Limit cycle behavior of smart fluid dampers under closed loop control

Semiactive vibration dampers offer an attractive compromise between the simplicity and fail safety of passive devices, and the weight, cost, and complexity of fully active systems. In addition, the dissipative nature of semiactive dampers ensures they always remain stable under closed loop control, unlike their fully active counterparts, However undesirable limit cycle behavior remains a possibility, which is not always property considered during the controller design. Smart fluids provide an elegant means to produce semiactive damping, since their resistance to flow can be directly controlled by the application of an electric or magnetic field. However the nonlinear behavior of smart fluid dampers makes it difficult to design effective controllers, and so a wide variety of control strategies has been proposed in the literature. In general, this work has overlooked the possibility of undesirable limit cycle behavior under closed loop conditions. The aim of the present study is to demonstrate how the experimentally observed limit cycle behavior of smart dampers can be predicted and explained by appropriate nonlinear models. The study is based upon a previously developed feedback control strategy, but the techniques described are relevant to other forms of smart damper control

Hardware-in-the-loop simulation of magnetorheological dampers for vehicle suspension systems

Magnetorheological (MR) fluids provide an elegant means to enhance vibration control in primary vehicle suspensions. Such fluids can rapidly modify their flow characteristics in response to a magnetic field, so they can be used to create semi-active dampers. However, the behaviour of MR dampers is inherently non-linear and as a consequence, the choice of an effective control strategy remains an unresolved problem. Previous research has developed a method to linearize the damper's force/velocity response, to allow implementation of classical control techniques. In the present study, this strategy is used to implement skyhook damping laws within primary automotive suspensions. To simulate the vehicle suspension, a two-degree-of-freedom quarter car model is used, which is excited by realistic road profiles. The controller performance is investigated experimentally using the hardware-in-the-loop-simulation (HILS) method. This experimental method is described in detail and its performance is validated against numerical simulations for a simplified problem. The present authors demonstrate that feedback linearization can provide significant performance enhancements in terms of passenger comfort, road holding, and suspension working space compared with other control strategies. Furthermore, feedback linearization is shown to desensitize the controller to uncertainties in the input excitation such as changes in severity of the road surface roughness

Temperature sensitive controller performance of MR dampers

Magnetorheological (MR) dampers can experience large temperature changes as a result of heating caused by energy dissipation, but control systems are often designed without consideration of this fact. Furthermore, due to the highly nonlinear behavior of MR dampers, many control strategies have been proposed and it is difficult to determine which is the most effective. This paper aims to address these issues through a numerical and experimental study of an MR mass isolator subject to temperature variation. A dynamic temperature dependant model of an MR damper is first developed and validated. Control system experiments are then performed using hardware-in-the-loopsimulations. Proportional, PID, gain scheduling, and on/off control strategies are found to be equally affected by temperature variation. Using simulations incorporating the temperature dependant MR damper model, it is shown that this is largely due to a change in fluid viscosity and the associated movement of the lower clipped optimal' control bound. This zero-volts condition determines how close any controller can perform to the ideal semiactive case, thus all types of controller are affected. In terms of relative performance, proportional and PID controllers perform equally well and outperform the on/off and gain scheduling strategies. Gain scheduling methods are superior to on/off control

Vibration isolation with smart fluid dampers: a benchmarking study

The non-linear behaviour of electrorheological (ER) and magnetorheological (MR) dampers makes it difficult to design effective control strategies, and as a consequence a wide range of control systems have been proposed in the literature. These previous studies have not always compared the performance to equivalent passive systems, alternative control designs, or idealised active systems. As a result it is often impossible to compare the performance of different smart damper control strategies. This article provides some insight into the relative performance of two MR damper control strategies: on/off control and feedback linearisation. The performance of both strategies is benchmarked against ideal passive, semi-active and fully active damping. The study relies upon a previously developed model of an MR damper, which in this work is validated experimentally under closed-loop conditions with a broadband mechanical excitation. Two vibration isolation case studies are investigated: a single-degree-of-freedom mass-isolator, and a two-degree-of-freedom system that represents a vehicle suspension system. In both cases, a variety of broadband mechanical excitations are used and the results analysed in the frequency domain. It is shown that although on/off control is more straightforward to implement, its performance is worse than the feedback linearisation strategy, and can be extremely sensitive to the excitation conditions

Vibration control strategies for proof-mass actuators

Proof-mass actuators have been considered for a broad range of structural vibration control problems, from seismic protection for tall buildings to the improvement of metal machining productivity by stabilizing the self-excited vibrations known as chatter. This broad range of potential applications means that a variety of controllers have been proposed, without drawing direct comparisons with other controller designs that have been considered for different applications. This article takes three controllers that are potentially suitable for the machining chatter problem: Direct velocity feedback, tuned-mass-damper control (or vibration absorber control), and active-tuned-mass-damper control (or active vibration absorber control). These control strategies are restated within the more general framework of Virtual Passive Control. Their performance is first compared using root locus techniques, with a model based on experimental data, including the low frequency dynamics of the proof-mass. The frequency response of the test structure is then illustrated under open and closed-loop conditions. The application of the control strategies to avoid machine-tool chatter vibrations is then discussed, without going into detail on the underlying physical mechanisms of chatter. It is concluded that virtual passive absorber control is more straightforward to implement than virtual skyhook damping, and may be better suited to the problem of machining chatter

On the performance and resonant frequency of electromagnetic induction energy harvesters

This paper investigates the linear response of an archetypal energy harvester that uses electromagnetic induction to convert ambient vibration into electrical energy. In contrast with most prior works, the in uence of the circuit inductance is not assumed negligible. Instead, we highlight parameter regimes where the inductance can alter resonance and derive an expression for the resonant frequency. The governing equations consider the case of a vibratory generator directly powering a resistive load. These equations are non-dimensionalized and analytical solutions are obtained for the system's response to single harmonic, periodic, and stochastic environmental excitations. The presented analytical solutions are then used to study the power delivered to an electrical load

Fuzzy stability analysis of regenerative chatter in milling

During machining, unstable self-excited vibrations known as regenerative chatter can occur, causing excessive tool wear or failure, and a poor surface finish on the machined workpiece. Consequently it is desirable to predict, and hence avoid the onset of this instability. Regenerative chatter is a function of empirical cutting coefficients, and the structural dynamics of the machine-tool system. There can be significant uncertainties in the underlying parameters, so the predicted stability limits do not necessarily agree with those found in practice. In the present study, fuzzy arithmetic techniques are applied to the chatter stability problem. It is first shown that techniques based upon interval arithmetic are not suitable for this problem due to the issue of recursiveness. An implementation of fuzzy arithmetic is then developed based upon the work of Hanss and Klimke. The arithmetic is then applied to two techniques for predicting milling chatter stability: the classical approach of Altintas, and the time-finite element method of Mann. It is shown that for some cases careful programming can reduce the computational effort to acceptable levels. The problem of milling chatter uncertainty is then considered within the framework of Ben-Haim's information-gap theory. It is shown that the presented approach can be used to solve process design problems with robustness to the uncertain parameters. The fuzzy stability bounds are then compared to previously published data, to investigate how uncertainty propagation techniques can offer more insight into the accuracy of chatter predictions

Fast chatter stability prediction for variable helix milling tools

Regenerative chatter is a well-known form of self-excited vibration that limits the productivity of machining operations, in particular for milling. Variable helix tools have been previously proposed as a means of avoiding regenerative chatter, and although recent work has analysed the stability of such tools there has not always been a strong agreement with experimentally observed behaviour. Furthermore, the analysis of variable helix tool stability can be tedious and numerically slow, compared to standard tools. Consequently it has been difficult to gain insight into the potential advantages of variable helix tools. The present work attempts to address these issues, by first developing an efficient approach to variable helix tool stability based upon the Laplace transform. Then, this new analysis method is used to demonstrate the importance of multi-frequency effects and nonlinear cutting stiffness. The work suggests that whilst variable-helix tools can have more operating regions that are stable, un-modelled behaviour (such as nonlinearity and multi-frequency effects) can have a critical influence on the accuracy of model predictions

Analytical prediction of chatter stability for variable pitch and variable helix milling tools

Regenerative chatter is a self-excited vibration that can occur during milling and other machining processes. It leads to a poor surface finish, premature tool wear, and potential damage to the machine or tool. Variable pitch and variable helix milling tools have been previously proposed to avoid the onset of regenerative chatter. Although variable pitch tools have been considered in some detail in previous research, this has generally focussed on behaviour at high radial immersions. In contrast there has been very little work focussed on predicting the stability of variable helix tools. In the present study, three solution processes are proposed for predicting the stability of variable pitch or helix milling tools. The first is a semi-discretisation formulation that performs spatial and temporal discretisation of the tool. Unlike previously published methods this can predict the stability of variable pitch or variable helix tools, at low or high radial immersions. The second is a time-averaged semi-discretisation formulation that assumes time-averaged cutting force coefficients. Unlike previous work, this can predict stability of variable helix tools at high radial immersion. The third is a temporal-finite element formulation that can predict the stability of variable pitch tools with a constant uniform helix angle, at low radial immersion. The model predictions are compared to previously published work on variable pitch tools, along with time-domain model simulations. Good agreement is found with both previously published results and the time-domain model. Furthermore, cyclic-fold bifurcations were found to exist for both variable pitch and variable helix tools at lower radial immersions

Magnetorheological landing gear: 1. A design methodology

Aircraft landing gears are subjected to a wide range of excitation conditions, which result in conflicting damping requirements. A novel solution to this problem is to implement semi-active damping using magnetorheological (MR) fluids. This paper presents a design methodology that enables an MR landing gear to be optimized, both in terms of its damping and magnetic circuit performance, whilst adhering to stringent packaging constraints. Such constraints are vital in landing gear, if MR technology is to be considered as feasible in commercial applications. The design approach focuses on the impact or landing phase of an aircraft's flight, where large variations in sink speed, angle of attack and aircraft mass makes an MR device potentially very attractive. In this study, an equivalent MR model of an existing aircraft landing gear is developed. This includes a dynamic model of an MR shock strut, which accounts for the effects of fluid compressibility. This is important in impulsive loading applications such as landing gear, as fluid compression will reduce device controllability. Using the model, numerical impact simulations are performed to illustrate the performance of the optimized MR shock strut, and hence the effectiveness of the proposed design methodology. Part 2 of this contribution focuses on experimental validation