# A NUMERICAL APPROACH FOR THE EVALUATION OF THE EFFECTS OF AIR RELEASE AND VAPOUR CAVITATION ON EFFECTIVE FLOW RATE OF AXIAL PISTON MACHINES

## Authors

• Andrea Vacca Industrial Engineering Department - University of Parma, Italy
• Richard Klop MAHA Fluid Power Lab., Purdue University, West Lafayette (IN), USA
• Monika Ivantysynova MAHA Fluid Power Lab., Purdue University, West Lafayette (IN), USA

## Keywords:

numerical models, cavitation, axial piston pumps, fluid properties

## Abstract

This work illustrates a numerical methodology for the description of effective flow rate of axial piston pumps and motors. The presented mathematical model is similar to classical lumped parameter approaches that are commonly used to simulate hydraulic units; however, this work uniquely utilises a mathematical formulation for compressible flows based on an original description of fluid density. Assuming the behaviour of typical mineral oil, the model can evaluate fluid density for all possible values of pressure while considering the ccurrence of gas cavitation (due to the release of air normally dissolved into liquid) below saturation pressure, and of vapour cavitation (due to liquid change of phase) below vapour pressure. The developed simulation model allows a description of several characteristics of the machine (i.e. instantaneous cylinder pressure and density, delivery and inlet flow rates, etc.) in its whole field of operation taking into account conditions of insufficient flow due to cavitation at the low pressure port. Tests were carried out on a swash plate type axial piston pump for open circuit applications to verify potentials of the developed numerical model. Experiments were conducted to test the pump under typical operating conditions as well as situations critical from the point of view of cavitation (high shaft speed, low values of inlet pressure), thus permitting the comparison between the prediction given by the developed model and experimental results over a wide range of data. Results highlight how fluid density changes can be used to characterize effective flow rate but also to justify, in particular operating conditions, the utilization of the approach for compressible flows. Results show that the developed model uniquely allows the calculation of effective flow rate through the pump at fair and extreme conditions, thus permitting the ability to predict limitations of the machine. Furthermore, the realistic prediction of pressures throughout the machine in these conditions leads the accurate predictions of pressure forces and of flow through the lubricating gaps that may be critical in other models.

## Author Biographies

### Andrea Vacca, Industrial Engineering Department - University of Parma, Italy

Andrea Vacca Born on June 2nd 1974, currently Andrea Vacca is Assistant Professor in Mechanical Enginnering at the University of Parma (Italy). At the same University, in 1999, he received his Master’s degree in Mechanical Engineering. In 2005 he became Ph. Doctor, at University of Florence, with a thesis in the field of Heat Transfer and Gas Turbine Blade Cooling Technology. His main research interests are the analysis and simulation of fluid power systems and components, such as valves, gear and piston pumps.

### Richard Klop, MAHA Fluid Power Lab., Purdue University, West Lafayette (IN), USA

Richard Klop Born on February 18th 1983 in Kalamazoo Michigan (USA). He received his B.S. Degree from Michigan State University, USA, with high honors in Mechanical Engineering in 2005. He received his MSE Degree at Purdue University, USA, in Agricultural and Biological Engineering in 2007. He is a Doctoral student at Purdue University in the area of acoustics and fluid power. His main research interest is noise control concepts for hydrostatic transmissions.

### Monika Ivantysynova, MAHA Fluid Power Lab., Purdue University, West Lafayette (IN), USA

Monika Ivantysynova Born on December 11th 1955 in Polenz (Germany). She received her MSc. Degree in Mechanical Engineering and her PhD. Degree in Fluid Power from the Slovak Technical University of Bratislava, Czechoslovakia. After 7 years in fluid power industry, she returned to university. In April 1996 she received a Professorship in fluid power & control at the University of Duisburg (Germany). From 1999 until August 2004 she was Professor of Mechatronic Systems at the Technical University of Hamburg-Harburg. Since August 2004 she is Professor in Mechanical Engineering and Agricultural and Biological Engineering at Purdue University, USA. She was approved as Maha named Professor in Fluid Power Systems and director of the Maha Fluid Power Research Center at Purdue University in November 2004. Her main research areas are energy saving actuator technology and model based optimization of displacement machines as well as modeling, simulation and testing of fluid power systems. Besides the book “Hydrostatic Pumps and Motors” published in German and English, she has published more than 90 papers in technical journals and at international conferences.

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