An experimental study of nonlinear viscoelastic bushing model for axial mode

A bushing is a device used in automotive suspension systems to cushion the force transmitted from the wheel to the frame of the vehicle. A bushing is essentially a hollow cylinder which is bonded to a solid metal shaft at its inner surface and a metal sleeve at its outer surface. The shaft is connected to the suspension and the sleeve is connected to the frame. The cylinder provides the cushion when it deforms due to relative motion between the shaft and sleeve. The relation between the force applied to the shaft or sleeve and its deformation is nonlinear and exhibits features of viscoelasticity. An explicit force-displacement relation has been introduced for multi-body dynamics simulations. The relation is expressed in terms of a force relaxation function and a method of determination by experiments on bushings has been developed. Solutions allow for comparison between the force-displacement behavior by experiments and that predicted by the proposed method. It is shown that the predictions by the proposed force-displacement relation are in very good agreement with the experimental results.     

An analytical solution for the spread extrusion of shaped sections

Spread extrusion could be used for manufacturing of wide profiles in the extrusion industry. In this paper a new method of design and analysis has been presented for such a problem. Special dies were designed for profiled sections such as square, rectangular, elliptical and cross shapes. These dies force the material to flow sideways and spread so as to extrude sections with wider dimensions than the initial billet or the maximum container diameter. The geometry of the deforming zone in the die was formulated and based upon that, a kinematically admissible velocity field was derived. Using this velocity, we estimated the field upper bound on extrusion power. Profile sections with different aspect ratios were investigated and the influence of other process parameters such as friction and reduction of area on the extrusion pressure were studied. Optimum die lengths for each die were calculated so as to minimize the extrusion pressure. Finite element analysis for the numerical simulation of the process was also carried out. The finite element results were also used as an aid to the design process of the extrusion dies. Dies were manufactured for different sections such as square, rectangle, and ellipse and cross shapes. Experiments were carried out to obtain data to verify the theory. Comparison of the results showed good agreement between the theoretical, numerical and experimental data. It was concluded the present method could be used to design dies for the spread extrusion of different shaped dies.     

An analytical solution of a finite bearing with an inclined journal

A solution of Reynolds' equation for a finite bearing with an inclined journal is attempted. A solution (pressure) is expanded as a series of circular trigonometric functions of β′, the coordinate corresponding to circumferential distances, with coefficients as functions of z, the coordinate corresponding to axial distances. Substitution of such a series for pressure in the equation gives an infinite set of coupled ordinary differential equations with varying coefficients. Forms of solutions of this set of equations are assumed in terms of arbitrary constants and with restrictions of continuity at zero values of the inclinations. The arbitrary constants are evaluated using differential equations and boundary conditions. The integrations of pressure for forces and torques are converted into single integrations which are readily evaluated by digital computer.     

An analytical solution to heat conduction with a moving heat source

This paper deals with an analytical solution to heat conduction in the medium subjected to a moving heat source. It evaluates the temperature distribution around a rectangular shape source moving at a constant speed along the axis of a bar. The transient temperature field from a moving heat source was analyzed using a Fourier series procedure. The most interesting result of the theory, is the derivation of a single formula capable of predicting the cooling time and cooling rate with a fairly good accuracy for ranges of temperature. Because of the passage of the heat source, the rise of temperature produced at a given near the source, tends to rapidly become constant. Several sample problems are discussed and illustrated, and comparisons with numerical approaches where these can also be used made. The results show that these solutions are in good agreement with the numerical results.     

A nonlinear analytical model for the squeeze-film dynamics of parallel plates subjected to axial flow

In this paper, we develop a theoretical model to predict the nonlinear fluid-structure interaction forces and the dynamics of parallel vibrating plates subjected to an axial gap flow. The gap is assumed small, when compared to the plate dimensions, the plate width being much larger than the length, so that the simplifying assumptions of 1D bulk-flow models are adequate. We thus develop a simplified theoretical squeeze-film formulation, which includes both the distributed and singular dissipative flow terms. This model is suitable for performing effective time-domain numerical simulations of vibrating systems which are coupled by the nonlinear unsteady flow forces, for instance the vibro-impact dynamics of plates with fluid gap interfaces. A linearized version of the flow model is also presented and discussed, which is appropriate for studying the complex modes and linear stability of flow/structure coupled systems as a function of the average axial gap velocity. Two applications of our formulation are presented: (1) first we study how an axial flow modifies the rigid-body motion of immersed plates falling under gravity; (2) then we compute the dynamical behavior of an immersed oscillating plate as a function of the axial gap flow velocity. Linear stability plots of oscillating plates are shown, as a function of the average fluid gap and of the axial flow velocity, for various scenarios of the loss terms. These results highlight the conditions leading to either the divergence or flutter instabilities. Numerical simulations of the nonlinear flow/structure dynamical responses are also presented, for both stable and unstable regimes. This work is of interest to a large body of real-life problems, for instance the dynamics of nuclear spent fuel racks immersed in a pool when subjected to seismic excitations, or the self-excited vibro-impact motions of valve-like components under axial flows.     

An existence condition for the inverse dynamics solution of a slewing Euler-Bernoulli beam

Causal inverse dynamics problem of a slewing flexible beam has been identified as being ill-posed because it violates the stability of solution. Such problem has been studied intensively for the past three decades due to its application to the tip tracking control of flexible-link manipulators. A well known remedy has been to modify the location of the boundary point, or the output function in tracking control. This paper re-examines the problem by analyzing a closed form solution. Such a solution is made possible by truncating the assumed modes beam deflection model after the first mode. An existence condition for the solution is established, which links to the deflection mode shape, payload inertia, and the location of boundary point. This condition indicates that for certain system parameters, causal solutions may exist. Existing remedies as suggested by many published results can be explained by the condition. Extension to a multi-mode model is discussed and examined through numerical simulations.     

An exact analytical solution for the self-weight deflection of circular plates of constant thickness

An exact analytical solution, not previously noted in the literature, for the self-weight deflection of a circular plate is obtained by superposition of various elementary solutions due to Love, and the accuracy of the existing approximate procedures is examined. The expressions for stress components are obtained using the axisymmetric stress-strain relations and the validity of the derived solution is justified by satisfying the field equations and the required boundary conditions.     

Comparison of analytical techniques for nonlinear vibrations of a parametrically excited cantilever

This paper is concerned with second-order approximations to the steady-state principal parametric resonance response of a vertically mounted flexible cantilever beam subjected to a vertical harmonic base motion. The unimodal form of the nonlinear equation describing the in-plane large amplitude parametric response of the beam, derived in Krishnamurthy (Ph.D. Thesis, Department of Mechanical Engineering, Washington State University, 1986) based on the previous analysis in Crespo da Silva and Glynn (Journal of Structural Mechanics 1978; 6:437–48), is analysed using the harmonic balance (HB) and the perturbation method of multiple time scales (MMS). Single term HB, two terms HB, and second-order MMS with reconstitution version I (Nayfeh and Sanchez, Journal of Sound and Vibration 1989; 24:483–97) and version II (Rahman and Burton, Journal of Sound and Vibration 1989; 133:369–79) approximations to the steady-sate frequency–amplitude curves of the principal parametric resonance for each of the first four natural modes of the cantilever beam are compared with each other and with those obtained by numerically integrating the unimodal equation of motion. The time transformation is used in obtaining these approximations; also detuning is used in obtaining the square of the forcing MMS approximations. The obtained results show that, for the problem under consideration, the MMS version II is, in comparison with MMS version I, simpler to apply and leads to qualitatively more accurate second-order results. These results, however, show that the MMS version II tends to produce appreciable over corrections to the first-order results and may breakdown at relatively low response amplitudes, whereas the two terms HB solutions tend to improve the first-order results and lead to fairly accurate results even for relatively large response amplitudes.     

An analytical solution of the ECAE process of bi-layer strip using a Bezier type streamline

Co-extrusion of strips of different strength and ductility is a process in the production of bimetal rods of desirable physical and mechanical properties. Equal channel angular extrusion (ECAE) is an innovative process for applying severe plastic deformation to materials. The present study is concerned with the ECAE of different bi-layer strips. Developing a kinematically admissible velocity field using a Bezier-type streamline is the aim of present research. In this analysis, using the mentioned velocity field and the upper bound theorem, the extrusion force as well as the strain distribution in the deformation zone of the ECAE process are predicted. The solution takes into account the die profile, friction conditions, strength, arrangement and thickness ratio of the layer materials. Experimental results of ECAE of aluminum/copper and aluminum/mild steel bi-layer strips showed a good agreement with the predicted results.

     

An analytical study on the performance analysis of a unit-injector system of a diesel engine

A numerical algorithm is developed to analyze the performance of a Unit-injector (UI) System for a diesel engine. The fundamental theory of the algorithm is based on the continuity equation of fluid dynamics. The loss factors that should be seriously regarded on the continuity equation are the compressibility effect of liquid fuel, the wall friction loss in high-pressure fuel lines of the system, the kinetic energy loss of fuel in the system, and the leakage of fuel out of the control volume. For an evaluation of the developed simulation algorithm, the calculation results are compared with the experimental outputs provided by the Technical Research Center of Doowon Precision Industry Co. (DPICO); the maximum pressure in the plunger chamber (P _p ) and total amount of fuel injected into a cylinder per cycle (Q_f) at each operational condition. The result shows that the average error rate (%)of P _p andQ _f are 2.90% and 4.87%, respectively, in the specified operational conditions. Hence, it can be concluded that the analytical simulation algorithm developed in this study can be reasonably applied to the performance prediction of newly designed UI system.     

A nonlinear viscoelastic model for one dimensional response of elastomeric bushings

Experience in analyzing suspension systems that contain elastomeric bushings has led engineers to conclude that it is essential to determine the correct bushing model in order to obtain accurate predictions of the dynamic behavior of the suspension system. In such a model, there must be a nonlinear relation between force and displacement, and viscoelastic effects must be included. It must also be computationally convenient in order to be useful in multi-body dynamics analysis.To this end, this paper presents a candidate nonlinear viscoelastic force-displacement relation which satisfies these criteria. This force-displacement relation depends on a force relaxation function, which is the relevant bushing property. Unfortunately, the idealized method for determining this property is experimentally unfeasible. Consequently, a practical method for determining this property from experimental data has been developed. Results of application of this procedure are presented for radial displacements of an elastomeric bushing. The resultant model is then used to predict forces due to various prescribed displacement histories. In comparing these forces with experimentally determined forces, good agreement was obtained.     

带有滞回的接触系统非线性动力学特性分析

考虑到机床导轨结合部系统在实际接触振动过程中具有滞回模型的特点,建立了分析该类系统的数学模型,同时讨论了系统在改变激振力条件下的非线性动力响应问题,最后得出激振力在一定范围内变化的情况下,系统出现了周期运动、倍周期分岔、混沌等运动形式的转化和演变过程。     

Non-uniform Euler-Bernoulli beams under a single moving oscillator: An approximate analytical solution in time domain

Dynamic responses of simply supported non-uniform beams traversed by a moving oscillator are analysed in this paper. An approximate analytical method based on Rayleigh-Ritz (R-R) formulation is developed. The fundamental approximate mode obtained from R-R method is used in the present formulation to determine the responses of the beam and the oscillator. Effects of surface irregularities on the displacement and acceleration responses of the beam and the vehicle are also analysed. The results are compared with those obtained using Finite element method (FEM). A numerical example is provided to illustrate the validity of the present method which shows that the proposed method is simple, computationally more efficient compared to FEM and gives fairly good results. Though the single-mode approach used in the present paper is a classical one and numerous studies on the responses of uniform beams under moving loads have been reported in the past, its application to non-uniform beams (for which there does not exist any closed form expression for mode shapes) under a moving load, especially a moving oscillator, is presented for the first time.     

一种简易工况法机动车排放质量分析系统

提出一种在工况法条件下机动车污染物排放总量及排放过程动态变化的测量系统,本法简单易行,可用于汽车维修,发动机检测,尾气排放质量检验等方面。     

An integrated manufacturing information system for mass sheet metal cutting

In order to reduce manufacturing cost and to improve the operational efficiency, some factories in the sheet-metal-related manufacturing industry centralize the production and management of sheet metal cutting. To support the centralized mass manufacturing paradigm, this paper presents an integrated manufacturing information system to achieve the high utilization of raw sheet material, lower the manufacturing cost, as well as to improve the operational efficiency and production management. The system architecture and some key technologies to implement this system are investigated, based on which, the whole information system is developed. This system integrates the functions of sheet metal part modeling and unfolding, nesting planning, automatic and interactive nesting, cutting process planning, NC-programming, off-line processing simulation and on-line monitoring. The system has been successfully utilized in industry, and an example of its application is described in the paper.     

Past,present and future of nonlinear system identification in structural dynamics

This survey paper contains a review of the past and recent developments in system identification of nonlinear dynamical structures. The objective is to present some of the popular approaches that have been proposed in the technical literature, to illustrate them using numerical and experimental applications, to highlight their assets and limitations and to identify future directions in this research area. The fundamental differences between linear and nonlinear oscillations are also detailed in a tutorial.     

一种非线性系统的自适应无模型预测控制方法

为了避免基于模型的控制方法在控制非线性系统时存在建模困难和模型失配的问题,提出一种非线性系统的自适应无模型预测控制方法。该方法首先将非线性系统转化为由一组伪偏导数描述的线性系统,然后利用一种改进的投影算法在线估计这组伪偏导数,得到被控系统的泛模型。根据得到的泛模型,推导出预测模型,在此基础上根据预测控制滚动的优化策略求解二次目标函数得出最优控制律。通过对CSTR过程进行仿真验证,结果表明该方法具有良好的跟踪性能和较强的鲁棒性。     

RRR-RRR六杆机构的MATLAB动力学求解

建立了曲柄、RRRⅡ级杆组动力学的矩阵数学模型,并编制了相应的M函数仿真模块,对给定的RRR-RRR六杆机构进行了建模和求解,其主要思想是以组成机构杆组为仿真模块,一方面降低了矩阵的阶数,另一方面便于搭建各种机构MATLAB求解模型,对各种低副机构进行动力学求解。     

General analytical shakedown solution for structures with kinematic hardening materials

The effect of kinematic hardening behavior on the shakedown behaviors of structure has been investigated by performing shakedown analysis for some specific problems. The results obtained only show that the shakedown limit loads of structures with kinematic hardening model are larger than or equal to those with perfectly plastic model of the same initial yield stress. To further investigate the rules governing the different shakedown behaviors of kinematic hardening structures, the extended shakedown theorem for limited kinematic hardening is applied, the shakedown condition is then proposed, and a general analytical solution for the structural shakedown limit load is thus derived. The analytical shakedown limit loads for fully reversed cyclic loading and non-fully reversed cyclic loading are then given based on the general solution. The resulting analytical solution is applied to some specific problems: a hollow specimen subjected to tension and torsion, a flanged pipe subjected to pressure and axial force and a square plate with small central hole subjected to biaxial tension. The results obtained are compared with those in literatures, they are consistent with each other. Based on the resulting general analytical solution, rules governing the general effects of kinematic hardening behavior on the shakedown behavior of structure are clearly.