Amplitude Of Vibration Response Research Articles

Modelling and dynamic characteristics of wind turbine drivetrain based on the variable coefficient sliding mode controller

Vibration is inevitable in operation of mechanical equipment, but severe vibrations will cause serious harm to wind turbines (WTs). This paper takes the drivetrain of 8 MW WT as the object, established a multi-body electromechanical coupling model of WT and verified the accuracy of the established model through the WT drivetrain in the laboratory. Subsequently, based on this model, time-frequency domain analysis was conducted on the vibration response of the WT drivetrain under different control strategies of the generator, and the influence of the generator control strategy on the vibration of the drivetrain was studied. The result shows that the generator control strategy has a significant impact on the vibration response amplitude of the drivetrain, but has a relatively small impact on the frequency component. Meanwhile, the sliding mode controller designed in this paper has good anti-interference ability, which can make the system quickly reach dynamic stability, and effectively suppress the vibration of the main components in the drivetrain. Under the new controller’s control, the transverse vibration displacement of some parts of the WT drivetrain can be reduced by up to nearly 60 %. This paper provides new ideas and new methods for the active vibration reduction control of WT drivetrain.

Effect of wear on the dynamic characteristics of a rigid rotor supported by journal bearings

The purpose of this work is to examine the effects of wear severity on the static and dynamic characteristics of journal bearings, and on the vibration response of a rigid rotor supported by journal bearings. Numerical simulations using MATLAB was conducted for three different operating regimes, namely low loaded operating regime (ϵ0=0.15\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\epsilon _0 = 0.15$$\\end{document}), moderately loaded operating regime (ϵ0=0.45\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\epsilon _0 = 0.45$$\\end{document}) and highly loaded operating regime (ϵ0=0.75\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\epsilon _0 = 0.75$$\\end{document}) with wear depth parameter ratio (δ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta$$\\end{document}) varied from 0 to 0.5 at increments of 0.1. Numerical results showed that the vibration response of the rotor generally increases with the increase of the wear depth for all cases of low, moderately and highly loaded operating regimes of the bearings. For the values of parameters considered in this work, it was shown that the vibration response amplitude of the rotor in worn journal bearings may be six times larger compared to the response amplitude of the rotor in non-worn bearings.

Experimental investigation on identification of lithologies and layered rock interface based on drilling vibration response

The rapid and accurate acquisition of lithologies and rock interfaces is an important prerequisite for guiding the development of oil gas and solid mineral resources as well as the construction of tunnel engineering. However, few studies have been conducted to identify the lithologies and rock interfaces using drilling information. The author used a drilling test platform and an integrated drilling information acquisition system to conduct drilling vibration tests on rock samples of limestone, sandstone, and coal with different lithologies and rock strengths. The test results indicated the following: 1) The drilling vibration response can characterize the properties of the lithology and rock strength and can be used as a key index to distinguish the lithologies and rock layer interface. 2) There were substantial differences in the drilling response (WOB and torque) and vibration response (vibration velocity, acceleration, and amplitude) of the single rock sample. The mean axial vibration velocities of coal, limestone, and sandstone were 5.6, 7.3, and 13.9 mm/s, respectively. The mean axial vibration accelerations were 9.2g, 32.3g, and 13.1g, respectively. The mean amplitudes of the rock surface were 402.6, 588.3, and 2003.8 μm, respectively. The mean weight on the bit was 1.3, 2.6, and 3.5 kN,1 respectively, and the mean torque was 12.3, 25.1, and 33.6 N m, respectively. 3) For the combined rock samples, the drilling and vibration responses of the layered rock interface showed an evident surge. 4) The rock strength affected the drilling and vibration responses. The stronger the rock, the higher was the drilling response (WOB and torque), higher the vibration acceleration, and lower the vibration speed and amplitude. The drilling vibration response displayed a high sensitivity to rock strength. It could effectively characterize the strength characteristics of the rock to accurately identify the lithologies and layered rock interface.

Experiments on flow-induced vibration of four flexible cylinders with large aspect ratio in a square configuration

A system consisting of four cylinders positioned in the quadrilateral arrangement represents the prevalent and fundamental constituent within pipe bundles and tube banks in numerous engineering scenarios. This research presents a laboratorial study on flow-induced vibration (FIV) exhibited by four flexible cylinders positioned within a square geometric arrangement. The uniform flows were produced by a carriage on the top of a towing tank. Considering flow velocities and structural parameters, Reynolds number could reach 16000. The spacing between the cylindrical centres was selected as 6.0 D (D denotes the outer diameter of cylinders), and two typical incidence angles 0° and 45° were examined. For each flexible cylinder model, strain gages at seven distinct measuring positions were utilized to collect the oscillation data in cross-flow (CF) and in-line (IL) directions. Principal vibration modes, response frequencies, response amplitudes and motion trajectories were presented to understand the FIV features. For incidence angles 0°, considering the four flexible cylinders as two sets of tandem cylinders arranged in parallel is not appropriate due to the proximate effect. The behaviours of the two upstream cylinders resembles those of the pair of cylinders positioned in a side-by-side configuration, whereas behaviours for the downstream cylinders are influenced by wake interference generated from leading cylinders. IL response frequencies decrease to the values close to the CF response frequencies, resulting in the elliptical-shaped motion trajectories with large IL displacements. For incidence angles 45°, the upstream cylinder displays characteristics akin to those of a solitary cylinder experiencing vortex-induced vibration (VIV). Reactions for the central pair of cylinders result from the amalgamation of VIV and wake-induced flutter. While, reactions observed for downstream cylinder are characterized by low frequencies, significant IL displacements and more chaotic trajectories.

Dynamics Modeling and Analysis of Rolling Bearings Variable Stiffness System with Local Faults

By analyzing the support of load-carrying rolling elements when the rolling elements fall into the fault position, the dynamics model of a rolling bearing variable stiffness system with local faults is proposed, considering the retention factor of the contact deformation. Then, this paper researches the change of effective contact stiffness, contact deformation, contact force, and the total effective stiffness of the rolling elements. The results show that the contact stiffness of the rolling elements abruptly decreases when the rolling elements fall into the fault position. The contact deformation and contact force of the load-carrying rolling elements in the load zone increase, rebalancing the external radial load while causing a sudden reduction in the total effective stiffness, resulting in the vibration of the system. When different rolling elements fall into the outer ring fault position, the change in total effective stiffness and the system response are equal in magnitude. Additionally, there is a significant outer race fault characteristic frequency accompanied by frequency multiplication in the fault characteristic spectrums. When different rolling elements fall into the inner race fault position, the total effective stiffness is modulated by the inner race rotation and varies dramatically, resulting in the amplitude of the system time domain vibration response also being modulated by the inner race rotation and varying dramatically. Additionally, there is a significant inner race rotational frequency accompanied by frequency multiplication, an inner race fault characteristic frequency accompanied by frequency multiplication, and a side frequency in the fault characteristic spectrums. The research can provide some reference for the effective diagnosis of the rolling bearing fault.

Nonlinear vibrations of four-degrees of freedom for piezoelectric functionally graded graphene-reinforced laminated composite cantilever rectangular plate with PPF control strategy

The nonlinear vibration suppression of the piezoelectric functionally graded graphene-reinforced laminated composite cantilever (PFG-GRLCC) rectangular plate with positive position feedback (PPF) control strategy is investigated firstly. The material properties of the graphene-reinforced structure are calculated through the Halpin–Tsai micromechanical model. Considering the transverse external excitation and the converse effect of piezoelectricity, the governing equations of motion are formulated through von Karman large deformation theory, the classical laminated plate theory, and Hamilton principle. After adding the PPF controllers, a four-degrees of freedom model for the close-loop vibration control system is achieved via Galerkin truncation technique. The average equations in the case of the primary resonance and 1:1:3:3 internal resonance can be obtained using the multiple scale perturbation (MSP) method. The amplitude–frequency response curves are studied by the numerical continuation algorithm. The detailed parametric analyses show that the PPF controller can effectively reduce the nonlinear vibration response amplitudes of the PFG-GRLCC rectangular plate. In addition, the results reveal the energy transform between the host system and the PPF controller. This work is expected to provide theoretical guidance for nonlinear large amplitude vibration reduction of graphene-reinforced structure.

Dynamic characteristics analysis of bilayer bio-inspired X-shaped vibration isolation structure

Based on the vibration isolation properties of the coupled toe-leg structure of the biped bird, a bilayer bio-inspired X-shaped vibration isolation structure (BBXVI) considering the coordination function between skeleton type and muscle/tendon is proposed in this research. The mapping relationships of equivalent restoring force–displacement and equivalent stiffness–displacement with various parameters are analyzed by statics, the parameter condition and the modulation of nonlinear behavior of the BBXVI to achieve quasi-zero stiffness (QZS) are investigated. Based on establishing dynamic model of the bilayer X-shaped structure, the effects of initial angle, rod-length ratio and rod length on dynamic characteristics and vibration transmissibility of the BBXVI subjected to displacement excitation are studied by incremental harmonic balance method (IHBM). The study found that the BBXVI presents excellent low frequency vibration isolation performance. With increasing α1, the QZS characteristic, vibration isolation bandwidth and response amplitude of the BBXVI increase first and then decrease. The larger rod-length ratio and longer rod length can increase the vibration isolation bandwidth and improve the vibration isolation performance. In addition, longer rod length could make the equivalent stiffness of the BBXVI gradually evolve from hardening spring to softening spring properties, and the vibration transmission property of the vibration isolation system is changed.

A Time Frequency Domain Based Approach for Ball Grid Array Solder Joint Fatigue Analysis Using Global Local Modeling Technique

AbstractThe fatigue life prediction of the electronic packages under dynamic loading conditions is an increasingly important area of research, with direct application in packaging industries. Current life prediction methodologies are, in general, developed through a finite element (FE) model that is correlated using an experimental data measured through sweep sine testing. The frequency response function (FRF) generated by using a sweep sine testing may suffer from leakage and windowing of the signal may not work correctly, which results in the shift in the amplitude and the resonance frequencies of the package. In consequence, there will be a significant deviation between the actual and the predicted natural frequencies and the amplitude of vibration response in the given excitation range, resulting in the longer time to fail the package during the laboratory based/virtual durability testing. Thus, it is necessary to develop a suitable validation technique in time/frequency domain to address this issue. In this paper, the step sine testing procedure is utilized to validate the FE model of a test vehicle consisting of a board level ball grid array chip package and the resonance-based fatigue testing is performed in the FE-based simulation. The global–local modeling approach is utilized to model the test vehicle and the volume average von Mises stress is used to predict the life of the solder joint. Following the numerical simulations, fatigue test is carried out in the test vehicle at the first resonance frequency obtained from the step sine test. Experimental results show that there are full openings of the corner balls in a very short interval of time. The results of the life prediction from the FE model and from experiments are comparable to each other thus validating the proposed methodology.

Investigation for the effect of stiffener on vibration response of engine cover of vehicle

Weight reduction and strengthening of the body is the major factor in automobile industries. It improves the fuel efficiency and safety factor of the vehicle. Inner engine cover is an important component of heavy vehicles. It is mounted inside the vehicle cabin. It reduces noise transfer from the engine and protects the engine from debris, dust etc. In this paper, we have focused on the effect of the stiffener and weight reduction of engine cover by optimizing design. The suitable material used for engine cover for low weight and low thermal conductivity is SMC polymer. This paper presents the static stress analysis, modal analysis and harmonic analysis of Engine Cover to identify the effect of stiffener and composite material on vibration response of engine cover. It is observed that the static deflection and vibration response amplitude of SMC polymer material Engine Cover is less as compared to other counterpart materials. This paper investigates the effect of stiffener on vibration response of engine cover using ANSYS Software.

Response of Composite Beam Structure under Unbalanced Excitation of Rice Threshing System

This paper studies the dynamic response of the support beam under the unbalanced excitation of the rice threshing system. The differential equation of motion of the supporting beam under the action of harmonic force is established by the modal superposition method, and its dynamic response is analyzed. It is found that the initial vibration of the supporting beam will fluctuate greatly when it is excited by the unbalanced force. In response to this problem, the application of composite beams as the support structure of the threshing system is proposed. The composite beam is mainly composed of uniform and isotropic Euler–Bernoulli beams that are parallel to each other, and the two beams are connected by elastic spring elements. Then, the vibration response of the composite beam structure under unbalanced forces is studied. The results show that the vibration of the composite beam is more stable when it is excited by the unbalanced drum. The overall vibration response amplitude is smaller than that with single support, and the vibration reduction effect is obvious. When the stiffness changes, the change trend of the response amplitude of beam 1 and beam 2 is opposite, that is, the stiffness increases, the vibration amplitude of beam 1 decreases, and the amplitude of beam 2 increases. This shows that the composite beam is suitable for the support structure of the harvester.

Implementation of the dynamic balancing approach of a rotating composite hollow shaft

Balancing is essential in rotating machinery, which is widely employed in many technical sectors, particularly in high-speed rotor-bearing systems. The mass balancing method of the hollow shaft manufactured of composite materials is investigated in this study over the whole speed range of the rotor. The main goal of the balancing technique is to generate a smooth-running machine by removing the commonality imbalance mass through the use of compensating mass unbalance. As a result, MATLAB code is created to produce a functioning mathematical model of the rotor-bearing system. The unbalanced rotor-bearing system finite element model is proposed to set the balancing mass of the composite hollow shaft at a selected speed rotor that allows minimizing the vibration response amplitude of the rotor as much as possible with minimal impact on the rest of the imbalance response within the speed range of the interest. As a consequence, this study validates the process for distributing imbalance in modelling balancing to balance the flexible hollow shaft with an unbalanced mass throughout the complete speed range of the shaft. The balance of the hollow shaft at the critical speed was observed in this approach, and the vibration amplitude was determined by adding extra mass at a specific angle

Stability Analysis of Electromechanical Coupling Torsional Vibration for Wheel-Side Direct-Driven Transmission System under Transmission Clearance and Motor Excitation

The wheel-side direct-driven transmission system (WDTS) is a new intelligent transmission technology, which has significant advantages in high-efficiency and few malfunctions for the electric bus. Based on the Lagrange–Maxwell equation, the WDTS electromechanical coupling dynamic model, whose effectiveness is verified by the PMSM speed, is constructed for analyzing the system torsional vibration destabilization characteristics. Then, by determining the resonance curve equation for the torsional vibration response amplitude of the WDTS with the direct multi-scale method, the influences of the torque ripple amplitude of the PMSM and the transmission clearance on the system torsional vibration stability are analyzed. The results indicate that the WDTS torsional vibration response shows complex nonlinear characteristics especially under the effect of the system transmission clearance, which has an important impact on the system stable operation. The research results can lay a theoretical foundation for the design of the WDTS of the electric bus.

Influence analysis of control signal phase on the vibration reduction effect of active constrained layer damping

The phase of the control signal applied on the piezoelectric constrained layer will have a direct influence on the vibration reduction effect in the process of implementing active constrained layer damping (ACLD) to the structure. Taking the ACLD cantilever beam system as the object, this paper focused on the study of the effect of control signal phase on the vibration suppression using the ACLD by establishing the experimental system and creating the relevant dynamic model. By analyzing the shear deformation of viscoelastic layer and combining piezoelectric equation, dynamic viscoelastic theory and mechanical analysis, a dynamic model of ACLD cantilever beam was created, which can effectively simulate two damping mechanisms and include the influence of control signal phase. The rationality of the dynamic model was verified by comparing the natural frequency and the time-domain vibration response corresponding to different control signal phases obtained by simulation and experiment. Using the presented dynamic model and the experimental results, the influence of the control signal phase on the vibration reduction effect was determined. Specifically, the control signal phase and the vibration response amplitude of the cantilever beam show a harmonic relationship centered on the response amplitude without control. The phase value corresponding to the best vibration reduction effect is not 180° like pure piezoelectric active vibration reduction and it is about 140° because of the hysteresis effect of viscoelastic material (for ZN-1 viscoelastic material selected in this study, the loss angle is about 40°).

Research on the Vibration Characteristics of Aviation Hydraulic Clamp and Pipeline Based on Hard Coating

Aviation hydraulic clamp-piping systems often experience damage due to vibration, which poses a great threat to the reliability and safety of the aircraft. In this paper, a hard coating is used as a new damping method to study the vibration characteristics of aviation hydraulic clamp-piping systems. Three kinds of coated clamp entities are obtained by optimization and preparation, and the combination of finite element simulation and experiment is used to analyze the vibration response of the high- and low-pressure rotor under fixed-frequency simple harmonic excitation, and the resonance response under sweep-frequency excitation of the aviation hydraulic clamp-piping system. Through orthogonal experiments, it is clear that 304 stainless steel clamps coated with 200-μm-thick YSZ-PTFE coating have the best vibration damping effect on the clamp-piping system; that is, the damping rate can reach 24.67% under fixed-frequency excitation, and swept frequency damping can reach 19.93%. The maximum error between the simulation and the experimental vibration response amplitude is 7.9%, which proves the correctness of the model and verifies that the YSZ-PTFE hard coating can significantly improve the vibration damping effect with very good application prospects.

Numerical simulation of surface roughness effects on the vortex-induced vibration of a circular cylinder at a subcritical Reynolds number

The Vortex-Induced Vibration (VIV) of a circular cylinder with different surface roughness is numerically simulated at a subcritical Reynolds number of 3900. The effects of surface roughness on the vibration response amplitude, hydrodynamic coefficients and wake vortex are analyzed. The results show that as surface roughness increases, four branches (initial, upper, super-upper and lower branches) appear in the VIV response for a smooth cylinder, and for a cylinder with a small surface roughness of K S / D = 2.5 × 10 − 3 , this response changes to three branches (initial, upper and lower branches). The vortex shedding for the initial and lower branches is 2S mode, and that for the upper and super-upper branches (lock-in range) is P + S − , P+S + and 2P modes. With increasing surface roughness, the maximum amplitude has little difference, and the width of the lock-in range increases. A large jump in the vortex phase at the transition of the initial and upper branches and a large jump in the total lift phase at the transition of the upper and lower branches are found, and these jumps are associated with a switch in the timing of vortex shedding (jump of the vortex phase: 2S mode to P + S − mode; jump of the lift phase: other modes to 2S mode). The results are significant for the development of flow and vibration control technology.

Lateral Parametric Vibration of Footbridge under Pedestrian Excitation considering the Time-Delay Effect

Pedestrian excitation may consequently cause large-scale lateral vibration of the long-span softness of footbridges. Considering the influence of structural geometric nonlinearity, a nonlinear lateral parametric vibration model is established based on the relationship between force and speed. Taking the London Millennium Footbridge as an example, the Galerkin method is applied to formulate parametric vibration equations. In addition, the multi-scale method is used to analyze the parametric vibration of footbridge system theoretically and numerically. The paper aims to find out the reasons for the large-scale vibration of the Millennium Footbridge by calculating the critical number of pedestrians, amplitude-frequency, and phase-frequency characteristics of the Millennium Footbridge during parametric vibration. On the other hand, the paper also studies the influence parameters of the vibration amplitude as well as simulates the dynamic response of the bridge during the whole process of pedestrians on the footbridge. Finally, the paper investigates influences of the time-delay effect on the system parameter vibration. Research shows that: the model established in the paper is reliable; the closer the walking frequency is to two times of the natural frequency, the fewer number of pedestrians are required to excite large vibrations; when the number of pedestrians exceeds the critical number in consideration of nonlinear vibration, the vibration amplitude tends to be stable constant-amplitude vibration, and the amplitude of vibration response is unstable constant-amplitude vibration when only linear vibration is considered; the following factors have an impact on the response amplitude, including the number of pedestrians on footbridge per unit time, damping, initial conditions, and the number of pedestrians in synchronized adjustment. At last, when considering the lag of the pedestrian’s force on the footbridge, the time-lag effect has no effect on the amplitude but has an effect on the time needed to reach a stable amplitude.

Nonlinear response analysis of aero-engine rotor bearing rub-impact system caused by horizontal yawing maneuver load

Based on the simplified aero-engine rotor system, a new nonlinear response prediction model of rotor bearing rub-impact system is established. Different from the traditional rotor system rub-impact model, based on the detailed characteristics of the blade–disc system, this paper considers the influence of the number of blades and the dynamic to static clearance on the rub-impact force. In addition, the influence of additional load on the established rotor-bearing system due to the change in the flight motion state of the horizontal yawing maneuver is also considered The Newmark-β numerical method is used to solve the system, and the effects of maneuver load and rub-impact stiffness on the nonlinear dynamics of the system are studied The results show that the system produces a kind of sub harmonic resonance rub-impact phenomenon, that is, the system will produce 1/2 sub harmonic resonance under the action of maneuver load near the double critical speed, which will increase the vibration response amplitude of the system. With the increase of maneuver load, the system always has complex nonlinear phenomenon; with the increase of rub-impact stiffness, the system produces a large number of frequency division and frequency multiplication components, which can be used as the characteristic frequency of rub-impact faults.

Optimization of the frequency tracking scheme for an adaptively tuned vibration absorber

Vibration absorbers can absorb vibration energy and reduce the vibration amplitude of the primary system. With adaptive tuning, an adaptively tuned vibration absorber (ATVA) can track the dominant frequency of the external excitation, and reduce the vibration response amplitude of the primary system under variable-frequency external excitation. To realize the optimal vibration reduction performance, the 100% frequency tracking scheme of the adaptively tuned absorber must be optimized. In this regard, a dynamic model of an undamped primary system and a vibration absorber is established based on vibration absorption theory, and alternative tuning schemes for these absorbers are investigated in this paper. Using ATVA with the 100% frequency tracking scheme as a reference, a frequency tracking scheme is optimized by the segmented intercept optimization method. This optimization method continuously tunes the ratio of the absorber natural frequency and external excitation frequency to minimize the response in the variable-frequency vibration regions. Hilbert-Huang transform (HHT) time-frequency analysis is performed on the vibration response to reveal the vibration reduction mechanism of the improved vibration absorber. The vibration reduction effects are verified by comprehensive analysis results and experimental results.

Vibration transmission characteristics of complex lubricating oil pipeline system

Considering the axial, lateral and torsional vibrations and considering the effect of Poisson coupling in the axial vibration, ignoring the effect of friction, based on the Timoshenko beam model, a dynamic model of the lubricating oil pipeline system with force and speed as variables is established. Using lubricating oil pumps and valves as vibration sources, the vibration characteristics of multi-branch lubricating oil pipeline systems including elbows are studied. The results show that due to the coupling of lubricating oil and pipeline structure, the vibration peak and peak frequency of pipeline system are significantly reduced, but the frequency lateral vibration response amplitude increases significantly at some characteristic frequency; when the pipeline support stiffness increases, the natural frequency of the pipeline increases, causing the peak frequency of pipeline vibration to shift to high frequency, and the peak frequency resolution increases.

Study on frequency domain response characteristics of straight pipe conveying fluid

In this paper, a transfer matrix method (TMM) for solving the frequency domain response of the straight pipe conveying fluid is established based on 14-equation model by Laplace transformation. The reliability of the method is verified by the frequency domain response results of fluid velocity and structural axial stress in the pipe under free boundary conditions. Then, based on the transfer matrix method, the influence of boundary conditions and fluid density on the frequency domain response characteristics of pipeline vibration is analyzed. The numerical results show that the boundary conditions have a significant effect on the amplitude of the vibration response of the pipeline, but the amplitude changes little under the fixed and simply supported boundary conditions. The vibration frequency is inversely proportional to the density, while the axial vibration response amplitude increases with the increase of fluid density, and the change of density has little effect on the transverse vibration response.