Dynamic Vibration Analysis Research Articles

Nonlinear dynamic modeling and vibration analysis for early fault evolution of rolling bearings

In rotating machinery, the condition of rolling bearings is paramount, directly influencing operational integrity. However, the literature on the fault evolution of rolling bearings in their nascent stages is notably limited. Addressing this gap, our study establishes an innovative nonlinear dynamic model for early fault evolution of rolling bearings based on collision impact. Firstly, considering the fault evolution characteristics, the influence of the rolling element and fault structure, the dynamic model of early fault evolution between the rolling element and the local fault is established. Secondly, according to the Hertzian contact deformation theory, a nonlinear dynamic model of rolling bearings expressed as mass-spring is established. Thirdly, the energy contribution method is used to integrate the fault evolution model and the nonlinear dynamic model of the rolling bearing. A nonlinear dynamic model of early fault evolution of the rolling bearing is proposed by using the Lagrangian equation. Comparing the simulation results of the nonlinear dynamic with the experimental results, it can be seen that the numerical model can effectively predict the evolution process and vibration characteristics of the fault evolution of rolling bearings in the early stage.

Dynamic modeling and vibration analysis for motorized spindle with uncertainties

Abstract Uncertainties inevitably exist in motorized spindle and it is difficult to accurately describe its dynamics based on a deterministic model. In this paper, a dynamic model of motorized spindle with uncertainty is proposed. The deterministic dynamic model of the motorized spindle rotor system is built by the finite element method, and the uncertainties are constructed by the polynomial chaotic expansion (PCE) method. The impact of each uncertainty parameter on the critical speed of the system is investigated by adopting the Sobol global sensitivity analysis method. The effects of uncertainties including the bearing stiffness, the material Young’s modulus, the disc mass and the unbalanced excitation on the vibration response of motorized spindle are analyzed. The modal experiments are carried out to verify the effectiveness of the model. The results show that the uncertainties have a great influence on the vibration characteristics of the motorized spindle system, in which the bearing stiffness mainly affects the high-order frequency response of the system, while the Young’s modulus affects all the order frequency response of the system. The influence of hybrid uncertainties on the frequency response of the system is more complex. This study provides a guidance to the design of motorized spindle.

Nonlinear dynamic modeling and vibration analysis for flexible tethered satellite systems under large deformations

The escalating threat posed by space debris necessitates innovative approaches for its removal. This article presents a comprehensive mathematical modeling and dynamic analysis of a flexible tethered satellite system (FTSS) in the post-capture phase, taking into account nonlinear strain effects for the flexible appendages. The FTSS consists of a rigid central body satellite, two identical flexible panels, and a towing mass that manipulates the satellite through a tether. We develop a detailed dynamic model that accurately represents the system’s three-dimensional motion, incorporating the rigid body’s 6 degrees of freedom (DOF), the tether’s 3 DOF motion, and two modal generalized coordinates for each panel. The extended Hamilton method is employed to derive this model, enabling us to investigate the conditions under which nonlinear strain considerations become critical. The findings of this article reveal that nonlinear strain effects can profoundly impact the system’s dynamics under certain geometric and forcing conditions, often overlooked in previous studies. In these scenarios, the panel strains exceed the linear regime, necessitating the use of nonlinear models for accurate representation. This work emphasizes the importance of incorporating nonlinear strain terms in the dynamic analysis of FTSSs, particularly when dealing with large deformations and high-amplitude vibrations encountered in debris removal applications.

Vision-based estimation method of crowd-induced vertical dynamic loading and vibration analysis

Most existing studies concentrating on human-induced loads on structures often rely on approximate formulas based on the loading from a single gait cycle, which inherently possess certain limitations. In this paper, a novel approach utilizing a multi-person 2D posture estimation model rooted in computer vision technology to real-time identify the posture of moving human bodies on construction sites is proposed. This approach works to deduce the reaction forces of moving bodies upon the floor by analyzing the motion characteristics of different body parts during their movement, ensuring an accurate estimation of structural loading. To validate the model’s accuracy, a series of tests were conducted, leveraging force measurement equipment to scrutinize the precision of load estimation during single-person motion. This examination seeks to ascertain the potential of the load prediction model in forecasting multi-person loads within actual project environments.

Dynamic modelling and vibration analysis of a bolted spigot joint structure considering mating interface friction: simulation and experiment

Dynamic modelling and vibration analysis of a bolted spigot joint structure considering mating interface friction: simulation and experiment

Dynamic modeling and vibration analysis of bolted flange joint disk-drum structures: Theory and experiment

Bolted flange joint disk-drum structures (BFJDSs) are key components in aero-engines, in which fatigue damage often occurs due to structural vibration. However, no study has so far given an effective theoretical dynamic model of BFJDSs. In this study, an effective dynamic model of BFJDSs is proposed. The present model considers the flange effect, non-uniform contact pressure of bolted joint, and bolt mass. The theoretical expression for describing the stiffness variation of bolted joints is presented. During the modeling process, the energy functions of disk, drum, and flange are obtained according to the Kirchhoff plate, Sanders’ shell, and Euler-Bernoulli beam theories, respectively. The non-uniform artificial spring technique is adopted to simulate the pressure distribution of bolted joint. This method is capable of taking into account the contact pressure, which is closer to real contact situation. The displacement functions of disk and drum are expanded by using the Chebyshev orthogonal polynomials, and the motion equations are obtained by employing the Lagrange equation. Then, the experimental studies are performed on BFJDSs to illustrate the effectiveness of the theoretical model. Finally, the frequency veering and coupling vibration phenomena are revealed. The comparison studies indicate that the established theoretical model can well predict the vibration characteristics of BFJDSs under both bolt looseness and no-looseness conditions. The maximum error can be reduced from 46.81% to 3.61% by using the present dynamic model.

Dynamic modelling and vibration analysis of gearbox bearings for a high-speed train with polygonal wheel

Dynamic modelling and vibration analysis of gearbox bearings for a high-speed train with polygonal wheel

Aeolian Vibration Dynamic Analysis of Large-Span, Relaxed Antenna Cable Net Based on Finite Particle Method

The large-span, relaxed antenna network is a large deformation flexible structure due to its low pre-tension level of the wires. Its dynamic analysis under a wind load belongs to dynamic and geometric nonlinear problems, which is very complex to accurately calculate and solve. This paper explores the possibility of the finite particle method (FPM) to the aeolian vibration analysis of a large-span, low stress-tensioned antenna cable net. In the FPM, the antenna network structure is discretized into a group of finite particles, where the motions of all particles follow Newton’s second law and can be solved dynamically using a central difference scheme. The effectiveness and applicability of the FPM were verified by comparing the calculation results of the finite element method and FPM. The FPM was used to study the effects of wind speed and the distribution of vibration on the aeolian vibration of antenna cable nets. The results showed that this method is suitable for studying the aeolian vibration of a large-span, low stress-tensioned antenna network and has high computational efficiency and accuracy.

Dynamic modeling and vibration analysis of double row cylindrical roller bearings with irregular-shaped defects

Dynamic modeling and vibration analysis of double row cylindrical roller bearings with irregular-shaped defects

Dynamic modeling and vibration analysis of an RV reducer with defective needle roller bearings

The rotate vector (RV) reducer's needle roller bearings (NRBs) are vulnerable to wear and flaws such as fatigue spalling of the raceway material. Studying the vibration mechanism and the excitation laws of NRB failures is essential to enhancing the RV reducer's performance and comprehending its operating state. This paper presents a dynamic model of the RV reducer based on the theory of contact multibody dynamics. It integrates internal and external raceway defects and takes into account the synchronous contact interaction between NRB groups and the crankshaft and cycloidal gears, as well as the time-varying mesh stiffness in the planetary gear transmission and cycloidal pin transmission. The study demonstrates that the rolling of bearings and the meshing of internal transmission components are the primary causes of vibration in a healthy RV reducer through experimental verification and dynamic simulation analysis of the system with and without NRB failures. Both the crankshaft rotation frequency and the cycloidal gear rotation frequency affect the vibration excitation source's characteristic frequency. The vibration amplitude of the RV reducer is influenced by bearing flaws on a periodic basis. The impact of internal raceway defects is greater than that of external raceway faults, resulting in a notable rise in vibration amplitude.

Numerical modelling of traffic-induced dynamic loading on a two-story residential building

BackgroundThis paper presents a numerical modelling procedure of dynamic loading due to traffic on a two-story residential building. In developing countries cities and towns, poor quality narrow road sections with high traffic density are common. In such cases, ground vibration due to traffic could be higher and lightweight buildings located closer are exposed to traffic-induced dynamic loading. Design codes require a proper assessment of such vibrations. However, a clear and definite procedure of assessment is not usually provided. This research presents an assessment procedure of dynamic loading due to traffic on a soil foundation system of light weight buildings based on numerical modeling. Traffic induced ground vibration acceleration amplitudes, frequencies and durations were measured, and the dynamic loads were calculated from measured vibration accelerations and vibrating mass of the vehicle. A two-story residential building with flexible square shallow footings was modelled together with the foundation soil using PLAXIS-2D. The dynamic load was modelled as harmonic loading considering the highest amplitude of vibration measured.ResultsOn the calculation stage, static loading analysis, dynamic loading analysis and free vibration dynamic analysis were carried out. A maximum increase in extreme total displacement of the soil to 22.03 mm was observed after the dynamic loading from 18.96 mm extreme total displacement due to static loading. Extreme effective mean stress in the soil increased to 112.81 kPa from 110.5 kPa, due to the dynamic loading. In addition, a differential settlement of 3.14 mm between two adjacent footings was observed after the traffic induced ground vibration. Furthermore, the Mohr–Coulomb plastic points were observed to be concentrated to the side of the soil-foundation system which the dynamic load was acting on.ConclusionThe regular exposure to traffic-induced vibrations may cause frequent change in stress and deformation response of the foundation-soil system. In areas where lightweight buildings are exposed to regular traffic induced vibrations, proper assessment of the effect should be carried out and measures should be taken to mitigate the problem. Improving road surfaces and limiting vehicle speed are possible remedial measures to reduce ground vibrations due to traffic.

Dynamic modeling and vibration analysis of planar pipeline with partial constrained layer damping treatment: Theoretical and experimental studies

As an important portion of pipeline systems, the vibration suppression analysis of the plane pipeline is of great significance for life prediction and vibration control. To reduce pipeline vibration by attaching constrained layer damping (CLD), the vibration characteristics of the Z-shaped pipeline (taking a Z-shaped pipeline in the planar pipeline as an example) with partial CLD treatment are investigated, and a modeling method is proposed. Based on the Timoshenko beam theory, the energy formulas of laminated straight pipeline with CLD and curved pipeline are developed. Artificial springs are introduced to establish the coupling between pipeline segments and consider the clamp constraint. Four kinds of polynomials are compared to expand the displacement functions, and the dynamic equitation is derived by employing the Lagrange equation. The rationality of the model is verified by a FE model and by in-plane and out-of-plane experimental test systems of the Z-shaped pipeline before and after CLD treatment. In addition, the results show that a change in the geometrical parameters of the pipeline can cause frequency alternation. The influence law of CLD thickness on the Z-shaped pipeline in-plane and out-of-plane is inconsistent. The modeling method can further provide a basis for nonlinear vibration analysis of pipeline systems.

Dynamic modeling and vibration analysis for the gear-rotor-bearing system with localized failures

Accurate identification of faults in gearbox requires a clear understanding of its vibration response. In this study, through establishing dynamic model and experimental observation, the vibration characteristics of gear-rotor-bearing systems with localized failures are investigated and discussed. Firstly, the models of the gear pair, rotor and bearing are integrated, a comprehensive model for gear-rotor-bearing systems is developed. Then the model for describing localized failures is established and supplemented to the system equations. By using the model, the influence of the spalling defect and bearing raceway failures on the dynamic response are analyzed. Moreover, multiple sets of experiments are conducted for verifying the model and analysis results. The paper explains that periodic shock will be generated due to the presence of localized failures, the vibration intensity of the faulty part at specific frequencies is greatly enhanced, and a series of harmonic frequency components will be generated. Additionally, due to the pulse force transmission, the operation state of other components is also seriously affected, and frequency modulation phenomenon between different components can be observed. The defect frequency of bearing outer raceway is commonly modulated with meshing frequency and cage frequency, while the inner raceway defect frequency and meshing frequency are modulated with shaft frequency, and the amplitude of harmonics caused by modulation is obviously increased under the excitation of localized failure.

Finite Element Based Static and Dynamic Vibration Analysis of a Beam with Axial Variation of Material Properties

Abstract: The study examines the vibration analysis of a damped cantilever beam with nonuniform variation in material properties using finite element methods. With power modification of material parameters in the axial direction, the static and dynamic response of a prismatic rectangular beam with damping has been examined. For the finite element approach, two noded beam elements with two degrees of freedom at each node were evaluated. The power law variation of material properties was used throughout the investigation. This research investigated the effects of proportional damping on displacement, velocity, and acceleration responses. The proposed beam's mass, stiffness, and damping matrices were calculated using Hamilton's concept. In the temporal domain, the Newmark Method has been utilized

Dynamic modeling and vibration analysis of planetary gear sets concerning mesh phasing modulation

This paper studies the changes in behavior, in terms of mesh phasing modulation, of planetary gear transmissions (PGTs) due to various gear pinhole position errors. An advanced model of the spur PGT is established to explore the effects of the position errors on mesh phasing relations and an analytical determination of the relative mesh phasing variation is derived. Furthermore, the vibration performance of planetary gears is investigated by developing a novel dynamic model and components of the vibration signals are clarified using the proposed model. Additionally, we further perform several experiments to measure the mesh phasing variations using strain gauges and collect the gear vibration signals using accelerometers. Finally, simulation and experimental results are compared to verify the proposed models, and the results indicate that the presented models provide the opportunity for the researchers to quantify the mesh phasing relations relative to the gear position errors as well as clarify the frequency modulation mechanism of gear vibrations in PGTs.

Dynamic modeling and vibration analysis of offshore wind turbine rotor system with insulated bearing under inclined shaft current damage

The offshore wind turbine is a device that uses the wind energy on the ocean to generate electricity. The voltage generated by offshore wind turbine can break down the insulated bearing and cause inclined shaft current damage. To explore the dynamic characteristics and influencing factors of offshore wind turbine rotor system, a dynamic model of offshore wind turbine rotor system is proposed. The insulating coating, inclined shaft current damage and contact characteristics are considered in the model. Through numerical simulation, the mapping relationship between vibration response and damage length is studied, the influence of the interaction between inclination angle and radial clearance on vibration response is analyzed, and the influence of the mass of insulating coating and speed on vibration response is discussed. The practicability of the model is proved by the experiment of physical prototype. The results show that, as the length of the shaft current damage increases from 10 × 10−5 m to 50 × 10−5 m, the strength of the vibration response increases. The coupling of the inclination angle of the shaft current damage and the radial clearance jointly promotes the enhancement of the vibration response. The enhancement effect of radial clearance is more significant than that of inclination angle. The increase of speed worsens the state of operation, and the state transitions from stable quasi-period to chaos.

Thermo-electro-mechanical dynamic and free vibration analysis of FGPM nanobeam with initial stress

Currently, nanostructures such as nanobeams, nanomembranes and nanoplates have been a hot area of research triggering. The contribution of this research article deals with both the effect of the free and dynamic vibration of a nanobeam as well as the use of the FGM material by integrating the piezoelectric effect. In fact, incorporating the initial stress for a nanoscale beam has not been considered yet. This paper displays an analysis of dynamic and free vibration of power-law functionally graded piezoelectric materials (FGPM) subjected to thermal-electro-mechanical loads with initial stress. The model was resolved based on nonlocal Timoshenko beams theory. The dimensionless fundamental frequency gradually improved with the new configuration of the FGPM nanobeam by 5% compared to the FGM nanobeam. The accuracy of this model is highlighted via numerical examples for different boundary conditions. To solve the governing equations, the polynomial differential quadrature method (PDQM) was elaborated and resolved numerically using MATLAB. For various configurations of the FGPM nanobeams, the effect of scaling parameters, volume fraction and slenderness ratios were discussed. In addition, for different edge conditions, variations of the first four frequencies with volume fraction indices and for different scaling parameters were set forward. This study corroborated that the power exponent, nonlocal parameter, slenderness ratio and thermo-electro-mechanical loads have significant effects on the dimensionless frequencies of various FGPM nanobeams. The present work provides an enlightening as guideline for the draft of a nanoscale beams based thermo-electro-mechanical actuators.

Dynamic modeling and vibration analysis of a flexible gear transmission system

Vibrations of gear transmission systems (GTSs) are the key problems in the machinery industry. In the previous vibration analysis of GTS, the rotor is usually regarded as a rigid part. The rigid-shaft gear-transmission dynamic system RGDS) model cannot solve the differences of vibrations of rotor at different axial positions. To solve this problem, a flexible-shaft gear- transmission system dynamic (FGDS) model is established by using the finite element method. In the FGDS, the GTSs is separated into some flexible shaft segments, gear meshing unit and bearing unit. The bearing stiffness, bearing contact force, time-varying meshing stiffness and damping force of gear are considered. The time- and frequency-domain vibrations of FGDS and RGDS model under different rotational speeds are compared and analyzed. Note that the FGDS can obtain more accurate results than the RGDS model. The vibrations from FGDS are less than those from RGDS model. This paper can give some new approach for the dynamic modeling and vibration analysis of flexible GTSs.

Dynamic modeling and nonlinear free vibration analysis of a rotating 3D beam induced by adjacent two revolute joints

Dynamic modeling and nonlinear free vibration analysis of a rotating 3D beam induced by adjacent two revolute joints

A Cartesian spatial discretization method for nonlinear dynamic modeling and vibration analysis of tensegrity structures

For vibration analysis of a tensegrity structure, the development of a dynamic model is a key step. A common issue in the traditional dynamic modeling methods for vibration analysis of tensegrity structures is that structural members are oversimplified. Member internal displacements, including those in longitudinal directions for bar and cable members and those in transverse directions for cable members, were neglected. This oversimplification would inevitably prevent the dynamic model of a tensegrity structure so developed from revealing accurate responses, especially for those in the high-frequency domain. To resolve this issue, a new method called the Cartesian spatial discretization method is developed for nonlinear dynamic modeling and vibration analysis of tensegrity structures. This method can successfully incorporate member internal displacements in dynamic modeling of a tensegrity structure by defining positions of structural members as a summation of internal terms and boundary-induced terms in a global Cartesian coordinate system. The proposed method is applied to vibration analysis of a planar Snelson’s X tensegrity structure, a three-dimensional tensegrity tower, and an irregular tensegrity grid in simulation, and compared with the Lagrangian method based on generalized coordinates, the commercial finite element analysis software ANSYS and the finite element analysis method in literatures, respectively. Results show that the proposed method is accurate in predicting dynamic responses of tensegrity structures, especially for vibration analysis in the high-frequency domain. It is also demonstrated that the proposed method is applicable to both simple and complex tensegrity structures, and computationally efficient as it converges in a super-linear rate by using only a small number of internal terms of member displacements.