Experimental investigation of a random repeated impact process

A simple random repeated impact process which has previously been investigated theoretically has now been investigated experimentally. The process, which consists of a ball bouncing on a randomly vibrating surface, is analogous to loss of contact situations which can occur in machinery and transportation systems where a hard rolling element separates from the rolling surface. Experimental data was acquired and processed by using a digital data acquisition system and associated software. The results were obtained in the form of histograms which could be directly compared with the predicted probability density functions. The agreement between the predicted behaviour and the measured results was excellent, and confirmed the dependence of the behaviour of the random process on the coefficient of restitution and the excitation level. Also, it was verified that the probability density function of table velocities at impact was distinct from the Gaussian density function of the excitation. Consequently the theoretical analysis previously developed has been validated with sufficient confidence to enable it to be applied to predictions of acoustic noise generated by the impact process.     

Force generation characteristics of standard heavyweight impact sources used in the sound generation of building floors

Several heavyweight impact sources have been used in applying standardized excitation forces to evaluate the noise generation characteristics of building floors. In this study, heavyweight sources (a bang machine and an impact ball) were filmed with a high-speed camera on the period of deformation and restitution of the impact. The generated impact force was measured, and the effects of the taken deforming shapes were investigated. Experimental modal analysis was performed to determine the natural frequencies and mode shapes of the impact sources. With respect to deforming shapes during impacts, the influence of the mode shapes was clearly demonstrated, especially for the impact ball. Using the measured modal properties, the impact force was predicted and compared to the measured excitation force. By comparing the transient variation of the excitation force and its frequency spectrum, the influence of the modal characteristics of the source on the generated impact force was investigated.     

Wheel/rail noise—Part III: Impact noise generation by wheel and rail discontinuities

This paper is part of a series of publications dealing with wheel/rail noise [1–4]. Except for comparing the relative importance of impact noise with rolling noise, this paper concerns itself exclusively with the impact noise generated by such discontinuities as rail joints, frogs, switches, and wheel flats.Studies show that above a certain critical train speed the wheel separates from the rail when the interface encounters certain types of discontinuities. This critical train speed is an important acoustical parameter, because the noise generation process obeys completely different laws in the speed ranges below and above it. From the geometry, the kinematics, and the dynamics of the wheel/rail system, analytical models have been developed to identify the major variables controlling the generation of impact noise. The validity of these models has been confirmed by both scale-model and full-scale experiments.The results of the study show the following: (1) at rail joints, the height difference—and not the width of the gap—is the controlling parameter; (2) below critical train speed, impact noise increases with increasing train speed and does not depend on the direction of travel; (3) above critical train speed, the intensity of impact noise increases with increasing train speed for travel in the step-up direction but is independent of the train speed for travel in the step-down direction; (4) in generating impact noise, wheel flats are equivalent to step-down rail joints, provided flat height equals height difference at the joint; (5) both the magnitude and spectrum of impact noise produced by wheel and rail discontinuities can be predicted from a simple wheel drop test. With the knowledge gained from both the analytical and the experimental studies, we have been able to identify feasible measures for the control of impact noise.     

Analyses of contact forces and vibration response for a defective rolling element bearing using an explicit dynamics finite element model

This paper provides insights into the physical mechanism by which defect-related impulsive forces, and consequently, vibrations are generated in defective rolling element bearings. A dynamic nonlinear finite element model of a rolling element bearing with an outer raceway defect was numerically solved using the explicit dynamics finite element software package, LS-DYNA. A hypothesis was developed to explain the numerical noise observed in the predicted vibrations and contact forces, and the noise frequencies were analytically estimated. In-depth analyses of the numerically estimated dynamic contact forces between the rolling elements and the raceways of a bearing, which are not measured in practice, and have not been reported previously, are presented in this paper. Several events associated with the traverse of the rolling elements through the outer raceway defect are elaborated, and the impulsive force generating mechanism is explained. It was found that the re-stressing of the rolling elements that occurs near the end of a raceway defect generates a burst of multiple short-duration force impulses. The modelling results also highlight that much higher contact forces and accelerations are generated on the exit of the rolling elements out of defect compared to when they strike the defective surface. A bearing with a machined outer raceway defect was tested in a controlled experiment; the measured acceleration response compared favourably with the numerically modelled acceleration results, thereby, validating the low- and high-frequency characteristics of the de-stressing and re-stressing of the rolling elements, respectively.     

Motion of grains down a bumpy surface

We summarize in this article an extensive experimental and theoretical effort carried out to understand the behavior of a single ball when rolling down a bumpy surface. This may appear to be a simple problem but in fact is one that displays a rich variety of different behaviors which allow us to understand better dissipative systems such as granular media. Studies performed previously have shown that the motion of the single ball on the rough surface can be characterized by three different dynamic regimes according to the different values of the two control parameters, the inclination angle theta and the ratio Phi=R/r, where R is the radius of the rolling ball and r the radius of the glass beads which make up the rough surface. The three regimes are a decelerated regime A, a stationary regime B, characterized by a constant average velocity and a jumping regime C. This result was found to be independent of the composition of the rolling ball and the rough surface. It has been demonstrated that regime B is characterized by a viscous-like friction force that appears for specific parameter values. This friction force can be explained by a model whose central ingredient is the geometry of the surface. The trajectory of the ball in regime B can be pictured as a driven random walk motion where the fluctuations of the local velocities are due to collisions of the moving sphere and the surface grains. A detailed analysis of diffusive properties of the motion is discussed. (c) 1999 American Institute of Physics.     

Measurement and analysis of rolling tire vibrations

This paper presents the measurement and analysis of rolling tire vibrations due to road impact excitations, such as from cobbled roads, junctions between concrete road surface plates, railroad crossings. Vibrations of the tire surface due to road impact excitations cause noise radiation in the frequency band typically below 500 Hz. Tire vibration measurements with a laser Doppler vibrometer are performed on a test set-up based on a tire-on-tire principle which allows highly repetitive and controllable impact excitation tests under various realistic operating conditions. The influence on the measured velocity of random noise, cross sensitivity and alignment errors is discussed. An operational modal analysis technique is applied on sequential vibration measurements to characterise the dynamic behaviour of the rolling tire. Comparison between the operational modal parameters of the rolling tire and the modal parameters of the non-rolling tire allows an assessment of the changes in dynamic behaviour due to rolling.     

Stochastic rolling of a rigid sphere in weak adhesive contact with a soft substrate

We study the rolling motion of a small solid sphere on a fibrillated rubber substrate in an external field in the presence of a Gaussian noise. From the nature of the drift and the evolution of the displacement fluctuation of the ball, it is evident that the rolling is controlled by a complex non-linear friction at a low velocity and a low noise strength (K), but by a linear kinematic friction at a high velocity and a high noise strength. This transition from a non-linear to a linear friction control of motion can be discerned from another experiment in which the ball is subjected to a periodic asymmetric vibration in conjunction with a random noise. Here, as opposed to that of a fixed external force, the rolling velocity decreases with the strength of the noise suggesting a progressive fluidization of the interface. A state (K) and rate (V) dependent friction model is able to explain both the evolution of the displacement fluctuation as well as the sigmoidal variation of the drift velocity with K. This research sets the stage for studying friction in a new way, in which it is submitted to a noise and then its dynamic response is studied using the tools of statistical mechanics. Although more works would be needed for a fuller realization of the above-stated goal, this approach has the potential to complement direct measurements of friction over several decades of velocities and other state variables. It is striking that the non-Gaussian displacement statistics as observed with the stochastic rolling is similar to that of a colloidal particle undergoing Brownian motion in contact with a soft microtubule.     

Experimental and numerical studies on the discrete noise about the cross-flow fan with block-shifted impellers

The experimental and numerical studies have been carried out to investigate the blade passage frequency (BPF) noise of a cross-flow fan (CFF) with the block-shifted impeller. Firstly, the aeroacoustic and aerodynamic features about the five different block-shifted impellers have been obtained experimentally. Secondly, the dynamic pressure sensors were put in the noise generating surfaces to investigate the pressure fluctuations generated by the shifted blocks in the near-field through the cross-correlation analysis. Thirdly, the two-dimensional (2D) unsteady flow field has been simulated by commercial CFD software and the vortex flow patterns and the unsteady force of the blade have been analyzed to detect the noise source about the CFF. Finally, the noise properties about the CFF were predicted by a hybrid method through the Farassat’s equation and the surface pressure fluctuations were provided by the CFD simulations. A simplified theory model has also been built up at the same time. The comparisons are made between the results of hybrid method and the theory model to validate the correctness of the noise prediction methods. The accuracy of these results was also evaluated by the corresponding experimental ones. The results indicate that the impellers with different block-shifted angles are the same in aerodynamic performance but different in the BPF noise. The relations between the shifted angles and the BPF noise levels have been predicted and discussed for the noise reduction.     

Noise of a turbulent boundary layer flow over smooth and rough plates at low mach numbers

The spectral levels of the quadrupole noise generated by a boundary layer flow over a smooth surface are calculated. Explicit dependences of the noise levels on the Reynolds number are obtained for the low-frequency and high-frequency ranges. It is shown that the logarithmic zone of the velocity profile is responsible for the region of the quadrupole noise spectrum with a hyperbolic dependence on frequency. A method of calculating the dipole noise of a boundary layer flow over a rough surface is developed. The method is based on the use of the combined probability density for the turbulent velocity fluctuations and the random dimensions of protuberances of the rough surface. The two constants involved in this theory are determined from a special experiment. It is shown that the surface roughness noticeably increases the radiation levels of a boundary layer flow in a certain frequency range.     

Noise impact assessment by utilizing noise map and GIS: A case study in the city of Chungju, Republic of Korea

In this study, a scheme to develop a noise map and noise impact assessment method using GIS has been suggested. After developing a road-traffic noise map for the city of Chungju, Republic of Korea, noise impact assessment was performed through analyzing the map. A 3-dimensional terrain model was generated using digital maps and building models were prepared using the information from draft and digital maps. To develop a noise evaluation model, a noise-source map for each road was generated. The noise levels at 25 locations close to roads were measured and compared with the expected noise levels to verify the developed noise map. An excess noise map was generated by comparing the road-traffic noise map with a noise-standard map. Using the excess noise map, the areas exceeding environmental noise standards were effectively evaluated through a GIS space analysis. The 3-dimensional facade noise map was generated to calculate the number of people exposed to a certain noise level.     

On the prediction of impact noise,V: The noise from drop hammers

In earlier papers in this series, the concepts of “acceleration” and “ringing” noise have been studied in relation to impact machines, and values of radiation efficiency have been obtained for the various types of structural components. In the work reported in this paper the predicted and measured noise radiation from a drop hammer, both in full-scale and in $\text{1}\text{3}\text{-}\text{scale}$ model form, were examined. It is found that overall noise levels (L_eq per event) can be predicted from vibration measurements to within ± 1·5 dB, and to within ±2·5 dB in one-third octave bands. In turn this has permitted noise reduction techniques to be examined by studies of local component vibration levels rather than overall noise, a method which provides considerable enlightenment at the design stage. It is shown that on one particular drop hammer, the noise energy is shared surprisingly uniformly over four or five sources, and that when these have been reduced, the overall noise reduction is severely limited by the “acceleration” noise from the “tup” or “hammer” itself. As this is difficult to eliminate without a basic change in forging technology, it follows that “tup” enclosure or modification of the sharpness of the final “hard” impact are the only means available for any serious noise reduction. Also indicated is the reliability of using model techniques, suitably scaled in frequency and impulse magnitude, in developing machinery with impact characteristics.     

The effects on noise of changes in wheel/rail system parameters

An analytical model has been developed that simulates the generation and propagation of wheel/rail noise. In the model, wheel/rail vibrations are induced by running surface roughness. The vibration responses are determined from considering contact stiffness effects and wheel/rail impedance interactions. Near field sound power levels are then calculated by combining the responses with radiation efficiencies, space-averaging the velocity squared on the wheel, and accounting for the decay of vibration along the rail. Finally, the noise levels predicted for the wayside are obtained from an analysis of the propagation that includes the effect of finite ground impedance. Good agreement exists between the analytical model and a series of validation measurements taken at DOT's Transportation Test Center in Pueblo, Colorado. A sensitivity analysis conducted for the parameters of a typical baseline system achieved significant changes in rolling noise only for reductions in wheel/rail contact stiffness, increases in wheel/rail contact area, and decreases in wheel/rail roughness through wheel truing and rail grinding.     

Vibration analysis of a rotating system due to the effect of ball bearing waviness

This research presents an analytical model to investigate vibration due to ball bearing waviness in a rotating system supported by two or more ball bearings, taking account of the centrifugal force and gyroscopic moment of the ball. The waviness of rolling elements is modelled by the sinusoidal function, and it is incorporated into the position vectors of the race curvature center. The Hertzian contact theory is applied to calculate the elastic deflection and non-linear contact force, while the rotor has translational and angular motions. Both the centrifugal force and gyroscopic moment of the ball and the waviness of the rolling elements are included in the kinematic constraints and force equilibrium equations of a ball to derive the non-linear governing equations of the rotor, which are solved by using the Runge–Kutta–Fehlberg algorithm to determine the new position of the rotor. The proposed model is validated by the comparison of the results of the prior researchers. This research shows that the centrifugal force and gyroscopic moment of the ball plays the important role in determining the bearing frequencies, i.e., the principal frequencies, their harmonics and the sideband frequencies resulting from the waviness of the rolling elements of ball bearing. It also shows that the bearing vibration frequencies are generated by the waviness interaction not only between the rolling elements of one ball bearing, but also between those of two or more ball bearings constrained by the rotor.     

Commercial road vehicle noise

A survey of the characteristics of the noise emitted by commercial vehicles has been made. The most important single parameter determining the noise of a modern diesel-engined vehicle is the engine speed. All of the other parameters such as load, road speed, etc., have only a secondary effect.The sources of noise on the vehicle are reviewed and it is shown how the characteristics of these sources determine the overall noise characteristics of the vehicle. It has been found that a simple model of the vehicle as a number of coincident point sources predicts the overall noise characteristics of the vehicle to ±2 dB(A). It is shown that there are two extremes of behaviour, the rolling noise controlled vehicle and the power unit noise controlled vehicle; the engine is currently the controlling noise source.Tyre noise has been investigated in some detail as comparatively little has been published previously on this source. Empirical relationships between the tyre noise and speed, tyre size and road surface roughness are given. It is concluded that tyre noise is generated by impacting between elements of the tyre tread and elements of the road surface.Modifications have been made to the engine, exhaust, intake and cooling fan of a 9 ton, 6 litre diesel engined truck which have reduced its ISO test noise level from 88 dB(A) to 80 dB(A). However, it is concluded that 80 dB(A) commercial vehicles are not yet feasible for production. In particular insufficient is known about cooling fan design.Finally cab noise has been investigated and it has been found to originate from the same source as the exterior noise, power unit airborne noise. Therefore any modifications to the power unit to reduce exterior noise will have a similar effect on interior noise. This is confirmed by the vehicle modifications mentioned above which reduced the maximum cab noise from 87 dB(A) to 79 dB(A).     

Identification of winter tires using vibration signals generated on the road surface

During the winter, traffic regulations state that automobile drivers must use winter tires on unsafe roads such as snowy expressways. The present report is concerned with the development of an automatic tire identification system that can discriminate winter tires from summer tires with high accuracy. The system detects the impact vibration signal that is specifically generated by winter tires when tread blocks with wide grooves strike the road surface during rolling. The signal is picked up by a commercially available vibration sensor. If the signal contains specified impact frequency components, the tire is judged to be a winter tire. Compared with the previous identification system, which used airborne tire/road noise, the proposed system has two advantages. First, it is unaffected by meteorological factors such as wind noise. Second, the proposed system performs well even when the target vehicle is traveling at low speed. We evaluate the performance of the system outdoors using a number of vehicles with various tires and demonstrate an overall improvement in identification accuracy for vehicles traveling at low or moderate speeds.     

Dynamics of a viscous ball rolling down on a rigid staircase

We theoretically investigate the motion of a ball rolling down on a periodical staircase. Our research is restricted in the case of completely inelastic collision when the ball falls down on the surface of the stairs. The ball is accelerated when it rolls cross the edge of the stair, while it is decelerated when it rolls on the horizontal surface due to the rolling friction. The competition between them causes two different regimes according to the parameters of the system. One is the steady moving regime in which the ball keeps moving forever, and the other is the still regime in which the ball finally stops after rolling on a finite number of stairs. The diagram of these two regimes is given in the reduced parameter space. The tendency that smaller scale of the staircase can keep moving on smaller inclined angle is found.     

The effects of environmental and classroom noise on the academic attainments of primary school children

While at school children are exposed to various types of noise including external, environmental noise and noise generated within the classroom. Previous research has shown that noise has detrimental effects upon children's performance at school, including reduced memory, motivation, and reading ability. In England and Wales, children's academic performance is assessed using standardized tests of literacy, mathematics, and science. A study has been conducted to examine the impact, if any, of chronic exposure to external and internal noise on the test results of children aged 7 and 11 in London (UK) primary schools. External noise was found to have a significant negative impact upon performance, the effect being greater for the older children. The analysis suggested that children are particularly affected by the noise of individual external events. Test scores were also affected by internal classroom noise, background levels being significantly related to test results. Negative relationships between performance and noise levels were maintained when the data were corrected for socio-economic factors relating to social deprivation, language, and special educational needs. Linear regression analysis has been used to estimate the maximum levels of external and internal noise which allow the schools surveyed to achieve required standards of literacy and numeracy.     

Particle filter-based relative rolling estimation algorithm for non-cooperative infrared spacecraft

The issue of feature point mismatching among infrared image sequence would bring big challenge to estimating the relative motion of non-cooperative spacecraft for it couldn’t provide the prior knowledge about its geometric structure and motion pattern. The paper introduces particle filter to precisely match the feature points within a desired region predicted by a kinetic equation, and presents a least square estimation-based algorithm to measure the relative rolling motion of non-cooperative spacecraft. The state transition equation and the measurement update equation of non-cooperative spacecraft are represented by establishing its kinetic equations, and then the relative pose measurement is converted to the maximum posteriori probability estimation via assuming the uncertainties about geometric structure and motion pattern as random and time-varying variables. These uncertainties would be interpreted and even solved through continuously measuring the image feature points of the rotating non-cooperative infrared spacecraft. Subsequently, the feature point is matched within a predicted region among sequence infrared image using particle filter algorithm to overcome the position estimation noise caused by the uncertainties of geometric structure and motion pattern. Finally, the position parameters including rotation motion are estimated by means of solving the minimum error of feature point mismatching using least square estimate theory. Both simulated and real infrared image sequences are induced in the experiment to evaluate the performance of the relative rolling estimation, and the experimental data show that the rolling motion estimated by the proposed algorithm is more robust to the feature extraction noise and various rotation speed. Meanwhile, the relative rolling estimation error would increase dramatically with distance and rotation speed increasing.     

Free vibration analysis of linear particle chain impact damper

Impact dampers have gained much research interest over the past decades that resulted in several analytical and experimental studies being conducted in that area. The main emphasis of such research was on developing and enhancing these popular passive control devices with an objective of decreasing the three parameters of contact forces, accelerations, and noise levels. To that end, the authors of this paper have developed a novel impact damper, called the Linear Particle Chain (LPC) impact damper, which mainly consists of a linear chain of spherical balls of varying sizes. The LPC impact damper was designed utilizing the kinetic energy of the primary system through placing, in the chain arrangement, a small-sized ball between each two large-sized balls. The concept of the LPC impact damper revolves around causing the small-sized ball to collide multiple times with the larger ones upon exciting the primary system. This action is believed to lead to the dissipation of part of the kinetic energy at each collision with the large balls.     

倾角和摩擦系数的不均匀性对伽利略斜面实验核心结果的影响

伽利略斜面实验的核心结果是小球走过的路程正比于时间的平方,但倾角和摩擦系数的局部不均匀性会导致局部加速度的不均匀性.本文用一个简化模型计入倾角和摩擦系数的不均匀性,数值计算发现这些不均匀性不仅引入随机误差,而且导致路程与时间偏离平方关系.如果保持倾角情况不变,减小摩擦系数使球从无滑滚动变为有滑滚动,路程与时间对于平方关系的偏离程度会增大而不是减小.这个结论虽然与直觉相反,但却与物理学史的相关研究得到的结论相符.为了排除小球被释放时的随机因素的影响,本文在实验中设计了零初速度释放小球的装置,还设计了一个更方便的测量摩擦系数的方法.