Session: Pumps 1

Paper Number: 110716

110716 - Modelling of Pumps and Motors as Source Flow Ripple and Source Impedance 

The fluid borne noise characteristics of hydraulic pumps and motors are commonly represented in the frequency domain using a source flow ripple spectrum in parallel with a source impedance spectrum. This is equivalent to Norton’s theorem for electrical sources in which the source is represented as a current source in parallel with a resistance or impedance. However strictly speaking Norton’s theorem is only valid for linear time-invariant sources, and a number of non-linearities and time-varying impedances are present in hydraulic machines.

In this paper, the validity of the source flow ripple and source impedance representation will be considered for a number of types of hydraulic pump. Because there are no practical means for direct and precise measurement of flow ripple at its source inside a pump, this is done through high-fidelity modelling and simulation. It is well known that the source flow ripple of piston-type pumps and motors depends strongly on fluid compression during the commutation phase when a cylinder opens to high or low pressure. It is found that for such machines the flow to or from a cylinder can have a strong dependence on the loading impedance, and this suggests that the Norton equivalent flow ripple and source impedance may be somewhat system dependent.

There are some indirect experimental methods for determining the source flow ripple and source impedance, and these fall into two main types: the ‘secondary source’ method, and the ‘two loads’ family of methods. Both are based on the measurement of pressure ripple at multiple points along a pipeline and the application of wave theory to estimate system flow ripple from those measurements. The source flow ripple and source impedance are then determined mathematically from the system flow ripple and system pressure ripple. These methods were simulated in this investigation, but the system flow ripple was obtained directly from simulation, eliminating experimental errors.

It was found that the simulated ‘secondary source’ method yielded physically realistic source impedance characteristics which were system independent – the same source impedance characteristics were obtained for a number of different loading conditions. However the source flow ripple was found to vary slightly with loading conditions. This suggests that the Norton equivalent model is not strictly system independent; however as a first approximation it is sufficient as the variations in source flow ripple are relatively small.

In the ‘two loads’ methods, measurements are taken at two different loading conditions, resulting in two simultaneous equations which can be solved to determine the two unknowns – source flow ripple and source impedance – at each frequency. The simulated ‘two loads’ method yielded source impedance results with a lot of physically unrealistic variation that depended strongly on the loading conditions. This is shown to be because the solution of the two simultaneous equations requires the two unknowns to be identical in the two equations. Differences in the actual source flow ripple at the two loading conditions result in spurious source impedance results, and it is found that small variations in source flow ripple between the two loading conditions can result in large errors in the source impedance.

Overall it is found that the source flow ripple obtained by the ‘two loads’ method is as precise and realistic as that obtained by the ‘secondary source’ method, with some variation with loading conditions in both methods. However the source impedance obtained by the ‘two loads’ method is vastly inferior because of errors implicit in the assumption of a Norton equivalent model.

Presenting Author: Nigel Johnston University Of Bath

Presenting Author Biography: Nigel Johnston is a Reader (associate professor) at the University of Bath, UK. His research interests are in the modelling and measurement of fluid-borne noise, pump, valve and flow dynamics in hydraulic fluid power and fuel systems, and in the development of more efficient fluid power systems. He was instrumental in the development of the ISO 10767 and ISO 15086 families of international standards for hydraulic fluid-borne noise measurement and analysis.