Nonlinear vibration analysis of mechanical systems with multiple joint clearances using the method of multiple scales

As the core control system of a rolling mill, the hydraulic automatic gauge control (HAGC) system is key to ensuring a rolling process with high speed, high precision and high reliability. However, a HAGC system is typically a mechanical-electric-hydraulic coupling system with nonlinear characteristics. The vertical vibration of the load easily occurs during the working process, which seriously affects the stability of the system and the causes are difficult to determine. In this work, the theory and method of nonlinear dynamics were employed. The load vertical vibration model of the HAGC system was established. Then, the multi-scale method was utilized to solve the obtained model, and the singularity theory was further applied to derive the transition set. Moreover, the research object of this article focused on some nonlinear factors such as excitation force, elastic force and damping force. The effects of the above feature parameters on bifurcation behavior were emphatically explored. The bifurcation characteristic of the load vertical vibration of the HAGC system was revealed. The research results indicate that the bifurcation curves in each sub-region, divided by the transition set, possess their own topological structure. The changes of the feature parameters, such as the nonlinear stiffness coefficient, liquid column height, nonlinear damping coefficient, and external excitation have an influence on the vibration amplitude of the HAGC system. By reasonably adjusting the nonlinear stiffness coefficient to effectively avoid the resonance region, the stability of the system will be facilitated. Furthermore, this is conducive to the system’s stability as it properly controls the size of the liquid column height of the hydraulic cylinder. The appropriate nonlinear damping coefficient can decrease the unstable area, which is beneficial to the stability of the system. However, large external excitation is not conducive to the stability of the system.

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“…Firstly, the small parameter factor ε and a series of slow-change time scales T n are employed [49,50].…”

Section: Analysis Of Bifurcation Characteristicmentioning

confidence: 99%

Bifurcation Characteristic Research on the Load Vertical Vibration of a Hydraulic Automatic Gauge Control System

et al. 2019

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“…From the manufacturing and operating points of view, the existence of a gap in the joints is necessary and unavoidable, because of manufacturing and assembly tolerances, and more importantly, to allow some flexibility and permit the relative motion between adjacent parts [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51]. If there is no lubricant in the mechanical joints, direct collisions take place in the mechanical systems causing vibration and fatigue phenomena [22,25,[52][53][54][55][56][57][58]. In some applications, the joints are designed to run with some fluid lubricant, with the purpose of reducing friction, wear and to provide load capacity to keep the joint elements apart [9,44,[59][60][61][62][63][64][65][66].…”

Section: Introductionmentioning

confidence: 99%

A comprehensive survey of the analytical, numerical and experimental methodologies for dynamics of multibody mechanical systems with clearance or imperfect joints

Tian

Flores

Lankarani

2018

Mechanism and Machine Theory

317

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A comprehensive survey of the literature of the most relevant analytical, numerical, and experimental approaches for the kinematic and dynamic analyses of multibody mechanical systems with clearance joints is presented in this review. Both dry and lubricated clearance joints are addressed here, and an effort is made to include a large number of research works in this particular field, which have been published since the 1960's. First, the most frequently utilized methods for modeling planar and spatial multibody mechanical systems with clearance joints are analyzed, and compared. Other important phenomena commonly associated with clearance joint models, such as wear, non-smooth behavior, optimization and control, chaos, and uncertainty and links' flexibility, are then discussed. The main assumptions procedures and conclusions for the different methodologies are also examined and compared. Finally, future developments and new applications of clearance joint modeling and analysis are highlighted.

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“…Perturbation methods such as the method of multiple scales (MMS) and Lindstedt-Poincaré (LP) method are effective at solving the transition curves and deriving analytical solutions for the Mathieu equation but have some limitations. The LP method can only obtain bounded asymptotic solutions for stable regions, not unbounded solutions for unstable regions [6][7][8][9][10]. The MMS can obtain asymptotic solutions for both stable and unstable regions in the case of δ ≥ 0 but is invalid when δ < 0 [7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

“…The LP method can only obtain bounded asymptotic solutions for stable regions, not unbounded solutions for unstable regions [6][7][8][9][10]. The MMS can obtain asymptotic solutions for both stable and unstable regions in the case of δ ≥ 0 but is invalid when δ < 0 [7][8][9][10][11]. In this paper, we propose a modified MMS that can obtain the bounded and unbounded solutions for not only δ ≥ 0 but also δ < 0.…”

Section: Introductionmentioning

confidence: 99%

Transverse oscillation of particles in the vicinity of resonances for a cyclotron

Zhou

Song

Chen

et al. 2019

Phys. Rev. Accel. Beams

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Transverse oscillation is an important issue in beam dynamics of cyclotrons and can be described by the Mathieu equation. We review the standard form of the Mathieu equation, d 2 u dθ 2 þ ðδ þ ε · cos 2θÞu ¼ 0, and propose a modification of the method of multiple scales (i.e., a perturbation method) so that the asymptotic analytical solutions of the Mathieu equation can be computed in the stable and unstable regions for both δ ≥ 0 and δ < 0. This method was applied to the nonlinear transverse oscillation equations for a cyclotron. Analytical solutions for transverse oscillation in the stable and unstable regions (i.e., vicinity of the resonances) were obtained, and the accuracy of these analytical solutions was confirmed by their close agreement with the direct numerical integration. Useful results such as the analytical solution of the transverse oscillation frequency, increasing rate of the amplitude in unstable regions, and the resonance width were also derived; the stable condition and driving terms of the resonances can be obtained from the analytical solutions.

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Nonlinear vibration analysis of mechanical systems with multiple joint clearances using the method of multiple scales

Cited by 37 publications

References 23 publications

Bifurcation Characteristic Research on the Load Vertical Vibration of a Hydraulic Automatic Gauge Control System

Bifurcation Characteristic Research on the Load Vertical Vibration of a Hydraulic Automatic Gauge Control System

A comprehensive survey of the analytical, numerical and experimental methodologies for dynamics of multibody mechanical systems with clearance or imperfect joints

Transverse oscillation of particles in the vicinity of resonances for a cyclotron

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