Stress calculation for plastic helical gears under a real transverse contact ratio

Calculation methods of plastic helical gears with a real transverse contact ratio have never been studied in depth. The methods used in some references assume a uniform load distribution along the line of contact or don’t take into consideration the effect of premature mesh between one or more pair of teeth during engagement, which is not in good agreement with numerical results. This paper is focused on analysis of plastic helical gears. The nonuniform load distribution obtained from the proposed mathematical model is based on the calculation of the real contact ratio representing the real number of pairs of teeth in contact. This model also leads to the distribution of the tooth bending stress and the contact stress along the area of contact.     

Experimental investigation of the effect of lead errors on helical gear and bearing vibration transmission characteristics

The characteristics of gear meshing vibration undesgo change as the vibration is transmitted from the gear to the housing. Therefore, vibration transmission characteristics of helical gear systems must be understood before the effective methods of reducing gear noise can be found. In this work, using a helical gear with different lead errors, the gear vibration in the rotational direction and the bearing vibration are measured. The frequency characteristics of gear and bearing vibration are investigated and a comparson is also provided.     

The forging of helical gears (II): comparisons of the forging processes

In this study, the forging processes of helical gears have been investigated wherein they have been classified into two types: the guiding type and the clamping types. These two types of forgings of helical gears have been analyzed by using the upper-bound method. New kinematically admissible velocity fields of the clamping-type forging of helical gears have been proposed, where an involute curve has been introduced to represent the tooth profile of the gear. The proposed velocity fields of the clamping-type forging of helical gears have been applied to the non-symmetric lateral extrusion forging and the result has been compared with the solution proposed by Plancak et al. [J. Mater. Process. Technol. 1992; 34:465–472]. Numerical calculations have been carried out to investigate the effects of various parameters, such as modules, number of teeth, helix angles and friction factors on the clamping-type forging of helical gears. For the forging of helical gears, the results of the upper-bound analysis of the clamping type have been compared with those of the guiding ones. Some experiments of the clamping-type forging were carried out with commercial aluminum alloy to show the validity of the analysis. Good agreement was found between the predicted values of the forging load and the experimental forging load.     

A new fault diagnosis algorithm for helical gears rotating at low speed using an optical encoder

Helical gears are widely used in gearboxes due to its low noise and high load carrying capacity, but it is difficult to diagnose their early faults based on the signals produced by condition monitoring systems, particularly when the gears rotate at low speed. In this paper, a new concept of Root Mean Square (RMS) value calculation using angle domain signals within small angular ranges is proposed. With this concept, a new diagnosis algorithm based on the time pulses of an encoder is developed to overcome the difficulty of fault diagnosis for helical gears at low rotational speeds. In this proposed algorithm, both acceleration signals and encoder impulse signal are acquired at the same time. The sampling rate and data length in angular domain are determined based on the rotational speed and size of the gear. The vibration signals in angular domain are obtained by re-sampling the vibration signal of the gear in the time domain according to the encoder pulse signal. The fault features of the helical gear at low rotational speed are then obtained with reference to the RMS values in small angular ranges and the order tracking spectrum following the Angular Domain Synchronous Average processing (ADSA). The new algorithm is not only able to reduce the noise and improves the signal to noise ratio by the ADSA method, but also extracts the features of helical gear fault from the meshing position of the faulty gear teeth, hence overcoming the difficulty of fault diagnosis of helical gears rotating at low speed. The experimental results have shown that the new algorithm is more effective than traditional diagnosis methods. The paper concludes that the proposed helical gear fault diagnosis method based on time pulses of encoder algorithm provides a new means of helical gear fault detection and diagnosis.     

Vibration analysis of the plates subject to distributed dynamic loads by using spectral element method

A spectral element method (SEM) is introduced for the vibration analysis of rectangular plates under distributed dynamic loads. In this paper, the spectral plate element matrix (often called the dynamic stiffness matrix) is formulated from the relation between the forces and displacement along the opposite two parallel edges. The distributed dynamic load is discretized into a sequence of equivalent line loads. The plate is then considered as a connection of two spectral plate element with the joint node line along which the equivalent line load acts. The spatial coordinate dependence of each equivalent line load is then removed through the spatial Fourier transformation so that the plate (2-D) problem becomes a simplified equivalent beam like (1-D) problem. The remaining solution procedures is therefore the same as that used for beam problems. Numerical tests show that the present SEM provides very accurate solutions when compared to finite element solutions.     

齿轮转子系统耦合振动新频率的有限元分析

利用有限元应用软件ANSYS建立了齿轮转子系统耦合振动分析的有限元计算模型。分析与计算了系统的耦合振动模态，在此基础上进行了谐响应分析，得到了系统的耦合振动响应图。该分析方法可广泛应用于齿轮转子系统的动力学设计。     

Research on transmission paths of a coupled beam-cylindrical shell system by power flow analysis

A power flow analysis based on a substructure approach is performed to exhibit vibration transmission in a complex coupled beam-cylindrical shell system. The system is divided into a shell substructure and a beam substructure, which are coupled by three spring-dampers. The theoretical receptance function of each substructure with a free-free interface condition is formulated by modal analysis to describe the dynamical behavior. On the basis of the receptance functions of the two substructures as well as synthesis through the geometrical compatibility and force balance conditions at the coupling interfaces, the dynamic characteristics of the coupled system are calculated. Both the input and transmitted powers within the system are estimated, and the influences of the excitation locations, the stiffness and loss factor of the spring-dampers on the vibration transmission are investigated as well. This paper was recommended for publication in revised form by Associate Editor Eung-Soo Shin G.P. Feng received his Ph.D. from the School of Mechanical Engineering at Shanghai Jiao Tong University. His research interests include vibration analysis, control and sound radiation, etc. Z.Y. Zhang received his Ph.D. from the School of Mechanical Engineering at Shanghai Jiao Tong University. Dr. Zhang is currently a Professor at the School of Mechanical Engineering at Shanghai Jiao Tong University in Shanghai, China. Y. Chen received his Ph.D. from the School of Mechanical Engineering at Shanghai Jiao Tong University. His research interests include vibration and shock analysis. H.X. Hua received his Ph.D. at the University of Brussels in Belgium. Dr. Hua is currently a Professor and Doctoral Supervisor at the School of Mechanical Engineering at Shanghai Jiao Tong University in Shanghai, China. His research interests include modal parameter identification, and analysis of vibration and shock.     

Application of the chebyshev-fourier pseudospectral method to the eigenvalue analysis of circular mindlin plates with free boundary conditions

An eigenvalue analysis of the circular Mindlin plates with free boundary conditions is presented. The analysis is based on the Chebyshev-Fourier pseudospectral method. Even though the eigenvalues of lower vibration modes tend to convergence more slowly than those of higher vibration modes, the eigenvalues converge for sufficiently fine pseudospectral grid resolutions. The eigenvalues of the axisymmetric modes are computed separately. Numerical results are provided for different grid resolutions and for different thickness-to-radius ratios.     

飞行器柔性起落架落震性能分析

以某型飞行器为原型,对该型飞行器进行了起落架缓冲器参数设计,并建立适用于ADAMS/Aircraft软件的起落架着陆性能仿真三维数字模型。进行了全刚性起落架全机落震仿真,验证起落架缓冲器初步设计结果基本满足落震缓冲性能要求。运用有限元软件对刚体起落架模型进行了柔性化处理,把起落架柔性因素考虑到缓冲性能分析中,建立简化数学模型对仿真结果加以分析验证。得出起落架柔性对缓冲器性能有一定影响的结论,并指出其影响的原因。对缓冲器参数设计具有指导意义。     

Vibration of a three-layered viscoelastic sandwich circular plate

The equations of motion for a three-layer sandwich circular plate with viscoelastic core are derived. The Donnell–Mushtari–Vlasov assumptions follow to simplify. For the case of iso-symmetric annular plate, five equations are further reduced to three equations. The assumed-mode method then yields the free and the forced solutions being characterized by six generalized coordinates for each circumferential wave number n. Due to the splitting of transversal and in-plane terms the study of vibration response can be reduced to the consideration of the SDOF linear oscillator with hysteretic damping. Numerical results first illustrated the frequency response function (FRF) for two different visco models and slight difference is observed. The effects of frequencies changes and damping due to viscoelastic material (VEM) core for several core-to-face thickness ratios are studied. The results, via the FRF's, show that a relatively thin visco (VEM) core can reduce vibration effectively, but as the core thickness exceeds it the damping gradually reduces. The embedded VEM core decreases the frequencies as expected. The damping effects upon individual modes are looked into as well. The results show that the n=0 mode is affected the most by VEM core.     

Vibration and stability of an Euler–Bernoulli beam with up to three-step changes in cross-section and in axial force

The paper treats the vibration of beams with up to three-step changes in cross-section and in which the axial force in each portion is constant but different. The system parameters are the step positions, the flexural rigidity, the mass per unit length and the axial force in the beam portions—all of which were normalized. The frequency equation for 16 combinations of classical boundary conditions are expressed as fourth-order determinants equated to zero. The first three frequency parameters are tabulated for sets of system parameters (arbitrarily chosen and which includes a stepped beams under tensile or compressive axial end force). Critical compressive end force which causes a stepped beam to buckle are tabulated. Buckling under a system of axial forces, one of which is critical is discussed and several critical combinations of the system parameters are tabulated. Beams of constant depth and step change in breadth, of constant breadth and step change in depth and shafts with step change in diameter are considered. It is shown that stepped shafts are inferior machine elements if dynamic properties are the prime consideration.     

Numerical and experimental analysis of a gear system with teeth defects

The modelling of a one-stage spur gear transmission by a two degrees of freedom system produces two modes: rigid body and elastic. The time varying meshing stiffness is the main internal excitation source for the transmission and governs the behaviour of the elastic mode. Deterioration of one or several teeth, which affects the gear mesh stiffness, is considered in this work. The beginning of crack or spalling are modelled respectively by tooth having localised and distributed defect and are taken into account in the model. Simulation results are analysed by cepstrum and spectrum techniques. It is found that cepstrum and spectrum techniques are very efficient for localised and distributed defects, respectively. Series of tests are made in the experimental setup. Spectrum and cepstrum analysis of the recorded responses, with and without defects, are compared with numerical results and confirms their usefulness in gear monitoring .     

Vibration analysis of a ferromagnetic plate subjected to an inclined magnetic field

The magnetic traction on a deformable ferromagnetic material is deduced based on the classical magnetoelastic model. The vibration frequency of a ferromagnetic beam subjected to an inclined magnetic field is analyzed by employing formulations of the magnetic force. The result for the condition of longitudinal magnetic field is the same trend as that of the previous experiment carried out by Takagi et al. [Analysis and experiment of dynamic deflection of a thin plate with a coupling effect. IEEE Transactions on Magnetics 1992;28(2):1259–62]. Moreover, experimental tests have been carried out to study the free vibration of a magnetic plate subjected to an inclined magnetic field.     

Vibration and reliability of a rotating beam with random properties under random excitation

In this paper, vibration and reliability of a rotating beam with random properties under random excitations are studied. The rotating beam is under a stochastic load modeled as a stationary white noise. The cross-sectional area, elasticity modulus, moment of inertia, shear modulus, damping coefficient, mass density and rotational speed are modeled as random variables. To develop the equations of motion, the finite element method and space state analysis are applied. In order to consider the randomness of properties, a second order perturbation method is used. The effects of rotational speed, setting angle, hub radius, variances of random properties, correlation of random variables and damping matrix forms on the vibration and reliability of rotating beams, are studied completely.     

Effects of a one-way clutch on the nonlinear dynamic behavior of spur gear pairs under periodic excitation

Nonlinear behavior analysis was used to verify whether a one-way clutch is effective for reducing the torsional vibration of a paired spur gear system under periodic excitation. The dynamic responses were studied over a wide frequency range by speed sweeping to check the nonlinear behavior using numerical integration. The gear system with a one-way clutch showed typical nonlinear behavior. The oscillating component of the dynamic transmission error was reduced over the entire frequency range compared to a system without a one-way clutch. The one-way clutch also eliminated unsteady continuous jump phenomena over multiple solution bands, and prevented double-side contact, even with very small backlash. Installing a one-way clutch on both sides of the gear system was more effective at mitigating the negative effects of external periodic excitation and various parameter changes than a conventional gear system without a one-way clutch.     

汽车变速器总成的噪声源及降噪措施

探讨了汽车变速器总成的多种噪声源,采取了相应的降噪措施.介绍了研究变速器降低噪声的意义,分析了噪声源(主要为齿轮系统和附属系统),并从设计和制造工艺上制定出了降噪措施.     

变刚度组合机构及其在隔振器设计中的应用

本文介绍了一种新型变刚度组合机构的组成及工作原理,分析了变刚度规律与机构中凸轮廓线的关系,讨论了各种典型变刚度规律的隔振效果,提出了在隔振器设计中应用变刚度组合机构的设计方法,给出了设计实例说明应用这种变刚度机构设计的隔振器,其隔振效果达到了先进隔振器的水平。     

Nonlinear vibration analysis of an axially moving drillstring system with time dependent axial load and axial velocity in inclined well

In this paper a nonlinear model was developed for a drillstring system in deviated well with axially moving motion and axial loading, using the perturbation techniques.The drillstring was considered as a simply supported axially moving rotor. Governing equations of motion were obtained based on Hamilton's principle and method of multiple scales was employed to solve the nonlinear motion equations in order to obtain the steady state response and stability region of the system.Then the effects of rotating speed, axial compression load, imbalance mass and nonlinear fluid force on the drillstring responses were investigated in detail and nonlinear natural frequencies and their corresponding mode shapes were presented.Analytical and numerical results reveal the rich and interesting nonlinear phenomena such as primary and parametric resonance that is being investigated for the first time in this study on the nonlinear vibration of the drillstring system.Finally in effort to validate the theoretical approach employed in this study, the numerical solutions obtained here were compared with a set of existing experimental data.     

The plastic extension of a chain of rings due to an axial impact load

The plastic response of a chain of circular rings due to an axial tensile impact load was investigated both experimentally and in part, analytically. Chains were built-up from circular aluminium rings and subjected to axial impact loading at one end. High-speed photography was employed to record the development of the deformation process. It was found that plastic collapse was progressively transmitted to neighbouring rings in the manner of a plastic wave. To investigate the situation analytically, a simplified approach was adopted which assumed rigid-perfectly plastic behaviour of the ring material and arrived at an equation of the same form as the classical one-dimensional elastic wave equation.     

The application of spectral kurtosis on Acoustic Emission and vibrations from a defective bearing

The application of Acoustic Emission (AE) technology for machine health monitoring is gaining ground as power tool for health diagnostic of rolling element bearing. This paper provides an investigation that compares the applicability of AE and vibration technologies in monitoring a naturally degraded roller bearing. This research is the first known attempt investigating the comparative effectiveness of applying the Kurtogram to both vibration and AE data from a defective bearing.