Rasmus Löfstrand Grip (KTH)

Published: 23 December 2009

A mechanical model of an axial piston machine

A mechanical model of an axial piston-type machine with a so-called wobble plate and Z-shaft mechanism is presented. The overall aim is to design and construct an oil-free piston expander demonstrator as a first step to realizing an advanced and compact small-scale steam engine system. The benefits of a small steam engine are negligible NOx emissions (due to continuous, low-temperature combustion), no gearbox needed, fuel flexibility (e.g., can run on biofuel and solar), high part-load efficiency, and low noise. Piston expanders, compared with turbines or clearance-sealed rotary displacement machines, have higher mechanical losses but lower leakage losses, much better part-load efficiency, and for many applications a more favourable (i.e., lower) speed. A piston expander is thus feasible for directly propelling small systems in the vehicular power range. An axial piston machine with minimized contact pressures and sliding velocities, and with properly selected construction materials for steam/water lubrication, should enable completely oil-free operation. An oil-free piston machine also has potential for other applications, for example, as a refrigerant (e.g., CO2) expander in a low-temperature Rankine cycle or as a refrigerant compressor.


An analytical rigid-body kinematics and inverse dynamics model of the machine is presented. The kinematical analysis generates the resulting motion of the integral parts of the machine, fully parameterized. Inverse dynamics is applied when the system motion is completely known, and the method yields required external and internal forces and torques. The analytical model made use of the “Sophia” plug-in developed by Lesser for the simple derivation of rotational matrices relating different coordinate systems and for vector differentiation. Numerical solutions were computed in MATLAB. The results indicate a large load bearing in the conical contact surface between the mechanism’s wobble plate and engine block. The lateral force between piston and cylinder is small compared with that of a comparable machine with a conventional crank mechanism.


This study aims to predict contact loads and sliding velocities in the component interfaces. Such data are needed for bearing and component dimensioning and for selecting materials and coatings. Predicted contact loads together with contact geometries can also be used as input for tribological rig testing. Results from the model have been used to dimension the integral parts, bearings and materials of a physical demonstrator of the super-critical steam expander application as well as in component design and concept studies.

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