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石棉
垫片
压延
成张机
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非石棉垫片压延成张机设计,石棉,垫片,压延,成张机,设计
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Time delay in a semi-active damper:modelling the bypass valveN. Janse van Rensburg*, J.L. Steyn, P.S. ElsDepartment of Mechanical and Aeronautical Engineering, University of Pretoria,Pretoria 0002, South AfricaAbstractRide comfort and handling of off-road vehicles can be significantly improved by replacingthe normal passive dampers in the vehicle suspension system with controllable, two-state,semi-active dampers. The hydraulic valve, which enables the semi-active damper character-istics to be controlled, is a critical component of a semi-active damper and has a markedinfluence on suspension performance. Models of the dynamics of a hydraulic bypass valveused on semi-active suspension systems for heavy vehicles were investigated. It is envisagedthat similar models will eventually be incorporated into a full vehicle, three-dimensionalsimulation study. Valve response time (or time delay) is used as a measure of model accuracybecause it is an important parameter in the performance of a semi-active damper. Modelswere created with AMESim, a commercial fluid power simulation environment, andMATLAB. AMESim was found to be capable of dealing with detailed and complex fluidpower models. Attempts to solve models of similar complexity in the MATLAB environmentwere unsuccessful due to numerical stiffness. Experimental work was conducted to obtaindynamic performance data with which to validate model integrity. Several external factorsinfluenced the valve behaviour during experiments. Test bench dynamics significantly influ-ences results and obscures the absolute accuracy of the models and the experimental data. Theinvestigation demonstrated an approach to creating fluid power models for this applicationthat can be used in simulation, but also indicated that substantial effort is required in theprocess. The accuracy of the current model is not sufficient for design purposes. # 2002ISTVS.Keywords: Hydraulic simulation; Semi-active suspension; Valve time delayJournal of Terramechanics 39 (2002) 3545/locate/jterra0022-4898/02/$22.00 # 2002 ISTVS.PII: S0022-4898(02)00002-2Abbreviations: AME, data relating to AMESim results; EXP, data relating to experimental results;DADS, dynamic analysis and design system* Corresponding author. Tel.: +1-734-207-5557; fax: +1-734-207-5556.E-mail address: neil (N.J. van Rensburg).1. IntroductionSeveral semi-active suspension systems for off-road military vehicles have beendeveloped in South-Africa since 1990 1. A two state semi-active damper formed thebasis of this development, consisting of a bypass valve fitted to a conventional pas-sive damper, with a computerised control system determining the damper state 2.In order to develop the semi-active suspension system for implementation on off-road vehicles, three-dimensional full vehicle dynamic models were compiled in theDADS environment 3,4. Extensive experimental validation was conducted on sev-eral vehicles over different off-road terrains. 1,4. The models and experimentsdemonstrated that significant improvement in ride quality could be achieved, inexcess of 40% based on BS 6841 weighted multi-axis RMS acceleration 4. Achievableimprovements decreased with an increase in vehicle speed over a specific terrain, indi-cating that suspension performance is significantly influenced by valve responsetimes.The aim of this study was to provide modelling of a specific hydraulic valve usedon a current prototype two-state semi-active suspension system. The valve in question(or parts thereof) furthermore has the potential for use in future hydro-pneumaticsystems currently under research or may serve as the basis for future developments5.Experimental work was conducted to acquire parameters needed in the modelsand to obtain dynamic performance data with which to verify the models. For thispurpose a hydraulic test bench at the University of Pretoria was used.NomenclatureAArea (relating to its subscript) (m2)cDamping coefficient (N s/m)CdOrifice flow coefficientFForce (N)kStiffness coefficient (N/m)mMass (kg)?PPressure difference (Pa)P:Derivative of pressure (Pa/s)QFlow rate (m3/s)VVolume (m3)xDisplacement (m)x:Velocity (m/s)x Acceleration (m/s2)?Fluid bulk modulus (Pa)?Fluid density (kg/m3)?Fluid kinematic viscosity (N2/s)36N.J. van Rensburg et al./Journal of Terramechanics 39 (2002) 35452. Hydraulic simulation overviewFluid power simulation poses considerable challenges. Most literature sourcesmake reference to some of these challenges. The following list serves as a shortsummary:? Hydraulic systems generally consist of large oil volumes in the connectingpipes and relatively small oil volumes in the control valves and other com-ponents. These highly different sized fluid volumes in any hydraulic systemgive rise to a stiff numerical problem. The small volumes have a very shorttime constant compared to the larger volumes. This causes an undesirablehigh frequency component in the solution that greatly affects the solver effi-ciency and stability 69.? Replacing the small (and generally insignificant) fluid volumes with incom-pressible ones can reduce the stiffness of a model. This adds differential alge-braic equations to the set of differential equations, which necessitate the use ofspecialised solving techniques and causes further numerical problems 7,9.? Fluid power phenomena are highly non-linear. Some parameters have to beobtained from lookup tables, or from empirical equations, thus adding inac-curacies to the model.? Many discontinuities arise. Typical examples include electrical signals, mas-ses with bump stops (end stops) and flow rates 7. Discontinuities adverselyaffect most numerical methods unless special precautions are taken.? Anumericalproblemariseswiththeuseofthewell-knownorificeflowequation.Q Cd?Affiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2? ?Pjj?s?sign?P1Singularities arise in the Jacobian matrix of the integration algorithm whenzero flow is reached. Altering the equation to include laminar and turbulentflow models can solve this problem 6,9.? There are many parameters in the model for which values have to be foundfrom the physical system. Often the physical system cannot be disassembledto measure these quantities. Techniques developed to overcome this probleminclude amongst others non-linear empirical models with parameters identi-fied from measured data 10.3. Mathematical modelsIn Fig. 1 the valve system layout is shown. It is not the system as fitted to vehicles,but is a comparable configuration used in the experimental work. The pilot valve(solenoid control valve) switches the pressure in the logic element control chamberto a high or low pressure. This allows the logic element state (open or closed) toN.J. van Rensburg et al./Journal of Terramechanics 39 (2002) 354537alter. The vehicle-mounted configuration differs in that the high and low-pressuresupplies needed by the pilot valve are taken from the damper chambers. A rectifiercircuit containing four check valves ensures that the alternating damper chamberpressures are separated into high and low pressure sources for use in the controlcircuit.Models of varying complexity were programmed in AMESim (Adaptive ModellingEnvironment for SIMulation) in the form of lumped parameter models. This type ofmodel assumes parameters such as mass and fluid volumes to be concentrated at asingle point in space. The following equations, shown in generalised and simplifiedform, are used to model the valve and test bench systems:lumped mass dynamicsmx cx: kx XF2lumped fluid compressibilityP:?VXQ3lumped flow restrictions (Laminar and turbulent approximations used)Q Q ?;?P;?;Cd4According to the lumped parameter approach, applying the equationXQ 0Fig. 1. System layout adapted for experimental work.38N.J. van Rensburg et al./Journal of Terramechanics 39 (2002) 3545on a control volume around any hydraulic node one is able to calculate the net flowrate causing a pressure variation in the volume. For a hydraulic network, thisapproach results in a system of differential equations that can be integrated to sup-ply the node pressures.Model compilation in AMESim is fast and intuitive. A small number of basichydraulic, mechanical and control elements enables one to construct customisedmodels. Model equations are automatically deduced and programmed according tothe graphical circuit layout created by selecting elements from the menu.Comparable models were programmed in MATLAB, but the solver used(MATLAB ODE15s) proved unstable with the inherent amount of numerical stiff-ness included in the model. The inclusion of discontinuity handling in the MATLABsolver, especially for mass bump stop implementation, proved effective and neces-sary, but places a further burden on the numerical method.To calibrate the modelling technique an AMESim model was compared to a testcase used by Piche and Ellman 6 to develop and test suitable numerical methods.The example by Piche and Ellman consists of two volumes fed by an ideal flowsource with a step input in flow rate. The two volumes are connected by orifices andhave a volume ratio of 1:1000 to introduce stiffness. Excellent correlation was foundbetween Piche and Ellmans results and AMESim results. A MATLAB model of thesame system also showed excellent correlation.An exponential rise and decay model was used for solenoid force. A full magneto-motive force model proved to be too detailed compared to the rest of the model andadded many additional parameters for which values had to be obtained.4. Experimental procedure and resultsThe test bench used for the experimental work consists of two pumps in paralleldelivering hydraulic oil via an instrumented supply line. The pumps are controlledindividually for flow and pressure by proportional solenoid valves. The test benchcapacity is 90 l/min at 30 MPa (300 bar). To obtain dynamic performance data amanifold block was manufactured to house a displacement transducer for dynamicmeasurement of logic element poppet displacement. The manifold block also containedseveral pressure measuring points and a cavity for the solenoid operated pilot valve.Valve response time (or time delay) is used as a measure of model accuracybecause it is an important parameter in the performance of a semi-active damper. Toprovide a uniform basis for determining the time delay, both the initial and finalsteady state values are determined, as well as the total change. Two additionalvalues are calculated where 5% of total change and 95% of total change has takenplace (see Fig. 2). The time from the valve actuation or trigger signal to the pointwhere 5% change has taken place is called the initial delay. Electro-magnetic tran-sients in the solenoid determine the initial delay. The time taken from the valveactuation signal to a 95% change is defined as the delay time. In this study thepressure drop across the valve and the displacement of the main valve poppet wereused for determination of the valve delay time.N.J. van Rensburg et al./Journal of Terramechanics 39 (2002) 354539Fig. 2. Definition of time delay.Fig. 3. Oscillatory behavior as measured (subscripts refer to Fig. 1).40N.J. van Rensburg et al./Journal of Terramechanics 39 (2002) 3545Many experiments were conducted to determine the steady state and dynamicbehaviour of individual components of the valve system. Only one representativetime domain correlation experiment is discussed in this article, while time delay datais analysed for the operating range.During testing of the valve system, unexpected vibration of the valve poppet, withcorresponding oscillation in flow and pressure, was encountered. With certain flowrates the poppet oscillated so severely that it contacted its seat. The effect was suffi-ciently serious that damage to the test bench or valve system could occur. A com-plicating factor was that oscillatory behaviour occurred on random occasions.Many possible causes for this problem were considered and investigated. Onlyafter including a test bench supply line model in the simulation could the cause beidentified as resonance resulting from supply line compliance. Typical time tran-sients measured are shown in Figs. 35. Since the observed oscillations were of largeamplitude, especially in the case of the displacement, the mean steady state value ofthe relevant parameter was used to determine the 5 and 95% values. The correlationbetween model and experimental results is carried out across the valve operatingrange by extracting and comparing the 95% delay times from the time domaintransients. Difficulty was experienced with the asymptotic behaviour of some transients,Fig. 4. Opening and closing control chamber pressure (PP) with system flow (Qin) at 22 l/min (subscriptsrefer to Fig. 1).N.J. van Rensburg et al./Journal of Terramechanics 39 (2002) 354541causing the calculated 95% point to be highly sensitive to small changes in transientbehaviour. This effect can create the incorrect impression that two transients withsimilar dynamics have substantially different delay values.A time delay of 100 to 400 ms was required for the valve to open or close (Fig. 4).This delay is longer than expected and can be attributed to the long test bench sup-ply line (total volume approximately 13 l) that has to be pressurised after the valvecloses.Due to low readings (resulting from low flow resistance) the drain line pressuretransients could not be used to determine the valve closing delay. However, the logicelement poppet displacement provides an accurate indication of the valve behaviourlargely independent of the experimental layout and test bench interference.The simulated poppet displacement is influenced by several factors. Even if thesimulated overall valve system pressure drop should match the measured value, themathematical distribution of orifice elements upstream and downstream of the logicelement may cause higher or lower pressure forces on the poppet itself.Fig. 5 indicates the time delay vs. the initial pressure difference for the operatingrange of the valve. The data is based on the logic element poppet displacement. Theerror in the delay trend based on displacement for the opening behaviour case(Fig. 5) can be explained as follows: In the time domain transients, the simulateddisplacement steady state value did not match the experimental steady state value(Fig. 4). Because the simulated poppet displacement steady state values are larger,the 95% delay value occurs at a later stage. (In calculating the 95% point, thetransients own steady state values are used.) If the steady-state value of the simu-lated results had matched the experimental values, the extracted delay trends wouldFig. 5. System delay trends based on displacement.42N.J. van Rensburg et al./Journal of Terramechanics 39 (2002) 3545show better correlation. The simulated delay trends follow the general shape of theexperimental delay trends but differ substantially in terms of time delay. This indi-cates that the model contains enough detail of the physical system to reproduce theoverall dynamic behaviour. However, the model is not accurate enough to be used indesign studies.In an attempt to explain the unsatisfactory correlation between experimental andsimulation results, a sensitivity analysis was performed on the AMESim valve andtest bench system model. This consisted of an automatic routine to simulate thesystem over a range of flow settings, each time with one parameter changed by plus10% and minus 10%. Except for the check valve cracking pressure, the parameterswith a large influence on the system response are exclusively related to the testbench.The test bench was originally designed for characterising hydraulic componentsand systems and has previously been used only in lower bandwidth applications.From the sensitivity analysis, resonance (due to supply line compliance) and the timedelay (attributed to supply line volume as well as pump control dynamics), it becameclear that the bandwidth of the test bench system was not sufficient for measuringthe valve system dynamics. This caused the test bench dynamics to influence boththe experimental, as well as the simulated values, obscuring actual valve dynamics.5. Conclusions and recommendationsThe aim of this study was to provide modelling of a specific hydraulic valve usedon a current prototype semi-active suspension system. Models were developed usingAMESim and MATLAB.It is concluded that:? AMESim was found to be useful in constructing a valid and detailed modelof the hydraulic damper bypass valve system and to have the ability to solvethe mathematical equations efficiently and with numerical stability.? Attempts to use the pre-programmed MATLAB ODE suite, mainly ODE15sto solve the stiffequations describing the valve system were not successful.Governing equations of the same complexity as that of the AMESim modelwould be programmable in MATLAB, but numerical solution of such amodel with standard MATLAB solvers seems improbable.? The system as modelled in this study contains fast acting subsystems. Themodels of these subsystems are sensitive to the physical parameter values oftheir components. The nature of hydraulic systems makes it difficult to obtainaccurate values for the parameters (either by experimental or analyticalmethods) for use in the model. This unavailability of accurate parametervalues and the need for parameter adjustment causes slow model develop-ment and errors in the simulated results.? The simplifying assumptions made in the models give a first order indicationof the expected system performance. Some of the assumptions made in thisN.J. van Rensburg et al./Journal of Terramechanics 39 (2002) 354543study (such as constant pressure and flow distributions and exponentialsolenoid behaviour) may however have a large effect on the simulatedresponse.? Test bench dynamics are significant and can obscure valve dynamics.Separation of test bench and valve dynamics is however very difficult.The following recommendations are made:? Computational fluid dynamics analysis can be used to create lookup tables toenhance the models accuracy in predicting flow forces and pressure dis-tributions acting on the poppet elements.? Detailed analysis of the magnetic circuit would aid in obtaining accuratesolenoid force characteristics that is important in the valve dynamic responsebehaviour.? Reconsideration of the test bench design, or detailed simulation of itsdynamics, is required before any further experimental correlation of simula-tion results can be undertaken.AcknowledgementsThe authors thank: Reumech Ermetek for providin
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