Frequency Response Of Critical Components Of A Hydraulic Servovalve

M. Singaperumal, Somashekhar. S. Hiremath and R. Krishnakumar

Department of Mechanical Engineering Indian Institute of Technology Madras

Chennai - 6000 36 (India). ABSTRACT The analyzed electrohydraulic servo valve is jet pipe type, is one of the mechatronics component used for precision flow control application. The jet pipe servo valves have one movable nozzle and two collector ports, from where fluid is ducted to the main valve spool. The servovalve analyzed here is basically used in fuel control application in Variable Geometry Actuation System (VGAS) of a gas turbine engine. It consists of several precision and delicate components. For the analysis the feedback spring assembly and jet pipe assembly of jet pipe servovalve are identified and conducted direct-solution steady-state dynamic analysis to study the response of the system for harmonic excitation. The assembly was subjected for analysis to ascertain the response for critical parameters like thickness of flexure tube and material for flexure tube. Key words: natural frequency, flexure tube, servovalve, feedback spring, and precision

1. INTRODUCTION

Electrohydraulic servovalve is one of the precision mechatronic components, used in many feedback control systems, working on jet engine and fighter aircrafts. In 1950, the electrohydraulic servovalve (EHSV) was conceived; to meet the U.S. aerospace program need for a precise hydraulic flow. EHSV pioneers considered using an electromechanical device to position the spool, but were limited by available electric motor and control technology. They rejected this bulky method in favour of a device using hydraulic pilot pressure to position the spool. Therefore the EHSV is an essential item of a servomechanism where fast speed of response, high power output and working fidelity are necessary [1]. The analyzed electrohydraulic servovalve of the jet pipe type, used for precision flow control application. It consists of several precision and delicate components. The performance of the valve depends on many parameters. During the developmental stage, it is very difficult to ascertain the functional parameters. Experimentation requires the valve and its components. Theoretical and simulation tools are available to predict the functional parameters. One of the powerful tools is solid modelling and FE simulation. Many attempts have been made in modeling the dynamic characteristics of servovalves particularly flapper type and allied components and models of varying complexity have evolved [2-5]. The complexity required is of course dependent upon the overall system dynamic performance which should be related to the probable dynamic characteristic of the servovalve suggested by the manufacturer. Less number of literatures is available on jet pipe type. A jet-pipe valve consists of a nozzle and a receiver block shown in Fig.1. The receiver block is having two closely spaced holes. The nozzle, or jet pipe, is arranged on a pivot so that it may be displaced from a neutral position. The jet pipe serves to convert pressure energy into the kinetic energy of a jet and directs this jet toward two receiver holes in the receiver block. When the jet of oil strikes the flat receiver block its kinetic energy is recovered in the form

of pressure. If the stream is directed exactly halfway between the receiver holes, the pressure in the two holes will be equal; the differential pressure, therefore, is zero. As the jet pipe is deflected, more oil will be directed at one hole than the other, raising the pressure in that hole and decreasing the pressure on the other, and thus creating a differential-pressure output. Pressure recovery in receiver holes is a function of jet pipe displacement relative to receiver plate and recovery falls off for larger jet displacements [6]. Theoretical investigation was conducted on various affecting parameters on the static pressure recovery in the receiver holes. The major parameters studied are distance between the receiver holes (web thickness), jet pipe nozzle diameter, receiver hole diameters, nozzle offset and nozzle stand-of distance [7]. Simulation study was done on pressure recovery in jet pipe servovalve [8]. The analytical and experimental investigation of a jet pipe controlled electropneumatic actuator for frequency response and time-domain force tracking was done [9]. The analyzed valve is miniature type having jet pipe and receiver diameters 3.4X10-4 m, the distance between the receiver holes 1X10-5 m and spool diameter 11 X10-3 m. Many attempts have been made in modeling the dynamic characteristics of servo valves and allied components and models of varying complexity have evolved 1,2,3,4. The complexity required is of course dependent upon the overall system dynamic performance which should be related to the probable dynamic characteristic of the servovalve suggested by the manufacturer. The analyzed servo valve is a miniature type having the jet pipe (D) and receiver hole diameters (d) as 3.0X10-4 m, the distance between the receiver holes as (W) 1X10-5 m and the spool diameter (Ds) as 10X10-3 m.

1.1 Operating description of jet pipe servovalve

The jet pipe electrohydraulic servovalve consists of two main assemblies, a torque motor assembly representing first stage and valve assembly representing the second stage. In-between the first and second stage, there is a mechanical feedback to stabilize the valve operation. The schematic representation of the two assemblies is shown in Fig.1. The valve operates as follows:

• Electrical current in the torque motor coils creates magnetic forces on the ends of the armature. Armature and jet pipe rotates about flexure tube support.

• Jet pipe deflection leads to move the more oil flow to one receiver hole than the other, creates a differential pressure across the spool end.

• Spool moves and opens pressure port ‘Ps’ to one of the control port and opens the other control port to tank ‘T’. During spool movement, it pushes the feedback spring connected between the jet pipe and spool, creating restoring torque on the jet pipe.

• As the feedback torque becomes equal to torque from magnetic forces, the jet pipe moves back to centered position (null position).

• Spool stops at a position where feedback spring torque becomes equal to torque in armature. This torque balance is said to be steady state operation of the servo valve. The resulting spool position opens a specified flow passage at the ports of the second stage of the valve.

Fig. 1: Schematic diagram of jet pipe assembly.

2. STEADY STATE DYNAMIC ANALYSIS

Generally the frequency extraction procedure performs eigenvalue extraction to calculate the natural frequencies and the corresponding mode shapes of a system. It will include initial stress and load stiffness effects due to preloads and initial conditions if *STEP, NLGEOM is used in the base state, so that small vibrations of a preloaded structure can be modeled. If initial stress effects are not included and there are no rigid body modes, stiffness matrix is positive definite; otherwise, it may not be. Negative eigenvalues normally indicate instability. The *FREQUENCY procedure uses eigenvalue techniques to extract the frequencies of the current system. The eigenvalue problem for the natural frequencies of an undamped finite element model is

)1(0)( 2 =+− NNMNM KM φω The structures subjected to continuous harmonic excitation, a “direct” steady state dynamic analysis procedure was used like “modal” procedure. A direct-solution steady-state dynamic analysis is a linear perturbation procedure, used to calculate a system’s linearized response to harmonic excitation. The formulation is based on the dynamic virtual work equation,

∫∫ ∫∫ =−++ )2(0.:.....

tdSuVdVduuVduuV V

cV

δσεδδαρδρ

Where .u and

..u are the velocity and acceleration, ρ is the density of material, Cα is the mass

proportional damping factor (part of the Rayleigh damping assumption), σ is the stress, t is the surface traction, and εδ is the strain variation that is compatible with the displacement variation uδ . The discretized form of this equation is

)3(0.

)(

..

=−++ NNM

NMm

MNMN PIuCuMuδ

Where the following definitions apply:

∫= dVNNM MNNM .ρ is the mass matrix,

∫= dVNNC MNC

NMm .)( αρ is the mass damping matrix,

∫= dVI NN σβ : is the internal load vector,

∫= dStNP NN . is the external load vector.

For the steady-state harmonic response we assume that the structure undergoes small harmonic vibrations about a deformed, stressed state, defined by the subscript 0. Since steady-state dynamics belongs to the perturbation procedures, the load and response in the step define the change from the base state. 2.1 Steady State Dynamic Analysis of Feedback Spring Assembly The feedback spring assembly consists of three parts namely feedback spring, spring guide and spring plate. Feedback spring and spring guide are fitted in the spring plate. The one end of the feedback spring is entering the second stage and fixed in spool valve with two null adjustable screws. The other end is fixed to jet pipe nozzle through the spring guide. Depending upon the geometry and nature of operation, FE model was created with suitable elements, material and boundary conditions. Fig.2 shows the solid and finite element model of feedback spring assembly with boundary and loading conditions.

Spring plate

Feedback spring

Clamp

F, Cload

Fig. 2: Solid and finite element model of feedback spring assembly.

Spring guide

The concentrated load of 0.33N was sweeped from 1 Hz to 1000 Hz and observed that the feedback spring assembly has the resonance at frequency 658 Hz, as shown in Fig. 4 Displacement vs. Frequency

0

0.005

0.01

0.015

0.02

0.025

0 200 400 600 800 1000 1200

Frequency (Hz)

Disp

lace

men

t (m

eter

)

Fig. 3: Frequency vs. Displacement of the feedback spring assembly end.

2.2 Steady State Dynamic Analysis of Jet Pipe Assembly The jet pipe assembly consists of armature, armature bush, flexure tube, jet pipe and jet pipe nozzle and oil supplying pipe as shown in Fig. 5

Clamp

Spring support F

F

Clamp Clamp

Armature

Connection pipe Flexure tube

Jet pipe

Nozzle

Fig. 4: Solid and finite element model of jet pipe assembly.

The jet pipe is supported by a thin walled flexure tube element. The flexure tube acts as a seal between the electromagnetic and hydraulic sections of the servovalve and hence ensures the dry torque motor operations. The applied torque on the armature rotates the jet pipe assembly around the flexure tube pivot. Similarly the restoring torque from the spool movement is transmitted to armature through this flexure tube. The stiffness of this flexure tube is very important from the dynamic response of the servovalve and was discussed, Somashekhar, et. al [10].. The steady state dynamic analysis was carried out on the jet pipe assembly. The finite element model is as shown in Fig. 5. Two concentrate loads of 0.94 N was applied on the armature to create the torque was sweeped from 1 Hz to 1000 Hz. The response of the assembly was studied at the jet pipe nozzle. Fig. 6 shows the displacement of jet pipe nozzle vs. frequency. It is seen that the resonance occurs at a frequency of 377 Hz The analysis was extended for different flexure tube thickness and different material, the result was shown in Table. 1 and Table.2.

Frequency vs. Jet pipe deflection

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0 100 200 300 400 500 600 700 800 900 1000

Frequency (Hz)

Jet p

ipe

defle

ctio

n (m

eter

)

nozzle end

Fig. 5: Frequency vs. Displacement of the jet pipe nozzle end.

Table 1: Frequency response of jet pipe assembly (Flexure tube material: UNS 17300)

t_flex (µm) F_arm (N) δarm (m) δjet (m) Resonance (Hz)

45 0.9414 3.164E-03 5.374E-03 464.2

50 0.9414 2.203E-03 3.732E-03 497.7

75 0.9414 6.403E-04 1.073E-03 657.9

100 0.9414 6.664E-04 1.092E-03 756.5

Table 2: Frequency response of jet pipe assembly (Flexure tube material: AISI 316)

t_flex (µm) F_arm (N) δarm (m) δjet (m) Resonance (Hz)

45 0.9414 9.389E-02 1.600E-01 376.5

50 0.9414 7.333E-03 1.245E-02 403.7

75 0.9414 8.555E-04 1.433E-03 533.7

100 0.9414 1.824E-03 2.999E-03 613.6

2.3 Steady State Dynamic Analysis of Jet Pipe and Feedback Spring Assembly with Spool as a Lumped Mass The steady state analysis was carried out on jet pipe and feedback spring assembly with spool as a lumped mass, placed on feedback spring end.

F

F

Clamp

Armature

Connection pipe

Support spring

Flexure tube

Feedback spring assembly

Fig. 6: Solid and finite element model of feedback spring and jet pipe assembly.

The displacement at feedback spring end, where lumped mass was placed was plotted against the frequency shown in Fig.7. The natural frequency of the system was found to be 46.4 Hz.

Frequency vs. Spool displacement

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

0 200 400 600 800 1000

Frequency (Hz)

Spoo

l dis

plac

emen

t (m

eter

)

spool

Fig. 7: Frequency vs. spool displacement.

3. CONCLUSION The feedback spring assembly and flexure tube are the critical components in jet pipe assembly. The steady state dynamic analysis was conducted studied the response of the system on feedback spring assembly and jet pipe assembly. The critical parameters like thickness and material of flexure tube was studied for the frequency response. Finally the assembly of jet pipe assembly and feedback spring assembly with spool as a lumped mass was studied for frequency sweep. 4. REFERENCES 1. Maskrey R. H, Thayer WJ. A Brief History of Electrohydraulic Servomechanisms.

Transactions of the ASME, June 1978, volume 100, p. 110-116. 2. Merrit, H. E. ‘Hydraulic Ccontrol Systems’. J. Wiley & Sons Inc. 3. Blackburn, J. F., Reethof, G., Shearer, J.L. ‘Fluid power control’. M. I. T. Press. 4. Walters, R. ‘Hydraulic and Electrohydraulic Servo Systems’. Iliffe Books. 5. Watton, J. ‘Fluid Power Systems: Modeling, Simulation, Analog and Microcomputer

Control’. Prentice hall international (UK) Ltd. 6. Dushkes SZ, Cahn SL. Analysis of Some Hydraulic Components used in Regulators and

Servo Mechanisms. Transactions of the ASME, May 1952. p. 595-601. 7. Somashekhar SH, Singaperumal M, Krishnakumar R. Design and Optimization of Parameters

Affecting to Static Recovery Pressure in Two Stage Jet Pipe Servovalve. ASME Conference, ESDA 2002, paper No. ESDA2002/DES-020.

8. Thoma, JU. Fluid mechanics, Bond Graphs a Jet Pipe Servo Valves, Modeling and Simulation of Systems .IMACS, p. 77-81.

9. Henri P.D, Hollerbach J. M, Nahvi A. An analytical and experimental investigation of a jet pipe controlled electro pneumatic actuator. IEEE Transactions on robotics and automation. Vol. 14, No. 6, 1998, p.601-610.

10. Somashekhar. S. Hiremath, M. Singaperumal and R. Krishnakumar Stiffness Analysis of Feedback Spring and Flexure Tube of Jet pipe Electrohydraulic Servovalve using Finite element method. 2002 ASME Joint U.S.-European Fluids Engg. Div. conference, July 14-18, 2002, Canada. Paper No. FEDSM20002-31304.