Steady-state responses of a belt-drive dynamical system under dual excitations

The stable steady-state periodic responses of a belt-drive system with a one-way clutch are studied. For the first time, the dynamical system is investigated under dual excitations. The system is simultaneously excited by the firing pulsations of the engine and the harmonic motion of the foundation. Nonlinear discrete-continuous equations are derived for coupling the transverse vibration of the belt spans and the rotations of the driving and driven pulleys and the accessory pulley. The nonlinear dynamics is studied under equal and multiple relations between the frequency of the fir- ing pulsations and the frequency of the foundation motion. Furthermore, translating belt spans are modeled as axially moving strings. A set of nonlinear piecewise ordinary differ- ential equations is achieved by using the Galerkin truncation. Under various relations between the excitation frequencies, the time histories of the dynamical system are numerically simulated based on the time discretization method. Further- more, the stable steady-state periodic response curves are calculated based on the frequency sweep. Moreover, the convergence of the Galerkin truncation is examined. Numer- ical results demonstrate that the one-way clutch reduces the resonance amplitude of the rotations of the driven pul- ley and the accessory pulley. On the other hand, numerical examples prove that the resonance areas of the belt spans are decreased by eliminating the torque-transmitting in the opposite direction. With the increasing amplitude of the foun- dation excitation, the damping effect of the one-way clutch will be reduced. Furthermore, as the amplitude of the firing pulsations of the engine increases, the jumping phenomena in steady-state response curves of the belt-drive system with or without a one-way clutch both occur.

Effectof Film Force Nonlinearity on Unbalance Responseof a Jeffcot RotorJournal Bearing System

The effect of oil film force nonlinearity on unbalance response of Jeffcot rotor elliptical bearing system is studied. Linear analysis is done by linearizing the bearing oil film dynamic forces and expressing them with stiffness and damping constants. Nonlinear dynamic simulation is done by taking the nonlinearity of bearing oil film dynamic force into full consideration, with the latter being expressed by a special database which is generated beforehand, and based on non stationary Reynolds equation and Reynolds boundary condition of film rupture. The linear and nonlinear unbalance responses of a Jeffcot rotor supported on a pair of elliptical bearings is studied. The resulting dynamic characteristics and rotor and journal whirling orbits are compared. While good consistancy between nonlinear and linear predictions is found under very small unbalance, significant or even drastic differences are found whenever the unbalance is not small, indicating the necessity of including the nonlinearity of oil film dynamic forces, especially when response to large unbalance is to be predicted.

SPHERICAL-SYMMETRIC STEADY-STATE RESPONSE OF PIEZOELECTRIC SPHERICAL SHELL UNDER EXTERNAL EXCITATION

Spherical-symmetric steady-state response problem of piezoelectric spherical shell in the absence of body force and free charges is discussed. The steady-state response solutions of mechanical displacement, stresses, strains, potential and electric displacement were derived Sram constitutive relations, geometric and motion equations for the piezoelectric medium under external excitation (i.e. applied surface traction and potential) in spherical coordinate system. As an application of the? general solutions, the problem of an elastic spherical shell with piezoelectric actuator and sensor layers was solved. The results could provide good theoretical basis for the spherical-symmetric dynamic control problem of piezoelectric intelligent structure. Furthermore, the solutions can serve as reference for the research of general dynamic control problem.

STEADY-STATE RESPONSES AND THEIR STABILITY OF NONLINEAR VIBRATION OF AN AXIALLY ACCELERATING STRING

The steady-state transverse vibration of an axially moving string with geometric nonlinearity was investigated. The transport speed was assumed to be a constant mean speed with small harmonic variations. The nonlinear partial-differential equation that governs the transverse vibration of the string was derived by use of the Hamilton principle. The method of multiple scales was applied directly to the equation. The solvability condition of eliminating the secular terms was established. Closed form solutions for the amplitude and the existence conditions of nontrivial steady-state response of the two-to-one parametric resonance were obtained. Some numerical examples showing effects of the mean transport speed, the amplitude and the frequency of speed variation were presented. The Liapunov linearized stability theory was employed to derive the instability conditions of the trivial solution and the nontrivial solutions for the two-to-one parametric resonance. Some numerical examples highlighting influences of the related parameters on the instability conditions were presented.

Influence of Operating Parameters on Unbalance in Rotating Machinery Using Response Surface Method

Wide range of rotating machinery contains an inherent amount of unbalance which leads to increase in the vibration level and related faults.In this work,the effect of different operating conditions viz.the unbalanced weight,radius,speed and position of the rotor disc on the unbalance in rotating machine are studied experimentally and analyzed by using Response Surface Methodology(RSM).RSM is a technique which consists of mathematical and statistical methods to develop the relationship between the inputs and outputs of a system by distinct functions.L27 Orthogonal Array(OA)was developed by using Design of Experiments(DOE)according to which experimentation has been carried out.Three accelerometer sensors were mounted to record the vibration responses(accelerations)in radially vertical,horizontal and axial directions.The responses recorded as root mean square values are then analysed using RSM.The relationship between response and operating factors has been established by developing a second order,non-linear mathematical model.Analysis of variance(ANOVA)has been performed for verification of the developed mathematical models.Results obtained from the analysis show that the unbalance weight and speed are most significant operating conditions that contribute the most to the effect the unbalance has on the rotating spindle.

DISTRIBUTION LAW OF RANDOM UNBALANCE RESPONSE OF MULTISTAGE BLOWER

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A CLOSED-FORM ALGORITHM FOR THE STEADY-STATE RESPONSE OF ELASTIC MECHANISMS

This paper presents a closed-form algorithm for the steady-state response of elastic mecha-nisms. Based on an analytic expression of the initial conditions, the steady-state response can beobtained by just one cycle of integration, thus the algorithm is of high efficiency. The algorithm isthen verified by comparing the computational results with the previously published experimental re-sults.

Semi-analytical steady-state response prediction for multi-dimensional quasi-Hamiltonian systems

The majority of nonlinear stochastic systems can be expressed as the quasi-Hamiltonian systems in science and engineering. Moreover, the corresponding Hamiltonian system offers two concepts of integrability and resonance that can fully describe the global relationship among the degrees-of-freedom(DOFs) of the system. In this work, an effective and promising approximate semi-analytical method is proposed for the steady-state response of multi-dimensional quasi-Hamiltonian systems. To be specific, the trial solution of the reduced Fokker–Plank–Kolmogorov(FPK) equation is obtained by using radial basis function(RBF) neural networks. Then, the residual generated by substituting the trial solution into the reduced FPK equation is considered, and a loss function is constructed by combining random sampling technique. The unknown weight coefficients are optimized by minimizing the loss function through the Lagrange multiplier method. Moreover, an efficient sampling strategy is employed to promote the implementation of algorithms. Finally, two numerical examples are studied in detail, and all the semi-analytical solutions are compared with Monte Carlo simulations(MCS) results. The results indicate that the complex nonlinear dynamic features of the system response can be captured through the proposed scheme accurately.

Auditory steady-state evoked response in diagnosing and evaluating hearing in infants

BACKGROUND: Auditory steady-state evoked response (ASSR) is one of the new objective electrophysiological methods to test hearing in infants. It can provide a reliable and complete audiogram with specific frequency to help the hearing diagnosis and rehabilitation of hearing and languaging following auditory screening. OBJECTIVE: To compare the response threshold of ASSR with auditory threshold of visual reinforcement audiometry (VRA) in infants failed in the hearing screening for investigating their hearing loss. DESIGN: A comparative observation. SETTINGS: Maternal and child health care hospitals of Guangdong province, Shunde city, Nanhai city and Huadu district. PARTICIPANTS: Totally 321 infants of 0-3 years undergoing ASSR test were selected from the Hearing Center of Guangdong Maternal and Child Health Care Hospital from January 2002 to December 2004. Informed consents were obtained from their guardians. There were 193 cases (60.2%) of 0-6 months, 31 cases (9.7%) of 7-12 months, 17 cases (5.3%) of 13-18 months, 14 cases (4.4%) of 19-24 months, 33 cases of 25-30 months, and 33 cases (10.2%) of 31-36 months. METHODS: ① The 321 infants failed in the hearing screening were tested under sleeping status, the ranges of response threshold distribution in ASSR of different frequencies were analyzed in each age group. ② The infants above 2 years old were also tested with VRA, and their response thresholds were compared between VRA and ASSR. ③ Evaluative standards: The response threshold was < 30 dB for normal hearing, 31-50 dB for mild hearing loss, 51-70 dB for moderate hearing loss, 71-90 dB for severe hearing loss, and > 91 dB for extremely severe hearing loss. MAIN OUTCOME MEASURES: ① ASSR results of the infants failed in the screening; ② Proportion of cases of each response threshold in each age group; ③ Comparison of ASSR response thresholds and VRA auditory thresholds in the infants of 2-3 years old. RESULTS: ①The response threshold was < 30 dB in 47.4% of the 321 infants failed in the initial hearing screening and secondary screening after 42 days. ② Severe to extremely severe hearing loss was detected in only 16 cases (8.3%) of the 193 infants of 0-6 months, in 9 cases (27.3%) of the 33 infants of 25-30 months, and 13 cases (39.4%) of the 33 infants of 31-36 months. Of the 193 infants of 0-6 months old who failed in the initial screening and the second screening after 42 days, the ASSR auditory threshold was < 30 dB in 97 cases (50.26%), 31-50 dB in 63 cases (32.6%), 51-70 dB in 17 cases (8.8%), 71-90 dB in 7 cases (3.6%), and > 91 dB in 9 cases (4.7%). ③ Among the 321 infants failed in the screening, the auditory threshold in the 6 age groups was < 30 dB in 47.4%, 31-50 dB in 27.1%, 51-70 dB in 8.4%, 71-90 dB in 6.2%, and > 91 dB in 10.9%. ④ The difference between ASSR response threshold and VRA auditory thresholds was 6-18 dB in the normal hearing group, mild and moderate hearing loss groups, and there was high correlation between them. The difference of ASSR and VRA thresholds was less than 5 dB between extremely severe and severe hearing loss groups, 5-13 dB between extremely severe and moderate-to-severe hearing loss groups (P < 0.05), and there was no significant differences between severe and moderate-to-severe hearing loss groups (P > 0.05). CONCLUSION: ① The hearing was normal in about half of the infants, although they failed in the primary screening and secondary screening. ② The proportion of the severity of hearing loss was increased along with aging. ③ Mild and moderate hearing losses are dominant in infants. ④ ASSR is reliable to evaluate the hearing of infants.

Investigation of Induced Unbalance Magnitude on Dynamic Characteristics of High-speed Turbocharger with Floating Ring Bearings

Due to operational wear and uneven carbon absorption in compressor and turbine wheels, the unbalance(me) vibration is induced and could lead to sub?synchronous vibration accidents for high?speed turbocharger(TC). There are very few research works that focus on the magnitude e ects on such induced unbalance vibration. In this paper, a finite element model(FEM) is developed to characterize a realistic automotive TC rotor with floating ring bearings(FRBs). The nonlinear dynamic responses of the TC rotor system with di erent levels of induced unbalance magni?tude in compressor and turbine wheels are calculated. From the results of waterfall and response spectral intensity plots, the bifurcation and instability phenomena depend on unbalance magnitude during the startup of TC. The sub?synchronous component 0.12× caused rotor unstable is the dominant frequency for small induced unbalance. The nonlinear e ects of induced unbalance in the turbine wheel is obvious stronger than the compressor wheel. As the unbalance magnitude increases from 0.05 gbration 1·mm to 0.2 g·mm, the vibration component changes from mainly 0.12× to synchronous vi×. When unbalance increases continuously, the rotor vibration response amplitude is rapidly growing and the 1× caused by the large unbalance excitation becomes the dominant frequency. A suitable un?balance magnitude of turbine wheel and compressor wheel for the high?speed TC rotor with FRBs is proposed: the value of induced un?balance magnitude should be kept around 0.2 g·mm.

Dynamic Response Analysis of Motorized Spindle System

As to motorized spindle system, this paper builds a simplified 3D model of spindle and bearing, performs structure modal analysis, reveals its dynamic characteristics under the free model; furthermore, modifies bearing radial stiffness and number of model and studies the change of modal parameters. On this basis, through the harmonic response analysis of the finite element model, dy- namic response characteristic caused by imbalance of monitored spindle system and law of vibration response to different amount of unbalance is analyzed.

THE GENERAL SOLUTION FOR DYNAMIC RESPONSE OF NONHOMOGENEOUS BEAM WITH VARIABLECROSSSECTION

In this paper by means of the exact analytic method [1], the general solution fordynamic response of nonhomogeneous beam with variable cross section is obtained un-der arbitrary resonant load and boundary conditions. The problem is reduced to solvea non-positive differential equation. Generally, it is not solved by variational method.By the present method, the general solution for this problem may be written as an ana-lytic form. Hence, it is convenient for structure optimizing problem. In this paper, itsconvergence is proved. Numerical examples are given at the end of the paper. which in-dicates satisfactory results can be obtained.

Steady-state response of a saturated half-space with an overlying dry layer subjected to a moving load

In this paper,the steady-state response of a saturated half-space with an overlying dry layer subjected to a moving rectangular load is investigated.The governing partial differential equations are solved using the Fourier transform.The solutions in time-space domain are expressed in terms of infinite Fourier type integrals,which can be evaluated only by numerical quadrature.Numerical results show that the influence of a drained or undrained interface on the response is related to the permeability of the underlying saturated soil.Moreover,the effect due to the upper dry layer is associated with the thickness of the layer.

突加不平衡下GTF发动机转子系统瞬态响应分析

针对GTF发动机低压转子系统突加不平衡瞬态响应问题,基于有限元法建立了考虑啮合单元、行星架单元、膜盘联轴器单元的多体接触、多转子耦合动力学模型,介绍了考虑非线性因素下突加不平衡瞬态响应计算方法,求解了低压转子系统的突加不平衡瞬态响应,并分析了关键部件刚度对突加不平衡的影响规律。结果表明:当风扇转子发生突加不平衡时,各部件均表现为振动幅值突增,后迅速趋于稳定,低压涡轮转子发生明显拍振,突加不平衡载荷主要由行星架结构和第1.5支点刚性支承承担;行星架刚度主要影响风扇转子突加不平衡响应、第1.5支点和行星架处的外传力;膜盘联轴器刚度主要影响增压级突加不平衡响应、转子在突加不平衡之后稳定运转情况。

压气机试验件转子对试验台转子横振不平衡响应的影响

重型燃气轮机压气机试验台系统的动力学性能由试验台转子与试验件转子共同决定。对于已经建成的试验台,在实际运转过程中,需要满足不同试验件的实验需求。因此,在设计试验件转子时,需要考虑其对试验台转子横振不平衡响应的影响。将未知试验件转子的动力学特性模化为试验台转子和试验件转子交界面上的机械阻抗,在交界面处利用机械阻抗综合法的阻抗匹配原理来确定试验件转子对试验台转子横振不平衡响应的影响,得出未知试验件转子的设计限制范围。最后,建立了某一试验台转子和试验件转子的动力学模型,分析了该系统的横向振动不平衡响应,验证了试验件转子不平衡响应的设计限制范围的有效性。研究结论为压气机试验件转子的设计提供了指导意见。

弹簧预紧力对轴承滚子不平衡量检测仪振动响应的影响

以圆柱滚子动不平衡量检测仪的气浮检测装置为研究对象,通过试验研究了不同预紧力对气浮检测装置振动响应的影响,建立振动系统-滚子动力学模型分析振幅的影响因素及弹簧预紧力对振动系统阻尼比的影响,结果表明:气浮检测装置的振动响应随动不平衡量的增加而增大,其主要受振动系统质量和阻尼比的限制;随着弹簧预紧力的增大,振动系统阻尼比先减小后增大,在预紧力为1.96 N时取得最小值;系统共振振幅只与阻尼比的变化有关,与滚子随转频衰减的离心力无关。

弹支干摩擦阻尼器对带有轴承共腔结构涡轴发动机的减振特性

为研究弹支干摩擦阻尼器在带有轴承共腔结构的涡轴发动机减振特性,基于阻尼器动静摩擦副的运动特征,提出弹支干摩擦阻尼器位于轴承共腔结构处的附加刚度和阻尼的计算方法,建立了弹支干摩擦阻尼器与涡轴发动机耦合的有限元模型。通过数值求解,分析不同支点阻尼器对涡轴发动机各阶模态减振效果及阻尼器对可控模态的减振机理。基于以上工作提出了阻尼器各阶模态减振设计方案。结果表明,通过设计弹支干擦阻尼器的支点位置、个数、正压力及控制转速区间等参数,可实现阻尼器对带有轴承共腔结构涡轴发动机各阶模态振动的有效控制,最大减振比达95.6%。

支承刚度各向异性对双转子系统进动状态的影响

为提高航空发动机的推重比,航空发动机静子系统的工程解决方案常引起转子系统支承刚度各向异性,进而对转子系统的动力学特性产生显著影响。针对支承刚度各向异性的双转子系统,建立动力学特性计算模型,在验证计算模型准确性的基础上,研究支承刚度各向同性和各向异性对双转子系统固有频率、进动状态和不平衡响应的影响。研究结果表明:支承刚度各向同性时,双转子系统Campbell图中的低阶固有频率线出现交叉,而支承刚度各向异性使低阶固有频率线具有相互分离的趋势。支承刚度各向同性时,不平衡力仅触发转子系统的正进动运动,转子进动轨迹为圆形;而支承刚度各向异性时,转子系统的反/正进动均被不平衡力触发,转子进动轨迹为椭圆形。支承刚度各向异性时,在某些转速下转子系统不同位置处的进动方向可能不同。支承阻尼减小转子系统反/正进动的振幅及反进动的转速区间,降低支承刚度各向异性对双转子系统动力学特性的不利影响。

大机动过载下不平衡转子的弯扭耦合振动分析

针对未来无人机承受较大机动过载的特点,基于Timoshenko梁以及圆盘单元理论建立任意机动飞行条件下不平衡转子系统的弯扭耦合振动有限元模型,分析大机动过载情况下转子的非线性响应特征。结果表明:机动飞行工况下,在弯曲自由度和扭转自由度上都产生了新的次谐振动频率成分;各频率成分幅值被放大,弯曲自由度和扭转自由度耦合增强;当转速超过1阶弯曲临界速度时,周期性明显变差。

Jeffcott转子-可倾瓦滑动轴承系统不平衡响应的非线性分析

考虑了可倾瓦滑动轴承的非线性油膜力,对Jeffcott转子-可倾瓦轴承系统的不平衡响应进行了非线性分析。以非定常雷诺方程和雷诺破膜条件为依据,生成了单瓦非线性油膜力数据库。根据可倾瓦滑动轴承的结构特点,对单瓦数据库进行插值和拼装以获得可倾瓦滑动轴承的非线性油膜力的瞬时值。通过计算得到了不同参数下,Jeffcott转子-可倾瓦轴承系统的轴颈和转子的涡动轨迹及振幅。计算结果与线性动力学所得的结果进行比较。两者在不平衡量比较小的情况下结果吻合良好,但在不平衡量很大时结果却有较大差别。可见在进行转子-可倾瓦轴承系统的非线性动力学分析时有必要计入可倾瓦滑动轴承油膜非线性的影响。