CFD Analysis of Gerotor Lubricating Pumps at High Speed: Geometric Features Influencing the Filling Capability

1. POLITECNICO DI TORINO - Italy Giorgio Altare – Massimo Rundo ASME/BATH 2015 Symposium on Fluid Power & Motion Control Chicago, October 12, 2015 CFD Analysis of Gerotor Lubricating Pumps at High Speed: Geometric Features Influencing the Filling Capability

2. Politecnico di Torino Dipartimento Energia Fluid Power Research Laboratory http://www.fprl.polito.it Summary • Model of the reference gerotor pump • Experimental validation • Simplified reference model • Influence of geometric parameters on filling: • Inlet pipe direction • Profile of the suction port • Height and diameter of the gears • Number of chambers 2 / 17

3. Politecnico di Torino Dipartimento Energia Fluid Power Research Laboratory http://www.fprl.polito.it Reference unit: gerotor lube pump Outlet port Inlet port Displacement = 19.8 cc/rev Diameter of the outer gear = 62.1 mm Gears thickness = 25 mm Delivery volume Double feeding Recess for axial balance Valve spool (blocked) shaft 3 / 17

4. Politecnico di Torino Dipartimento Energia Fluid Power Research Laboratory http://www.fprl.polito.it inlet volume tank portion pipe variable chambers delivery volume atmospheric pressure blind port CFD model (PumpLinx) About 600 000 cells outlet pressure axial leakage (3 layers) radial leakage (3 layers) Equilibrium Dissolved Gas Model 4 / 17 Tip clearance Tooth of the inner gear

5. Politecnico di Torino Dipartimento Energia Fluid Power Research Laboratory http://www.fprl.polito.it Test rig at FPRL P1 P2 P1, P2: miniature pressure transducers on the pump 5 / 17

6. Politecnico di Torino Dipartimento Energia Fluid Power Research Laboratory http://www.fprl.polito.it Tests as function of speed (open circuit) Constant delivery pressure (4 bar) Constant temperature (40 °C) Max error 7% Theoretical Config. R1 R2 1 no no 2 yes no 3 yes yes R2 R1 Good evaluation of the limit speed 6 / 17

7. Politecnico di Torino Dipartimento Energia Fluid Power Research Laboratory http://www.fprl.polito.it and as function of inlet pressure (closed circuit) Constant delivery pressure (4 bar) Constant temperature (40 °C) P1 0.06 bar 7 / 17 2%

8. Politecnico di Torino Dipartimento Energia Fluid Power Research Laboratory http://www.fprl.polito.it Reference simplified model • Same rotors used for model validation • Simplified geometry of the suction side • Rotors fed from one side only • Ideal timing • Leakages only between the gears Operating conditions • Speed = 5000 rpm • Delivery pressure = 4 bar • Temperature = 40 °C Flow rate = 50.34 L/min Volumetric efficiency = 50.8% (square cross section, radial position) 8 / 17

9. Politecnico di Torino Dipartimento Energia Fluid Power Research Laboratory http://www.fprl.polito.it Influence of inlet direction  0° : Tangential cocurrent direction of rotation 180° : Tangential countercurrent inlet volume 90°:axial Max improvement (from 51% to 59%) with axial inlet radial axial 9 / 17

10. Politecnico di Torino Dipartimento Energia Fluid Power Research Laboratory http://www.fprl.polito.it Comparison of axial velocity fields  = 90°  = 180° Direction of rotation Lower contraction coefficient 10 / 17 15 m/s 0 m/s Analyzed chamber

11. Politecnico di Torino Dipartimento Energia Fluid Power Research Laboratory http://www.fprl.polito.it Influence of inlet port profile   = 0°  Ideal timing  > 0°  Closing delay Radial inlet pipe Flow area of a chamber Volumetric efficiency 11 / 17

12. Politecnico di Torino Dipartimento Energia Fluid Power Research Laboratory http://www.fprl.polito.it Influence of pump displacement Ref. V1 V2 Thickness (mm) 25 16.67 12.5 Displacement (cc/rev) 19.8 13.2 9.9 Speed (rpm) 5000 7500 10000 Same theoretical flow rate (99 L/min) 12 / 17

13. Politecnico di Torino Dipartimento Energia Fluid Power Research Laboratory http://www.fprl.polito.it H12.5mm H25mm 10 000 rpm 5 000 rpm Axial velocity fields Low axial velocity regions 13 / 17

14. Politecnico di Torino Dipartimento Energia Fluid Power Research Laboratory http://www.fprl.polito.it Influence of external diameter (D) • Same thickness (H) • Same displacement • Ideal timing • Different eccentricity (e) The chamber flow area is always larger with higher external diameters  better filling 14 / 17 Greater frontal surface

15. Politecnico di Torino Dipartimento Energia Fluid Power Research Laboratory http://www.fprl.polito.it Influence of axial thickness (H) • Same diameter (D) • Same displacement • Ideal timing • Different eccentricity (e) 15 / 17

16. Politecnico di Torino Dipartimento Energia Fluid Power Research Laboratory http://www.fprl.polito.it Influence of the number of chambers (N) • Same diameter (D) • Same axial height (H) • Same displacement • Ideal timing • Different eccentricity (e) Reduction of N • Higher volume to be filled • Shorter extension of suction port • Larger flow area • Lower speed of outer gear • Lower internal radius of inner gear 16 / 17

17. Politecnico di Torino Dipartimento Energia Fluid Power Research Laboratory http://www.fprl.polito.it Conclusion • Good agreement with experimental results in terms of evaluation of limit speed for complete filling • Outcomes from simulations: • Axial inlet must be preferred (worst case with radial direction) • The shaped rim is equivalent to a 4 deg delay with radial rim • Only high delay angles are really effective • Low speed / high displacement better than high speed / low displ. • Height must be lowered by increasing the eccentricity • Small increment of the diameter not necessarily detrimental • Slight improvement with a few chambers 17 / 17

18. Fluid Power Research Laboratory www.fprl.polito.it Politecnico di Torino