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New analysis model for rotor-bearing systems based on plate theory

Zhinan ZHANG, Mingdong ZHOU, Weimin DING, Huifang MA

《机械工程前沿（英文）》 2019年第14卷第4期页码 461-473 doi: 10.1007/s11465-019-0525-2

摘要： The purpose of this work is to develop a new analysis model for angular-contact, ball-bearing systems on the basis of plate theory instead of commonly known approaches that utilize spring elements. Axial and radial stiffness on an annular plate are developed based on plate, Timoshenko beam, and plasticity theories. The model is developed using theoretical and inductive methods and validated through a numerical simulation with the finite element method. The new analysis model is suitable for static and modal analyses of rotor-bearing systems. Numerical examples are presented to reveal the effectiveness and applicability of the proposed approach.

关键词： rotor-bearing system rolling element bearing plate theory finite element analysis

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Dynamics analysis of a cracked dual-disk over-hung rotor-bearing system

CHEN Hong, LI He, WEN Bang-chun, ZHANG Xiao-wei

《机械工程前沿（英文）》 2006年第1卷第2期页码 204-208 doi: 10.1007/s11465-006-0002-6

摘要： A dynamic model of a dual-disk vertical over-hung rotor-bearing system is developed, taking into account nonlinear oil-film force. Its dynamic behaviors are investigated by numerical Runge-Kutta method. Its bifurcation and chaos characteristics are analyzed with crack fault and without crack fault. By analyzing the bifurcation plot, Poincare section plots and amplitude spectra, we found that the crack greatly influences the dynamic characteristics of the rotor-bearing system. Because of the strong effect of the nonlinear oil-film force and crack to the system, 1/2 times, 1/3 times frequency components appear in the response spectrum map. The results may bring up theoretical references for fault diagnosis of rotor-bearing systems.

关键词： nonlinear oil-film diagnosis bifurcation dynamic numerical Runge-Kutta

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Dynamic analysis of a rig shafting vibration based on finite element

Van Thanh NGO, Danmei XIE, Yangheng XIONG, Hengliang ZHANG, Yi YANG

《机械工程前沿（英文）》 2013年第8卷第3期页码 244-251 doi: 10.1007/s11465-013-0264-8

摘要：

In recently, finite elements method (FEM) has been used most popular for analysis of stress, vibration, heat flow and many other phenomena. Taking a rig shafting as an example, this paper studies the lateral vibration of the rig shafting with multi-degree-of-freedom by using FEM. The FEM model is created and the eigenvalues and eigenvectors are calculated and analyzed to find natural frequencies, critical speeds, mode shapes and unbalance responses. Then critical and mode shapes are determined. Finally, responses of unbalance force are analyzed in case of undamped and damped system, and peaks of response are compared.

关键词： Finite element method (FEM) lateral vibration rig shafting rotor-bearing system dynamic characteristics

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Vibratory behaviors of Jeffcott system on cylindrical roller bearings

Hao WU, Jianwen WANG, Qi AN

《机械工程前沿（英文）》 2009年第4卷第3期页码 305-309 doi: 10.1007/s11465-009-0036-7

摘要： A Jeffcott rotor system of cylindrical roller bearings is studied in detail. Its critical speed is calculated by a new calculation method with roller bearing stiffness and damping. The influences of bearing parameters, such as the roller length, rotor mass, distance between the bearings and the kinematics viscosity of oil on the system critical speed are numerically studied, and the influences of an oil film and damping on the critical speed are also studied. Regular curves of the relationship between the geometric parameters and the system critical speed are obtained. The results show that with increasing roller length and radial load, the critical speed increases; and with increasing rotor mass and the distance between the bearings and the kinematics viscosity, the critical speed decreases. This means that an oil film will decrease the critical rotational speed of the rotor system.

关键词： roller bearing bearing-rotor system design value critical rotational speed

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Analysis of stability and nonlinear response of rotor system with elliptical sliding bearing supports

LU Yanjun, LIU Heng, YU Lie, LI Qi, JIANG Ming, ZHANG Zhiyu

《机械工程前沿（英文）》 2007年第2卷第1期页码 37-45 doi: 10.1007/s11465-007-0006-x

摘要： Based on the variational constraint approach, the variational form of Reynolds equation in hydrodynamic lubrication is revised continuously to satisfy certain constraints in the cavitation zone of oil film field. According to the physical characteristic of oil film, an eight-node isoparametric finite element method is used to convert the revised variational form of Reynolds equation to a discrete form of finite dimensional algebraic variational equation. By this approach, a perturbance equation can be obtained directly on the finite element equation. Consequently, nonlinear oil film forces and their Jacobian matrices are calculated simultaneously, and compatible accuracy is obtained without increasing the computational costs. A method, which is a combination of predictor corrector mechanism and Newton Raphson method, is presented to calculate equilibrium position and critical speed corresponding to Hopf bifurcation point of bearing-rotor system, as by-product dynamic coefficients of bearing are obtained. The timescale, i.e., the unknown whirling period of Hopf bifurcation solution of bearing-rotor system is drawn into the iterative process using Poincar?Newton Floquet method. The stability of the Hopf bifurcation solution can be detected when estimating Hopf bifurcation solution and its periods. The nonlinear unbalanced periodic responses of the system are obtained by using PNF method and path-following technique. The local stability and bifurcation behaviors of periodic motions are analyzed by Floquet theory. Chaotic motions are analyzed by Lyapunov exponents. The numerical results revealed the rich and complex nonlinear behavior of the system, such as periodic, quasiperiodic, jumped solution, chaos, and coexistence of multisolution, and so on.

关键词： computational corrector mechanism predictor corrector multisolution quasiperiodic

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Influence of the Mechanical Seals on the Dynamic Performance of Rotor–Bearing Systems

XU Hua, ZHU Jun

《机械工程前沿（英文）》 2006年第1卷第1期页码 96-100 doi: 10.1007/s11465-005-0008-5

摘要：

In this paper, to consider the effects of mechanical seals, a lumped-mass model and the transfer matrix method are used to establish the equations for the dynamics performance of rotor bearing system. The general inverted iteration method is also used to solve the eigenvalue problem of these equations. To check the response of the rotor bearing system under unbalance motivation, the Gauss method is used to calculate the dynamic response of the constrained vibration. The results, based on the dynamic properties calculation of a typical mechanical spiral seal, such as stiffness coefficients and damping coefficients, exert the influence of the mechanical seal on the rotor bearing system of the high-speed machinery. Meanwhile, some structure parameters that may affect the dynamic performance and forced vibration under unbalance motivation of the rotor bearing system considering mechanical seals are analyzed in the paper. The analysis results show that the mechanical seal more or less has effects on the rotor bearing system. The mechanical seal has much more effects on the flexible rotor bearing system than on the rigid one. For instance, in a certain case, if the effects of the mechanical seal were taken into account, the system s critical speed may increase by 70 80%.

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Stability and coupling dynamic behavior of nonlinear journal active electromagnetic bearing rotor system

LU Yanjun, HEI Di, WANG Yuan, DAI Rong, LU Yanjun, LIU Heng, YU Lie

《机械工程前沿（英文）》 2008年第3卷第2期页码 193-199 doi: 10.1007/s11465-008-0023-4

摘要： The stability and coupling dynamic behavior of a journal active electromagnetic bearing rotor system are analyzed. The gyroscopic effect is considered in the rotor model. The system equations are formulated by combining equations for rotor motion and decentralized proportional integral differential (PID) controllers. A method combining the predictor-corrector mechanism and the Netwon-Raphson method is presented to calculate the critical speed at the corresponding Hopf bifurcation point of the system. For periodic motions, a continuation method combining the predictor-corrector mechanism and shooting method is presented. Nonlinear unbalanced periodic motions and their stability margins are obtained using the shooting method and established continuation method for periodic motions. With the change of control parameters, the system local stability and bifurcation behaviors are obtained using the Floquet theory. The numerical examples show that the schemes not only significantly save computing cost, but also have high precision.

关键词： proportional integral bifurcation corresponding integral differential predictor-corrector mechanism

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Stability and dynamics of rotor system with 45° slant crack on shaft

Yanli LIN, Xiaohui SI, Fulei CHU

《机械工程前沿（英文）》 2011年第6卷第2期页码 203-213 doi: 10.1007/s11465-011-0131-4

摘要：

Crack on a shaft is one of the common damages in a rotor system. In this paper, transverse vibrations are calculated to compare the influences of transverse crack and slant crack on the rotor system. Results show that the vibration amplitude of the rotor system with a 45° slant crack on the shaft is larger than that with a transverse crack when the two types of crack have the same depth and the rotor system runs in the same condition. Stability and dynamic characteristics of the rotor system with a 45° slant crack on the shaft under torsional excitation are analyzed by considering opening and closing of the crack. It is shown that the instability of the transverse vibration of the rotor system increases with increasing difference between the bending stiffness in two main directions, and the vibration is stable when the two bending stiffness are identical. The spectrum analysis of the steady-state response reveals that the gravity and the eccentricity produce different frequency components, and when the two bending stiffness are identical, the multiple frequency components of the torsional excitation disappear. Further investigation shows that the vibration amplitudes in combined frequencies increase rapidly in transversal, torsional, and axial vibration with increasing slant crack depth. The results are helpful for the understanding the dynamic behavior of a rotor system with a slant crack on a shaft and can be used for the detection of the slant crack on a shaft.

关键词： rotor dynamics slant crack stability torsional excitation open and close

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Balancing method without trial weights for rotor systems based on similitude scale model

Ruiduo YE, Liping WANG, Xiaojie HOU, Zhong LUO, Qingkai HAN

《机械工程前沿（英文）》 2018年第13卷第4期页码 571-580 doi: 10.1007/s11465-018-0478-x

摘要：

A balancing method without trial weights based on the dynamic similitude scale model was proposed as a solution to the balancing problem of a large-scale rotor system. This method could be used to directly obtain the required coefficients for the balancing problem of the prototype system through a similarity model test without a prototype test. Thus, the weight test process of the prototype system was effectively eliminated in the proposed balancing method. First, with the rotor system as the research object, the analytical expression of the influence coefficient was derived on the basis of rotor dynamics theory. Then, through calculation and dimensional analysis methods, the similitude relationships of the rotor system and the influence coefficient were deduced on the basis of dynamic similitude theory. The correctness of the proposed similitude relationships was verified through numerical simulation and experiment. The balancing method without trial weights was proposed based on the similitude relationship of the influence coefficient. The effect of the balancing method without trial weights was compared with that of the traditional influence coefficient method through numerical simulation, and the results verified the correctness and effectiveness of the proposed balancing method. The results of this study provide theoretical supplements for the balancing method and the similitude design of the rotor system.

关键词： rotor system dynamic similitude balancing without trial weights influence coefficient

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Experimental and theoretical investigations of the lateral vibrations of an unbalanced Jeffcott rotor

Ali ALSALEH, Hamid M. SEDIGHI, Hassen M. OUAKAD

《结构与土木工程前沿（英文）》 2020年第14卷第4期页码 1024-1032 doi: 10.1007/s11709-020-0647-y

摘要： The current work experimentally explores and then theoretically examines the lateral vibrations of an unbalanced Jeffcott rotor-system working at several unbalance conditions. To this end, three conditions of eccentric masses are considered by using a Bently Nevada RK-4 rotor kit. Measurements of the steady-state as well as the startup data at rigid and flexible rotor states are captured by conducting a setup that mimics the vibration monitoring industrial practices. The linear governing equation of the considered rotor is extracted by adopting the Lagrange method on the basis of rigid rotor assumptions to theoretically predict the lateral vibrations. The dynamic features of the rotor system such as the linearized bearing induced stiffness are exclusively acquired from startup data. It is demonstrated that, with an error of less than 5%, the proposed two-degrees-of-freedom model can predict the flexural vibrations at rigid condition. While at flexible condition, it fails to accurately predict the dynamic response. In contrast to the other works where nonlinear mathematical models with some complexities are proposed to mathematically model the real systems, the present study illustrates the applicability of employing simple models to predict the dynamic response of a real rotor-system with an acceptable accuracy.

关键词： rotor-dynamics Jeffcott rotor lateral vibrations Lagrange method system-equivalent stiffness sleeve bearings oil film induced stiffness

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Performance investigation on ultrasonic levitation axial bearing for flywheel storage system

Taijiang PENG, Zhigang YANG, Junwu KAN, Fengjun TIAN, Xiaohong CHE,

《机械工程前沿（英文）》 2009年第4卷第4期页码 415-419 doi: 10.1007/s11465-009-0051-8

摘要： The bearing is an important basic mechanical part for supporting a shaft. A flywheel storage system needs a type of noncontact support bearing to enhance the speed of the axis. A magnetic suspension bearing is one type of noncontact bearing but has electromagnetic interference to other electric equipment. Based on the performance research of ultrasonic levitation technology, a novel noncontact bearing called ultrasonic bearing is presented, which consists of a special piezoelectric vibrator supporting the load. Experiments are carried out to study the relationships among the amplitude of the vibrator and levitation clearance, the highest speed of the axis, and the frictional moment of the axis. Results show that the levitation clearance becomes smaller gradually with increasing load; the rotation speed is up to 8946 r/min, and the friction moment is only 2.095×10 N·m when the levitation clearance is 8.53 μm. The ultrasonic bearing is highlighted because of its simple structure, strong levitation ability, and low friction moment.

关键词： ultrasonic bearing flywheel storage system piezoelectric ceramic piezoelectric vibrator

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A novel NN based rotor flux MRAS to overcome low speed problems for rotor resistance estimation in vector

Venkadesan ARUNACHALAM,Himavathi SRINIVASAN,A. MUTHURAMALINGAM

《能源前沿（英文）》 2016年第10卷第4期页码 382-392 doi: 10.1007/s11708-016-0421-y

摘要： This paper presents a new neural network based model reference adaptive system (MRAS) to solve low speed problems for estimating rotor resistance in vector control of induction motor (IM). The MRAS using rotor flux as the state variable with a two layer online trained neural network rotor flux estimator as the adaptive model (FLUX-MRAS) for rotor resistance estimation is popularly used in vector control. In this scheme, the reference model used is the flux estimator using voltage model equations. The voltage model encounters major drawbacks at low speeds, namely, integrator drift and stator resistance variation problems. These lead to a significant error in the estimation of rotor resistance at low speed. To address these problems, an offline trained NN with data incorporating stator resistance variation is proposed to estimate flux, and used instead of the voltage model. The offline trained NN, modeled using the cascade neural network, is used as a reference model instead of the voltage model to form a new scheme named as “NN-FLUX-MRAS.” The NN-FLUX-MRAS uses two neural networks, namely, offline trained NN as the reference model and online trained NN as the adaptive model. The performance of the novel NN-FLUX-MRAS is compared with the FLUX-MRAS for low speed problems in terms of integral square error (ISE), integral time square error (ITSE), integral absolute error (IAE) and integral time absolute error (ITAE). The proposed NN-FLUX-MRAS is shown to overcome the low speed problems in Matlab simulation.

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Study on wave rotor refrigerators

Yuqiang DAI, Dapeng HU, Meixia DING

《化学科学与工程前沿（英文）》 2009年第3卷第1期页码 83-87 doi: 10.1007/s11705-009-0075-y

摘要： As a novel generation of a rotational gas wave machine, the wave rotor refrigerator (WRR) is an unsteady flow device used for refrigeration, in whose passages pressured streams directly contact and exchange energy due to the movement of pressure waves. In this paper, the working mechanism and refrigeration principle are investigated based on the one-dimensional unsteady flow theory. A basic limitation on main structural parameters and operating parameters is deduced and the wave diagram of WRR to guide designing is sketched. The main influential factors are studied through an experiment. In the DUT Gas Wave Refrigeration Studying and Development Center (GWRSDC) lab, the isentropic efficiency can now reach about 65%. The results show that the WRR is a feasible and promising technology in pressured gas refrigeration cases.

关键词： wave rotor refrigeration unsteady flow theory wave diagram

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Air bearing center cross gap of neutron stress spectrometer sample table support system

Yang LI,Yunxin WU,Hai GONG,Xiaolei FENG

《机械工程前沿（英文）》 2016年第11卷第4期页码 403-411 doi: 10.1007/s11465-016-0405-y

摘要：

A support system is the main load-bearing component of sample table for neutron stress spectrometer, and air bearing is an important element of a support system. The neutron stress spectrometer sample table was introduced, and the scheme for air bearing combination was selected. To study the performance of air bearing center cross gap, finite element models (FEMs) were established based on air motion and Reynolds equations, effects of air supply pressure, and gap parameters on the overturning moment and bearing capacity of air bearing center cross gap were analyzed. Results indicate that the width, depth, and height differences of the marble floor gap played important roles in the performance of the air bearing. When gap width is lesser than 1 mm and gap depth is lower than 0.4 mm, bearing capacity and overturning moment would vary rapidly with the variation of the width and depth. A gap height difference results in the bearing capacity dropping rapidly. The FEM results agree well with experimental results. Further, findings of the study could guide the design of the support system and marble floor.

关键词： neutron stress spectrometer sample table support system air bearing center cross gap simulation experiment

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Optimization model for rotor blades of horizontal axis wind turbines

LIU Xiong, CHEN Yan, YE Zhiquan

《机械工程前沿（英文）》 2007年第2卷第4期页码 483-488 doi: 10.1007/s11465-007-0084-9

摘要： This paper presents an optimization model for rotor blades of horizontal axis wind turbines. The model refers to the wind speed distribution function on the specific wind site, with an objective to satisfy the maximum annual energy output. To speed up the search process and guarantee a global optimal result, the extended compact genetic algorithm (ECGA) is used to carry out the search process. Compared with the simple genetic algorithm, ECGA runs much faster and can get more accurate results with a much smaller population size and fewer function evaluations. Using the developed optimization program, blades of a 1.3 MW stall-regulated wind turbine are designed. Compared with the existing blades, the designed blades have obviously better aerodynamic performance.

关键词： population extended algorithm developed optimization accurate