Showing papers on "Damper published in 2002"

Optimal placement of dampers for passive response control

Abstract: The effectiveness of viscous and viscoelastic dampers for seismic response reduction of structures is quite well known in the earthquake engineering community. This paper deals with the optimal utilization of these dampers in a structure to achieve a desired performance under earthquake-induced ground excitations. Frequency-dependent and -independent viscous dampers and viscoelastic dampers have been considered as the devices of choice. To determine the optimal size and location of these dampers in the structure, a genetic algorithm is used. The desired performance is defined in terms of several different forms of performance functions. The use of the genetic approach is not limited to any particular form of performance function as long as it can be calculated numerically. For illustration, numerical examples for different building structures are presented showing the distribution and size of different dampers required to achieve a desired level of reduction in the response or a performance index. Copyright © 2002 John Wiley & Sons, Ltd.

Vibration Control of a Suspension System via a Magnetorheological Fluid Damper

Abstract: Semi-active control systems are becoming more popular because they offer both the reliability of passive systems and the versatility of active control without imposing heavy power demands. It has been found that magneto-rheological (MR) fluids can be designed to be very effective vibration control actuators. The MR fluid damper is a semi-active control device that uses MR fluids to produce a controllable damping force. The objective of this paper is to study a single-degree-of-freedom suspension system with an MR fluid damper for the purpose of vibration control. A mathematical model for the MR fluid damper is adopted. The model is compared with experimental results for a prototype damper through finding suitable model parameters. In this study, a sliding mode controller is developed by considering loading uncertainty to result in a robust control system. Two kinds of excitations are inputted in order to investigate the performance of the suspension system. The vibration responses are evaluated in both ti...

Neural network emulation of inverse dynamics for a magnetorheological damper

Abstract: The dynamic behavior of a magnetorheological (MR) damper is well portrayed using a Bouc–Wen hysteresis model. This model estimates damper forces based on the inputs of displacement, velocity, and voltage. In some control applications, it is necessary to command the damper so that it produces desirable control forces calculated based on some optimal control algorithms. In such cases, it is beneficial to develop an inverse dynamic model that estimates the required voltage to be input to the damper so that a desirable damper force can be produced. In this study, we explore such a possibility via the neural network (NN) technique. Recurrent NN models will be constructed to emulate the inverse dynamics of the MR damper. To illustrate the use of these NN models, two control applications will be studied: one is the optimal prediction control of a single-degree-of-freedom system and the other is the linear quadratic regulator control of a multiple-degree-of-freedom system. Numerical results indicate that, using t...

Free Vibrations of Taut Cable with Attached Damper. I: Linear Viscous Damper

Abstract: Free vibrations of a taut cable with an attached linear viscous damper are investigated in detail using an analytical formulation of the complex eigenvalue problem. This problem is of considerable practical interest in the context of stay-cable vibration suppression in bridges. An expression for the eigenvalues is derived that is independent of the damper coefficient, giving the range of attainable modal damping ratios and corresponding oscillation frequencies in every mode for a given damper location without approximation. This formulation reveals the importance of damper-induced frequency shifts in characterizing the response of the system. New regimes of behavior are observed when these frequency shifts are large, as is the case in higher modes and for damper locations further from the end of the cable. For a damper located sufficiently near the antinode in a given mode, a regime of solutions is identified for which the damping approaches critical as the damper coefficient approaches a critical value. A regime diagram is developed to indicate the type of behavior in each mode for any given damper location.

Earthquake response of elastic SDF systems with non‐linear fluid viscous dampers

Abstract: The steady-forced and earthquake responses of SDF systems with a non-linear fluid viscous damper (FVD) are investigated. The energy dissipation capacity of the FVD is characterized by the supplemental damping ratio ζsd and its non-linearity by a parameter designated α. It is found that the structural response is most effectively investigated in terms of ζsd and α because (1) these two parameters are dimensionless and independent, and (2) the structural response varies linearly with the excitation intensity. Damper non-linearity has essentially no influence on the peak response of systems in the velocity-sensitive spectral region, but differences up to 14% were observed in the other spectral regions. The structural deformation is reduced by up to 25% when ζsd= 5%; and by up to 60% when ζsd= 30%. Non-linear FVDs are advantageous because they achieve essentially the same reduction in system responses but with a significantly reduced damper force. For practical applications, a procedure is presented to estimate the design values of structural deformation and forces for a system with non-linear FVD directly from the design spectrum. It is demonstrated that the earthquake-induced force in a non-linear FVD can be estimated from the damper force in a corresponding system with linear FVD, its peak deformation, and peak relative velocity; however, the relative velocity should not be approximated by the pseudo-velocity as this approximation introduces a large error in the damper force. Finally, a procedure is presented to determine the non-linear damper properties necessary to limit the structural deformation to some design value or the structural capacity for a given design spectrum. Copyright © 2002 John Wiley & Sons, Ltd.

H8 Control Performance of a Full-Vehicle Suspension Featuring Magnetorheological Dampers

Abstract: Summary This paper presents an investigation of the feedback control performance of a full-vehicle suspension system featuring magnetorheological (MR) dampers. A cylindrical MR damper is designed and manufactured by incorporating a Bingham model of aMR fluid which is commercially available. After evaluating the field-dependent damping characteristics of the MR damper, a full-vehicle suspension system installed with 4 independent MR dampers is constructed and its governing equations of motion which include vertical, pitch and roll motions are derived. A H 8 controller which has inherent robustness against system uncertainties is formulated by treating the sprung mass of the vehicle as uncertain parameter. This is accomplished by adopting the loop shaping design procedure. For the demonstration of a practical feasibility, control performance characteristics for vibration suppression of the proposed MR suspension system are evaluated under various road conditions through the hardware-in-the-loop simulation (...

Tuned mass dampers for response control of torsional buildings

Abstract: This paper presents an approach for optimum design of tuned mass dampers for response control of torsional building systems subjected to bi-directional seismic inputs. Four dampers with fourteen distinct design parameters, installed in pairs along two orthogonal directions, are optimally designed. A genetic algorithm is used to search for the optimum parameter values for the four dampers. This approach is quite versatile as it can be used with different design criteria and definitions of seismic inputs. It usually provides a globally optimum solution. Several optimal design criteria, expressed in terms of performance functions that depend on the structural response, are used. Several sets of numerical results for a torsional system excited by random and response spectrum models of seismic inputs are presented to show the effectiveness of the optimum designs in reducing the system response. Copyright © 2002 John Wiley & Sons, Ltd.

Efficiency of a simple approach to damper allocation in MDOF structures

Abstract: A simple approach to the design of optimal damper configurations has recently been suggested. This practical method is designated simplified sequential search algorithm (SSSA). Although some comparisons showed that the efficiency of the SSSA is similar to that of more sophisticated methods, a more comprehensive investigation is needed in order to gain more insight into its effectiveness. In this study, the SSSA is applied to several regular building models with different natural periods, numbers of storeys, levels of added damping, and different ground motions. Only one type of passive energy dissipation device is considered: linear viscous dampers. It is concluded that, in the case of regular buildings, the SSSA will generally lead to efficient damper configurations, particularly for low-to-medium-rise buildings and for a number of dampers equal to or greater than 1.5–2 times the number of storeys. The resulting damper configurations are found to be sensitive to ground motion characteristics, especially for low levels of supplemental damping. Copyright © 2002 John Wiley & Sons, Ltd.

Passive and semi-active seismic response control of a cable-stayed bridge

Abstract: Effectiveness of passive and semi-active seismic response control on a cable-stayed bridge was studied by numerical analyses. An existing cable-stayed bridge which has fixed-hinge connections between deck and towers is modeled and its connections were replaced by isolation bearings and dampers. The isolation bearings are of elastic and hysteretic type. The dampers are of linear and variable type. The variable damper uses semi-active control that incorporates a pseudo-negative stiffness algorithm. A pseudo-negative stiffness hysteretic loop produced by the variable damper, combined with a positive stiffness curve of the deck-tower connections, creates nearly rigid–perfectly plastic force–deformation characteristics with a large damping ratio. The damping ratio for the main mode of the bridge for both passive and semi-active control was also calculated. Soil-structure interaction and three-dimensional effects on structural responses were studied. Copyright © 2002 John Wiley & Sons, Ltd.

Noise and vibration suppressors

Abstract: In order to form a noise suppressor in a hose of e.g. a motor vehicle, modular portions are connected in series to define suppression chambers with particular noise suppression characteristics. Those characteristics are due to the volume of each chamber, to the size of the apertures from the chambers to the central duct of the suppressor, and optionally due to spacers which are inserted into at least one aperture of the chambers to alter the effective open area of that aperture. Such spacers may also be used in which the noise suppressor is not modular. Where modular portions are used, it is preferable that each chamber is bounded by parts of two modular portions. A wall of one modular portion may then close the chamber in another modular portion, making the manufacture of the modular portions easier. Also disclosed is the use of a mass acting as a damper, which may be a noise suppressor as previously discussed, within a hose. The mass is connected to the hose by resilient means, e.g. electrometric material.

Vibrations of a shallow cable with a viscous damper

Abstract: The optimal tuning and effect in terms of modal damping of a viscous damper mounted near the end of a shallow cable are investigated. The damping properties of free vibrations are extracted from the complex wavenumber. The full solution for the lower modes is evaluated numerically, and an explicit and rather accurate analytical approximation is obtained, generalizing recent results for a taut cable. It is found that the effect of the damper on the nearly antisymmetric modes is independent of the sag and the stiffness parameter. In contrast, the nearly symmetric modes develop regions of reduced motion near the ends, with increasing cable stiffness, and this reduces the effect of the viscous damper. Explicit results are obtained for the modal damping ratio and for optimal tuning of the damper.

Free Vibrations of Taut Cable with Attached Damper. II: Nonlinear Damper

Abstract: Free vibrations of a taut cable with a nonlinear power-law damper attached near the end are considered. An approximate analytical solution for the amplitude-dependent effective damping ratios in each mode is developed by assuming the same form of solution as for the linear damper and minimizing the mean-square error in the force equilibrium at the damper. An asymptotic approximate solution for small frequency shifts reveals a nondimensional grouping of parameters allowing the development of an amplitude-dependent universal estimation curve for the power-law damper. The shape of the universal curve is slightly different for each value of the damper exponent, but for a given exponent the curve is nearly invariant over the same range of parameters as the universal curve for the linear damper. This formulation yields insights into the dependence of nonlinear damper performance on mode number and amplitude of oscillation, suggesting potential advantages that may be offered by a nonlinear damper over a traditional linear damper.

Thermostat incorporating a carbon dioxide sensor suitable for reading using potentiostat techniques, and environmental control system incorporating such thermostat

Abstract: A system for monitoring and modifying the quality and temperature of air within a conditioned space includes a blower unit, an optional damper unit for selectively admitting outside air into the conditioned space, a temperature moderating unit and a control unit. The control unit includes a thermostat and conventional temperature control apparatus for selectively activating the temperature moderating unit to maintain the desired temperature in the conditioned space. The control unit also incorporates CO 2 concentration measuring and control apparatus which employs a small CO 2 sensor. The CO 2 sensor includes upper and lower electrodes with an intermediate solid electrolyte. A voltage having a cyclic waveform is applied across the upper and lower electrodes, and the current through the CO 2 sensor is read at at least one predetermined voltage representing a CO 2 peak. The measured current is representative of the CO 2 concentration. CO 2 concentration modifying apparatus is responsive to sensing a first predetermined CO 2 concentration for turning on the blower unit and, optionally, to sensing a second, higher, predetermined CO 2 concentration for actuating the damper unit to admit outside air.

Harmonic analysis of a magnetorheological damper for vibration control

Abstract: Semi-active control systems are becoming more popular because they offer both the reliability of passive systems and the versatility of active control systems without imposing heavy power demands. In particular, it has been found that magnetorheological (MR) fluids can be designed to be very effective vibration control actuators, which use MR fluids to produce controllable damping force. The objective of this paper is to study a single-degree-of-freedom (SDOF) isolation system with an MR fluid damper under harmonic excitations. A mathematical model of the MR fluid damper with experimental verification is adopted. The motion characteristics of the SDOF system with the MR damper are studied and compared with those of the system with a conventional viscous damper. The energy dissipated and equivalent damping coefficient of the MR damper in terms of input voltage, displacement amplitude and frequency are investigated. The relative displacement with respect to the base excitation is also quantified and compared with that of the conventional viscous damper through updating the equivalent damping coefficient with changing driving frequency. In addition, the transmissibility of the MR damper system with semi-active control is also discussed. The results of this study are valuable for understanding the characteristics of the MR damper to provide effective damping for the purpose of vibration isolation or suppression.

Coaxial wind turbine apparatus having a closeable air inlet opening

Abstract: A coaxial wind turbine apparatus which includes a pair of rearward-mounted, spring-loaded fins to orient the air inlet opening to face the direction of the oncoming wind and close a damper panel or shutter array at the air inlet opening during very high wind conditions. Thereby, the pair of rearward-mounted, spring-loaded fins stabilizes the apparatus during strong ambient wind conditions and minimizes damage to the rotating turbine wheel in the presence of a strong wind.

Adjustable damper actuator

Abstract: An actuator for controlling the position of a damper. It is an adjustable damper actuator that can actuate a damper to have positions that are other than fully open and fully closed. The actuator has adjustable stops for attaining a partially closed or partially open damper as the operator wants. This actuator is useful for zone heating and air-conditioning as well as for providing a continuous supply of make-up air at low flow rates.

The Squeeze Film Damper over four decades of investigations. Part II: Rotordynamic analyses with rigid and flexible rotors

Abstract: The present paper is aimed at summarizing the main results of the investigation regarding the application of the Squeeze Film Damper (SFD). Part I of the paper illustrated the constructive aspects and the operating features of this component, with reference to the related published work. Herein is a brief review of a number of theoretical and experimental analyses, regarding the dynamic behavior of rigid and flexible rotors supported with SFDs, with parallel examination of the main models adopted for the study. Advantages and drawbacks of SFDs are thus directly inferred from rotordynamic evaluation. Recent and current investigation, with particular regard to unconventional, improved SFDs, is briefly outlined in the concluding section of the paper.

The Influence of Damper Properties on Vehicle Dynamic Behaviour

Abstract: This paper details a non-linear hysteretic physical shock absorber model, and the processes utilised to identify the constituent parameters. In the current paper the model parameters are extracted from experimental data for the ‘sport’ setting of a prototype front shock absorber for a vehicle in the luxury class. The model is validated by comparing simulated results to experimental data for a test damper, for three discrete frequencies of sinusoidal excitation of 1,3 and 12 Hz. Finally the shock absorber model is included in a quarter car vehicle ride model and output characteristics are compared to those obtained with classical damper representations. INTRODUCTION The detailed dynamic properties of dampers are known to influence substantially some of the subtle, and yet nevertheless hugely important, refinement aspects of vehicle ride and handling. However, damper properties are typically characterised by quasi-steady properties for vehicle simulation purposes. The classic 14 speed test [1], for example, involves subjecting a damper to 14 differing frequency levels of fixed amplitude sinusoidal excitation, and then plotting the peak force values obtained versus the relevant test velocity. Such a representation of shock absorber behaviour is clearly deficient for the purpose of vehicle simulations as only a snap shot view of the damper’s behaviour is utilised and much information is discarded. As a direct consequence the process of damper valve tuning is still carried out to a great extent via ride work. This consists of ride engineers subjectively rating the performance of the prototype vehicle(s) over a series of test tracks/ride routes. The damper valve is then possibly adjusted to improve the vehicle’s ride/handling or to obtain characteristics expected for that class of vehicle. This process is clearly open to subjective evaluation which may vary driver to driver, and even from one day to the next. A more scientific approach to the issue of damper tuning, via vehicle simulations, would offer a number of significant benefits. This is simply due to the fact that the bulk of the damper selection process could be carried out prior to the manufacture of any vehicle prototypes, and this technique would be far less subjective in nature. Such an approach would necessitate an improved method of characterising the damper, such that the important dynamic features are represented, and comprehension of the links between more subtle features of the damper response. The current paper attempts to address the aforementioned requirement for improved damper characterisation in the context of the ‘sport’ setting of a triple rate prototype adaptive shock absorber. SHOCK ABSORBER MODELLING APPROACH In order to select the optimum damper modelling strategy for a ‘virtual damper tuning environment’, the suitability of the differing approaches found within published literature were determined with respect to the following criterion: Ability to capture damper non-linearity and dynamic behaviour. Flexibility to model different shock absorber types. Ease of model generation (Experiment/Parameter identification). Suitability for use in vehicle simulations. Usefulness as a predictive tool. Clearly black box methods such as the Restoring Force Mapping method [2-5] and neural networks [6], do not satisfy the need for a predictive tool as they are inherently non-tuneable. The same applies to elementary models constructed with spring and ideal viscous damping elements [7,8]. The required need for tuneable elements for this damper model application lends itself to an explicit physical model, where the damper control force is related to physical parameters that govern the dampers internal flows and pressures. The high detail model developed by Lang [9,10], for a twin tube shock absorber, was the first physical model that actually aimed to predict damper behaviour over a wide range of operating conditions. This 87 parameter model gave good correlation with experiment, but both simulation and parameter identification processes were highly iterative. It was also very specific to the shock 2002-01-0319 The Influence of Damper Properties on Vehicle Dynamic Behaviour Adrian Simms and David Crolla Copyright © 2002 Society of Automotive Engineers, Inc. The University of Leeds, School of Mechanical Engineering absorber under investigation. It did however identify the contribution of internal compliance’s to the hysteretic nature of dampers. More recently models by Duym [11-13], Lang and Sonnenburg [14] and Herr et al [16] attempted to generate more readily identifiable physical damper models. Each of these models are similar in overall structure in that they consist of a pressure model(s) and valve pressure/flow characterisations. The pressure models are a selection of first order non-linear differential equations, which are utilised to determine the various internal chamber pressures, and are derived from pressure dependent oil compressibility models. For the pressure/flow model Duym [11-13] identified valve parameters from several simple dynamometer tests and an additional ‘incompressible’ model (see definitions); these parameters were then used to analytically determine valve flows for given pressure drops in the main model. In contrast Lang and Sonnenburg [15] used experimentally obtained pressure/flow data, and Herr et al evaluated the pressure flow characteristics of the differing valve components using Computational Fluid Dynamics (CFD). In the absence of a large database of pressure/flow data for differing valve formulations, as was available to Lang and Sonnenburg, this non parametric form of pressure model does not satisfy the required criteria of tune-ability. The CFD approach is a time consuming process requiring detailed modelling even for varying damper valves of the same basic architecture. As a result of the aforementioned considerations the damper modelling approach to be taken is one of a physical model similar to that of Duym [11-13]. SHOCK ABSORBER ARCHITECTURE, AXES SYSTEMS AND SIGN CONVENTIONS The prototype shock absorber, in the ‘sport’ setting, falls into the mono-tube category; the only flow paths for the internal hydraulic fluid are thus through the piston’s valves (see Figure 1). The additional ‘softer’ damper settings, which are achieved by the solenoid activation of additional flow paths, will not be considered in this paper. The mono-tube shock absorber consists of a rebound chamber and a compression chamber which are both oil filled. A high pressure nitrogen gas volume, typically 20-30 Bar, is present at the end of the pressure tube, separated from the damper fluid by way of a floating piston. Expansion and compression of this gas volume compensates for the differing volumetric changes encountered in bump and rebound strokes as a result of the piston rod’s presence in the rebound chamber. Several valve assemblies are present on the piston, one for compression and one for extension strokes. The flow path architecture of these valves are outlined in Figure 1. For low damper velocities the preloaded blowoff valve remains closed and the net pressure/flow characteristic can be described by the series combination of the port channel and the fixed bleed. For higher velocities the blow-off valve progressively opens thus reducing the rate of increase of damper force with respect to velocity. Figure 1. Mono-tube layout / axis system (top), and flow path architecture (bottom). MONO-TUBE DAMPER MODEL The twin-tube damper model presented in [11-13] is a compressible model which is used solely for the purpose of simulations. To yield a readily identifiable damper model the parameters of the compressible model of [1113] were identified by fitting an additional incompressible model to experimental data from which the hysteresis had been removed as described in [16,17]. As a result of the differing model architectures the pressure/flow model, required for the parameter identification processes, was different to that of the full compressible model. In this paper a single pressure/flow model will be derived for a mono-tube shock absorber for the parameter identification process, and the valve pressure/flow characteristics will then be supplied to the compressible damper model in the form of a simple look-up table. This modelling approach should yield more rapid simulations and additional robustness without compromising model tune-ability. As will be discussed later this can also yield improvements in model accuracy and flexibility; for non-standard valve architectures it will now only be necessary to derive a single new pressure/flow model. Leak Restriction Port Restriction P1 P2 Rebound Chamber Preb Compression chamber, Pcom x , x Gas phase, Pcom,gas Piston valve assembly

An experimental study of a semiactive magneto-rheological fluid variable damper for vibration suppression of truss structures

Abstract: The purpose of this paper is to demonstrate that vibrations of a truss structure can be suppressed nicely by a magneto-rheological (MR) fluid variable damper for semiactive vibration suppression. A variable MR fluid damper was designed and fabricated for this study. The principal characteristics of an MR damper were measured in dynamic tests, and a mathematical model of the damper was proposed. To investigate if the variable damper effectively suppresses the vibration of actual truss structures, semiactive vibration suppression experiments were performed using a cantilevered ten-bay truss beam. The experimental result has shown that the vibration was suppressed nicely by the variable MR damper, and that was compared with that of an electro-rheological (ER) damper investigated in previous research. The MR damper showed a higher performance than that of the ER damper.

Energy-efficient variable-air-volume (VAV) system with zonal ventilation control

Abstract: A ventilation and air-conditioning system uses a first variable-air-volume system to cool and dehumidify fresh outside air and deliver it through a first duct to a mixing box located downstream. The system also uses a second variable-air-volume system to further cool and dehumidify recycled air and deliver it through a second duct to the mixing box where the fresh and recycled air are able to mix prior to ventilation into a room or office. The system uses a carbon dioxide sensor and a temperature sensor to provide feedback signals to a control system, which in turn regulates fan speeds and damper openings in order to provide optimal cooling and ventilation and to conserve energy when cooling and ventilation requirements are low.

State-Switched Absorber for Vibration Control of Point-Excited Beams:

Abstract: A system that has the capability to make instantaneous changes in its mass, stiffness, or damping may be termed a state-switchable dynamical system. Such a system will display different dynamical responses dependent upon its current state. State-switchable stiffness may be practically obtained through the control of the termination impedance of piezoelectric stiffness elements. If such a switchable stiffness element is incorporated as part of the spring element of a vibration absorber, the change in stiffness causes a change in the resonance frequencies of the system, thereby instantaneously 'retuning' the state-switched absorber to a new frequency. In between state switches, the operation of such a device is passive, being fundamentally a passive vibration absorber. This concept has improved performance over classical passive vibration absorbers or dampers, particularly for disturbances with multiple spectral components. This paper considers the application of such a device for the purpose of vibration control on beams subjected to harmonic point-force excitation.

Experimental Verification of Seismic Response of Building Frame with Adaptive Sliding Base-Isolation System

Abstract: The paper presented herein investigates the ability of an adaptive seismic isolation system to protect structures subjected to disparate earthquake ground motions. The isolation system consists of sliding isolation bearings in combination with an adaptive hydraulic damper. The damping capacity of the hydraulic damper can be modified in real time to respond to the effects that the earthquake ground motion has on the structure. An experimental laboratory implementation of the adaptive isolation system within a scale-model building structure is described. Analytical models of the isolation system components and the test structure are developed and calibrated through experimental system identification tests. Results from experimental shaking table tests are then used to validate the results from numerical simulations which utilized the analytical models. Although the adaptive base-isolation system results in a complex nonlinear dynamic system, the analytical predictions agreed reasonably well with the experim...

Performance Analysis of ER/MR Impact Damper Systems Using Herschel-Bulkley Model

Abstract: Performance analysis for electrorheological (ER) and magnetorheological (MR) fluid-based impact damper systems is evaluated on the basis of the Herschel-Bulkley shear model. Generally, ER-MR dampers have been analyzed based on the simple Bingham-plastic shear model. However, the Bingham-plastic shear model cannot well describe the behavior of the damper under conditions of high velocity and high field input. Therefore, in this study, the Herschel-Bulkley shear model, in which the constant postyield plastic viscosity in the Bingham model is replaced with a power law model dependent on shear rate, is used to assess the performance of ER-MR impact damper systems. In doing so, an ER-MR impact damper system is proposed and its governing equation of motion is derived on the basis of the Herschel-Bulkley shear model. Then, computer simulation is done to analytically evaluate characteristics of the ER-MR impact damper system under impact loads for constant current input and embedding end-stop on-off control algorithm. As an important parameter in the Herschel-Bulkley shear model, effects of the flow behavior index, n, that is the degree of shear thinning or shear thickening, on the performance of the impact damper system are shown.