Electro-Hydraulic Servo Valve Construction, Models and Use

Electro-Hydraulic Servo Valve Construction, Models and Use From Merritt, H. E., Hydraulic Control Systems, J. Wiley, 1967.The input to an electro-hydraulic (EH) servovalve is typically a current or a differential current that powers an electromagnetic torque motor. The differential current Δi is typically supplied by an amplifier to avoid excess loading of the interface to the computer or controller. In the simplest (but not typical) form, the torque motor moves a spool valve as shown below. The spool valve allows the hydraulic fluid to pass from the supply to the return across two variable metering orifices with a controlled flow rate Q L. If the spool is shifted in the other direction the direction of flow will reverse. Since the clearances between the spool and the valve body is small, the forces required to move a large spool are large. Hence the single stage or direct acting EH valve is limited to low rates of flow (small valves). Figure 7-11 from Merritt shows the pictorial representation of the motion system in this case.In order to achieve higher flow rates, a two or three stage servovalve may be necessary. In this case the torque motor controls the first stage valve that actuates the spool on the second stage. The first stage valve is typically not a spool valve but either a flapper-nozzle valve or a jet pipe valve. The flapper-nozzle is more common. For these valvesflow passes from the nozzle through a cylindrical area between the nozzle and the flat flapper that is near to it. As shown in Fig 7-14 and 7-17 from Merritt, the EH valve uses one flapper between two nozzles to produce a differential pressure that is applied to each side of the spool. The displacement of the flapper from a neutral position is powered by the torque motor and resisted by a torsional spring. The “fixed upstream orifice” in both types of valve is important to allow the pressure on either end of the spool to be below the supply pressure. A small flapper motion creates an imbalanced pressure in one direction or the other on the ends of the spool of the second stage. Obviously the spool will tend to move in response to this imbalance and allow flow Q L to the actuator. Since continued imbalance in pressure would quickly move the spool to its limits of travel, a form of feedback connects the motion of the spool to the effective displacement of the flapper. A very small spool displacement will result in a large flow at high pressures typically used.Two common forms of feedback are illustrated in the figures from Merritt. Direct position feedback moves the nozzle with the spool as shown in Fig 7-14. Thus the equilibrium position of the spool is 1:1 with the position of the flapper. Fig 1-17 shows the force feedback arrangement in which a feedback leaf spring applies a force to the flapper to restore equilibrium. The ratio between the spring constant of this spring and the torsional spring on the torque motor determine the ratio between motion of the flapper and the spool.Valve ModelsMathematical models of the EH valve can be constructed at various levels of detail depending on the purpose of the model. The models may represent the nonlinear square root relation between pressure and flow, or may be linearized about an operating position. When designing the valve itself, a more detailed model is typically required than when modeling the system controlled by a well designed valve. The model of the dynamics of the electromagnetic behavior is typically ignored or aggregated into the overall valve behavior, for example. Block diagram 7-18 shows a very detailed model of the force feedback valve that is simplified in the block diagram of Fig 8-5 constructed for analysis of the valve in a position control system. The transfer function of Equation (8-17) excerpted from Merritt is further simplified. This is the form you should hope to apply to a system design. Some of the parameters of this model are readily calculated, provided by the manufacturer or obtained from manufacturer’s specifications. Other terms in (8-17) are better identified from aggregate measurements of the system’s overall behavior. Even in this case it is generally desirable to compare the identified parameters to estimates based on first principles. The effective bulk modulus βe is an example. It depends not only on the compressibility of the pure fluid, but the effect of entrained air and vapor and the expansion of the walls containing a fluid. These effects are very hard to compute directly but they result in an increased compressibility (decrease bulk modulus), so the limiting case can be estimated from knowledge of the ideal properties.The most common model of the load used for system design assumes the load is essentially an inertia and that⎟⎟⎠⎞⎜⎜⎝⎛++⎟⎟⎠⎞⎜⎜⎝⎛+−=1241222s s s n T s K V D K x D K h h n L ce e tm ce v m q m ωδωβθ where the variables are given below, along with the units in the metric system:1/sec variable,Laplace essdimensionl ), labeled (sometimes system hydraulic of ratio damping rad/secsystem, hydaulic of frequency naturaless dimensionl rotation, ontrolled rotation/c motor ratio,gear m)-(N torque load applied externally N/mmodulus,bulk effective system m valve,exiting fluid by compressed volume )/sec)/(N/m (m t,coefficien leakage mm nt,displaceme spool valve liters/rad nt,displaceme motor liters/mm gain, flow valve radrotation,motor 2323============s n T V K x D K h h L e t ce v m q m ξδωβθPossible simplifications, refinements and extensions of this model are numerous:o The simplest valve model would give the steady state flow for a given electrical input. As one can see from the final value theorem and the blocks representing the valve in Merritt’s Figure 8-5, for a step input (i.e. s s e /1)(=θ) to the error signal,amplitude)(input x gain)constant (a 1)(lim )(lim 0=⋅==→→∞s d e v s t v K K K t x s x sThus if the valve dynamics are fast compared to those of the load, one canessentially ignore the dynamics of the electrical drive and the electromagnetics of the valve, leaving the effect of the valve as a constant.o A more accurate model of the servo valve spool motion is given by a first orsecond order transfer function. The Merritt model shows a fourth order model for the electrical drive and spool dynamics but today’s electrical drives are so fast that their dynamics may be ignored. See the Moog Company’s venerablepublication, “Transfer Function for Moog Servovalves” by Thayer for example models and parameters for a high performance servo valve.o For an example extension, consider T L which is shown in the block diagram as an external input, when it is likely to be dependent on the flow through the valve. This would be represented with a feedback loop representing the effects of inertia, compliance, damping, etc. of the load.o There are other connections that are of interest. The pressure in the actuator willreduce the pressure drop across the valve orifice. This effect is not explicit in the block diagram and would require further considerations of the back pressure if it is a substantial fraction of the supply pressure.Identification of Hydraulic System ParametersThe model requires coefficients to be known within reasonable accuracy to be of any value. Some of the values can be measured directly, such as lengths and volumes. Otherparameters may be determined in groups by certain experiments. This is particularly true of the valve model.To “identify” the parameters of any dynamic experiments, a number of experiments can be performed. They include steady state measurements, time-domain measurements such as step responses, and frequency response measurements either from sinusoidal or other inputs. Often these experiments identify a coefficient of the transfer function that is a grouping of physical constants. In most cases it may be desirable to check the identified coefficients with the feasible range of values of the physical constants.One difficulty is the measurement in an open loop fashion due to the presence of a pure integrator in the system. Small amounts of flow through the valve in the null position cause the position to drift to the limits of travel. One alternative is to provide a position feedback which eliminates the drift although it alters the response. The true response has to be back calculated in these circumstances.MOOG INC. CONTROLS DIVISION, EAST AURORA, NY 14052TRANSFER INTRODUCTIONFUNCTIONS FOR MOOG SERVOVALVESIt is often convenient in servoanalysis or in system synthesis work to represent an electrohydraulic servovalve by a sim-plified, equivalent transfer function. Such a representation is, at best, only an ap-proximation of actual servovalve perform-ance. However, the usefulness of lineartransfer functions for approximatingequipment presently used by Moog tomeasure servovalve dynamic response.Another difficulty in assigning simplified, linear transfer functions to represent servovalve response is that these valves are highly complex devices that exhibit high-order, nonlinear responses. If a first, second, or even third-order transfer function is selected to represent servovalve dynamics, still only an approximation to actual response is possible. Fortunately, for most physical systems, the servovalve is not the primary dynamic element, so it is only necessary to represent valve response throughout a relatively low frequency spectrum. For instance, if a servovalve-actuator is coupled to a load which exhibits a 50 cps resonant frequency, it is meaningful only to represent valve dynamic response in the frequency range to 50 cps. Similarly, for lower response physical systems,the contribution of valve dynamics throughout a correspondingly smaller frequency range need be considered. This simplification of actual servo response should be applied whenever practicable, for the reduced analytical task associated with the system analysis is obvious.These approximations to servovalve response have resulted in such expressions as "the equivalent time constant of the servovalve is - seconds" or "the apparent natural frequency of the servovalve is -radians /second." If a representation of servovalve response throughout the frequency range to about 50 cps is sufficient, then a first-order expression is usually adequate. Figure I shows a typical valve dynamic response, together with the response of a first-order transfer function. The first-order approximation is seen to be quite good throughout the lower frequency region. The time constant for the first-order transfer function (i.e., the equivalent servovalve time constant) is best established by curve fitting techniques. If a quick approximation is desired, the equivalent time constant should correspond to the 45°phase point rather than the 0.7SS Y M B O L SF R E Q U E N T L Y U S E Ddifferential current m ainput to servovalve in’/sec (cis)to the loadservovalve differential sensitivity,as defined time constants sec.natural frequencies rad/sec.damping ratiosnondimensionaltond Ordercpr20014061105TO ACTUATORThese servovalves provide a differ-ential pressure output in response to theelectrical input current. The static Figure 6.A small droop, or decrease in the con-trolled pressure with flow, does occur,even throughout the null region. This droop is usually small in pressure-control servovalves; however, in some applica-tions even a small droop can significantlyalter the system response. InAPPENDIX IANALYTICANALYSIS OFSERVOVALVEDYNAMICSIt is possible to derive meaningful transfer functions for electrohydraulic servovalves, and several papers have reported such work (ref). Unfortunately, servovalves are complex devices and have many nonlinear characteristics which are significant in their operation. These nonlinearities include: electrical hysteresis of the torque motor, change in torque-motor output with displacement, change in orifice fluid-impedance with flow and with fluid characteristics, change in orifice discharge coefficient with pressure ratio, sliding friction of the spool, and others.Many servovalve parts are small so have a shape which is analytically non-ideal. For example, fixed inlet orifices are often 0.006 to 0.008 inch in diameter. Ideally, the length of the orifice would be small with respect to its diameter to avoid both laminar and sharp-edge orifice effects; however, this becomes physically impractical with small orifices due to lack ofstrength for differential pressure loading, and lack of material for adequate life with fluid erosion. Therefore, the practical design from the performance standpoint is not necessarily the ideal design from the analytical standpoint.Experience has shown that these non-linear and non-ideal characteristics limit the usefulness of theoretical analysis of servovalve dynamics in systems design. Instead, the more meaningful approach is to approximate measured servovalve response with suitable transfer functions, as discussed in the body of this technical bulletin.The analytic representation of servo-valve dynamics is useful during prelim-inary design of a new valveconfiguration, or when attempting toalter response of a given design byparameter variation. Analysis alsocontributes to a clearer understandingof servovalve operation.Rather elaborate analyses ofservovalve dynamic response havebeen performed at Moog, includingcomputer studies which involve severalnonlinear effects, and up to eightdynamic orders (excluding any loaddynamics). Unfortunately, thesecomplex analyses have not contributedsignificantly to servovalve design due touncertainties and inaccuraciesassociated with the higher-order effects.These analyses have been extremelyuseful when reduced to their simplerform. A very adequate transfer functionrepresentation for the basic Type 30mechanical feedback servovalve isgiven in Figure 12. This simplifiedrepresentation results from the followingassumptions:1. An ideal current source (infiniteimpedance) is used.2. Negligible load pressure exists.3. All nonlinearities can either beapproximated by linear dynamiceffects, or can be neglected.4. The armature/flapper can be rep-resented as a simple lumped-parameter system.5. Perturbation conditions can beapplied to the hydraulic amplifierorifice characteristics.6. Fluid compressibility and viscosityeffects are negligible.7. Motions of the flapper are smallwith respect to spool motion.8. The forces necessary to move thespool are small with respect to thedriving force available.The last assumption implies that thedifferential pressure across the spool isnegligible during dynamic conditions. If so, then spool mass, friction, flow forces, and other spool force effects can be neglected. At first this assumption may seem unreasonable; but it can be shown to be quite valid, and the simplification which results more than justifies its use.The simplified block diagram is a third order system consisting of the armature/ flapper mass, damping and stiffness, together with the flow-integration effect of the spool. The spool, in this case, is analogous to the piston of a simple position servoloop.The rotational mass of the armature/ flapper is quite easy to calculate. The effective stiffness of the armature/flapper is a composite of several effects, the most important of which are the centering effect of the flexure tube, and the decentering effect of the permanent magnet flux. The latter is set by charge level of the torque motor, and is individuallyadjusted in each servovalve to meetprescribed dynamic response limits. Thedamping force on the armature/flapper islikewise a composite effect. Here, it is knownfrom experience that the equivalent ζ is about0.4.The hydraulic-amplifier orifice bridge reducesto a simple gain term with the assumptionslisted earlier. This gain is the differential flowunbalance between opposite arms of thebridge, per increment of flapper motion.Internal loop gain of the servovalve isdetermined by the following parameters.The hydraulic amplifier flow gain, K2, can berelated to nozzle parameters by the following:Any of the loop gain parameters can bealtered to change servovalve response. Forexample, the following changes wouldincrease internal servovalve loop gain: (1)smaller spool diameter, (2) larger nozzlediameter, (3) higher nozzle pressure drop, (4)higher torque motor charge level. The highertorque motor charge gives a lower k f whichincreases loop gain, but this also lowers thenatural frequency of the first stage.Unfortunately, the directions of these twoeffects are not compatible in that higher loopgain cannot be used with a lower naturalfrequency first stage. Therefore, an optimumcharge level exists which produces maximumloop gain for the stability margin desired.。