scholarly journals Analysis of the Dynamic Stiffness, Hysteresis Resonances and Complex Responses for Nonlinear Spring Systems in Power-Form Order

2021 ◽  
Vol 11 (16) ◽  
pp. 7722
Author(s):  
Qingtao Wang ◽  
Zhiyong Zhang ◽  
Yongheng Ying ◽  
Zhaojun Pang
Keyword(s):  
Normal Load ◽  
Dynamic Stiffness ◽  
Mechanical Systems ◽  
Contact Fatigue ◽  
Period Doubling ◽  
Excitation Amplitude ◽  
Hertzian Contact ◽  
Restoring Force ◽  
Nonlinear Spring ◽  
Stiffness Characteristics

Power-form nonlinear contact force models are widely adopted in relatively moving parts of macro (e.g., rolling bearings considering Hertzian contact restoring force between rolling elements and bearing raceways) or micro (e.g., the micro cantilever probe system of atomic force microscopy) scale mechanical systems, and contact resonance could cause serious problems of wear, contact fatigue, vibration, and noise, which has attracted widespread attention. In the present paper, the softening/hardening stiffness characteristics of continuous and one-sided contact power-form nonlinear spring models are addressed, respectively, by the analysis of the monotone features of resonant frequency-response skeleton lines. Herein, the period-n solution branch and its stability characteristics are obtained by the harmonic balance and alternating frequency/time domain (HB–AFT) method and Floquet theory. Compared with previous studies, this paper will furtherly clarify the influences of externally normal load, the power form exponent term, and excitation amplitude on the softening/hardening stiffness characteristics of general power-form spring systems. In addition, for a power-form system with a one-sided contact, the phenomena of primary and super/sub-harmonic hysteretic resonances inducing period-doubling, folding bifurcation, the coexistence of multiple solutions are demonstrated. Besides, it gives the evolution mechanism of two types of intermittency chaos in a one-sided contact system. The overall results may have certain basic theoretical significance and engineering values for the control of vibration and noise in contact mechanical systems.

scholarly journals Vibration Characteristics of Rolling Mill System under Constraints of the Nonlinear Spring Force and Friction Force from Hydraulic Cylinder

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Zhaolun Liu ◽  
Guixiang Pan ◽  
Jiahao Jiang ◽  
Bin Liu
Keyword(s):  
Friction Force ◽  
Rolling Mill ◽  
Period Doubling ◽  
Time History ◽  
Hydraulic Cylinder ◽  
Excitation Amplitude ◽  
System Stability ◽  
External Excitation ◽  
Nonlinear Spring ◽  
Spring Force

Considering the two kinds of nonlinear constraints of rolling mill hydraulic cylinder, spring force and friction force, the vibration model of rolling mill system is established. The amplitude frequency response equations are obtained by using the average method. Comparing the time history curves of vertical vibration displacement of rolling mill system under the nonlinear spring force and friction force, the amplitude frequency characteristic curves are simulated. The external excitation amplitude is viewed as the bifurcation parameter, and the system bifurcation response changing with the external excitation amplitude is analyzed. The influence of the external excitation amplitude on the system stability is studied. The results indicate that the increase of the nonlinear spring force makes the rolling mill system’s unstable area to become wider, and the influence on the rolling mill system of nonlinear friction force behaves as the damping characteristics; the vibration of rolling mill system is alternating between the periodic, period-doubling, and the chaotic motion. The research results provide a theoretical support for restraining the vibration of the rolling mill system in the actual production process.

Identification of Impact Damping of Two Elastic Bodies

1999 ◽  
Author(s):  
Haiyan Hu ◽  
Dongping Jin
Keyword(s):  
Contact Force ◽  
Time History ◽  
Hertzian Contact ◽  
New Technique ◽  
Restoring Force ◽  
Nonlinear Spring ◽  
Elastic Bodies ◽  
Measured Time ◽  
The Impact ◽  
Impact Damping

Abstract The contact force of two impacting elastic bodies is widely modeled as the parallel combination of a nonlinear spring and a nonlinear dashpot. The restoring force of the nonlinear spring can be determined according to the Hertzian contact law in elasticity, while the model and corresponding parameters of the nonlinear damping force have to be identified through experiments. The current approaches of damping identification are based on the measured time histories of both contact force and relative approaching velocity of two impacting bodies. In this paper, a new technique is presented for the damping identification on the basis of measured time history of the contact force only. Hence, the tough problem of measuring the relative approaching velocity of two impacting bodies just before impact is removed. The efficacy test of the new technique is given in the paper through an example of identifying the impact damping of a pair of clamped beams.

Design and analysis of a vibration isolation system with cam–roller–spring–rod mechanism

2021 ◽  
pp. 107754632110005
Author(s):  
Yonglei Zhang ◽  
Guo Wei ◽  
Hao Wen ◽  
Dongping Jin ◽  
Haiyan Hu
Keyword(s):  
Vibration Isolation ◽  
Dynamic Stiffness ◽  
Experimental Studies ◽  
Excitation Amplitude ◽  
Isolation System ◽  
Vibration Isolation System ◽  
Stiffness Characteristic ◽  
Negative Stiffness Mechanism ◽  
Isolation Systems ◽  
Vibration Isolation Performance

The vibration isolation system using a pair of oblique springs or a spring-rod mechanism as a negative stiffness mechanism exhibits a high-static low-dynamic stiffness characteristic and a nonlinear jump phenomenon when the system damping is light and the excitation amplitude is large. It is possible to remove the jump via adjusting the end trajectories of the above springs or rods. To realize this idea, the article presents a vibration isolation system with a cam–roller–spring–rod mechanism and gives the detailed numerical and experimental studies on the effects of the above mechanism on the vibration isolation performance. The comparative studies demonstrate that the vibration isolation system proposed works well and outperforms some other vibration isolation systems.

Observation of Fatigue Fracture on PEEK Shaft against Alumina Bearing’s Ball under One-Point Rolling Contact

2016 ◽  
Vol 878 ◽  
pp. 137-141 ◽  
Author(s):  
Hitonobu Koike ◽  
Genya Yamaguchi ◽  
Koshiro Mizobe ◽  
Yuji Kashima ◽  
Katsuyuki Kida
Keyword(s):  
Fatigue Fracture ◽  
Rolling Contact Fatigue ◽  
Rolling Direction ◽  
Contact Fatigue ◽  
Rolling Contact ◽  
Hertzian Contact ◽  
Subsurface Crack ◽  
Mechanical Elements ◽  
The One ◽  
Alumina Ball

Tribological fatigue failure of the machined PEEK shaft was investigated through the one-point type rolling contact fatigue test between a PEEK shaft and an alumina ball, in order to explore fatigue fracture mechanism of frictional parts working at high frequency in various mechanical elements. Due to Hertzian contact of cyclic compressive stress, the subsurface crack occurred within approximately 300 μm depth from thesurface and propagated along the rolling direction. After that, the subsurface crack propagation direction changed toward the surface. The flaking occurred on the raceway of the PEEK shaft when the subsurface crack reached to the PEEK shaft surface.

Two Groups of Chaotic Vibrations in a Single-Degree-of-Freedom Maglev System

1997 ◽  
Author(s):  
Zhixiang Xu ◽  
Hideyuki Tamura
Keyword(s):  
Magnetic Levitation ◽  
Excitation Frequency ◽  
Power Spectra ◽  
Period Doubling ◽  
Excitation Amplitude ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Moving Base ◽  
Period Doubling Bifurcations

Abstract In this paper, a single-degree-of-freedom magnetic levitation dynamic system, whose spring is composed of a magnetic repulsive force, is numerically analyzed. The numerical results indicate that a body levitated by magnetic force shows many kinds of vibrations upon adjusting the system parameters (viz., damping, excitation amplitude and excitation frequency) when the system is excited by the harmonically moving base. For a suitable combination of parameters, an aperiodic vibration occurs after a sequence of period-doubling bifurcations. Typical aperiodic vibrations that occurred after period-doubling bifurcations from several initial states are identified as chaotic vibration and classified into two groups by examining their power spectra, Poincare maps, fractal dimension analyses, etc.

Thermal Effects in Contact Fatigue Under Oscillatory Normal Load

1965 ◽  
Vol 87 (1) ◽  
pp. 177-184 ◽  
Author(s):  
R. A. Burton ◽  
J. C. Tyler ◽  
P. M. Ku
Keyword(s):  
Energy Dissipation ◽  
Dynamic Load ◽  
Normal Load ◽  
Fatigue Cracks ◽  
Thermal Transformation ◽  
Contact Fatigue ◽  
Contact Temperature ◽  
Flat Specimen ◽  
Exponential Relationship ◽  
Specimen Temperature

Experiments are reported wherein contact fatigue was brought about by the application of an oscillatory normal load between a ball and a flat specimen. Plots of the flat-specimen temperature versus time showed that a rapid temperature rise occurred in the initial stage of crack formation, and thus provided an early indication of fatigue. Thermal resistances were measured for the apparatus components as well as the specimen contact. Using these, it was possible to apply the measured flat-specimen temperature to obtain estimates of the contact temperature as well as the energy dissipation rate prior to the incidence of fatigue cracks. It was shown that the contact temperature did not rise sufficiently to produce annealing in the test specimens. Thus, toroidal rings of hardened and softened material in the stressed zone could not be attributed to thermal transformation of the bearing steel. It was also shown that energy dissipation due to cyclic loading varied in approximate exponential relationship with dynamic load, and decreased upon increase of static load when dynamic load was maintained constant.

Dynamic Property Analysis of Damping Rubber in Rail Fastenings under Different Deformation Condition

2014 ◽  
Vol 494-495 ◽  
pp. 706-710
Author(s):  
Bin Zhang ◽  
Yan Yun Luo ◽  
Zhi Nan Shi
Keyword(s):  
Mechanical Model ◽  
Dynamic Stiffness ◽  
Excitation Frequency ◽  
Nonlinear Damping ◽  
Deformation Condition ◽  
Damping Force ◽  
Restoring Force ◽  
Dynamic Mechanical ◽  
Large Distortion ◽  
Hydraulic Servo

This paper studies the experimental research on dynamic characteristics of the damping rubber in high elastic fastening by the electro-hydraulic servo movement tester. Based on a hypothesis superposition theory of nonlinear elastic restoring force and nonlinear damping force, a non-linear dynamic mechanical model is proposed. The dynamic stiffness and damping parameters of the rubber are obtained in different deformation conditions based on the dynamic mechanical model. The dynamic stiffness is analyzed, and the results show that dynamic stiffness is closely related to excitation frequency and amplitude. Furthermore the dynamic stiffness is analyzed under different free surface of rubber components by using FEM. That also reveals the changeable characteristics and affected factors of the damping rubber of the high elastic fastenings in large distortion condition.

scholarly journals Nonlinear Static and Dynamic Stiffness Characteristics of Support Hydraulic System of TBM

2019 ◽  
Vol 32 (1) ◽  
Author(s):  
Jianfeng Tao ◽  
Junbo Lei ◽  
Chengliang Liu ◽  
Wei Yuan
Keyword(s):  
Hydraulic System ◽  
Vibrational Energy ◽  
Dynamic Stiffness ◽  
Operating Conditions ◽  
Static Stiffness ◽  
Railway Tunnel ◽  
Relief Valve ◽  
Component Structure ◽  
Stiffness Characteristics ◽  
Stable Stage

AbstractFull-face hard rock tunnel boring machines (TBM) are essential equipment in highway and railway tunnel engineering construction. During the tunneling process, TBM have serious vibrations, which can damage some of its key components. The support system,an important part of TBM, is one path through which vibrational energy from the cutter head is transmitted. To reduce the vibration of support systems of TBM during the excavation process, based on the structural features of the support hydraulic system, a nonlinear dynamical model of support hydraulic systems of TBM is established. The influences of the component structure parameters and operating conditions parameters on the stiffness characteristics of the support hydraulic system are analyzed. The analysis results indicate that the static stiffness of the support hydraulic system consists of an increase stage, stable stage and decrease stage. The static stiffness value increases with an increase in the clearances. The pre-compression length of the spring in the relief valve affects the range of the stable stage of the static stiffness, and it does not affect the static stiffness value. The dynamic stiffness of the support hydraulic system consists of a U-shape and reverse U-shape. The bottom value of the U-shape increases with the amplitude and frequency of the external force acting on the cylinder body, however, the top value of the reverse U-shape remains constant. This study instructs how to design the support hydraulic system of TBM.

scholarly journals From Hertzian contact to spur gears: analyses of stresses and rolling contact fatigue

2019 ◽  
Vol 20 (6) ◽  
pp. 626 ◽  
Author(s):  
Guillaume Vouaillat ◽  
Jean-Philippe Noyel ◽  
Fabrice Ville ◽  
Xavier Kleber ◽  
Sylvain Rathery
Keyword(s):  
Rolling Contact Fatigue ◽  
Contact Fatigue ◽  
Spur Gear ◽  
Point Of View ◽  
Rolling Contact ◽  
Hertzian Contact ◽  
Spur Gears ◽  
Realistic Representation ◽  
Contact Fatigue Life ◽  
Surface Microgeometry

The study of rolling contact fatigue in spur gears requires a good comprehension of all the phenomena occurring at the material scale. On a numerical point of view, a realistic representation of the material and of the load repartition function of the local micro-geometries is needed. However the resulting models are often complex and time-consuming. So, this work aims at developing a model meeting these specificities. Thus, different sections of the spur gear material granular geometry are simulated first. Secondly, the contact pressure fields are computed accurately relatively to the simulated surface microgeometry. Then, the influence of several parameters on their rolling contact fatigue life is highlighted. Among friction, sliding coefficient, load variation and roughness, these individual or combined parameters are taken into account in the model, tested and their impact stressed out. Finally, a fatigue criteria based on rolling contact fatigue micro-cracks nucleation at grain boundaries is proposed in order to compare simulations and influencing parameters to the reference.

Effect of Lubricant on Surface Rolling Contact Fatigue Cracks

2010 ◽  
Vol 97-101 ◽  
pp. 793-796 ◽  
Author(s):  
Khalil Farhangdoost ◽  
Mohammad Kavoosi
Keyword(s):  
Fatigue Crack ◽  
Fatigue Cracks ◽  
Rolling Contact Fatigue ◽  
Contact Fatigue ◽  
Rolling Contact ◽  
Hertzian Contact ◽  
Element Analysis ◽  
Crack Face ◽  
Hertzian Contact Stress ◽  
Model Of Friction

This study performed the finite element analysis of the cycle of stress intensity factors at the surface initiated rolling contact fatigue crack tip under Hertzian contact stress including an accurate model of friction between the faces of the crack and the effect of fluid inside the crack. A two-dimensional model of a rolling contact fatigue crack has been developed with FRANC-2D software. The model includes the effect of Coulomb friction between the faces of the crack. The fluid in the crack was assumed not only to lubricate the crack faces and reduce the crack face friction coefficient but also to generate a pressure.

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