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INSTRUMENTATION PROBLEMS INVOLVED IN THE MEASUREMENT OF THE TRANSIENT RESPONSE OF AN HYDRAULIC SERVOMECHANISM

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T H E MEASUREMENT OF T H E T R A N S I E N T RESPONSE OF AN H Y D R A U L I C S E R V O M E C H A N I S M

R M DAVIES« and T H LAMBERT-1

A B S T R A C T

Research into the performance of a high pressure valve controlled jack type hydraulic servomechanism necessitated accurate dynamic measure- ments of displacements and pressures.

The response of the system was so fast that measurement of the violent motions resulting from step displacements posed severe instrumentation problems.

Inaccessibility of the ram chambers required investigation of strain gauge techniques for the measurement of high frequency pressure fluc- tuations.

Various techniques for overcoming these problems are critically discus- sed and the methods adopted are justified.

I N T R O D U C T I O N

A number of instrumentation problems were encountered in the investigation of the transient response of a high performance hydraulic servomechanism. The device, which is a valve controlled hydraulic jack used as a powered flying control in a fighter aircraft, is shown diagrammatically in Fig. 1. Input displacement signals (y) are fed to the valve spindle by the pilot's control column; the ram piston being anchored to the aircraft structure, and the output to the control surface (x) being

!, - Department of Mechanical Engineering, University College London, England Fig. 1. Diagram of experi-

mental apparatus.

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taken from the jack body. Ideally the transfer function of such a device is represented by a simple exponential lag but the effects of inertial load, compressibility and leakage together with non-linear effects such as Coulomb friction between the ram piston and chamber, and non-linear port area vs valve displacement and valve flow vs pressure difference characteristics modify the response considerably [1, 2].

In order to analyse the transient response of the jack a step displacement input is desirable. In practice a true step can never be achieved since it involves infinite velocities but an input approximating to a fast ramp is satisfactory provided that the rise time is small compared with the response time of the output. Even with the output of the jack slugged with high inertial loads and with the system running at

1500 lbf /'m 2

— half its rated supply pressure, the response time of the output was in the order of 10 ms and an input rise time of less than 1 ms was required in order to satisfactorily simulate a step input.

Consideration of the inertia forces associated with the mass of the moving parts of the valve and the inductive time constants of the electrical windings precluded the use of solenoid devices for obtaining the step and a mechanical spring-trigger arrangement as shown in Fig. 2 was adopted.

Compression spring | Step

amplitude

7Ό valve

Trigger Fig. 2. Trigge r mechanis m for initiatin g step inputs .

For the purpose of analysis it was required that accurate dynamic time records of the following parameters should be obtained:

(i) input displacement (y) (ii) output displacement (x)

(iii) ram chamber pressures (pj and p?).

D I S P L A C E M E N T M E A S U R E M E N T S

The experimental programme envisaged a series of tests in which the step displace­

ment amplitude would be varied between 0.025 in and 0.100 in with various inertial loads connected to the output of the jack. The general character of the input and

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output displacements can be seen from Fig. 3, and the following requirements for the displacement transducer can be enumerated

(1) It must be capable of measuring displacement up to 0.100 in, which occur at high velocities.

(2) It must be rugged since the input to the system is of a violent nature — similar in fact to a hammer blow.

(3) It must have good resolution as the oscillatory part of the transient is of small amplitude. This was of particular importance as the presence of Coulomb friction between the ram piston and chamber produced a peculiar "flat- topped" oscillation or stopping motion at low amplitudes (Fig. 3), (see also [3]).

Fig. 3 . T i m e r e c o r d s of i n p u t a n d o u t p u t t o s h o w g e n e r a l c h a r a c t e r . ( S t e p size 0 . 0 7 5 i n ; t i m e m a r k e r s v i s i b l e o n i n p u t t r a c e , 0 . 0 1 0 sec p e r i o d . )

(4) It must be accurately linear if measurements are to be made from the recorded transient.

(5) It must have a sufficiently high output to permit the low amplitude "tail" of the transient oscillation to be recorded with standard instruments.

Working on the principle that the simplest is often the best, consideration was initially given to a linear displacement transducer of the resistance potentiometer type. At that time the only commercially available transducer of that type, guaranteeing good linearity was one consisting of a static wire wound cylindrical element with a moving wiper. Some difficulty was experienced in attaching such transducers to the input and output of the system. The sensing finger of the trans­

ducer was a plain 1/16 in diameter spindle which was internally spring loaded towards one end of its travel. Clearly these light springs could not be expected to provide the high acceleration or deceleration required if the wiper was to follow the violent motion of the input displacement. Some form of rigid connection between the transducer and input member was required with all the associated alignment difficulties.

A record of output displacement using these transducers is shown in Fig. 4. The presence of the individual wires on the resistance bobbin can clearly be seen and it

Fig. 4. T i m e r e c o r d of o u t p u t s h o w i n g i n a d e q u a t e r e s o l u t i o n of w i r e w o u n d d i s p l a c e m e n t t r a n s d u c e r .

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is apparent that the general character of the oscillatory part of the transient response is completely masked by the inadequate resolution of the transducer.

In order to overcome the deficiency in resolution attempts were made to mecha­

nically amplify the signals using a lever system as shown in Fig. 5. The lever was

Fig. 5. D i a g r a m of l e v e r for m e ­ c h a n i c a l a m p l i f i c a t i o n of d i s p l a ­ c e m e n t s i g n a l s .

made from aluminium plate in the shape shown to give a high stiffness in the plane of motion. This was considered necessary in view of the impact nature of the displacement. The failure of this attempt is shown in Fig. 6 which is a record of the

Fig. 6. S p u r i o u s o s c i l l a t i o n s o f l e v e r o b s c u r i n g a s t e p i n p u t .

input displacement. Significant oscillations of the lever at its natural frequency are evident and the need to guard against this spurious response both in the design and application of transducers for this type of motion is clearly important.

The discouraging results obtained with d.c. resistive transducers led to conside­

ration of a.c. systems. These can be conveniently divided into amplitude and frequency modulated systems. The former category can generally be further subdivided into variable capacity devices which are only suitable for small displa­

cements, and variable inductance devices which are more common and which generally take the form of differential transformers [4}. These are commercially available for both rotary and linear motion but generally work with carrier frequencies between 50 c/s and a few Kc/s, making them inadequate for the accurate measurement of high speed phenomenon. The carrier filter after demodu­

lation must be very carefully designed if it is not to affect signal response and even if demodulation is dispensed with an accurate envelope can rarely be drawn through only a few widely spaced peaks of the carrier.

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Attempts were therefore made to produce a differential transformer type of transducer which would work satisfactorily with carrier frequencies in the region of 100 Kc/s. Initially a soft iron core was used but considerable distortion of the output carrier waveform prompted the replacement of this with a ferrite rod. A record of output displacement using this type of transducer is shown in Fig. 7.

Fig. 7. T i m e r e c o r d s of m o d u l a t e d i n p u t a n d o u t p u t d i s p l a c e m e n t t r a c e s f r o m d i f f e r e n t i a l t r a n s f o r m e r t r a n s d u c e r s h o w i n g p h a s e i n a c c u r a c y .

Demodulation and filtering of the signal has not been carried out and the envelope represents the output displacement. Examination of the output trace shows that the envelope is not symmetrical and that the upper and lower edges show a phase displacement relative to one another.

It is easily shown that such an effect may occur at lower carrier frequencies due to velocity effects (it was in fact observed in early experiments using a carrier frequency of 2 Kc/s). Its occurrence with a carrier of 100 Kc/s, however, is surprising, but at this stage it was felt that the method was creating more problems than it solved and attention was given to other alternatives.

Consideration was also given to the use of frequency modulated systems. Generally these use carrier frequencies in the order of several hundred kilocycles per second and should therefore be capable of measuring fast transients. Proximity type trans­

ducers are very convenient to use but for this application showed some disadvantages.

The sensitivity of these gauges is greatest when the mean gap is small, but conver­

sely linearity is best when the mean gap is large compared with the variation. The mean gap length required for good linearity in this instance was so great that the sensitivity would have been too low to permit accurate measurement of the small amplitude oscillatory part of the transient. This type of transducer is most suitable for the measurement of small total displacements and was successfully employed to check the rigidity of the anchor point of the ram piston rod (see Fig. 1).

Other forms of variable inductance transducers using frequency modulation techniques which do not suffer from these disadvantages are available. These have a sensing finger which must be rigidly attached to the moving part and show good linearity over the whole of the travel. Apart from the disadvantages associated with the more complex electronic circuitry there is no reason why these gauges should not be successful in this type of application. The only factor that prevented their use in this instance was delivery time.

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At this stage in the investigation attention was again given to the simple resistive type of element. The major defect of the previous application of this type of transducer had been the poor resolution associated with the wire wound resistive element. Infinite resolution can be obtained with a carbon track but at the time of the investigation straight carbon tracks with guaranteed linearity were not readily available. The fact that the required displacement was small compared with the total length of track encouraged the authors to investigate the linearity of low cost carbon track elements intended for use as pre-set resistors in electronic circuits.

A number of these were tested and it was found that the linearity was remarkably good over the range of displacements required (i.e. 0—0.100 in). The remaining problem therefore was the type of wiper to be used. Experience gained with the lever used for mechanical amplification emphasised the need for rigid mounting if spurious oscillations of the measuring system were to be avoided. The system found to be most satisfactory is shown in Fig. 8. The wiping element consists of a silver

plated relay contact rigidly mounted in a paxalin block which is directly attached to the part whose displacement is to be measured. The contact pressure between the track and wiper is obtained by adjusting the fixed track in contact with the wiper. This simple arrangement was found to give very satisfactory results and several hundreds of transient tests were performed using these transducers to measure input and output displacements (see Fig. 3). Due to the rather crude method of obtaining contact pressure between the wiper and track and also due to the high velocities involved, some track failures were experienced. These took the form of local surface fatigue of the track and were evidenced by spikes or gaps appearing on the oscillograph traces. The ease and low cost of track replacement made occasional failures quite acceptable.

body

Fig. 8. D i a g r a m of l i n e a r c a r b o n t r a c k d i s p l a c e m e n t t r a n s d u c e r .

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P R E S S U R E M E A S U R E M E N T S

Measurements of the rapid pressure fluctuations occurring in the ram chambers were required in order to support and verify the theoretical analysis of the jack perfor­

mance. In order to reduce the effects of compressibility and dilation in the connec­

tions between the valve and jack, these bodies of the members were incorporated in a single aluminium alloy die casting which included all the communicating oil ways.

Fortunately access to one side of the ram chamber was available through a plugged end to an oil gallery and attention was directed towards measuring the pressure fluctuations by means of a commerical pressure transducer fitted at this point.

The two essential requirements of such a transducer were that it should have a small internal volume and a high frequency response in order to be able to reproduce faithfully the rapid fluctuations that were expected to occur in the chambers. Since the pressures in the ram chambers approximate under quiescent conditions to one half of the supply pressure and dynamic fluctuations occur about this relatively high mean value it was also desirable that the transducer should be of the high output type.

Three types of transducer were readily available, the Bourdon tube type in which the deflection of the free end of the tube was used to move a wiper across a resistive track, the variable inductance type, and the unbonded strain gauge type.

The high internal volume and inertia of the first type compelled its rejection on the grounds of inadequate frequency response. The variable inductance type appeared to be quite promising but experience with this type of displacement transducer suggested that only frequency modulated systems with the associated electronic complexity could be expected to give reliable results. Leaving these aside, therefore, experiments were carried out using unbonded strain gauge transducers. These had a perfectly adequate frequency response but gave a relatively low output requiring preamplification (a gain of 250—500 times) before the signal could be fed to a recording oscilloscope.

The problem of obtaining pressure records from the other ram chamber was more severe. No access point was available and the low factor of safety associated with military aircraft components and the notch sensitivity of the aluminium alloy made any attempt to gain access by drilling the casting a hazardous undertaking.

These very factors, however, which made tampering with the casting undesirable suggested an alternative solution. Simple calculations showed that the hoop strains occurring at the outer diameter of the jack cylinder could be measured using high resistance electrical strain gauges fixed to the outside of the jack body. The question remained as to whether these strains would be a faithful measure of the pressures inside the chambers. Under dynamic conditions the pressures in each half of the jack cylinder will be different and bending effects must be present in the cylinder walls.

If these effects altered the hoop strains at the location of the gauges cross-coupling between the two signals would occur and the strain gauge outputs could not be used to monitor the chamber pressures. St. Vernant showed that the effects of

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Fig. 9. I d e n t i c a l t i m e r e c o r d s of p r e s s u r e m e a s u r e d u s i n g c o m m e r c i a l p r e s s u r e t r a n s d u c e r a n d s t r a i n g a u g e m o u n t e d h o o p - w i s e o n j a c k b o d y .

discontinuities in a loading system are quite localised and it was hoped that by fixing the gauges one cylindrical diameter away from the piston in the axial direction this cross-talk could be eliminated. The justification for this is shown in Fig. 9, which compares the outputs from the pressure transducer and the appropriate strain gauge.

In fact records from the two taken on transparent film could be overlaid to give virtually complete co-incidence.

The hoop-wise strain gauges posed the same problem as the commercial pressure transducer in that in each case the signal outputs were of the order of a few hundred microvolts and required appreciable preamplification before they could be fed to the recording oscilloscope. As measurements of the steady state pressure values were also required these preamplifiers had to be d. c. coupled, but no high degree of long term d. c. level stability was necessary in view of the nature of the experimental tests. Long term gain stabilty was more necessary in order to avoid frequent, calibration. A commercial thermionic preamplifier having excellent long-term freedom from drift and high gain stability was initially tried, but the hight noise level associated with this device (approximately 60 //V referred to input) completely masked the more interesting characteristics of the transient. As most of this noise appeared to be shot noise associated with the thermionic valves a simple long-tailed pair amplifier using Silicon transistors [5J was built. The differential input of this device gave the additional advantage of a measure of in-phase rejection and allevia­

ted the screening requirements for the strain gauge bridges and leads. These preamplifiers proved to be completely satisfactory, the only significant source of noise being traced to the reference resistors in the strain gauge bridge which had to be selected to give a completely clean trace. The long term d. c. stability of the amplifiers was considerably improved by mounting them in blocks of expanded polystyrene.

C O N C L U S I O N S

The writers feel that the main conclusion to be drawn from this work is the value of the simple approach. In the case of the displacement measurements a good deal of time and effort was wasted in trying to develop a. c. transducers for measuring fast transients while the much simpler d. c. system was capable of giving satisfactory results. It is not suggested that a properly designed frequency modulated system is not capable of giving equally good results but it is questionable whether the

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Fig. 10. Complet e transien t re › cor d usin g experimentall y evol›

ved instrumentation .

advantages of such a system justify the additional complexity, particularly with the advent of metal oxide film resistors which should enable infinite resolution trans­

ducers to be produced with a high degree of linearity over their whole displacement range. The results shown in Fig. 6 clearly indicate the care needed in the design and application of transducers for the meassurement of "shock" or impact type motions if spurious results are to be avoided.

The value of simplicity is further demonstrated in the section on pressure measure­

ment. The simple solutions finally adopted for the pressure transducers and preamp­

lifiers are shown to be capable of giving results equal to and in some cases superior to those from more sophisticated systems.

The authors feel a high degree of confidence in the results after the above instru­

mentation investigation and a typical composite transient is shown in Fig. 10. A large number of transients of this system were recorded in which parameters were varied over a wide range and the results with the instrumentation finally adopted were found to be accurate and repeatable.

R E F E R E N C E S

1. Lambert , ˙ an d Davies , R M , Investigatio n of th e respons e of a n hydrauli c servo - mechanis m wit h inertia l load . / l.icch Eng. Sci. 5 ( 1 9 6 3 ) 281.

2. Davies , R M an d Lambert , ˙ , Transien t respons e of a n hydrauli c servomechanis m flexibl y connecte d t o a n inertia l load . / Mech Eng. Sci. 6 (1964) 32.

3. Davies , R M an d Lambert , ˙ , Transien t oscillatio n of t w o degre e of freedo m system s wit h Coulom b damping . Proceedings of Eleventh International Congress of Appl.

Mechanics. Springe r Verlag , in press .

4. D i g h t o n , D T R, A differentia l transforme r gaug e an d amplifie r for measurin g smal l smal l displacements . Electronic Engineering. Fe b ( 1 9 5 3 ) .

5. Mullar d Referenc e Manua l of Transisto r Circuits , p . 271. 1st ed. , I960 .

Ábra

Fig. 7.  T i m e  r e c o r d s of  m o d u l a t e d  i n p u t  a n d  o u t p u t  d i s p l a c e m e n t  t r a c e s  f r o m  d i f f e r e n t i a l  t r a n s f o r m e r  t r a n s d u c e r  s h o w i n g  p h a s e  i n a c c u r a c y
Fig. 8.  D i a g r a m of  l i n e a r  c a r b o n  t r a c k  d i s p l a c e m e n t  t r a n s d u c e r
Fig. 9.  I d e n t i c a l  t i m e  r e c o r d s of  p r e s s u r e  m e a s u r e d  u s i n g  c o m m e r c i a l  p r e s s u r e  t r a n s d u c e r  a n d  s t r a i n  g a u g e  m o u n t e d  h o o p - w i s e  o n  j a c k  b o d y
Fig. 10.  Complet e transien t re › cor d usin g experimentall y evol›

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