scholarly journals Nonlinear response of gear system based on a novel backlash model with coupling dynamic change and surface topography

2021 ◽  
Author(s):  
Xin Yu ◽  
Yunyun Sun ◽  
Hongguang Li ◽  
Shijing Wu
Keyword(s):  
Surface Topography ◽  
Vibration Amplitude ◽  
Nonlinear Response ◽  
Contact Region ◽  
Dynamic Change ◽  
Time History ◽  
Spur Gear ◽  
Phase Portraits ◽  
Average Height ◽  
Coupling Dynamic

Abstract Backlash is one of main nonlinear internal excitation factors in gear transmission system and therefore has been widely concerned. Most existing models of backlash are based on a random constant, which ignore the dynamic characteristics of backlash itself and the effects of surface topography. To model the backlash precisely, in this paper, the constant part of backlash is revised through average height of all asperities in contact region related to surface roughness by fractal method. Simultaneously, the dynamic part is modeled considering the displacement of gear center motion that comes from shaft deformation in coupling dynamic meshing. A complete backlash model consisting of the two parts is established subsequently and a corresponding close-loop algorithm is proposed to solve system dynamics by coupling mesh stiffness and time varying pressure angle. Through time history charts, phase portraits and Poincare mapping as well as frequency spectrograms, calculation results clearly demonstrate the comprehensive effects of dynamic backlash on the nonlinear dynamics involving vibration amplitude, frequency and chaotic characteristics of a spur gear pair. The effects of surface topography on backlash and system nonlinear response including vibration amplitude and chaotic features are also analyzed, therefore dynamic backlash and surface topography are important factors that cannot be ignored in gear issue. The comparison with experimental data as well as other previous models is conducted to verify the superiority of proposed model.

scholarly journals Numerical Study of the Seismic Response of an Instrumented Building with Underground Stories

2021 ◽  
Vol 11 (7) ◽  
pp. 3190
Author(s):  
Edmundo Schanze ◽  
Gilberto Leiva ◽  
Miguel Gómez ◽  
Alvaro Lopez
Keyword(s):  
Seismic Response ◽  
Soil Structure ◽  
Numerical Study ◽  
Time History ◽  
Building Design ◽  
Average Height ◽  
The Real ◽  
Vibration Data ◽  
Finite Element Software ◽  
Stiffness Reduction

Engineering practitioners do not usually include soil–structure interactions in building design; rather, it is common to model and design foundations as embedded joints with joint–based reactions. In some cases, foundation structures are modeled as rigid bodies, embedding the first story into lower vertical elements. Given that the effects of underground floors on the seismic response are not generally included in current building design provisions, it has been little explored in the literature. This work compares and analyzes models to study the effects of different underground stories modeling approaches using earthquake vibration data recorded for the 16–story Alcazar building office in downtown Viña del Mar (Chile). The modeling expands beyond an embedded first story structure to soil with equivalent springs, representing soil–structure interaction (SSI), with varying rigid soil homogeneity. The building was modeled in a finite element software considering only dead load as a static load case because the structure remained in the framing stage when the monitoring system was operating. The instruments registered 72 aftershocks from the 2010 Maule Earthquake, and this study focused on 11 aftershocks of different hypocenters and magnitudes to collect representative information. The comparisons between empirical records and models in this study showed a better fit between the model and the real vibration data for the models that do consider the SSI using horizontal springs attached to the retaining walls of the underground stories. In addition, it was observed that applying a stiffness reduction factor of 0.7 to all elements in deformation verification models for average–height buildings was suitable to analyze the behavior under small earthquakes; better results are obtained embedding the structure in the foundation level than embedding in the street level; the use of horizontal springs with Kuesel’s model with traction for the analysis of the structure yields appropriate results; it is necessary to carefully select the spring constants to be used, paying special attention to the vertical springs. Even though the results presented herein indicate that the use of vertical springs to simulate the SSI of the base slab can result in major differences concerning the real response, it is necessary to obtain more data from instrumentation across a wider variety of structures to continue to evaluate better design and modeling practices. Similarly, further analyses, including nonlinear time–history and high–intensity events, are needed to best regulate building design.

scholarly journals Parametric and Internal Resonances of an Axially Moving Beam with Time-Dependent Velocity

2013 ◽  
Vol 2013 ◽  
pp. 1-18 ◽  
Author(s):  
Bamadev Sahoo ◽  
L. N. Panda ◽  
G. Pohit
Keyword(s):  
Internal Resonance ◽  
Multiple Scales ◽  
Time History ◽  
Mean Value ◽  
Phase Portraits ◽  
Axially Moving Beam ◽  
Internal Resonances ◽  
Moving Beam ◽  
Axially Moving ◽  
The Stability

The nonlinear vibration of a travelling beam subjected to principal parametric resonance in presence of internal resonance is investigated. The beam velocity is assumed to be comprised of a constant mean value along with a harmonically varying component. The stretching of neutral axis introduces geometric cubic nonlinearity in the equation of motion of the beam. The natural frequency of second mode is approximately three times that of first mode; a three-to-one internal resonance is possible. The method of multiple scales (MMS) is directly applied to the governing nonlinear equations and the associated boundary conditions. The nonlinear steady state response along with the stability and bifurcation of the beam is investigated. The system exhibits pitchfork, Hopf, and saddle node bifurcations under different control parameters. The dynamic solutions in the periodic, quasiperiodic, and chaotic forms are captured with the help of time history, phase portraits, and Poincare maps showing the influence of internal resonance.

scholarly journals A study of nonlinear coupling dynamic characteristics of the cold rolling mill system under different rolling parameters

2017 ◽  
Vol 9 (7) ◽  
pp. 168781401771370 ◽  
Author(s):  
Hai Xu ◽  
Ling-Li Cui ◽  
De-Guang Shang
Keyword(s):  
Fault Diagnosis ◽  
Cold Rolling ◽  
Dynamic Characteristics ◽  
Rolling Mill ◽  
Vibration Amplitude ◽  
Strip Thickness ◽  
Drive System ◽  
Nonlinear Coupling ◽  
Cold Rolling Mill ◽  
Coupling Dynamic

The dynamic characteristics of the mill and the drive system are mutually coupled and affected closed-loop system. However, most research has considered only the vibration of the drive system or the vibration of the mill to determine the cause of the accident in the equipment condition monitoring and fault diagnosis process. Condition monitoring and fault diagnosis based on this type of approach can lead to misdiagnosis or missed diagnosis in determining faults in actual systems. So, in this study, a dynamic model of the coupling between a mill and its drive system was developed to study the interaction of the mill and the drive system with the goal of increasing the accuracy of diagnostic methods and to improve the quality of the rolled material. A nonlinear coupling dynamic model was formulated to represent the relation between the gearbox vibration amplitude and various time-varying parameters to study the effects of various parameters on the drive system vibration characteristic under unsteady lubrication. Simulations results showed that increasing the strip speed, the input strip thickness, or the output strip thickness or decreasing the lubricating oil temperature or the roller radius caused the vibration amplitude of the drive system to increase. The vibration frequency caused by variations in the strip inlet or outlet thickness can be transmitted to the drive system, and gear meshing frequency of the gearbox can be transmitted to the mill. Test data from an actual cold rolling mill verified the accuracy of the model. The model was shown to be capable of simulating the mutually coupled and affected mechanism between a mill and its drive system.

scholarly journals Nonlinear Dynamic Characteristic Analysis of a Coated Gear Transmission System

Coatings ◽  
2020 ◽  
Vol 10 (1) ◽  
pp. 39
Author(s):  
Yangyi Xiao ◽  
Liyang Fu ◽  
Jing Luo ◽  
Wankai Shi ◽  
Minglin Kang
Keyword(s):  
Dynamic Characteristic ◽  
Time History ◽  
Spur Gear ◽  
Transmission System ◽  
Gear Transmission ◽  
Phase Curve ◽  
Gear Pair ◽  
Characteristic Analysis ◽  
Mesh Stiffness ◽  
Gear Transmission System

Coatings can significantly improve the load-carrying performance of a gear surface, but how they affect the vibration characteristic of the system is an urgent issue to be solved. Taking into account the nonlinear factors like the variable mesh stiffness, friction, backlash, and transmission error, a six-degree-of-freedom spur gear transmission system with coatings is presented. Meanwhile, the finite element method is applied to acquire the time-varying mesh stiffness of the coated gear pair in the engagement process. With the support of the time-history curve, phase curve, Poincare map, and fast Fourier transform spectrum, the dynamic characteristics and the effects of the coating elastic modulus on vibration behaviors of a gear transmission system are minutely dissected by using a numerical integration approach. Numerical cases illustrate that the dynamic characteristic of a gear transmission system tends toward a one-period state under the given operating condition. They also indicate that, compared with softer coatings, stiffer ones can properly enhance the transmission performance of the coated gear pair. Numerical results are also compared with previous studies, and can establish a theoretical basis for dynamic design and vibration control of the coated gear transmission system.

Random Disordered Periodical Input Induced Chaos in Discontinuous Systems

2019 ◽  
Vol 29 (01) ◽  
pp. 1950002 ◽  
Author(s):  
Di Liu ◽  
Yong Xu
Keyword(s):  
Noise Intensity ◽  
Stochastic Systems ◽  
Time History ◽  
Phase Portraits ◽  
System Response ◽  
Unperturbed System ◽  
Discontinuous Systems ◽  
Stable And Unstable Manifolds ◽  
Stochastic Force ◽  
Onset Of Chaos

In this paper, we extend the random Melnikov method from stochastic systems with a continuous vector field to discontinuous systems driven by a random disordered periodic input under the assumption that the unperturbed system is a piecewise Hamiltonian system. By measuring the distance of the perturbed stable and unstable manifolds, the nonsmooth random Melnikov process can be derived in detail, and then the mean square criterion for the onset of chaos is established in the statistical sense. It is shown that the threshold for the onset of chaos depends on the stochastic force and a scalar function of hypersurface. Finally, an example is given to analyze the chaotic dynamics using this extended approach, and discuss the effects of noise intensity on the dynamical behaviors of the system. The results indicate that the increase of the noise intensity will result in a chaotic motion of the discontinuous stochastic system and the changes of possible chaotic degree in the phase space. At the same time, the effects of noise intensity on chaos are further investigated through the system response including time history and phase portraits, Poincaré maps and [Formula: see text]-[Formula: see text] test.

Nonlinear Dynamics of a NEMS Carbon Nanotube Resonator

2012 ◽  
Author(s):  
Laura Ruzziconi ◽  
Mohammad I. Younis ◽  
Stefano Lenci
Keyword(s):  
Nonlinear Response ◽  
Ritz Method ◽  
Single Mode ◽  
Reduced Order Model ◽  
Phase Portraits ◽  
Order Model ◽  
Reduced Order ◽  
Combined Use ◽  
Dynamic Voltage ◽  
Carbon Nanotube Resonator

In this study we consider a slacked CNT and analyze the nonlinear response under electrostatic and electrodynamic actuation. We introduce a reduced-order model, which takes into account the single-mode dynamics and is derived via the Ritz method and the Padé approximation. The overall scenario of the device behavior is investigated when both the frequency and the electrodynamic voltage are varying. Extensive numerical simulations are performed by the combined use of frequency response diagrams, attractor-basins phase portraits, and frequency-dynamic voltage behavior chart. Our aim is that of illustrating the richness of the nonlinear events that may undergo in the device due to the coupling of mechanical and electrical nonlinearities. We observe that the CNT exhibits coexisting competing attractors, which lead to a versatile behavior. We examine the multistability in detail. The response is explored not only at low electrodynamic voltages, where the safe jump between attractors is ensured, but also at large electrodynamic excitation, where the inevitable escape (dynamic pull-in) becomes impending. We detect the theoretical boundaries of appearance and disappearance of the main attractors, which provide a complete description of the response.

Torsional Vibration of a Spur Gear System With Time-Varying and Square Nonlinearities

2013 ◽  
Author(s):  
Qian Ding ◽  
Wei Zhang
Keyword(s):  
Torsional Vibration ◽  
Excitation Frequency ◽  
Harmonic Balance Method ◽  
Spur Gear ◽  
Gear System ◽  
Phase Portraits ◽  
Resonant Peak ◽  
Time Varying ◽  
Frequency Spectra ◽  
Input Torque

This paper investigates the torsional vibration of a spur gear system with time-varying and square nonlinearities, by both the analytical method and numerical simulation. First, the equations of motion of a rotating spur gear system are established. Then a single-dof equivalent system is induced to describe the relative motion or torsional vibration of the gears. The harmonic balance method is used to obtain the steady-state response. Influence of the input torque on the response is discussed and a phenomenon, one resonant peak split up into two peaks when the input torque is high enough is revealed. Last, numerical simulations are carried out and bifurcation diagrams and amplitude-frequency curve is given by taking the excitation frequency as control parameter. Selected typical motions are also presented in detail by time-histories, phase portraits, Poincaré map and frequency spectra.

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