This paper describes a method of modelling time-varying flow in hydraulic pipelines which may be incorporated into time domain simulations of hydraulic systems operating with variable time steps. A previously reported finite element method is extended. New approximations to frequency-dependent friction for laminar and turbulent flow are presented. These are applicable to this finite element method as well as the method of characteristics and finite difference methods. Simulation results are compared against theory and excellent agreement is found.
Simulation of flow and pressure variations in fluid pipelines using finite difference and finite element models can give unrealistic results, corresponding to errors in natural frequencies. A novel finite element model of hydraulic pipelines has been developed, using an interlacing grid system. The grid spacing is non-uniform and is optimized, using a genetic algorithm, to make some or all of the undamped natural frequencies of the model as close as possible to exact theoretical ones for a uniform pipe with the extreme boundary conditions of either constant pressure or no flow. Inaccuracies in the highest natural frequencies may be acceptable because of the effect of frequency-dependent friction and limited system frequency response. The optimized model gives accurate results in time domain simulation, and it allows variable properties and a variable integration step to be readily accommodated.
The steel pushing V-belt continuously variable transmission (CVT) is now commercially available in the automobiles of a number of manufacturers but to date it has not led to a significant reduction in fuel consumption. To develop its full potential it is necessary to have a good mathematical model of the system. A number of models have been described in recent years but all make use of a Coulomb friction model for the shear connection between the belt and the pulleys. This paper proposes a friction model based on elastohydrodynamic theory. It is shown that there is good agreement between measured and calculated slip values for the transmission which justifies use of the model.
Flexible hoses used within a hydraulic circuit can reduce the levels of both pressure fluctuations and structural vibration. An important application is in automotive power steering where tubular inserts and restrictors are often used inside a hose to enhance the reduction of pressure ripple. The performance of a hose assembly in the frequency domain is usually specified by an impedance matrix relating pressure and flow ripple at the ends. However, these quantities are coupled to fluctuating axial tension and motion of the hose walls and it is desirable to have a 4 × 4 impedance matrix relating the complex amplitudes of all these quantities. A convenient method of experimentally measuring this matrix is presented. As well as allowing investigation of the main structural and fluid transmission from the hose assembly to the subsequent pipework, the 4 × 4 impedance matrix provides a way of obtaining the dynamic properties of hose walls under realistic conditions for use in further studies.
Hydraulic pipeline dynamics play an important role in many real systems, for example in Diesel fuel injection, anti-skid braking, under-sea oil production and hydraulic control in general. When investigating the behaviour of such systems by simulation it is necessary to have suitable numerical models for the line. An excessively complicated model wastes computing time, but an inadequate one fails to predict the behaviour satisfactorily. A first step in deciding upon a suitable model is to look at the relationship between the frequency content of transient operations in the system and the natural frequencies of the lines. Rapid transients can be initiated by such things as valve operation, actuators reaching the end of their travel and cavitation and air release. A second important criterion is the amount of damping in the lines caused by fluid friction. This may be steady or frequency dependent friction in laminar or turbulent flow. On the one hand, increasing the complexity of the friction model employed makes the computations more involved. On the other hand, friction may limit the amount of higher frequency motion and consequently make the computations simpler. This paper examines the requirements for line models under different circumstances, and how these requirements can be met. Discussions are illustrated with results on practical systems. NOMENCLATURE Fluid Power. Edited by T. Maeda. (c) 1993 E & FN Spon. ISBN 0 419 19100 3.
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