoelectric gravimeter corresponds to a real device and this model can be used for further studies of a dual-channel piezoelectric gravimeter motion parameters.

Mathematical Model of Root Crop Digging with Longitudinal Vibrations

The problem how to reduce damage to tubers when they are dug up is urgent. For the new design of a vibrating digging working body for root crops the mathematical model of longitudinal vibrations of a root crop in the soil is developed as an elastic body in an elastically damped medium. The Ostrogradsky-Hamilton variational principle is applied for the analytical description of the process. The Ritz method was applied to find the frequencies of natural vibrations, the amplitudes of forced vibrations of a root crop as a solid elastic body when it is captured by a vibrating digging body. The frequency equation for the discussed vibrational process was obtained. The values of the first proper frequency of longitudinal vibrations of the considered elastic body of the root crop with specific geometric physical parameters are found. Graphs of the dependence of the first natural frequency upon the elastic deformation coefficient, the damping coefficient of the soil as an elastic damping medium are obtained. When the soil damping coefficient changes within 0 to 10 N∙s²∙m^–3, the first proper frequency changes within 500 to 750 s^-1 (80 to 119 Hz) at soil elastic deformation coefficient 2∙10⁵ N∙m^–3. Dependence of the elastic body forced vibration amplitude upon the change in the amplitude of the disturbing force have been obtained. When the amplitude of the disturbing force changes within 100 to 600 N, the amplitude of forced vibrations of the root crop body changes within 0.30 to 0.68 mm.

RELATIONSHIP BETWEEN PROCESSING TEMPERATURE AND INTERRUPTION IN THE GRINDING PROCESS

This article discusses issues related to the processing of grinding wheels with an intermittent working surface and their influence on the grinding process. To solve this problem, it was necessary to first identify the relationship between the discontinuity of the process and the shock load. Next, determine the trajectory of movement of the forming point of the circle. A diagram of the movement of the center of mass of the circle and the forces acting on it is constructed. Equations are derived that determine these displacements. A system of equations describing the movement of the spindle axis under the action of cutting forces and power imbalance of the wheel is presented. The relationship between the frequency, amplitude of forced vibrations and displacements of the axis under the action of a harmonic disturbing force has been established. Theoretical calculations are confirmed by practical results. Based on the movement of the forming point of the circle, the parameters of the profile of the machined surface are set. The influence of the discontinuity of the process on the grinding temperature is considered.