hydrulic valve18.pdf

Time delay in a semi-active damper: modelling the bypass valve N. Janse van Rensburg*, J.L. Steyn, P.S. Els Department of Mechanical and Aeronautical Engineering, University of Pretoria, Pretoria 0002, South Africa Abstract Ride comfort and handling of off -road vehicles can be signifi cantly improved by replacing the 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 marked infl uence on suspension performance. Models of the dynamics of a hydraulic bypass valve used on semi-active suspension systems for heavy vehicles were investigated. It is envisaged that similar models will eventually be incorporated into a full vehicle, three-dimensional simulation study. Valve response time (or time delay) is used as a measure of model accuracy because it is an important parameter in the performance of a semi-active damper. Models were created with AMESim, a commercial fl uid power simulation environment, and MATLAB. AMESim was found to be capable of dealing with detailed and complex fl uid power models. Attempts to solve models of similar complexity in the MATLAB environment were unsuccessful due to numerical stiff ness. Experimental work was conducted to obtain dynamic performance data with which to validate model integrity. Several external factors infl uenced the valve behaviour during experiments. Test bench dynamics signifi cantly infl u- ences results and obscures the absolute accuracy of the models and the experimental data. The investigation demonstrated an approach to creating fl uid power models for this application that can be used in simulation, but also indicated that substantial eff ort is required in the process. The accuracy of the current model is not suffi cient for design purposes. # 2002 ISTVS. Keywords: Hydraulic simulation; Semi-active suspension; Valve time delay Journal of Terramechanics 39 (2002) 3545 0022-4898/02/$22.00 # 2002 ISTVS. PII: S0022-4898(02)00002-2 Abbreviations: 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. Introduction Several semi-active suspension systems for off -road military vehicles have been developed in South-Africa since 1990 1. A two state semi-active damper formed the basis of this development, consisting of a bypass valve fi tted 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 the DADS environment 3,4. Extensive experimental validation was conducted on sev- eral vehicles over diff erent off -road terrains. 1,4. The models and experiments demonstrated that signifi cant improvement in ride quality could be achieved, in excess of 40% based on BS 6841 weighted multi-axis RMS acceleration 4. Achievable improvements decreased with an increase in vehicle speed over a specifi c terrain, indi- cating that suspension performance is signifi cantly infl uenced by valve response times. The aim of this study was to provide modelling of a specifi c hydraulic valve used on 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-pneumatic systems currently under research or may serve as the basis for future developments 5. Experimental work was conducted to acquire parameters needed in the models and to obtain dynamic performance data with which to verify the models. For this purpose a hydraulic test bench at the University of Pretoria was used. Nomenclature AArea (relating to its subscript) (m2) c Damping coeffi cient (N s/m) Cd Orifi ce fl ow coeffi cient FForce (N) k Stiff ness coeffi cient (N/m) mMass (kg) ?P Pressure diff erence (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) 3545 2. Hydraulic simulation overview Fluid power simulation poses considerable challenges. Most literature sources make reference to some of these challenges. The following list serves as a short summary: ? Hydraulic systems generally consist of large oil volumes in the connecting pipes and relatively small oil volumes in the control valves and other com- ponents. These highly diff erent sized fl uid volumes in any hydraulic system give rise to a stiff numerical problem. The small volumes have a very short time constant compared to the larger volumes. This causes an undesirable high frequency component in the solution that greatly aff ects the solver effi - ciency and stability 69. ? Replacing the small (and generally insignifi cant) fl uid volumes with incom- pressible ones can reduce the stiff ness of a model. This adds diff erential alge- braic equations to the set of diff erential equations, which necessitate the use of specialised solving techniques and causes further numerical problems 7,9. ? Fluid power phenomena are highly non-linear. Some parameters have to be obtained 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 fl ow rates 7. Discontinuities adversely aff ect most numerical methods unless special precautions are taken. ? Anumericalproblemariseswiththeuseofthewell-knownorifi cefl owequation. Q Cd?A ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffiffi 2? ?Pjj ? s ?sign?P1 Singularities arise in the Jacobian matrix of the integration algorithm when zero fl ow is reached. Altering the equation to include laminar and turbulent fl ow models can solve this problem 6,9. ? There are many parameters in the model for which values have to be found from the physical system. Often the physical system cannot be disassembled to measure these quantities. Techniques developed to overcome this problem include amongst others non-linear empirical models with parameters identi- fi ed from measured data 10. 3. Mathematical models In Fig. 1 the valve system layout is shown. It is not the system as fi tted to vehicles, but is a comparable confi guration used in the experimental work. The pilot valve (solenoid control valve) switches the pressure in the logic element control chamber to a high or low pressure. This allows the logic element state (open or closed) to N.J. van Rensburg et al./Journal of Terramechanics 39 (2002) 354537 alter. The vehicle-mounted confi guration diff ers in that the high and low-pressure supplies needed by the pilot valve are taken from the damper chambers. A rectifi er circuit containing four check valves ensures that the alternating damper chamber pressures are separated into high and low pressure sources for use in the control circuit. Models of varying complexity were programmed in AMESim (Adaptive Modelling Environment for SIMulation) in the form of lumped parameter models. This type of model assumes parameters such as mass and fl uid volumes to be concentrated at a single point in space. The following equations, shown in generalised and simplifi ed form, are used to model the valve and test bench systems: lumped mass dynamics mx cx : kx X F2 lumped fl uid compressibility P : ? V X Q3 lumped fl ow restrictions (Laminar and turbulent approximations used) Q Q ?;?P;?;Cd4 According to the lumped parameter approach, applying the equation X Q 0 Fig. 1. System layout adapted for experimental work. 38N.J. van Rensburg et al./Journal of Terramechanics 39 (2002) 3545 on a control volume around any hydraulic node one is able to calculate the net fl ow rate causing a pressure variation in the volume. For a hydraulic network, this approach results in a system of diff erential equations that can be integrated to sup- ply the node pressures. Model compilation in AMESim is fast and intuitive. A small number of basic hydraulic, mechanical and control elements enables one to construct customised models. Model equations are automatically deduced and programmed according to the 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 MATLAB solver, especially for mass bump stop implementation, proved eff ective and neces- sary, but places a further burden on the numerical method. To calibrate the modelling technique an AMESim model was compared to a test case 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 fl ow source with a step input in fl ow rate. The two volumes are connected by orifi ces and have a volume ratio of 1:1000 to introduce stiff ness. Excellent correlation was found between Piche and Ellmans results and AMESim results. A MATLAB model of the same 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 and added many additional parameters for which values had to be obtained. 4. Experimental procedure and results The test bench used for the experimental work consists of two pumps in parallel delivering hydraulic oil via an instrumented supply line. The pumps are controlled individually for fl ow and pressure by proportional solenoid valves. The test bench capacity is 90 l/min at 30 MPa (300 bar). To obtain dynamic performance data a manifold block was manufactured to house a displacement transducer for dynamic measurement of logic element poppet displacement. The manifold block also contained several 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 accuracy because it is an important parameter in the performance of a semi-active damper. To provide a uniform basis for determining the time delay, both the initial and fi nal steady state values are determined, as well as the total change. Two additional values are calculated where 5% of total change and 95% of total change has taken place (see Fig. 2). The time from the valve actuation or trigger signal to the point where 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 valve actuation signal to a 95% change is defi ned as the delay time. In this study the pressure drop across the valve and the displacement of the main valve poppet were used for determination of the valve delay time. N.J. van Rensburg et al./Journal of Terramechanics 39 (2002) 354539 Fig. 2. Defi nition 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) 3545 Many experiments were conducted to determine the steady state and dynamic behaviour of individual components of the valve system. Only one representative time domain correlation experiment is discussed in this article, while time delay data is analysed for the operating range. During testing of the valve system, unexpected vibration of the valve poppet, with corresponding oscillation in fl ow and pressure, was encountered. With certain fl ow rates the poppet oscillated so severely that it contacted its seat. The eff ect 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. Only after including a test bench supply line model in the simulation could the cause be identifi ed as resonance resulting from supply line compliance. Typical time tran- sients measured are shown in Figs. 35. Since the observed oscillations were of large amplitude, especially in the case of the displacement, the mean steady state value of the relevant parameter was used to determine the 5 and 95% values. The correlation between model and experimental results is carried out across the valve operating range by extracting and comparing the 95% delay times from the time domain transients. Diffi culty was experienced with the asymptotic behaviour of some transients, Fig. 4. Opening and closing control chamber pressure (PP ) with system fl ow (Qin) at 22 l/min (subscripts refer to Fig. 1). N.J. van Rensburg et al./Journal of Terramechanics 39 (2002) 354541 causing the calculated 95% point to be highly sensitive to small changes in transient behaviour. This eff ect can create the incorrect impression that two transients with similar dynamics have substantially diff erent 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 valve closes. Due to low readings (resulting from low fl ow resistance) the drain line pressure transients could not be used to determine the valve closing delay. However, the logic element poppet displacement provides an accurate indication of the valve behaviour largely independent of the experimental layout and test bench interference. The simulated poppet displacement is infl uenced by several factors. Even if the simulated overall valve system pressure drop should match the measured value, the mathematical distribution of orifi ce elements upstream and downstream of the logic element may cause higher or lower pressure forces on the poppet itself. Fig. 5 indicates the time delay vs. the initial pressure diff erence for the operating range of the valve. The data is based on the logic element poppet displacement. The error 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 simulated displacement 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, the transients 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 would Fig. 5. System delay trends based on displacement. 42N.J. van Rensburg et al./Journal of Terramechanics 39 (2002) 3545 show better correlation. The simulated delay trends follow the general shape of the experimental delay trends but diff er substantially in terms of time delay. This indi- cates that the model contains enough detail of the physical system to reproduce the overall dynamic behaviour. However, the model is not accurate enough to be used in design studies. In an attempt to explain the unsatisfactory correlation between experimental and simulation results, a sensitivity analysis was performed on the AMESim valve and test bench system model. This consisted of an automatic routine to simulate the system over a range of fl ow settings, each time with one parameter changed by plus 10% and minus 10%. Except for the check valve cracking pressure, the parameters with a large infl uence on the system response are exclusively related to the test bench. The test bench was originally designed for characterising hydraulic components and systems and has previously been used only in lower bandwidth applications. From the sensitivity analysis, resonance (due to supply line compliance) and the time delay (attributed to supply line volume as well as pump control dynamics), it became clear that the bandwidth of the test bench system was not suffi cient for measuring the valve system dynamics. This caused the test bench dynamics to infl uence both the experimental, as well as the simulated values, obscuring actual valve dynamics. 5. Conclusions and recommendations The aim of this study was to provide modelling of a specifi c hydraulic valve used on a current prototype semi-active suspension system. Models were developed using AMESim and MATLAB. It is concluded that: ? AMESim was found to be useful in constructing a valid and detailed model of the hydraulic damper bypass valve system and to have the ability to solve the mathematical equations effi ciently and with numerical stability. ? Attempts to use the pre-programmed MATLAB ODE suite, mainly ODE15s to solve the stiff equations describing the valve system were not successful. Governing equations of the same complexity as that of the AMESim model would be programmable in MATLAB, but numerical solution of such a model with standard MATLAB solvers seems improbable. ? The system as modelled in this study contains fast acting subsystems. The models of these subsystems are sensitive to the physical parameter values of their components. The nature of hydraulic systems makes it diffi cult to obtain accurate values for the parameters (either by experimental or analytical methods) for use in the model. This unavailability of accurate parameter values 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 fi rst order indication of the