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Making the eye blink - Modelling the operation of the Gateshead Millennium Bridge
Abstract
This paper considers the system dynamics associated with a hydraulic system moving a large flexible structure, namely the Gateshead Millennium Bridge. The hydraulic components possess a range of non-linear characteristics, which become coupled to the bridge structural dynamics. The bridge structure is lightly damped and may be represented by a linear model, provided that the amplitudes of vibrational modes are small enough to maintain positive cable tensions. The limiting amplitudes were known at the design stage and the hydraulic circuit had to ensure that these were not exceeded during operation, which may include various conditions of wind loading, emergency stops and variability of components. System design was achieved through an extensive iterative process of simulation that included all operational procedures to eliminate problematic circuits that would have caused instability or excessive bridge oscillations. The actual bridge and coupled hydraulic circuits underwent a series of commissioning trials and no undue problems were experienced. This indicated that the simulation procedures developed greatly reduced the risks associated with a unique structure actuated by a bespoke hydraulic circuit.
... Future machine systems would benefit significantly if their operational capabilities and precision under hydraulic actuation could be increased. Although hydraulically actuated systems offer high power densities and are capable of delivering large forces over long strokes (e.g. 3 MN over 3 m to open the Gateshead Millennium Bridge [1]), they have a relatively low bandwidth, typically between 1 and 100 Hz. Piezoelectric actuators, on the other hand, have relatively high force capacity and bandwidth (. 1 kHz), but their stroke lengths are several orders of magnitude lower than hydraulic actuators. ...
The performance of hydraulically actuated machine systems could be improved with the use of valves that have high bandwidth and high flowrates under low pressure drops. Although high flowrates can be achieved using very large spool strokes and/or diameters, the overall bandwidth of the valve will be reduced. Research has therefore been undertaken on a prototype valve design incorporating the Hörbiger plate principle, which utilizes multiple metering edges to allow high flowrates to be obtained at low pressure drops and small poppet displacements. The valve is directly activated using a piezoelectric actuator to achieve a fast dynamic response. Valve performance is assessed using a mathematical model that includes the piezoelectric actuator and power amplifier, the supply flow, fluid squeeze forces, end stop response, and valve mechanical components. The steady state relationship between valve flow, force and pressure drop, and the fluid inertance, were determined using computational fluid dynamics software. The simulation model has been validated using test data obtained from experimental tests undertaken on a prototype valve. Good agreement is obtained between the predicted and measured results and it is shown that the valve is capable of opening or closing fully in less than 1.5 ms, and can pass a flow of 65 l/min at a pressure drop of 20 bar.
Movable bridges are interesting and feasible solutions at the crossover point of transportations, providing fascinating landscapes and significant engineering challenges. This paper presents a new structural system applied to a movable cable-stayed footbridge. It is an S-shaped curved bridge suspended by cables, and can be opened with a moving mechanism coupled with the torsional deformation. In this paper, we clarify the mechanical behavior of the structural system through a preliminary analysis. We propose novel concepts of the twistable deck, aiming to improve the dynamic performance of the structural system. We trace the moving process of the structure by decoupling the elastic deformation and the rigid displacement. We confirm the validity and versatility of the proposed structural system through the optimal shapes for the footbridges in different cases with respect to the symmetricity and serviceability. The concept of the movable structural system proposed herein is believed to be feasible for application to the design of movable footbridges based on the preliminary analysis.
In order to expand the operational capabilities of hydraulically actuated systems the development of new valves to allow of enhanced flow rates and bandwidth performance is required. Previously, the technical challenge in developing such valves was the need for large spool strokes to achieve the desired flow rates. However, this would then hinder the dynamic response of the valve. To increase flow without reducing dynamic performance it is proposed that the use of multiple metering edges is appropriate. This is achievable using the Hörbiger plate valve principle and direct connection to a piezoelectric actuator. This paper examines the design criteria associated with such a valve. Simulations undertaken as part of its construction and design show that improved flow rates can be achieved. Results from these simulations are then included in orifice equations to further predict flow as a function of plate separation. Finally a simulation was undertaken to determine the total forces acting on the valve, and the forces on the piezoactuator were found to be compressive under normal conditions, which should lead to predictable and stable operation.
Structural integrity management is key to the safe and economic operation of offshore structures. Presently, regular manual inspections are conducted. This is expensive, time consuming, and prone to human error. This paper investigates the possibility of using the bicoherence function of the measured structural acceleration to provide automatic early detection of damage in an offshore structure. The method is shown to be insensitive to typical operating parameter variations and to variations in wave excitation force, and demonstrates that very small changes in stiffness of individual structural members are detectable from measurements of global structural motion.
This paper addresses a controller design methodology for the hydraulic actuation of non-linear multi-body systems. It takes account of system uncertainties, envisaged system changes through added mass, positioning speed requirements, and vibration control. A mathematical model developed in the companion paper, Part 1, describes an experimental multi-body structure that is actuated by a hydraulic system. It is used to generate H∞-based position and active vibration controllers to meet the actuation requirements at the design stage. Experimental tests were undertaken with the developed H∞ controllers to demonstrate their accuracy and stability of motion control. The results are compared to ‘base level’ tests completed using a more traditional proportional-integral (PI) controller. In contrast with the instability experienced using PI control, the design process associated with the H∞ controllers ensures accurate closed loop stability over the range of system variations.
Modern engineering design is leading towards structures that are complex and lightweight. These structures often contain flexible and rigid components actuated through large displacements by a non-linear hydraulic system. Due to the increased system complexities, there is a need to define structural models that can be easily coupled to models of the hydraulic system for use in the design of suitable controllers. The current paper develops a modular system model composed of rigid and flexible structural components coupled directly to a non-linear hydraulic system. The resulting model allows for changes to be made to the hydraulic and structural components in an independent manner such that the entire system may be incorporated in a single simulation domain. A structural damping matrix is introduced that allows a control system designer to assign realistic modal damping ratios to well established modes, and higher damping to modes with significant uncertainty. This allows for increased steady-state accuracy and model run-time efficiency, which is beneficial to the controller design process presented in Part 2. The system modelling approach is applied to a hydraulically actuated experimental rig for validation purposes.
This paper investigates the use of the bicoherence function of measured structural acceleration to provide automatic early detection of damage in an offshore structure. A detailed simulation model is developed, including realistic wave loading, and is used to assess the performance of the method. The method is shown through analytical and numerical analysis to be insensitive to typical operating parameter variations and to variations in wave excitation force. It is demonstrated that very small changes in stiffness of individual structural members are detectable from measurements of global structural motion.
The computer simulation package BATHfp has been developed at the Fluid Power Centre, University of Bath to perform transient time domain simulations of fluid power systems. Utilities are provided which allow new models to be introduced into the component database. This enables the package to be tailored to particular dedicated areas of interest such as aircraft flight controls, braking and landing gear and fuel flow systems. This paper describes the application of BATHfp to aircraft hydraulic systems. An example is taken of an electrohydraulic position control system which uses an actuator to move an aileron according to a desired schedule. Parametric variations are made to illustrate how system performance can be improved.
Accurate mathematical models of hydrostatic pumps and motors are required in the synthesis and analysis of hydraulic systems. Increasingly the models are used in computer simulation work where the performance of the machines must be represented over a wide range of operating conditions.
Examination of test data has shown significant differences in the real performance characteristics of hydrostatic machines compared to the characteristics predicted by classical models based on simple linear theory. This paper describes these differences and shows the way that the characteristics can change with different designs of machine.
A mathematical model is developed which may be adapted to describe the wide range of characteristics associated with the different designs. This model has shown good agreement with test data.
Recommendations are made for more comprehensive performance tests to provide the data required for more accurate models.
This paper starts by describing the structure of the London Millennium Footbridge. The bridge opened on 10 June 2000. During the opening day unexpected lateral movements occurred as pedestrians crossed the bridge. The paper describes the events of opening day and the research and analysis that were carried out as a result of these movements. The lateral force exerted by pedestrians on the moving deck surface is found to be related to the movement. The results show that the phenomenon is not related to the technical innovations of the bridge and that the same phenomenon could occur on any bridge with a lateral frequency below about 1.3Hz loaded with a sufficient number of pedestrians. A selection of other bridges, including one road bridge, found to have exhibited the same phenomenon, are listed. The paper describes the development of a retrofit to control the vibrations. This involves the use of fluid-viscous dampers and tuned mass dampers to achieve damping levels in excess of 20% of critical. The results of tests on the bridge with a prototype installation of a small number of the proposed dampers are presented, which show that the performance of the damping scheme conforms with analytical predictions.
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