Mathematical Modeling and Parameter Identification of a Planar Servo-Pneumatic Test Facility. Part I: Mathematical Modeling and Computer Simulation

High quality multi-axis test facilities used for testing heavy loads and large structures of industrial equipment are usually simulated, designed and controlled based on reduced model equations neglecting the inertia properties of the actuators. The design and control of servo-pneumatic test facilities used for testing small and light structures must take into account extended test facility models including the various inertia properties of the actuators. In this paper (Part I) an extended test facility model is presented including the various inertia properties and joints of the actuators. These extended model equations are represented in a form well suited to be directly implemented in control algorithms based on exact linearization techniques for real time control. This is done by stepwise projecting the inertia properties of the various actuator housings and actuator pistons down to the common mass of the test table and payload. The resulting extended model equations have the same form as the reduced model equations. They only include more complex system matrices and vector functions. These compact model equations turn out to be suitable for an efficient nonlinear controller design of these test facilities. Computer simulations and associated laboratory experiments show the necessity to use extended model equations in case of testing small and light structures. In Part II of this paper [1] the inertia parameters of the planar test facility will be identified in laboratory experiments.     

考虑关节摩擦的空间机器人动力学建模与参数辨识

研究了考虑关节摩擦影响的空间机器人系统的动力学建模与参数辨识问题．采用单向递推组集方法和虚功率原理建立了含有关节摩擦的多体系统动力学方程,推导了关节摩擦对系统动力学方程的贡献,采用基于腕力传感器信号和最小二乘法的辨识方法进行了系统惯性参数的辨识．数值仿真结果验证了数学模型的正确性与辨识方法的有效性．     

Mathematical Modeling, Control, Computer Simulation and Laboratory Experiments of a Spatial Servopneumatic Parallel Robot

In this paper, the special construction of a parallel robot, called spatial servopneumatic multi-axis test facility, will be discussed. The investigations include the following aspects: (i) the laboratory set-up of the robot, (ii) various results obtained in laboratory experiments, taking into account quite different control algorithms and command-input signals, (iii) a comparison of the laboratory experiments with the computer simulations of Part I of this paper, and ({vi}) a quality check of the results compared with the cost of the different controller realizations. The results of both the computer simulations and the laboratory experiments show: (i) The dynamic behavior of the parallel structure can be tremendously improved by using sophisticated nonlinear control algorithms. (ii) This improvement has to be paid by a drastically increased amount of work for deriving the model equations and control algorithms, and by augmented hardware cost of the sensing elements and controller electronics. (iii) Carefully developed model equations and identified model parameters provide theoretical models of the complex parallel structure that are very close to reality. This enables the design engineer to systematically investigate constructive alternatives of the design parameters, sensor and actuator concepts, and control strategies of the MAP prior to their hardware realization.This work has been supported by the German Science Foundation (DFG) under Contract No. Ha 1666/6-3.     

Experiments and Material Parameter Identification Using Finite Elements. Uniaxial Tests and Validation Using Instrumented Indentation Tests

In this article, we focus our attention on the relation between instrumented indentation tests and the prediction by means of finite element calculations. To this end, a finite strain viscoplasticity model of Perzyna-type with non-linear isotropic and kinematic hardening is calibrated at experimental data of steel S690QL. A particular concept for conducting uniaxial tensile and compression tests is taken up in order to represent the basic rate-dependent material behavior. In this respect, an algorithmic framework of material parameter identification using finite elements is proposed leading to a two-stage procedure in the case of the underlying rate-dependent constitutive model. On the basis of the termination points of relaxation the rate-independent equilibrium stress state can be identified and all viscous parts of the model are obtained using rate-dependent loading paths. Finally, use is made of finite elements for predicting indentation experiments, which results in a critical view on modeling and parameter identification on the basis of experimental results occurring in instrumented indentation tests.     

Nonlinear Dynamics of a Rigid Unbalanced Rotor in Journal Bearings. Part II: Experimental Analysis

In the first part of the present investigation [9], the dynamic behaviour of a rigid rotor supported on plain journal bearings was studied, focusing particular attention on its nonlinear aspects. In the present paper an experimental confirmation of the theoretical results is sought. The steel rotor of the experimental rig was given a constant circular cross section in order to fix in an easy way the two distances between supports corresponding, respectively, to the values of the parameter assigned in [9]. Two steel rings, each one with a series of holes and a clamping screw, were mounted onto the rotor with a small clearance. This arrangement made it possible to fix the positions of the rings and their holes respect to the rotor, so as to realize a pre-estabilished unbalance. The two bronze journal bearings were characterised by a relatively low length/diameter ratio, and a relatively high value of the radial clearance and were lubricated with oil delivered from a thermostatic tank. In this way, despite the relative lightness of the rotor, the dimensionless static eccentricity _s was given the high values that were apt to realize the operating conditions assumed in the theoretical analysis. The rotor was driven by means of a d.c. motor connected to a toothed belt-drive. Varying the rotor speed in the range 1000 ÷ 10000 r.p.m., made it possible to assign the values of the modified Sommerfeld number assumed in the theoretical analysis. Three pairs of eddy-current probes were mounted in order to detect the trajectories of three points (C₁, C and C₂) suitably fixed along the rotor axis. These orbits were finally put in comparison with the corresponding ones previously obtained through numerical analysis. The comparison pointed out that the experimental data were in good agreement with the theoretical predictions, despite the approximations that characterise the theoretical model and the unavoidable errors affecting measures in the course of the experimental test.     

The dynamics of coupled planar rigid bodies. II. Bifurcations,periodic solutions,and chaos

We give a complete bifurcation and stability analysis for the relative equilibria of the dynamics of three coupled planar rigid bodies. We also use the equivariant Weinstein-Moser theorem to show the existence of two periodic orbits distinguished by symmetry type near the stable equilibrium. Finally we prove that the dynamics is chaotic in the sense of Poincaré-Birkhoff-Smale horseshoes using the version of Melnikov's method suitable for systems with symmetry due to Holmes and Marsden.     

Analytical and Experimental Analysis of Wing Rock

The paper deals with the study of an analytical model of wingrock, based on parameter identification of experimental data. Theexperiments were performed in the Aeronautical Laboratory of Politecnicodi Torino, in the D3M Low Speed Wind Tunnel, on a80° delta wing. Free-to-roll tests have been used todetermine build-up and limit cycle characteristics of wing rock. Flowvisualization techniques were also utilized in order to track vortexpositions. The characteristics of the limit cycle (oscillation amplitudeand frequency) were compared in detail with reference results obtainedin other laboratories. An analytical nonlinear model was derived.Parameters were identified by means of the least-squares approximationof experimental data with coherent initial conditions. The consistencyof time histories, reproduced by numerical integration, was alsoanalyzed. This formulation correctly predicts stable limit cycles for awide range of airspeeds, angles of attack and release roll angles.     

Mathematical Modeling,Control, Computer Simulation and Laboratory Experiments of a Spatial Servopneumatic Parallel Robot

In this paper (Part I), the special construction of a controlled parallel structure, called spatial servopneumatic multi-axles test facility (MAP), will be theoretically and numerically investigated and controlled. The investigations include the following steps: (i) design of mathematical models of different complexity of both, the test facility mechanics in terms of DAEs and ODEs (a multi-body system which contains 13 rigid bodies under spatial motion, connected by joints), and the servopneumatic actuators; (ii) construction of different linear and nonlinear (model based) control algorithms; (iii) development of a computer simulation program of the MAP; and (iv) evaluation of various computer simulation runs, obtained by applying different control algorithms and spatial command-input signals. The results show that the efficiency of the control algorithms is closely related to their complexity and cost. In order to check the closeness to reality of the computer simulation results and their benefit for industrial applications, laboratory experiments must be formed with the same MAP, the same control algorithms, and applying the same command-input signals which have been used in the computer simulations. These experimental investigations will be presented in Part II of the paper.     

Modeling the Dynamics and Kinematics of a Telescopic Rotary Crane by the Bond Graph Method: Part II

Simulation of a rotary telescopic crane for which a detailed nonlinearbond graph model has been established in Part I of this study, isrealized utilizing experimental actual system for geometrical anddynamical parameters. With the intention of comparing the real system andthe model and of verifying the sufficiency of the model accuracy,various scenarios are defined corresponding to different loading andoperating conditions. Of the scenarios defined, impulse response, timeresponse and static response are used to experimentally gather such system parameters and variables as damping coefficient, cylinderdisplacements, and stiffness of the telescopic boom, respectively.Following, the simulation for two dissimilar scenarios which are staticresponse and impulse response is undergone and results are presented.     

Experimental Investigation of the Nonlinear Response of a Hanging Cable. Part II: Global Analysis

The nonlinear dynamics of the same experimental model of an internally resonant hanging elastic cable considered in Part I [1] are addressed here from the point of view of the global system behaviour in the control parameter space. Synthetic results of systematic response measurements, made at different amplitudes of the support motion in frequency ranges including meaningful external resonance conditions, are reported and discussed. Attention is devoted to the detection of the most robust classes of motion. Quite complicated overall pictures of regular response regions with variable contributions from different planar and nonplanar cable modes are observed, as well as several regions of quasiperiodic and chaotic responses. Sample quantitative characterizations of nonregular motions are presented. Some experimental results are also observed against the background of the nonlinear dynamic phenomena exhibited by a theoretical model of a continuous cable with four-degrees-of-freedom.     

Spontaneous radial capillary impregnation across a bank of aligned micro-cylinders. Part II: Experimental investigations

This paper presents an experimental approach to study the capillary impregnation of a liquid across an array of parallel micro-cylinders. The technique presented successfully validates the theoretical findings of part I, and provides a methodology to calculate the fill time and the overall capillary impregnation dynamics for any arbitrary cylindrical sample made of aligned micro-cylinders, by taking into account the role of the trapped gas, which opposes and slows down the inward capillary flow.     

Unified nano-mechanics based probabilistic theory of quasibrittle and brittle structures: II. Fatigue crack growth, lifetime and scaling

This paper extends the theoretical framework presented in the preceding Part I to the lifetime distribution of quasibrittle structures failing at the fracture of one representative volume element under constant amplitude fatigue. The probability distribution of the critical stress amplitude is derived for a given number of cycles and a given minimum-to-maximum stress ratio. The physical mechanism underlying the Paris law for fatigue crack growth is explained under certain plausible assumptions about the damage accumulation in the cyclic fracture process zone at the tip of subcritical crack. This law is then used to relate the probability distribution of critical stress amplitude to the probability distribution of fatigue lifetime. The theory naturally yields a power-law relation for the stress-life curve (S-N curve), which agrees with Basquin's law. Furthermore, the theory indicates that, for quasibrittle structures, the S-N curve must be size dependent. Finally, physical explanation is provided to the experimentally observed systematic deviations of lifetime histograms of various ceramics and bones from the Weibull distribution, and their close fits by the present theory are demonstrated.     

Size effects and idealized dislocation microstructure at small scales: Predictions of a Phenomenological model of Mesoscopic Field Dislocation Mechanics: Part II

In Part I of this set of two papers, a model of mesoscopic plasticity is developed for studying initial-boundary value problems of small scale plasticity. Here we make qualitative, finite element method-based computational predictions of the theory. We demonstrate size effects and the development of strong inhomogeneity in simple shearing of plastically constrained grains. Non-locality in elastic straining leading to a strong Bauschinger effect is analyzed. Low shear strain boundary layers in constrained simple shearing of infinite layers of polycrystalline materials are not predicted by the model, and we justify the result based on an examination of the no-dislocation-flow boundary condition. The time-dependent, spatially homogeneous, simple shearing solution of PMFDM is studied numerically. The computational results and an analysis of continuous dependence with respect to initial data of solutions for a model linear problem point to the need for a nonlinear study of a stability transition of the homogeneous solution with decreasing grain size and increasing applied deformation. The continuous-dependence analysis also points to a possible mechanism for the development of spatial inhomogeneity in the initial stages of deformation in lower-order gradient plasticity theory. Results from thermal cycling of small scale beams/films with different degrees of constraint to plastic flow are presented showing size effects and reciprocal-film-thickness scaling of dislocation density boundary layer width. Qualitative similarities with results from discrete dislocation analyses are noted where possible.We discuss the convergence of approximate solutions with mesh refinement and its implications for the prediction of dislocation microstructure development, motivated by the notion of measure-valued solutions to conservation laws.     

Modeling the Dynamics and Kinematics of a Telescopic Rotary Crane by the Bond Graph Method: Part I

Cranes employed for load transfer are large volume machines and canbe designed to accomplish linear, planar or spatial motions dependingon the intended use. Understanding the dynamic behavior of thesesystems, which have a load-carrying capacity of hundreds of tonnes, ishighly noteworthy for system design, control, and work safety. Inthis study, a theoretical model of a spatially actuated telescopic rotarycrane is obtained with provided assumptions using Bond Graph techniques.Following the modeling of an actuation system and of a main structure,unification of these two is accomplished. Since the overall system consistsof high nonlinearity originating from geometric nonlinearity, gyroscopicforces, hydraulic compressibility, and elastic boom structure, the resultingderivative causality problem caused by rigidly coupled inertia elementsis addressed for this highly nonlinear system and consequential systemstate-space equations are presented.     

Dynamics of a Rigid Unbalanced Rotor with Nonlinear Elastic Restoring Forces. Part II: Experimental Analysis

In Part I, theoretical analysis of the dynamic behaviour of a rigid rotor with nonlinear elastic restoring forces was carried out. In this part (Part II), an experimental confirmation of the theoretical data from that analysis was sought. With this aim, an experimental model was set up consisting mainly of a practically rigid rotor clamped onto a small diameter piano wire symmetrical to the wire supports. These supports were rigid and equipped with roller bearings and a device that made it possible to adjust the initial tension in the wire so as to make the elastic restoring forces less or more linear. The rotor was dynamically unbalanced and was driven by an asynchronous motor regulated by means of an inverter in order to adjust the rotor speed. A series of tests was performed on this rig with different values of the initial tension in the wire, and the trajectories of two points on the rotor axis were recorded in the course of the tests. These trajectories were obtained, under the hypothesis of similarity, from the orbits covered by two given sections of the wire and detected with two pairs of capacitive transducers. The collected data was compared with the theoretical results from Part I of the present investigation. Comparison of the collected data with the corresponding theoretical results made it possible to infer that system nonlinearity in the presence of small damping can give rise to motions that are periodic, whether synchronous or not, or quasi-periodic, but never chaotic.     

Elongated bubbles in microchannels. Part II: Experimental study and modeling of bubble collisions

The collision of elongated bubbles has been studied along adiabatic glass microchannels of 509 and 790 μm internal diameters for refrigerant R-134a. The slug flow regime obtained here comes from the nucleation process inside a micro-evaporator located upstream. Using an optical measurement technique based on two lasers and two photodiodes, it was possible to determine the vapor bubble length distributions at the exit of the micro-evaporator and 70 mm downstream and thus characterize both diabatic and adiabatic bubble collisions. The database includes 412 coupled sets of distributions involving thousands of bubbles. Half of the database has been obtained under diabatic conditions and the second half under adiabatic conditions.     

Dynamic Models of Simple Judgments: II. Properties of a Self-Organizing PAGAN (Parallel, Adaptive, Generalized Accumulator Network) Model for Multi-Choice Tasks

This is the second of two papers comparing connectionist and traditional stochastic latency mechanisms with respect to their ability to account for simple judgments. In the first, we reviewed evidence for a self-regulating accumulator module for two- and three-category discrimination. In this paper, we examine established neural network models that have been applied to predicting response time measures, and discuss their representational and adaptational limitations. We go on to describe and evaluate the network implementation of a Parallel Adaptive Generalized Accumulator Network (PAGAN), based on the interconnection of a number of self-regulating, generalized accumulator modules. The enhancement of PAGAN through the incorporation of distributed connectionist representation is briefly discussed.     

Analysis of Wet Pressing of Paper: The Three-Phase Model. Part II: Compressible Air Case

In this study we consider a model of wet pressing of paper. We use the techniques and results from the first part of this paper, where a simplified model is studied in details. The model is, using suitable transformation, rewritten in the standard parabolic-hyperbolic form. Numerical solution for typical example is given and the effects of plastic deformations of paper are investigated. Finally, the model is employed to adres the problem of choosing an optimal pressing regime.     

Very large amplitude vibrations of flexible structures: Experimental identification and validation of a quadratic drag damping model

This article presents a theoretical, numerical and experimental study of resonant structures undergoing very large amplitude vibrations. The purpose of this work is to validate a model for the damping due to the action of the air on a structure’s single-mode response in the steady-state. Experiments are performed on cantilever beams and beam assemblies of various sizes, from centimetric to micrometric, under harmonic base excitation. Dimensionless linear and nonlinear modal damping coefficients are simultaneously identified by means of frequency-domain identification techniques. These measurements demonstrate the pertinence of the presented model.     

Planar laser-induced fluorescence (PLIF) measurements of liquid film thickness in annular flow. Part II: Analysis and comparison to models

Film thickness distributions in upward vertical air–water annular flow have been determined using planar laser-induced fluorescence (PLIF). Film thickness data are frequently used to estimate interfacial shear and pressure loss. This film roughness concept has been used in a number of models for annular flow of varying complexity. The PLIF data are presently applied to the single-zone interfacial shear correlation of Wallis; the more detailed model of Owen and Hewitt; and the two-zone (base film and waves) model of Hurlburt, Fore, and Bauer. For the present data, these models all under-predict the importance of increasing liquid flow on pressure loss and interfacial shear. Since high liquid flow rates in annular flow induce disturbance wave and entrainment activity, further modeling in these areas is advised.