The pitch-heave dynamics of transportation vehicles

The analysis and design of suspensions for vehicles of finite length using pitch-heave models is presented. Dynamic models for the finite length vehicle include the spatial distribution of the guideway input disturbance over the vehicle length, as well as both pitch and heave degrees-of-freedom. Analytical results relate the vehicle front and rear accelerations to the pitch and heave natural frequencies, which are functions of vehicle suspension geometry and mass distribution. The effects of vehicle asymmetry and suspension contact area are evaluated. Design guidelines are presented for the modification of vehicle and suspension parameters to meet alternative ride quality criteria

Hydrodynamics of Suspensions of Passive and Active Rigid Particles: A Rigid Multiblob Approach

We develop a rigid multiblob method for numerically solving the mobility problem for suspensions of passive and active rigid particles of complex shape in Stokes flow in unconfined, partially confined, and fully confined geometries. As in a number of existing methods, we discretize rigid bodies using a collection of minimally-resolved spherical blobs constrained to move as a rigid body, to arrive at a potentially large linear system of equations for the unknown Lagrange multipliers and rigid-body motions. Here we develop a block-diagonal preconditioner for this linear system and show that a standard Krylov solver converges in a modest number of iterations that is essentially independent of the number of particles. For unbounded suspensions and suspensions sedimented against a single no-slip boundary, we rely on existing analytical expressions for the Rotne-Prager tensor combined with a fast multipole method or a direct summation on a Graphical Processing Unit to obtain an simple yet efficient and scalable implementation. For fully confined domains, such as periodic suspensions or suspensions confined in slit and square channels, we extend a recently-developed rigid-body immersed boundary method to suspensions of freely-moving passive or active rigid particles at zero Reynolds number. We demonstrate that the iterative solver for the coupled fluid and rigid body equations converges in a bounded number of iterations regardless of the system size. We optimize a number of parameters in the iterative solvers and apply our method to a variety of benchmark problems to carefully assess the accuracy of the rigid multiblob approach as a function of the resolution. We also model the dynamics of colloidal particles studied in recent experiments, such as passive boomerangs in a slit channel, as well as a pair of non-Brownian active nanorods sedimented against a wall.Comment: Under revision in CAMCOS, Nov 201

Series active variable geometry suspension application to comfort enhancement

This paper explores the potential of the Series Active Variable Geometry Suspension (SAVGS) for comfort and road holding enhancement. The SAVGS concept introduces significant nonlinearities associated with the rotation of the mechanical link that connects the chassis to the spring-damper unit. Although conventional linearization procedures implemented in multi-body software packages can deal with this configuration, they produce linear models of reduced applicability. To overcome this limitation, an alternative linearization approach based on energy conservation principles is proposed and successfully applied to one corner of the car, thus enabling the use of linear robust control techniques. An H∞ controller is synthesized for this simplified quarter-car linear model and tuned based on the singular value decomposition of the system's transfer matrix. The proposed control is thoroughly tested with one-corner and full-vehicle nonlinear multi-body models. In the SAVGS setup, the actuator appears in series with the passive spring-damper and therefore it would typically be categorized as a low bandwidth or slow active suspension. However, results presented in this paper for an SAVGS-retrofitted Grand Tourer show that this technology has the potential to also improve the high frequency suspension functions such as comfort and road holding

Magnetic bearings: Fifty years of progress

Magnetic bearings are just beginning to be flown in spacecraft systems, but their development spans more than 50 years. The promise of completely noncontacting, unlubricated rotating systems operating at speeds substantially beyond the range of conventional bearings, and with no wear and virtually no vibration, has provided the incentive to develop magnetic bearing technology for many diverse applications. Earnshaw theorized in 1842 that stable magnetic suspension is not possible in all three spatial directions unless the magnetic field is actively controlled. Since that time, researchers have attempted to successfully support spinning rotors in a stable manner. Development of magnetic suspension systems over the past fifty years has included progress on both passive (permanent magnet) and active (electromagnet) systems. The improvements in bearing load capacity, stiffness, and damping characteristics are traced. The trends in rotor size, rotational kinetic energy, and improvements in active control systems capabilities are also reviewed. Implications of superconductivity on suspension system design and performance are discussed

Contact tribology also affects the slow flow behavior of granular emulsions

Recent work on suspension flows has shown that contact mechanics plays a role in suspension flow dynamics. The contact mechanics between particulate matter in dispersions should depend sensitively on the composition of the dispersed phase: evidently emulsion droplets interact differently with each other than angular sand particles. We therefore ask: what is the role of contact mechanics in dispersed media flow? We focus on slow flows, where contacts are long-lasting and hence contact mechanics effects should be most visible. To answer our question, we synthesize soft hydrogel particles with different friction coefficients. By making the particles soft, we can drive them at finite confining pressure at all driving rates. For particles with a low friction coefficient, we obtain a rheology similar to that of an emulsion, yet with an effective friction much larger than expected from their microscopic contact mechanics. Increasing the friction coefficient of the particles, we find a flow instability in the suspension. Particle level flow and fluctuations are also greatly affected by the microscopic friction coefficient of the suspended particles. The specific rheology of our "granular emulsions" provides further evidence that a better understanding of microscopic particle interactions is of broad relevance for dispersed media flows

Towards an analytical description of active microswimmers in clean and in surfactant-covered drops

Geometric confinements are frequently encountered in the biological world and strongly affect the stability, topology, and transport properties of active suspensions in viscous flow. Based on a far-field analytical model, the low-Reynolds-number locomotion of a self-propelled microswimmer moving inside a clean viscous drop or a drop covered with a homogeneously distributed surfactant, is theoretically examined. The interfacial viscous stresses induced by the surfactant are described by the well-established Boussinesq-Scriven constitutive rheological model. Moreover, the active agent is represented by a force dipole and the resulting fluid-mediated hydrodynamic couplings between the swimmer and the confining drop are investigated. We find that the presence of the surfactant significantly alters the dynamics of the encapsulated swimmer by enhancing its reorientation. Exact solutions for the velocity images for the Stokeslet and dipolar flow singularities inside the drop are introduced and expressed in terms of infinite series of harmonic components. Our results offer useful insights into guiding principles for the control of confined active matter systems and support the objective of utilizing synthetic microswimmers to drive drops for targeted drug delivery applications.Comment: 19 pages, 7 figures. Regular article contributed to the Topical Issue of the European Physical Journal E entitled "Physics of Motile Active Matter" edited by Gerhard Gompper, Clemens Bechinger, Holger Stark, and Roland G. Winkle

Effective Viscosity of Dilute Bacterial Suspensions: A Two-Dimensional Model

Suspensions of self-propelled particles are studied in the framework of two-dimensional (2D) Stokesean hydrodynamics. A formula is obtained for the effective viscosity of such suspensions in the limit of small concentrations. This formula includes the two terms that are found in the 2D version of Einstein's classical result for passive suspensions. To this, the main result of the paper is added, an additional term due to self-propulsion which depends on the physical and geometric properties of the active suspension. This term explains the experimental observation of a decrease in effective viscosity in active suspensions.Comment: 15 pages, 3 figures, submitted to Physical Biolog

Rotors on Active Magnetic Bearings: Modeling and Control Techniques

In the last decades the deeper and more detailed understanding of rotating machinery dynamic behavior facilitated the study and the design of several devices aiming at friction reduction, vibration damping and control, rotational speed increase and mechanical design optimization. Among these devices a promising technology is represented by active magnetic actuators which found a great spread in rotordynamics and in high precision applications due to (a) the absence of all fatigue and tribology issues motivated by the absence of contact, (b) the small sensitivity to the operating conditions, (c) the wide possibility of tuning even during operation, (d) the predictability of the behavior. This technology can be classified as a typical mechatronic product due to its nature which involves mechanical, electrical and control aspects, merging them in a single system. The attractive potential of active magnetic suspensions motivated a considerable research effort for the past decade focused mostly on electrical actuation subsystem and control strategies. Examples of application areas are: (a) Turbomachinery, (b) Vibration isolation, (c) Machine tools and electric drives, (d) Energy storing flywheels, (e) Instruments in space and physics, (f) Non-contacting suspensions for micro-techniques, (g) Identification and test equipment in rotordynamics. This chapter illustrates the design, the modeling, the experimental tests and validation of all the subsystems of a rotors on a five-axes active magnetic suspension. The mechanical, electrical, electronic and control strategies aspects are explained with a mechatronic approach evaluating all the interactions between them. The main goals of the manuscript are: • Illustrate the design and the modeling phases of a five-axes active magnetic suspension; • Discuss the design steps and the practical implementation of a standard suspension control strategy; • Introduce an off-line technique of electrical centering of the actuators; • Illustrate the design steps and the practical implementation of an online rotor selfcentering control technique. The experimental test rig is a shaft (Weight: 5.3 kg. Length: 0.5 m) supported by two radial and one axial cylindrical active magnetic bearings and powered by an asynchronous high frequency electric motor. The chapter starts on an overview of the most common technologies used to support rotors with a deep analysis of their advantages and drawbacks with respect to active magnetic bearings. Furthermore a discussion on magnetic suspensions state of the art is carried out highlighting the research efforts directions and the goals reached in the last years. In the central sections, a detailed description of each subsystem is performed along with the modeling steps. In particular the rotor is modeled with a FE code while the actuators are considered in a linearized model. The last sections of the chapter are focused on the control strategies design and the experimental tests. An off-line technique of actuators electrical centering is explained and its advantages are described in the control design context. This strategy can be summarized as follows. Knowing that: a) each actuation axis is composed by two electromagnets; b) each electromagnet needs a current closed-loop control; c) the bandwidth of this control is depending on the mechanical airgap, then the technique allows to obtain the same value of the closed-loop bandwidth of the current control of both the electromagnets of the same actuation axis. This approach improves performance and gives more steadiness to the control behavior. The decentralized approach of the control strategy allowing the full suspensions on five axes is illustrated from the design steps to the practical implementation on the control unit. Furthermore a selfcentering technique is described and implemented on the experimental test rig: this technique uses a mobile notch filter synchronous with the rotational speed and allows the rotor to spin around its mass center. The actuators are not forced to counteract the unbalance excitation avoiding saturations. Finally, the experimental tests are carried out on the rotor to validate the suspension control, the off-line electrical centering and the selfcentering technique. The numerical and experimental results are superimposed and compared to prove the effectiveness of the modeling approach