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

Abstract

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.