Synchronization characteristics of a rotor-pendula system in multiple coupling resonant systems

2017 ◽  
Vol 232 (10) ◽  
pp. 1802-1822 ◽  
Author(s):  
Pan Fang ◽  
Yongjun Hou
Keyword(s):  
Dynamic Characteristics ◽  
Transformation Method ◽  
Stable Phase ◽  
Coupling Coefficients ◽  
Synchronous State ◽  
Rotation Direction ◽  
Pendula System ◽  
Resonant Systems ◽  
The Stability ◽  
Synchronous Behavior

The problem is motivated by observations of a rotor-pendula system, which derived from a new shale shaker. To grasp the dynamic characteristics of the shale shaker, the key research is exploring the synchronous mechanism for the system, since synchronous state between rotors is closely related to the dynamic characteristics of the system. In this paper, the dynamic equation of the rotor-pendula system is firstly derived by applying Lagrange’s equations. Through Laplace’s transformation method, the approximate responses of the system in synchronous state are obtained, which is determined coupling coefficients and synchronous state of the system. Then, the synchronous balance equation and the stability criterion of the system are obtained with Poincaré method on which stable phase difference and synchronous behavior can be ascertained. To verify the correctness of the theoretical analysis, numerical simulations are implemented by Runge–Kutta method, and it is shown that the synchronous behavior is determined by the geometry parameters, coupling coefficients, and rotor rotation direction.

Dynamic Characteristics of Spiral-Grooved Opposed-Hemisphere Gas Bearings

2016 ◽  
Vol 139 (3) ◽  
Author(s):  
Guangwei Yang ◽  
Jianjun Du ◽  
Weiping Ge ◽  
Tun Liu ◽  
Xiaowei Yang
Keyword(s):  
Dynamic Characteristics ◽  
Degrees Of Freedom ◽  
Dynamic Stiffness ◽  
Translational Motion ◽  
Coupling Coefficients ◽  
Dynamic Coefficients ◽  
Large Eccentricity ◽  
The Stability ◽  
Stiffness And Damping ◽  
Gas Bearing

The traditional eight-coefficient bearing model only considers the translational motion of the bearings and neglects the tilting motion and coupling effects between them. In this paper, the dynamic characteristics of the spiral-grooved opposed-hemisphere gas bearing considering five degrees-of-freedom are studied, and 50 dynamic coefficients including the translational, tilting, and coupling components are completely calculated. The Reynolds equations and their perturbed equations are solved by the finite element method to obtain the dynamic stiffness and damping coefficients. The effects of the tilting motion on the dynamic coefficients and response are analyzed, respectively. The results show that the coupling coefficients between the translational and tilting motions, which have been neglected in most previous studies, are significant at large eccentricity ratio. But these coupling coefficients have little effect on the dynamic response. On the other hand, the influences of the tilting motion on the synchronous response and natural frequency are remarkable and will decrease the stability of the rotor bearing system.

scholarly journals Investigation for Synchronization of a Rotor-Pendulum System considering the Multi-DOF Vibration

2016 ◽  
Vol 2016 ◽  
pp. 1-22 ◽  
Author(s):  
Yongjun Hou ◽  
Pan Fang
Keyword(s):  
Lagrange Equation ◽  
Transformation Method ◽  
Spring Stiffness ◽  
Balance Equations ◽  
Pendulum System ◽  
Dimensionless Equation ◽  
Coupling Relationship ◽  
The Stability ◽  
Synchronous Behavior ◽  
Laplace Transformation Method

This work is a continuation for our published literature for vibration synchronization. A new mechanism, two rotors coupled with a pendulum rod in a multi-DOF vibration system, is proposed to implement coupling synchronization, and the dynamics equation of mechanism is derived by Lagrange equation. In addition, the coupling relationship between the vibrobody and the pendulum rod is ascertained with the Laplace transformation method, based on the dimensionless equation of the dynamics system. The Poincare method is employed to study the synchronization state between the two unbalanced rotors, which is converted into that of existence and the stability of solutions for synchronization-balance equations. The obtained results are supported by computer simulations. It is demonstrated that the values of the spring stiffness coefficient, the length of the pendulum, and the angular installation of the pendulum are important parameters with respect to the synchronous behavior in the rotor-pendulum system.

scholarly journals Synchronous state of unbalanced rotors in a three-dimensional space and far-resonance system

2019 ◽  
Vol 234 (1) ◽  
pp. 108-122
Author(s):  
Pan Fang ◽  
Huan Peng ◽  
Du Changcheng ◽  
Min Zou ◽  
Duyu Hou ◽  
...  
Keyword(s):  
Dynamic Characteristics ◽  
Dimensional Space ◽  
Damping Ratio ◽  
Three Dimensional ◽  
Parameter Method ◽  
Synchronous State ◽  
Rotation Direction ◽  
Key Factor ◽  
Screening Efficiency ◽  
Three Dimensional Space

The unreasonable dynamic characteristics results in decrease of screening efficiency of the vibrating screen. However, the synchronous behavior of motors is key factor to determine dynamic characteristics of the screens. In this paper, two unbalanced rotors actuated with motors in a three-dimensional space are proposed. To understand the synchronous mechanism, the dynamic equation of the system is firstly confirmed based on Lagrangian formulation; meanwhile, synchronization condition of the system is calculated with average and small parameter method; then, synchronization stability of the system is explored by Lyapunov method; finally, some numerical simulations are given to validate the theoretical computations. It is found that, to implement the stable synchronous rotation between the rotors, the values of the parameter in this system must be satisfied by synchronous condition and synchronous stability; the synchronous state is determined by the rotation direction, the damping ratio, the frequency ratio, and the motor position; the system is a planar motion when the identical mass rotors oppositely actuated, but the system is a spatial motion in the other cases.

MASTER STABILITY FUNCTIONS FOR SYNCHRONIZED COUPLED SYSTEMS

1999 ◽  
Vol 09 (12) ◽  
pp. 2315-2320 ◽  
Author(s):  
LOUIS M. PECORA ◽  
THOMAS L. CARROLL
Keyword(s):  
Simple Form ◽  
Coupled Systems ◽  
Stability Function ◽  
Coupled Oscillator ◽  
Synchronous State ◽  
Master Stability Function ◽  
Stability Functions ◽  
The Stability

We show that many coupled oscillator array configurations considered in the literature can be put into a simple form so that determining the stability of the synchronous state can be done by a master stability function which solves, once and for all, the problem of synchronous stability for many couplings of that oscillator.

Dynamic analysis and control of an active engine mount system

2002 ◽  
Vol 216 (11) ◽  
pp. 921-931 ◽  
Author(s):  
Y-W Lee ◽  
C-W Lee
Keyword(s):  
Transfer Function ◽  
Dynamic Characteristics ◽  
Performance Test ◽  
Adaptive Controller ◽  
Lms Algorithm ◽  
Equivalent Mass ◽  
Engine Mount ◽  
Active Engine ◽  
The Stability ◽  
Mass Spring

Dynamic characteristics of a prototype active engine mount (AEM), designed on the basis of a hydraulic engine mount, have been investigated and an adaptive controller for the AEM has been designed. An equivalent mass-spring-damper AEM model is proposed, and the transfer function that describes the dynamic characteristics of the AEM is deduced from mathematical analysis of the model. The damping coefficient of the model is derived by considering the non-linear flow effect in the inertia track. Experiments confirmed that the model precisely describes the dynamic characteristics of the AEM. An adaptive controller using the filtered-X LMS algorithm is designed to cancel the force transmitted through the AEM. The stability of the LMS algorithm is guaranteed by using the secondary path transfer function derived on the basis of the dynamic model of the AEM. The performance test in the laboratory shows that the AEM system is capable of significantly reducing the force transmitted through the AEM.

The stability of onoratoite, Sb8O11Cl2, in the supergene environment

2014 ◽  
Vol 78 (7) ◽  
pp. 1671-1675 ◽  
Author(s):  
Adam J. Roper ◽  
Peter Leverett ◽  
Timothy D. Murphy ◽  
Peter A. Williams
Keyword(s):  
Significant Influence ◽  
Secondary Phase ◽  
Low Ph ◽  
Stable Phase ◽  
Supergene Zone ◽  
A Value ◽  
Solubility Studies ◽  
The Stability ◽  
Very High

AbstractSynthesis and solubility studies of onoratoite have been undertaken to determine the role of this rare secondary phase in the immobilization of Sb and the conditions responsible for its formation in the supergene zone. Solubility studies were undertaken at 298.15 K. A value of ΔGfθ (Sb8O11Cl2, s, 298.15 K) = –2576 ±12 kJ mol–1 was derived. Calculations involving sénarmontite, Sb2O3, klebelsbergite, Sb4O4SO4(OH)2 and schafarzikite, FeSb2O4, show that onoratoite is a thermodynamically stable phase only at negligible activities of SO42–(aq) and low activities of Fe2+(aq), at low pH and very high activities of Cl–(aq). This explains why onoratoite is such a rare secondary phase and why it cannot exert any significant influence on the dispersion of Sb in the supergene environment.

A Variable Viscosity Approach for the Analysis of Steady State and Dynamic Characteristics of Two-Lobe Journal Bearing With TiO2 Based Nanolubricant

2017 ◽  
Author(s):  
Ashutosh Kumar ◽  
Sashindra Kumar Kakoty
Keyword(s):  
Steady State ◽  
Dynamic Characteristics ◽  
Journal Bearing ◽  
Volume Fraction ◽  
Variable Viscosity ◽  
Flow Coefficient ◽  
Viscosity Model ◽  
Nano Lubricant ◽  
The Stability ◽  
Stiffness And Damping

Steady-state and dynamic characteristics of two-lobe journal bearing, operating on TiO2 based Nano-lubricant has been obtained. The effective viscosity is obtained by using Krieger-Dougherty viscosity model for a given volume fraction of nanoparticle in the base fluid. Various bearing performance characteristics are then obtained by solving modified Reynolds equation for variable viscosity model and couple stress model. The stiffness and damping coefficients are also determined for various values of the volume fraction of the nanoparticle in the nanofluid. Results reveal that load carrying capacity and flow coefficient increase whereas friction variable decreases without affecting the stability condition of two-lobe journal bearing operating on TiO2 based nanolubricant. On the other hand attitude angle and dynamic coefficients remains constant for all the values of volume fraction of nanoparticle.

scholarly journals Dynamic Characteristics and Experimental Research of a Two-Span Rotor-Bearing System with Rub-Impact Fault

2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Rui Zhu ◽  
Guang-chao Wang ◽  
Qing-peng Han ◽  
An-lei Zhao ◽  
Jian-xing Ren ◽  
...  
Keyword(s):  
Dynamic Characteristics ◽  
Critical Speed ◽  
Great Influence ◽  
Experimental Platform ◽  
Rotating Machine ◽  
Rotor Bearing ◽  
Before And After ◽  
Analysis System ◽  
The Stability ◽  
Bearing System

Rotor rub-impact has a great influence on the stability and safety of a rotating machine. This study develops a dynamic model of a two-span rotor-bearing system with rubbing faults, and numerical simulation is carried out. Moreover, frictional screws are used to simulate a rubbing state by establishing a set of experimental devices that can simulate rotor-stator friction in the rotor system. Through the experimental platform and its analysis system, the rubbing experiment was conducted, and the vibration of the rotor-bearing system before and after the critical speed is observed. Rotors running under normal condition, local slight rubbing, and severe rubbing throughout the entire cycle are simulated. Dynamic trajectories, frequency spectrum diagrams, chart of axis track, and Poincare maps are used to analyze the features of the rotor-bearing system with rub-impact faults under various parameters. The vibration characteristics of rub impact are obtained. Results show that the dynamic characteristics of the rotor-bearing system are affected by the change in velocity and degree of impact friction. The findings are helpful in further understanding the dynamic characteristics of the rub-impact fault of the two-span rotor-bearing system and provide reference for fault diagnosis.

Biquadratic Digital Phase-Compensator Design with Stability-Margin Controllability

2019 ◽  
Vol 28 (04) ◽  
pp. 1950068 ◽  
Author(s):  
Tian-Bo Deng
Keyword(s):  
Stability Margin ◽  
Transformation Method ◽  
Second Order ◽  
Approximation Accuracy ◽  
Parameter Transformation ◽  
Practical Applications ◽  
Compensator Design ◽  
Novel Method ◽  
Design Idea ◽  
The Stability

This paper proposes a novel method for the design of a recursive second-order (biquadratic) all-pass phase compensator with controllable stability margin. The design idea stems from the generalized stability triangle (GST) derived by the author for the second-order biquadratic digital filter. Based on the GST, a parameter-transformation method is proposed on the transformations of the denominator coefficients of the transfer function of the biquadratic phase compensator. The transformations convert the original denominator coefficients to other new parameters, and any values of those new parameters can guarantee that the GST condition is always satisfied. Optimizing the new parameters yields a biquadratic phase compensator that definitely meets a prespecified stability margin. That is, a biquadratic all-pass phase compensator can be designed to have an arbitrarily specified stability margin. This in turn avoids the occurrence that a recursive phase compensator may become unstable in the practical applications. Thus, the resulting biquadratic phase compensator has robust stability, which is extremely important during the practical filtering operations. A design example is given to show the stability margin guarantee as well as the approximation accuracy.

scholarly journals Universal Walking Control Framework of Biped Robot Based on Dynamic Model and Quadratic Programming

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Xiaokun Leng ◽  
Songhao Piao ◽  
Lin Chang ◽  
Zhicheng He ◽  
Zheng Zhu
Keyword(s):  
Motion Control ◽  
Dynamic Characteristics ◽  
Control Method ◽  
Constraint Equation ◽  
Biped Robot ◽  
Equation System ◽  
Whole Body ◽  
Optimal Controller ◽  
Control Framework ◽  
The Stability

Biped robot research has always been a research focus in the field of robot research. Among them, the motion control system, as the core content of the biped robot research, directly determines the stability of the robot walking. Traditional biped robot control methods suffer from low model accuracy, poor dynamic characteristics of motion controllers, and poor motion robustness. In order to improve the walking robustness of the biped robot, this paper solves the problem from three aspects: planning method, mathematical model, and control method, forming a robot motion control framework based on the whole-body dynamics model and quadratic planning. The robot uses divergent component of motion for trajectory planning and introduces the friction cone contact model into the control frame to improve the accuracy of the model. A complete constraint equation system can ensure that the solution of the controller meets the dynamic characteristics of the biped robot. An optimal controller is designed based on the control framework, and starting from the Lyapunov function, the convergence of the optimal controller is proved. Finally, the experimental results show that the method is robust and has certain anti-interference ability.

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