Analysis of gear rattle by means of a wavelet-based signal processing procedure

In the paper a wavelet-based signals processing technique for the experimental detection of the gear rattle produced by the teeth impacts in lightly loaded gears is proposed. The Discrete Wavelet Transform is used to decompose the signal of the angular relative motion of an helical gear pair, and the wavelet decomposition details are adopted to analyze the dynamic behavior under rattle condition. In particular the procedure permits to evaluate the quality of the impacts between the teeth, discriminating between the two different sides of teeth contacts when there is a double-sided rattle condition. This technique enables, moreover, to define new indices for metrics of gear rattle especially useful in order to conduct comparisons for different operative conditions. Some examples of application of the proposed technique are reported in the paper adopting experimental signals acquired by two high resolution incremental encoders on a specific gear pair test rig. The experimental investigations regard comparative analyses with respect to the speed fluctuations amplitude, the rattle frequency and the lubrication regime.     

Landing gear noise control using perforated fairings

Landing gears of commercial aircraft make an important contribution to total aircraft noise in the approach configuration. Using fairings to shield components from high speed impingement reduces noise. Furthermore, perforating these fairings has been confirmed by flight tests to further enable noise reduction. Following an earlier fundamental study of the application of perforated fairings, a study has been performed to investigate and optimize the benefits of bleeding air through landing gear fairings. By means of wind tunnel tests, an aerodynamic and acoustic survey has been performed on a simplified generic main landing gear to explore the influence of （perforated） fairings on the lower part of the gear. The results show that for this specific case, the application of impermeable fairings reduces noise in the mid- and high frequency range by shielding sharp edged components from high velocity impingement. However, below 1 kHz the noise is shown to increase significantly. Application of the perforations is shown to diminish this low frequency increase whilst maintaining the reduction in the mid- and high frequency range. The aerodynamic and acoustic measurements point in the direction of the separated flow of the fairings interacting with the downstream gear components responsible for the low frequency noise increase. Bleeding of the air through the fairings reduces the large scale turbulence in the proximity of these components and hence diminishes the low frequency noise increase.     

Radial flexible bearings suitable stiffness estimation

This article describes a technique for the differential bearings noise reduction. Noise results from the mechanical looseness of the differential gear and connected elements and it is activated by the vibrations of the engine. A test rig for simulation of the phenomenon outside vehicle has been designed and behavior of the differential bearing has been analyzed. Analytical software that is capable to classify the types of the noise has been created. The mathematical model enables estimation of suitable range of differential bearings radial stiffness. Finally, the selected solution is tested on the test rig, thus the technique is verified.     

Experimental research for robust design of power transmission components

In the future progress of technical systems it is impossible to avoid the power transmission (PT) components. Mechatronical technical systems will include the innovated PT components with high-level quality indicators. The article proposes the application of the new approaches to those components design in order to challenge innovation and inventions. The main objective is to define the design parameters in terms of reliability, vibration and noise as design constraints in the stage of the Embodiment design of PT components. Robust design is provided by using the axiomatic method in this way. Reliability as the design constraint of PT components is defined and modeled in a specific way suitable for this purpose and application. Also, the model of gear vibrations and gear units noise generation is presented in a new way suitable for applying as the design constraint. Those design constraints provide design parameters definition in an efficient way, with high-level service quality indicators. The presented models are based on a great volume of experimental data about service conditions probability, gear and bearing failure probability, gear units vibration and modal behavior etc. Theoretical knowledge and models are insufficient yet to provide the necessary data. The article contains presentation of testing methods and data processing oriented to provide data necessary for the application in the suggested approach to PT components design.     

Effect of rotation direction of a rotary tiller on draft and power requirements in a Bangkok clay soil

Experiments were conducted in a Bangkok clay soil to evaluate the performance of a rotary tiller equipped with reverse or conventional blades. The conventional rotary tiller was equipped with C-type blades whereas the reverse-rotary tiller had new types of blades. Tests were conducted on wet land as well as in dry land. Tests were conducted at tractor forward speeds of 1.0, 1.5 and 2.0 km/h. A power-take-off (PTO) power consumed was calculated from the PTO torque and speed. The results indicated that the PTO power consumption was less for the reverse-rotary tiller compared to the conventional tiller for all passes and forward speeds. For both rotary tillers, power consumption decreased as the number of passes increased, whereas power consumption increased when the forward speed was increased. At all forward speeds, the power consumption was the highest during the first pass and lowest during the third pass. The maximum difference of PTO power requirement was after the first pass at 1.0 km/h forward speed. The reverse-rotary tiller consumed about 34% less PTO power under this condition.     

一飞机发动机动力特性分析

确定计算模型时，发动机定子按实际刚度，采用NASTRAN70．0程序对发动机整机进行了动力分析，分析结果与试验进行了比较，吻合度优于美国GE公司计算结果。作者认为造成偏磨故障的原因是弹性环压死，使压气机转子与定子反向平动的第六阶临界转速上升到接近放气阀门关闭时转速所致。根据动力响应计算结果，装配工艺采取措施后，克服了此偏磨故障。     

Dynamic behavior of gear pumps: effect of variations in operational and design parameters

This work presents a wide number of results about the influence that variations in terms of operational and design parameters play on the dynamic behavior of external gear pumps. These results are obtained by using a non-linear lumped-parameter kineto-elastodynamic model developed and experimentally assessed with the aim of including all the important dynamic effects. On the one hand, the effects of variations in the operational parameters—namely output pressure, rotational speed and oil viscosity—are analysed; on the other hand, the effects of modifications of some design parameters are shown: clearances and relief groove dimension. The results in terms of gear eccentricity, pressure evolution, pressure forces, gear accelerations and variable forces exciting the pump casing enlighten the dynamic behavior of gear pumps and give useful indications for design improvements and vibration and noise reduction. As regards specifically gear accelerations as well as forces exciting the casing, they strongly increase with both output pressure and rotational speed, but variations in rotational speed in the operational range give lower effects. Conversely, the modifications of the clearances give negligible effects, while the relief groove dimension is very important: the larger the relief grooves are, the higher the gear accelerations and forces exciting the casing become.     

Finite element analysis of post-buckling dynamics in plates—Part I: An asymptotic approach

Various static and dynamic aspects of post-buckled thin plates, including the transition of buckled patterns, post-buckling dynamics, secondary bifurcation, and dynamic snapping (mode jumping phenomenon), are investigated systematically using asymptotical and non-stationary finite element methods. In part I, the secondary dynamic instability and the local post-secondary buckling behavior of thin rectangular plates under generalized (mechanical and thermal) loading is investigated using an asymptotic numerical method which combines Koiter’s nonlinear instability theory with the finite element technique. A dynamic multi-mode reduction method—similar to its static single-mode counterpart: Liapunov–Schmidt reduction—is developed in this perturbation approach. Post-secondary buckling equilibrium branches are obtained by solving the reduced low-dimensional parametric equations and their stability properties are determined directly by checking the eigenvalues of the resulting Jacobian matrix. Typical post-secondary buckling forms—transcritical, supercritical and subcritical bifurcations are observed according to different combinations of boundary conditions and load types. Geometric imperfection analysis shows that not only the secondary bifurcation load but also changes in the fundamental post-secondary buckling behavior are affected. The post-buckling dynamics and the global analysis of mode jumping of the plates are addressed in part II.     

An instrumentation system to measure the loads acting on the tractor PTO bearing during rotary tillage

Application of rotary tillage has been increased due to less tillage passes required, reduced draft, and greater efficiency through reduction in wheel slippage. Early failure of the bearing of tractor power take-off (PTO) shaft was observed in tractors of power range 30–35 horsepower during rotary tillage. An instrumentation setup involving an extended octagonal ring transducer (EORT) was developed and installed at the bottom of the bearing to measure the axial load and the vertical component of the radial load. The horizontal component of radial load was measured by strain gauges. Based on measured loads, the bearing life was assessed. Independent variables were: operating depth, number of blades, gear setting, engine speed, and tyre size. The average axial and radial loads varied from 786–3869 N, and 134–430 N, respectively. However, bearing experienced very high peak loads during each trial. The peak axial and radial loads was recorded between 1081–7534 N and 566–1794 N, respectively. The estimated bearing life based on peak loads was 171.98–28341.39 h. Based on the findings, it may be concluded that the average loads were not sufficient to cause quick failure of PTO bearing, rather sudden peak loads might be the root cause of early failure.     

线绳驱动转速提升式低频俘能器的设计与研究

俘获周围环境中丰富的低频机械能对减少废旧电池数量、实现自维持传感器、降低传感器网络的使用和维护成本等具有重要意义, 但传统的振动型俘能器对低频机械能的俘获效果不佳. 为了有效收集周围环境中的低频机械能, 本文提出一种线绳驱动、具备转速提升功能的电磁式俘能器, 首先借助线绳驱动转轴结构将低频振动转换为双向旋转运动, 再通过刚度自动改变的拨片和磁齿轮将双向旋转运动转换为转速更高的单向旋转运动, 从而提高输出功率. 对所提出的俘能器建立了机电耦合动力学模型, 并通过样机制作和实验测试证实了理论模型的正确性. 实验研究表明, 在激励幅值40 mm和激励频率2 Hz的条件下, 通过本文设计制作的2.5倍转速提升功能的磁齿轮, 可将线绳驱动电磁式俘能器的最大输出功率增加至7.82 mW, 比对应的无磁齿轮提升转速的线绳驱动电磁式俘能器的最大输出功率(3.22 mW)高约143%. 在相同的激励条件下, 制作的俘能器的交流电能经过桥式整流器转换为直流后, 可在1.2 s内将220 μF储能电容器的电压从0 V提升至1.5 V. 在低频、不规则的振动激励下, 所制作的俘能器仍可提供0.35 mW的输出功率, 为设计高性能低频俘能器提供一条可行的解决方案.      

Biomechanical and dynamic mechanism of locust take-off

The biomimetic locust robot hopping vehicle has promising applications in planet exploration and reconnaissance. This paper explores the bionic dynamics model of locust jumping by using high-speed video and force analysis. This paper applies hybrid rigid-flexible mechanisms to bionic locust hopping and studies its dynamics with emphasis laid on the relationship between force and jumping performance. The hybrid rigid-flexible model is introduced in the analysis of locust mechanism to address the principles of dynamics that govern locust joints and mechanisms during energy storage and take-off. The dynamic response of the biomimetic mechanism is studied by considering the flexi- bility according to the locust jumping dynamics mechanism. A multi-rigid-body dynamics model of locust jumping is established and analyzed based on Lagrange method; elastic knee and tarsus mechanisms that were proposed in previous works are analyzed alongside the original bionic joint configurations and their machinery principles. This work offers primary theories for take-off dynamics and establishes a theoretical basis for future studies and engineering applications.     

Variable knot-based spline approximation recursive Bayesian algorithm for the identification of Wiener systems with process noise

Wiener systems consist of a linear dynamic block in cascade with static nonlinearity. One of the challenging issues in the identification of a process noise disturbed Wiener system is that the influence of noise is difficult to eliminate. For Wiener systems with process noise, traditional algorithms will result in biased estimates. To solve this problem, a novel recursive Bayesian algorithm based on variable knot spline approximation is proposed in this paper. First, a spline function is taken to approximate the inverse function of the nonlinear part, which can achieve excellent extrapolation and eliminate oscillatory behaviors. A knot selection method is then presented to achieve accurate estimates. Furthermore, a knot variation strategy to improve the accuracy of the spline approximation is described. Finally, the proposed algorithm is validated through a numerical simulation.     

On the effect of multiple parallel nonlinear absorbers in palliation of torsional response of automotive drivetrain

Torsional vibrations transmitted from the engine to the drivetrain system induce a plethora of noise, vibration and harshness (NVH) concerns, such a transmission gear rattle and clutch in-cycle vibration, to name but a few. The main elements of these oscillations are variations in the inertial imbalance and the constituents of combustion power torque, collectively referred to as engine order vibration. To attenuate the effect of these transmitted vibrations and their oscillatory effects in the drive train system, a host of palliative measures are employed in practice, such as clutch pre-dampers, slipping discs, dual mass flywheel and others, all of which operate effectively over a narrow band of frequencies and have various unintended repercussions. These include increased powertrain inertia, installation package space and cost. This paper presents a numerical study of the use of multiple Nonlinear Energy Sinks (NES) as a means of attenuating the torsional oscillations for an extended frequency range and under transient vehicle manoeuvres. Frequency–Energy Plots (FEP) are used to obtain the nonlinear absorber parameters for multiple NES coupled in parallel to the clutch disc of a typical drivetrain configuration. The results obtained show significant reduction in the oscillations of the transmission input shaft, effective over a broad range of response frequencies. It is also noted that the targeted reduction of the acceleration amplitude of the input shaft requires significantly lower NES inertia, compared with the existing palliative measures.     

Energy dissipation mechanism and experiment of particle dampers for gear transmission under centrifugal loads

As a passive means of vibration reduction, particle damping is mainly applied to the horizontal or vertical steady field. However, it is seldom applied to centrifugal fields. Under high speed and heavy loading, the vibration of tooth surfaces of gear transmissions becomes more severe shortening gear service life and augmenting noise. Under centrifugal loading, the particle system exhibits different characteristics, for example, particles are extruded at the end farthest from the center. We investigated gears with drilled via holes filled with damping particles. Using the discrete-element method, we developed an energy dissipation model for the particle system accounting for friction and inelastic collisions. Energy dissipation and damping characteristics of this system were analyzed. Experiments were also conducted with the gear system having different particle filling rates. The results show that this filling rate is an important parameter associated with particle damping in a centrifugal field. An unsuitable filling rate would significantly reduce damping effectiveness. With changes in rotation speed and load, the gear transmission system has different optimal filling rates. The results provide guidelines for the application of particle damping in centrifugal fields of gear transmissions.     

The use of plasma actuators for bluff body broadband noise control

Experiments were conducted using plasma actuators to control broadband noise generated by a bluff body flow. The motivation behind the study was to explore the potential of plasma actuators to reduce landing gear noise during approach phase of an aircraft. The control effectiveness of both dielectric barrier discharge and sliding discharge plasma actuators were tested in laboratory environment, using a representative bluff body consisting of a circular cylinder and an oblique strut. Noise measurements were taken in an anechoic chamber using a phased microphone array and far-field microphones. Results showed that the upstream directed plasma forcing, located at ±90 deg on the upstream cylinder with respect to the approaching flow, could effectively attenuate the broadband noise radiated from the wake flow interaction with the downstream strut. With the same AC electrical power consumption, the sliding discharge with additional DC voltage was found to be more effective due to its elongated plasma distribution and higher induced flow momentum. Measurements using particle image velocimetry suggested that the flow speed impinging on the downstream strut was reduced by the upstream plasma forcing, contributing to the reduced noise.     

Stochastic Vibration Model of Gear Transmission Systems Considering Speed-Dependent Random Errors

A dynamic and stochastic simulation model is developed for analyzing the vibration of gear transmission systems with consideration of the influence of the time-variant stiffness, loads, and gear transmission errors. The gear transmission system is viewed as a non-linear, time-correlated and stationary stochastic system. The transmission errors of gears are decomposed into harmonic and random components based on the spectral analysis. To simulate the random component, a second order Markov process with time-variant parameters considering influence of rotational speed is proposed and the method to determine the model parameters based on the random error of measured gear transmission error is developed. A simulation system is developed. The input to the simulation system is a white Gaussian noise process and harmonic errors, and the output is the rotational vibration acceleration of gears. Experiments are carried out to verify the proposed model. The influences of the random error on vibration acceleration are examined using the developed simulation system.     

Finite element analysis of post-buckling dynamics in plates. Part II: A non-stationary analysis

With the secondary bifurcation and the local post-secondary buckling behavior being analyzed in Part I, Part II of this study consists of developing an adaptive non-stationary load sweeping algorithm to investigate post-buckling dynamics and mode jumping phenomena of generally (mechanically and thermally) loaded thin plates in a global context. The non-stationary sweeping procedure has the merits of adapting large load steps to capture static characteristics of stable equilibrium paths both before and after mode jumping and reduce automatically the step size to ensure a dynamic transition between the two stable branches. Thus, it is computationally effective. Furthermore, by adopting the non-stationary sweeping scheme, this procedure can avoid spurious convergence of the transient response to an unstable equilibrium.Corresponding to different post-secondary bifurcation forms, which are determined using asymptotical finite element analysis developed in Part I, subsequent buckling patterns of various complexity occurring after mode jumping are obtained using the method developed in this article. Qualitative changes in post-buckled patterns are observed after the occurrence of the secondary bifurcation or the mode jumping. Free vibration analysis using the tangent stiffness matrix obtained from the converged static or dynamic solutions shows a vibration modal shifting phenomena occurs during the process of the load sweep. The spurious convergence phenomenon caused by the application of the traditional hybrid static–dynamic method is found and explained.     

Bifurcation and chaos analysis of multistage planetary gear train

A nonlinear time-varying dynamic model for a multistage planetary gear train, considering time-varying meshing stiffness, nonlinear error excitation, and piece-wise backlash nonlinearities, is formulated. Varying dynamic motions are obtained by solving the dimensionless equations of motion in general coordinates by using the varying-step Gill numerical integration method. The influences of damping coefficient, excitation frequency, and backlash on bifurcation and chaos properties of the system are analyzed through dynamic bifurcation diagram, time history, phase trajectory, Poincaré map, and power spectrum. It shows that the multi-stage planetary gear train system has various inner nonlinear dynamic behaviors because of the coupling of gear backlash and time-varying meshing stiffness. As the damping coefficient increases, the dynamic behavior of the system transits to an increasingly stable periodic motion, which demonstrates that a higher damping coefficient can suppress a nonperiodic motion and thereby improve its dynamic response. The motion state of the system changes into chaos in different ways of period doubling bifurcation, and Hopf bifurcation.     

Evaluation of a 6.71 kW power tiller for draft and drawbar power on tar roads

A 6.71 kW power tiller was evaluated for draft and drawbar power on tar roads. The effect of mounting 40 kg of wheel ballast was also studied. Polynomial regression analysis was used to establish the relationship between draft and wheel slip, drawbar power and wheel slip, drawbar power and fuel consumption, and drawbar power and specific fuel consumption. The results of the study showed draft values of 2107, 2110 and 2110 N in second low, third low and first high gears at an engine speed of 150o rpm with a 15% wheel slip. The respective draft values at engine speed of 2000 rpm with a 15% wheel slip were 2172, 2189 and 2212 N. With the mounting of 40kg wheel ballast there was an increase in draft of 217, 207 and 291 N at 1500 rpm, and 328, 306 and 344 N at 2000 rpm of the engine with a 15% wheel slip in second low, third low and first high gears, respectively. The increase in drawbar power with 40 kg ballast was 10.88%, 7.83% and 20.13% at 1500 rpm and 18.89%, 16.56% and 14.88% at 2000 rpm of engine over the drawbar power available with zero ballast. The fuel consumption with the use of wheel ballast was slightly more than the fuel consumption without any ballast.     

Effect of noise on erosion of safe basin in power system

We study the effect of Gaussian white noise on erosion of safe basin in a simple model of power system whose safe basin is integral in the absence of noise. The stochastic Melnikov method is first applied to predict the onset of basin erosion when the noise excitation is present in system. And then the eroded basins are simulated according to the necessary restrictions for the system’s parameters. It is found that for the noisy power system when the noise intensity σ is greater than a threshold, basin erosion occurs and as σ is further increased basin erosion is aggravated. These studies imply that random noise excitation can induce and enhance the basin erosion in the power system.