SiC颗粒增强6061铝合金滑动磨损的周期性与随机性

采用自制盘 -块式高速摩擦试验机研究了SiC颗粒增强 6 0 6 1铝合金试盘同颗粒增强橡胶试块对摩时的滑动磨损行为 ,在滑动速度为 2 0m/s和 40m/s条件下 ,通过持续试验、间歇试验和重复试验 ,考察了试盘磨损行为的周期性和磨损量变化的随机性 .基于对磨损行为的风险率的分析 ,提出了磨损统计模型 ,结合试验数据讨论了周期磨损量概率分布的某些特殊性质 .结果表明 ,周期磨损量的概率平均值及分散程度与滑动速度有关 ,而其下限值与速度无关     

Medium frequency dynamic investigation of the railway wheelset-track system using a discrete-continuous model

Summary In the paper, dynamic interaction between elastic high-speed-train car wheelset and track is studied using a discrete-continuous mechanical model. The model enables to investigate the influence of the parametric excitation from the track as well as static and dynamic unbalances of wheels and brake disks on the dynamic response of the wheelset running at various speeds on the track of various average vertical stiffness. From the results of numerical simulation it follows that particularly severe periodic resonances occur for the track of large stiffness, yielding high vertical dynamic contact forces between the wheels and rails. The maximum dynamic response has been obtained for parameters corresponding to the conditions at which the phenomenon of grumbling noise generation is usually observed in reality. Received 21 January 1997; accepted for publication 29 February 1997     

高速涡轮增压器轴承-转子系统不平衡响应及稳定性分析

汽车涡轮增压器广泛采用浮环轴承支承的小型轻质转子系统,以实现100 000~300 000 r/min的工作转速,提高发动机功率和动力性能,并降低燃油消耗和排放. 在此超高速工况下,动压油膜的强非线性作用和转子固有的不平衡效应使该系统呈现出复杂的动力学现象,其中油膜涡动、振荡、跳跃、倍周期分岔和混沌等非线性动力学行为对增压器的健康运转意义重大,因而备受关注. 本文作者从摩擦学动力学耦合的角度出发,基于流体动压轴承润滑理论和有限差分法计算非稳态油膜压力,结合达朗贝尔原理和传递矩阵法建立了转子离散化动力学方程,提出了一种由双油膜浮环支承的涡轮增压器转子系统动力学模型,并从转子轨迹、轴承偏心率、频谱响应、庞加莱映射和分岔特性等方面比较分析,描述了该非线性轴承-转子系统的不平衡效应及油膜失稳特征. 结果表明:转子一般在相对低速下作稳定的单周期不平衡振动,在高转速下其被油膜失稳引起的次同步涡动所抑制,但不平衡量的增加可阻碍转子以拟周期运动通向混沌运动的路径;适当不平衡补偿下,由于内、外油膜间交互的非线性刚度和阻尼作用,在油膜失稳区间之间的中高速区会出现适合增压器健康运转的稳定区间.      

Existence of planar flame fronts in convective-diffusive periodic media

We prove the existence of planar travelling wave solutions in a reaction-diffusion-convection equation with combustion nonlinearity and self-adjoint linear part in R ⁿ, n1. The linear part involves diffusion-convection terms and periodic coefficients. These travelling waves have wrinkled flame fronts propagating with constant effective speeds in periodic inhomogeneous media. We use the method of continuation, spectral theory, and the maximum principle. Uniqueness and monotonicity properties of solutions follow from a previous paper. These properties are essential to overcoming the lack of compactness and the degeneracy in the problem.     

Development of a dynamic simulation model of a towed seeding implement

As the size of western Canadian farms increase and the productivity demands on seeding equipment rise, improvement in the depth consistency performance of seeding implements at higher seeding speeds is a future focus of equipment designers. The objective of this work was to develop a dynamic simulation tool for predicting the motion of a hoe-opener style seeding implement with independent row units. The model was developed using simple low-order models available in the literature to compute the forces generated at soil-tire and soil-tool interfaces. By maintaining low computational cost, early-stage parameter sensitivity and design trade-off studies can assess the risk of a given design change. The amplitude of the power spectral density (PSD) of simulated row unit motion was typically lower with sharper peaks than measured results up to 3.3 m/s; these differences were due to both input amplitude differences, and the sensitivity of the model itself. Frequency agreement of major measured and simulated PSD peaks was acceptable considering the model simplifications. Row unit motion was dominated by two phenomena – a strong periodic input in the terrain surface, and feedback between the hoe-opener and packer wheel of the row unit.     

Dynamic crack growth under Rayleigh wave

A nonuniform crack growth problem is considered for a homogeneous isotropic elastic medium subjected to the action of remote oscillatory and static loads. In the case of a plane problem, the former results in Rayleigh waves propagating toward the crack tip. For the antiplane problem the shear waves play a similar role. Under the considered conditions the crack cannot move uniformly, and if the static prestress is not sufficiently high, the crack moves interruptedly. For fracture modes I and II the established, crack speed periodic regimes are examined. For mode III a complete transient solution is derived with the periodic regime as an asymptote. Examples of the crack motion are presented. The crack speed time-period and the time-averaged crack speeds are found. The ratio of the fracture energy to the energy carried by the Rayleigh wave is derived. An issue concerning two equivalent forms of the general solution is discussed.     

Design of piezoaeroelastic energy harvesters

We design a piezoaeroelastic energy harvester consisting of a rigid airfoil that is constrained to pitch and plunge and supported by linear and nonlinear torsional and flexural springs with a piezoelectric coupling attached to the plunge degree of freedom. We choose the linear springs to produce the minimum flutter speed and then implement a linear velocity feedback to reduce the flutter speed to any desired value and hence produce limit-cycle oscillations at low wind speeds. Then, we use the center-manifold theorem to derive the normal form of the Hopf bifurcation near the flutter onset, which, in turn, is used to choose the nonlinear spring coefficients that produce supercritical Hopf bifurcations and increase the amplitudes of the ensuing limit cycles and hence the harvested power. For given gains and hence reduced flutter speeds, the harvested power is observed to increase, achieve a maximum, and then decrease as the wind speed increases. Furthermore, the response undergoes a secondary supercritical Hopf bifurcation, resulting in either a quasiperiodic motion or a periodic motion with a large period. As the wind speed is increased further, the response becomes eventually chaotic. These complex responses may result in a reduction in the generated power. To overcome this adverse effect, we propose to adjust the gains to increase the flutter speed and hence push the secondary Hopf bifurcation to higher wind speeds.     

Coarsening Fronts

We characterize the spatial spreading of the coarsening process in the Allen–Cahn equation in terms of the propagation of a nonlinear modulated front. Unstable periodic patterns of the Allen–Cahn equation are invaded by a front, propagating in an oscillatory fashion, and leaving behind the homogeneous, stable equilibrium. During one cycle of the oscillatory propagation, two layers of the periodic pattern are annihilated. Galerkin approximations and the Conley index for ill-posed spatial dynamics are used to show existence of modulated fronts for all parameter values. In the limit of small amplitude patterns or large wave speeds, we establish uniqueness and asymptotic stability of the modulated fronts. We show that the minimal speed of propagation can be characterized by a dichotomy which depends on the existence of pulled fronts. The main tools here are an Evans function type construction for the infinite-dimensional ill-posed dynamics and an analysis of the complex dispersion relation based on Sturm–Liouville theory.     

Criticality of Hopf bifurcation in state-dependent delay model of turning processes

In this paper the non-linear dynamics of a state-dependent delay model of the turning process is analyzed. The size of the regenerative delay is determined not only by the rotation of the workpiece, but also by the vibrations of the tool. A numerical continuation technique is developed that can be used to follow the periodic orbits of a system with implicitly defined state-dependent delays. The numerical analysis of the model reveals that the criticality of the Hopf bifurcation depends on the feed rate. This is in contrast to simpler constant delay models where the criticality does not change. For small feed rates, subcritical Hopf bifurcations are found, similar to the constant delay models. In this case, periodic orbits coexist with the stable stationary cutting state and so there is the potential for large amplitude chatter and bistability. For large feed rates, the Hopf bifurcation becomes supercritical for a range of spindle speeds. In this case, stable periodic orbits instead coexist with the unstable stationary cutting state, removing the possibility of large amplitude chatter. Thus, the state-dependent delay in the model has a kind of stabilizing effect, since the supercritical case is more favorable from a practical viewpoint than the subcritical one.     

Existence of multidimensional traveling waves in the transport of reactive solutes through periodic porous media

We prove the existence of multidimensional traveling-wave solutions to the scalar equation for the transport of solutes (contaminants) with nonlinear adsorption and spatially periodic convection-diffusion-adsorption coefficients under the assumption that the nonlinear adsorption function satisfies the Lax and Oleinik entropy conditions. In the nondegenerate case, we also prove the uniqueness of the traveling waves. These traveling waves are analogues of viscous shock profiles. They propagate with effective speeds that depend on the periodic porous media only up to their mean states, and are given by an averaged Rankine-Hugoniot relation. This is a direct consequence of the fact that the transport equation is in conservation form. We use the sliding domain method, the continuation method, spectral theory, maximum principles, and a priori estimates. In the degenerate case, the traveling waves are weak solutions of a degenerate parabolic equation and are only Holder continuous. We obtain them by taking suitable limits on the non-degenerate traveling waves. The uniqueness of the degenerate traveling waves is open.     

Design of a one-dimensional flexible structure for desired load-bearing capability and axial displacement

A flexible spine is capable of bearing both transverse and axial external loads. At the same time, it is observed in animals that the spine deforms substantially during their motion and this allows the body to move e?ciently and achieve high speeds. This paper deals with the modeling and design of one-dimensional flexible objects for a desired load-carrying capability and axial deflection. The flexible one-dimensional object is modeled as a serial chain of rigid segments connected by one-degree-of-freedom rotary joints with torsional springs and dampers at the joints. For a desired transverse and axial loading, optimization techniques are used to obtain the values of orientation of the rigid segments, the joint stiffness and damping, which gives the desired axial displacement and the shape. It is shown that changing the orientation or the shape of the one-dimensional structure has more effect than changing the stiffness at the joints. Various types of loading and axial deflections are considered and the optimization procedure is illustrated through numerical examples. The response of such a flexible structure to a transient periodic loading is also obtained.     

Spinodal Decomposition and Coarsening Fronts in the Cahn–Hilliard Equation

We study spinodal decomposition and coarsening when initiated by localized disturbances in the Cahn–Hilliard equation. Spatio-temporal dynamics are governed by multi-stage invasion fronts. The first front invades a spinodal unstable equilibrium and creates a spatially periodic unstable pattern. Secondary fronts invade this unstable pattern and create a coarser pattern in the wake. We give linear predictions for speeds and wavenumbers in this process and show existence of corresponding nonlinear fronts. The existence proof is based on Conley index theory, a priori estimates, and Galerkin approximations. We also compare our results and predictions with direct numerical simulations and report on some interesting bifurcations.     

Numerical Continuation of Solutions and Bifurcation Analysis in Multibody Systems Applied to Motorcycle Dynamics

It is shown how the equations of motion for a multibody system can be generated in a symbolic form and the resulting equations can be used in a program for the analysis of nonlinear dynamical systems. Stationary and periodic solutions are continued when a parameter is allowed to vary and bifurcations are found. The variational or linearized equations and derivatives with respect to parameters are also provided to the analysis program, which enhances the efficiency and accuracy of the calculations. The analysis procedure is firstly applied to a rotating orthogonal double pendulum, which serves as a test for the correctness of the implementation and the viability of the approach. Then, the procedure is used for the analysis of the dynamics of a motorcycle. For running straight ahead, the nominal solution undergoes Hopf bifurcations if the forward velocity is varied, which lead to periodic wobble and weave motions. For stationary cornering, wobble instabilities are found at much lower speeds, while the maximal speed is limited by the saturation of the tyre forces.     

Dispersion relations and mode shapes for waves in laminated viscoelastic composites by variational methods

The propagation of oscillatory waves through periodic elastic composites has been analysed on the basis of the Floquet theory. This leads to self-adjoint differential equation systems which it was proved convenient to solve by variational methods. Many composites, such as the light-weight high-strength boron-epoxy material, consist of strong reinforcing components in a plastic matrix. The latter can exhibit viscoelastic properties which can have a significant influence on wave propagation characteristics. Replacement of the elastic constant by the viscoelastic complex modulus changes the mathematical structure so that the differential equation system is no longer self-adjoint. However, a modification of the variational principles is suggested which retains formal self-adjointness, and yields variational principles which contain additional boundary terms. These are applied to the determination of wave speeds and mode shapes for a laminated composite made of homogeneous elastic reinforcing plates in a homogeneous viscoelastic matrix for plane waves propagating normally to the reinforcing plates. These results agree well with the exact solution which can be evaluated in this simple case. The variational principles permit solutions for periodic, but otherwise arbitrary variation of material properties.     

Unsteady velocity field measurements at the outlet of an automotive supercharger using particle image velocimetry (PIV)

Particle image velocimetry (PIV) was used to study air flow characteristics at the outlet of an automotive supercharger. Instantaneous velocity fields were analyzed to yield ensemble-averaged velocities and Reynolds stresses, and the ensemble-averages were used to determine maximum velocity and exit flow angle as a function of blade position for various speeds and pressure ratios. The results show that the flow exits the supercharger as a high-speed jet that not only varies in the parallel plane but also in the perpendicular plane, generating a complex three-dimensional flow. The flow varies in the magnitude and the angle at which it leaves the supercharger with the change in blade position and follows a periodic behavior. The maximum velocity at which the flow exits the supercharger also follows a periodic behavior with a variation of 25–30% observed for all the cases. In the parallel plane, the exit angles are periodic every 60° of blade rotation and vary by as much as 40°, whereas periodic behavior with every 120° of blade rotation and a variation of 60° is observed in the perpendicular plane. Variation in flow with blade position is also observed in the velocity and turbulence profiles, with periodic behavior with every 60° blade rotation. The velocity and velocity fluctuation profiles show that the unsteady nature of the flow is most significant close to the outlet, and these unsteady variations diminish 58 mm downstream of the outlet. An exit flow pattern of a Fig. 8 is generated as the flow leaves the blades with one complete blade rotation of 120° for all the cases, except 4000 rpm, pressure ratio 1.4, where the flow exits in a circular pattern.     

On a New Route to Chaos in Railway Dynamics

Cooperrider's mathematical model of a railway bogie running on a straight track has been thoroughly investigated due to its interesting nonlinear dynamics (see True [1] for a survey). In this article a detailed numerical investigation is made of the dynamics in a speed range, where many solutions exist, but only a couple of which are stable. One of them is a chaotic attractor.Cooperrider's bogie model is described in Section 2, and in Section 3 we explain the method of numerical investigation. In Section 4 the results are shown. The main result is that the chaotic attractor is created through a period-doubling cascade of the secondary period in an asymptotically stable quasiperiodic oscillation at decreasing speed. Several quasiperiodic windows were found in the chaotic motion.This route to chaos was first described by Franceschini [9], who discovered it in a seven-mode truncation of the plane incompressible Navier–Stokes equations. The problem investigated by Franceschini is a smooth dynamical system in contrast to the dynamics of the Cooperrider truck model. The forcing in the Cooperrider model includes a component, which has the form of a very stiff linear spring with a dead band simulating an elastic impact. The dynamics of the Cooperrider truck is therefore non-smooth.The quasiperiodic oscillation is created in a supercritical Neimark bifurcation at higher speeds from an asymmetric unstable periodic oscillation, which gains stability in the bifurcation. The bifurcating quasiperiodic solution is initially unstable, but it gains stability in a saddle-node bifurcation when the branch turns back toward lower speeds.The chaotic attractor disappears abruptly in what is conjectured to be a blue sky catastrophe, when the speed decreases further.     

Nonlinear analysis of a rub-impact rotor-bearing system with initial permanent rotor bow

A general model of a rub-impact rotor-bearing system with initial permanent bow is set up and the corresponding governing motion equation is given. The nonlinear oil-film forces from the journal bearing are obtained under the short bearing theory. The rubbing model is assumed to consist of the radial elastic impact and the tangential Coulomb type of friction. Through numerical calculation, rotating speeds, initial permanent bow lengths and phase angles between the mass eccentricity direction and the rotor permanent bow direction are used as control parameters to investigate their effect on the rub-impact rotor-bearing system with the help of bifurcation diagrams, Lyapunov exponents, Poincaré maps, frequency spectrums and orbit maps. Complicated motions, such as periodic, quasi-periodic even chaotic vibrations, are observed. Under the influence of the initial permanent bow, different routes to chaos are found and the speed when the rub happens is changed greatly. Corresponding results can be used to diagnose the rub-impact fault in this kind of rotor systems and this study may contribute to a further understanding of the nonlinear dynamics of such a rub-impact rotor-bearing system with initial permanent bow.     

Nonlinear steady states of hyperelastic membrane tubes conveying a viscous non-Newtonian fluid

We study possible steady states of an infinitely long tube made of a hyperelastic membrane and conveying either an inviscid, or a viscous fluid with power-law rheology. The tube model is geometrically and physically nonlinear; the fluid model is limited to smooth changes in the tube’s radius. For the inviscid case, we analyse the tube’s stretch and flow velocity range at which standing solitary waves of both the swelling and the necking type exist. For the viscous case, we first analyse the tube’s upstream and downstream limit states that are balanced by infinitely growing upstream (and decreasing downstream) fluid pressure and axial stress caused by fluid viscosity. Then we investigate conditions that can connect these limit states by a single solution. We show that such a solution exists only for sufficiently small flow speeds and that it has a form of a kink wave; solitary waves do not exist. For the case of a semi-infinite tube (infinite either upstream or downstream), there exist both kink and solitary wave solutions. For finite-length tubes, there exist solutions of any kind, i.e. in the form of pieces of kink waves, solitary waves, and periodic waves.     

滚波演化中聚合过程的数值模拟研究

滚波是一种重力作用下自由液面失稳诱发的水面波动现象, 通常可分为具有相对稳定波形和波速的周期性滚波与波形和波速不断变化的不规则滚波(自然滚波). 不规则滚波的相互作用和发展演化过程十分复杂, 至今对其认识尚不成熟. 本文采用基于雷诺平均Navier-Stokes方程的立面二维数值模型, 对不规则滚波发展过程中的吸收聚合和追赶聚合现象进行了数值模拟研究. 分析了两种聚合模式的演化过程, 给出了滚波聚合过程中完整的波形、波速、速度剖面以及湍流黏性等重要信息. 结果表明滚波的聚合过程是不规则滚波演化和增长的重要机制, 在特定条件下滚波增长由自然增长模式转变为以吸收聚合和追赶聚合为主的增长模式. 滚波聚合过程中, 依次经历后波追赶、爬升、与前波合并、内部流场调制等多个步骤, 最终形成一个具有更大波长和波高的滚波. 本文发现了在3个滚波间距较近的情况下, 会发生二重聚合现象, 即后两个滚波首先聚合, 然后与前波进一步聚合形成一个新的滚波.      

Time-harmonic wave propagation in a pre-stressed compressible elastic bi-material laminate

The dispersive behaviour of time-harmonic waves propagating along a principal direction in a perfectly bonded pre-stressed compressible elastic bi-material laminate is considered. The dispersion relation which relates wave speed and wavenumber is obtained by formulating the incremental boundary value problem and the use of the propagator matrix technique. At the low wavenumber limit, depending on the pre-stress, both the fundamental mode and the next lowest mode may have finite phase speeds. For the higher modes which have infinite phase speeds in the low wavenumber region, an expression to determine the cut-off frequencies is obtained. At the high wavenumber limit, the phase speeds of the fundamental mode and higher modes tend to phase speeds of the surface wave, the interfacial wave or the limiting phase speed of the composite. For numerical examples, either a two-parameter compressible neo-Hookean material or a two-parameter compressible Varga material is assumed.