How To Simulate A Hydrostatic Displacement Unit

Transcription

1 O&P Simulation of hydrostatic displacement units 1 Using modern CAE tools to simulate hydrostatic displacement units Dipl.-Ing. Michael Deeken Institute of Fluid Power Drives and Controls (IFAS) Steinbachstrasse 53, Aachen, Germany Phone: / , Fax: / Head: Prof. Dr.-Ing. H. Murrenhoff post@ifas.rwth-aachen.de Abstract Modern CAE tools are currently being used to simulate hydrostatic displacement units within the framework of a research project being carried out at the Institute of Fluid Power Drives and Controls (IFAS) with the financial backing of the German Industrial Research Foundation (SiF) and a syndicate of companies. One of the focal points of this research project is the user-friendly application of the enhanced PUMA program, whereby the simulation includes an investigation of the tribological contacts in a hydrostatic displacement unit and an analysis of the pulsations. Simulation, i.e. calculation of a tribological contact's dynamic performance, is preceded by a complex modelling process. The model, which includes installation of a differential system, is produced by means of the MSC.ADAMS CAE tool. The Institute's own menu and dialog structures were implemented in MSC.ADAMS to facilitate parameterization of the model. Design engineering data can now be entered using an interactive dialog. The simulation model is generated automatically in a subsequent stage. This procedure is available for the tribological piston/cylinder, slipper/swash plate, piston drum/control plate and piston/slipper contacts in an axial piston machine. A complete moving apparatus can also be modelled in order to analyse pulsations. The hydraulic part of the simulation model is linked to the mechanical part by means of simulation coupling with the DSHplus program.

2 O&P Simulation of hydrostatic displacement units 2 Introduction In recent years, the numerical calculation of tribological contacts and pulsations in hydrostatic displacement units has become increasingly significant for the design engineering of such machines. Different approaches can be found in [2], [3], [5-7] and [8]. As the development of simulation programs progresses to Windows-based systems, the software maintenance and updating of an independent program becomes very time-consuming and expensive. In this respect, the further development of specialised simulation programs offers a means of incorporating the calculation of tribological contacts into tools that are already available on the market. Widely used throughout the automotive sector, the MSC.ADAMS program offers a solution in the field of multi-body simulation. One of the reasons for choosing this program was that it provides a means of creating user-defined interactive dialogs and menus. Sponsored by the German Industrial Research Foundation (SiF) and a syndicate of companies, a user-friendly tool for calculation of tribological contacts in hydrostatic displacement units is currently being developed at the Institute of Fluid Power Drives and Controls (IFAS) within the framework of a research project. The focal points of this project include the development of an interface to the design engineer, which is usually presented in the form of a menu structure. The research project is aiming to automatically create simulation models from entered parameters in order to analyse the various contacts, e.g. the contacts between slipper and swash plate and between piston drum and control plate. Examples of the created simulation models are shown in Figure 1 (control plate / piston drum) and Figure 2 (piston / bushing).

3 O&P Simulation of hydrostatic displacement units 3 Figure 1: Tribological contact between piston drum and control plate Figure 2: Tribological contact between piston and bushing Implementation of the PUMA program in MSC.ADAMS The PUMA program (for pump and motor design) was presented in [7]. It is a Delphibased independent program version. This section describes the version created for the MSC.ADAMS multi-body simulation program. The simulation tool offers a means of creating user-defined menu structures, which generate the required functions, e.g. automatic creation of simulation models. The structure is illustrated in Figure 3. Starting from a logic operation in the main menu (PUMA), 5 possible options appear as sub-items. These include the "piston/bushing", "slipper/swash plate", "piston/slipper" and "piston drum/control plate" contacts. The "axial piston unit" subitem permits generation of a complete moving apparatus, which can be used to simulate pulsations. The third level of the menu structure is concerned with model parameterization. This is where design engineering parameters for the driving mechanism can be entered, e.g. pitch diameter, piston diameter etc., as well as the surface parameters. The tribological contacts take the surface roughness and the orientation of the asperities of roughness into consideration. These parameters influence the build-up of pressure in the lubricating gap. Furthermore, the boundary conditions for the temperature may also be specified on this level. The actual tribological contacts are generated in the "tribological contact" sub-item.

4 O&P Simulation of hydrostatic displacement units 4 create model piston/bushing surface parameters PUMA slipper/ swash plate piston/slipper tribological parameters piston drum/ control plate axial piston unit Figure 3: Menu structure Figure 4 shows the procedure, using the contact between slipper and swash plate as an example. The tribological force is exerted between the slipper and the swash plate. It is calculated from the displacement and velocity input values, where the Reynolds' equation is solved iteratively with integration of the corresponding forces from the calculated pressure field. All of the other model bodies are linked together by joints and friction. This means, for example, that piston and bushing are joined together by a cylindrical joint that permits two degrees of freedom of movement. The computational core is embedded by means of a dynamic link library (dll). This library contains the functions required to calculate the tribological force, whereby the functions in the library are called up by the tribological force in each of the simulation stages to be calculated.

5 O&P Simulation of hydrostatic displacement units 5 Reibung Reibung Gleitschuh Druckkraft Entlastung Buchse Kolben F Tribologie Translation: Druckkraft = Force of pressure Reibung = Friction Buchse = Bushing Kolben = Piston Tribologie = Tribology Gleitschuh = Slipper Entlastung = Relief Figure 4: Principle of a tribological contact Translations: Druckverteilung im Spalt = Distribution of pressure in the gap Äußere Kräfte = External forces Mehrkörpersimulation mit MSC.ADAMS = Multi-body simulation with MSC.ADAMS Verluste = Losses Figure 5: Simulation structure

6 O&P Simulation of hydrostatic displacement units 6 The procedure is shown in Figure 5. The multi-body simulation program solves the equations required to calculate the forces and movement of solid bodies in a dynamic simulation. The distribution of pressure in the gap is calculated from the displacement, e.g. piston in the bushing [1]. The functions in the library are used for this. The resulting pressure distribution is used to calculate the forces in the gap. If the calculated forces and displacement values are within certain error tolerances, the simulation enters a new stage. An automatically generated model and the associated interactive dialog are shown in Figure 6. Figure 6: Model parameterization The potential offered by the use of modern CAE tools can be demonstrated with reference to two simulation examples. These focus on the contact between piston drum and control plate and the contact between piston and bushing respectively.

7 O&P Simulation of hydrostatic displacement units 7 Simulation examples for piston drum / control plate The tribological contact between the piston drum and the control plate constitutes a hydrodynamic bearing. The purpose of this bearing is to absorb the tilting moment of the piston drum with reference to a level contact. The tilting moment on the piston drum is produced by the piston forces acting on the cylinder bottom. The force resulting from the piston forces is located off centre on a figure-eight trajectory. The torque generated here causes the piston drum to tilt over around the knuckle point, which is located at the point where the shaft axis intersects the line joining the ball joint centre points. The effects of the tilting movement on the gap between piston drum and control plate are shown in Figure 7. F An v y τ v τ p τ p τ v F Ab Zylinder Kolbentrommel v y p n p 1 p n. ϕ x z x y Niere des Steuerspiegels Steuerspiegel Translation: Zylinder = Cylinder Kolbentrommel = Piston drum Niere des Steuerspiegels = Kidney-shaped opening in the control plate Steuerspiegel = Control plate Figure 7: Piston drum

8 O&P Simulation of hydrostatic displacement units 8 The tilting movement about the knuckle point produces a velocity in the lubricating gap, as shown on the right-hand side of Figure 7. This movement and the reduction from high pressure to housing pressure give rise to various types of fluid friction. The velocity causes transverse stresses in the fluid film. The pressure flow also generates fluid friction which takes a semi-circular form. The build-up of pressure in the convergent lubricating gap produced by the tilting movement of the piston drum is evident in the lower section of Figure 7. This pressure build-up generates the reaction forces to the pressure forces in the cylinders, whereby the pressure is built up as a result of the tilting movement about the x and y-axes, as well as the trapped oil effect produced by the movement of the piston drum along the z-axis. This displacement is shown in Figure 8. The displacement is applied over a revolution. It is evident that piston is controlled into the high-pressure zone. The piston drum is pushed in a negative direction along the z-axis, i.e. against the control plate. Only then does the counter-pressure build up in the lubricating gap as a result of trapped oil effects. If the piston is controlled out of the high-pressure zone, this increases the gap between piston drum and control plate. Attention must be given to the fact that the displacement shown in the figure relates to a clearance between piston drum and control plate, which is located on the rotation axis Piston drum displacement Displacement 300 bar Displacement 200 bar Travel [mm] Angle [ ] Figure 8: Piston drum displacement

9 O&P Simulation of hydrostatic displacement units 9 The relationship between displacement and balancing force is also evident in Figure 9. The simulation model comprises the piston forces, which exert a force on the cylinder bottom as a function of the angle of rotation. The four pistons controlled into the high-pressure zone are shown in kn. They achieve a force of around 3 kn for this model. A spring presses the piston drum against the control plate. This is intended to prevent the piston drum lifting away from the control plate any further. Figure 9: Simulation results Example of simulation for piston/bushing The hydrodynamic bearing between piston and bushing absorbs the transverse forces produced as a result of the swash plate construction [4]. The transverse forces acting on the centre of the ball joint cause the piston to tilt. The tilting movement gives rise to a convergent or divergent lubricating gap like that produced at the contact between control plate and piston drum. The nature of the gap depends on the direction of movement and the operating mode. The displacement produced from the lubricating gap is shown in Figure 10 and the transverse forces are shown in Figure 11.

10 O&P Simulation of hydrostatic displacement units 10 Verlagerungen Kolben Querkräfte Kolben Weg [mm] Verlagerung in x-richtung Verlagerung in y-richtung Kraft [kn] 3.00 Querkraft x-richtung Querkraft in y-richtung Winkel [ ] Winkel [ ] Translations: Translations: Verlagerung Kolben = displacement piston Querkräfte Kolben = transverse force piston Verlagerung in x-richtung = displacement along the x-axis Querkraft in x-richtung = transverse force along x-axis Verlagerung in y-richtung = displacement along the y-axis Querkraft in y-richtung = transverse force along y-axis Weg = displacement Kraft = force Winkel = angle Winkel = angle Figure 10: Displacement Figure 11: Transverse forces The frictional force of the piston and the restoring moments are shown in Figure 12 and Figure 13 Kolbenreibkraft Kolbenreibkraft 0.15 Reibkraft [kn] Winkel [ ] Translations: Kolbenreibkraft = fritional force piston Reibkraft = fritional force Winkel = angle Figure 12: Frictional force of the piston Drehmoment [Nm] Rückstellmomente Kolben Drehmoment um x-achse Drehmoment um y-achse Winkel [ ] Translations: Rückstellmomente Kolben = restoring torque piston Drehmoment um x-achse = torque about the x-axis Drehmoment um y-achse = torque about the y-axis Drehmoment = Torque

11 O&P Simulation of hydrostatic displacement units 11 Figure 13: Restoring moments Summary This article describes a means of calculating complex tribological contacts using a conventional multi-body simulation tool. Modelling can be simplified and automated using the integration of user-defined interactive dialogs and menus, which are capable of performing specific functions. Two simulation examples were described with reference to the contact between the piston drum and the control plate, and between the piston and the bushing. The work described in this article was carried out within the framework of a research project at the Institute of Fluid Power Drives and Controls (IFAS) under the leadership of Prof. Dr.-Ing. H. Murrenhoff. The project was sponsored by the German Industrial Research Foundation (SiF). We would like to take this opportunity to thank the SiF and the participating companies for their support. Bibliography: [1] M.Deeken Simulation der tribologischen Kontakte in einer Axialkolbenmaschine [Simulation of the tribological contacts in an axial piston machine], O+P 11-2/2003 pages [2] A. Kleist Berechnung von Dicht- und Lagerfugen in Hydrostatischen Maschinen [Calculation of sealing and bearing joints in hydrostatic machines], Dissertation RWTH Aachen 2002 [3] M. Liu Dynamisches Verhalten hydrostatischer Axialkolbengetriebe Schriftenreihe des Instituts für Konstruktionstechnik Ruhr [Dynamic performance of hydrostatic axial piston transmissions series of publications issued by the Ruhr Institute for Design Engineering] Bochum University Volume [4] H. Murrenhoff Grundlagen der Fluidtechnik Teil1: Hydraulik

12 O&P Simulation of hydrostatic displacement units 12 [Fundamental principles of fluid technology Part 1: Hydraulics], Script for lecture, RWTH Aachen 2001 [5] L. Olems Ein Beitrag zur Bestimmung des Temperaturverhaltens der Kolben-Zylinder Baugruppe von Axialkolbenmaschinen in Schrägscheibenbauweise [Article on determination of the thermal characteristic of the piston/cylinder assembly in swash-plate type axial piston machines] Dissertation TU Hamburg-Harburg 2001 [6] H. Rahnejat Multi-Body Dynamics Vehicles, Machines and Mechanisms, ISBN ] [7] G. Sanchen Auslegung von Axialkolbenpumpen in Schrägscheibenbauweise mit Hilfe der numerischen Simulation [Using numerical simulation to design swash-plate type axial piston pumps], Dissertation RWTH Aachen 2003 [8] U. Wieczorek Ein Simulationsmodell zur Beschreibung der Spaltströmungen in Axialkolbenmaschinen der Schrägscheibenbauart [A simulation model to describe the gap flow in swash-plate type axial piston machines], Progress report VDI Series 7 No