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Effect of entrained air on dynamic characteristics of hydraulic servosystem with asymmetric linear motor

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Sommario

Si effettua una ricerca teorica sugli effetti dell'aria catturata sul comportamento dinamico di un servo-sistema idraulico. L'equazione non lineare del sistema, messa in forma adimensionale, viene linearizzata per ottenere la rigidità, il rapporto di smorzamento e la frequenza naturale in una forma adimensionale generalizzata che include gli effetti di restringimento, perdita, rapporto d'area, contenuto percentuale d'aria e il processo di cambiamento di stato dell'aria. Si sviluppa un nomogramma che aiuta a determinare rapidamente le proprietà dinamiche in maniera diretta senza alcun calcolo. L'analisi mostra che una diminuzione del rapporto d'area o un aumento nella quantità d'aria trascinata dentro il sistema riduce sia il rapporto di smorzamento sia la frequenza naturale. Un'eccessiva cattura d'aria può portare a instabilità. L'equazione non lineare viene anche risolta numericamente con un metodo di Runge-Kutta del quart'ordine che mostra un accordo con la soluzione lineare. La soluzione numerica mostra che anche il processo di cambiamento di stato dell'aria ha un'influenza significativa sul suddetto comportamento dinamico. Si prepara un diagramma di stabilità che collega due variabili di grande importanza, cioè il rapporto d'area e il contenuto percentuale d'aria, col restringimento come parametro, che facilita la stima del contenuto d'aria ammissibile per sistemi con un dato rapporto d'area, o alternativamente quando è vero-simile che il contenuto d'aria nell'olio sia elevato; con l'aiuto di questo grafico si possono scegliere valori opportuni di restringimento e/o rapporto d'area.

Summary

A theoretical investigation into the effect of entrained air on dynamic behaviour of hydraulic servosystem is made. The nonlinear system equation developed in dimensionless form is linearised to obtain stiffness, damping ratio and natural frequency in generalised dimensionless form that includes the effects of underlap, leakage, area ratio, per cent air content and the process of change of state of air. A nomogram is developed that helps in quick determination of the dynamic properties directly without any computation. The analysis shows that a decrease in area ratio or an increase in the amount of air entrained into the system reduces both damping ratio and natural frequency. An excessive air entrainment may even lead to instability. The original nonlinear system equation is also solved numerically by fourth order RK-method which shows qualitative agreement with the linear solution. The numerical solution shows that the process of change of state of air also has significant influence on the said dynamic behaviour. A stability chart is prepared relating two most important variables, viz. area ratio and per cent air content, with underlap as a parameter, that facilitates the estimation of allowable air content for a system with given area ratio, or alternatively where the air content in oil is likely to be high; with the help of this graph suitable of underlap and/or area ratio can be selected.

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Abbreviations

V i :

initial enclosed volume of fluid

A 1 :

piston end cylinder area

A 2 :

rod end cylinder area

x :

nett valve displacement

y :

output displacement

L :

cylinder length

d :

valve sleeve diameter

u s :

supply underlap

u t :

exhaust underlap

r :

reference step input

x p :

reference port length

P 1 :

piston end cylinder pressure

P s :

constant supply pressure

p :

fluid density

c d :

orifice discharge coefficient

β oil :

bulk modulus of oil

K L :

laminar leakage coefficient

{ie51-01}:

reference flow {ie51-02}

t :

time

M :

mass of the load

f b :

viscous load coefficient

P at :

atmospheric pressure

T :

reference time ({ie51-03})

∈:

percentage of air entrained (by volume)

n :

polytropic index

X :

dimensionless nett valve displacement (x/x p )

Y :

dimensionless output displacement (y/x p )

Z :

dimensionless reference step input (r/x p )

τ:

dimensionless time (t/T)

n :

dimensionless supply underlap (u s /x p )

v :

lap ratio (u t /u s )

k :

area ratio (A 2/A 1)

ø:

dimensionless leakage parameter ({ie51-04})

P 1 :

dimensionless piston end cylinder pressure (P 1/P s )

p at :

dimensionless atmospheric pressure (P at /P s )

p ℓ :

dimensionless load pressure (P L /P s )

β 0 :

dimensionless oil bulk modulus (β oil/P s )

θ:

dimensionless cylinder length (L/x p )

m :

dimensionless inertia load parameter (Mx p /A 1 P s T 2)

γ1 :

dimensionless viscous load parameter (f b x p /A 1 P s T)

β mix :

effective bulk modulus of air-oil mixture

λ:

compressibility parameter (β oil/{β}mix)

References

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  2. Goodwin A.B.,Power Hydraulics, B.I. Publication, 1964, pp. 222–225.

  3. Merritt H.E.,Hydraulic Control Systems, J. Wiley and Sons, Inc., 1967, pp. 14–18.

  4. Radhakrishnan P. andSundaram S.,Effect of compressibility due to entrained air on the performance of a hydraulic system, Proc. 7th AIMTDR Conf., June, 1976, pp. 285–288.

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Author information

Authors and Affiliations

  1. Mechanical Engineering Department, I.I.T., Kharagpur, on deputation from B.E. College, 711103, Howrah, India

    B. N. Datta (Research Scholar)

  2. Mechanical Engineering Department, I.I.T., Kharagpur, India

    Akella S. R. Murty (Professor)

  3. Mechanical Engineering Department, I.I.T., Kharagpur, India

    G. L. Sinha (Professor and Head)

Authors
  1. B. N. Datta
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  2. Akella S. R. Murty
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  3. G. L. Sinha
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Datta, B.N., Murty, A.S.R. & Sinha, G.L. Effect of entrained air on dynamic characteristics of hydraulic servosystem with asymmetric linear motor. Meccanica 21, 51–57 (1986). https://doi.org/10.1007/BF01556317

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  • DOI: https://doi.org/10.1007/BF01556317

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