Abstract

Gerotors are inexpensive positive displacement pumps commonly used in hydrostatic transmissions, fuel injection, and automotive lubrication systems. In these pumps, leakages at the tooth tips of the gears are the major source of volumetric losses that prevents their usage in high pressure applications. However, due to the curvature of typical gear profiles, the flow relations available in the literature do not accurately model this leakage flow. In this paper, a novel tooth tip leakage flow model is developed based on dimensional analysis. Key geometric and flow parameters are identified and a set of computational fluid dynamics (CFD) simulations are conducted on the tooth tip geometry to establish the flow relationship. This relationship is first verified with the analytical formulation derived from Reynolds equation. Then, an experimental setup is designed to reproduce the flow conditions at the tooth tip of gerotors. Experiments are conducted for a range of geometric and flow parameters, and results from the experiments are used to validate the proposed leakage flow model. The tooth tip leakage flow model developed and validated in this work is valuable for pump designers in determining the impact of gear geometry and clearances on volumetric performance of the pump. Moreover, the model can be readily used in any lumped parameter based simulation tool permitting a fast and accurate prediction of the tooth tip leakage flow and hence the volumetric efficiency of the unit.

References

References
1.
Bonandrini
,
G.
,
Mimmi
,
G.
, and
Rottenbacher
,
C.
,
2009
, “
Theoretical Analysis of Internal Epitrochoidal and Hypotrochoidal Machines
,”
Proc. Inst. Mech. Eng., Part C
,
223
(
6
), pp.
1469
1480
.10.1243/09544062JMES1163
2.
Karamooz Ravari
,
M. R.
,
Forouzan
,
M. R.
, and
Moosavi
,
H.
,
2012
, “
Flow Irregularity and Wear Optimization in Epitrochoidal Gerotor Pumps
,”
Meccanica
,
47
(
4
), pp.
917
928
.10.1007/s11012-011-9473-6
3.
Mancò
,
S.
,
Nervegna
,
N.
,
Rundo
,
M.
,
Armenio
,
G.
,
Pachetti
,
C.
, and
Trichilo
,
R.
,
1998
, “
Gerotor Lubricating Oil Pump for IC Engines
,”
SAE Trans.
,
107
(
3
), pp.
2267
2283
. www.jstor.org/stable/44736689
4.
Schweiger
,
W.
,
Schoefmann
,
W.
, and
Vacca
,
A.
,
2011
, “
Gerotor Pumps for Automotive Drivetrain Applications: A Multi Domain Simulation Approach
,”
SAE Int. J. Passenger Cars—Mech. Syst.
,
4
(
3
), pp.
1358
2272
.10.4271/2011-01-2272
5.
Gamez-Montero
,
P. J.
, and
Codina
,
E.
,
2007
, “
Flow Characteristics of a Trochoidal-Gear Pump Using Bond Graphs and Experimental Measurement—Part 2
,”
Proc. Inst. Mech. Eng., Part I
,
221
(
3
), pp.
347
363
.10.1243/09596518JSCE251
6.
Pellegri
,
M.
, and
Vacca
,
A.
,
2017
, “
Numerical Simulation of Gerotor Pumps Considering Rotor Micro-Motions
,”
Meccanica
,
52
(
8
), pp.
1851
1870
.10.1007/s11012-016-0536-6
7.
Pellegri
,
M.
,
Vacca
,
A.
,
Devendran
,
R. S.
,
Dautry
,
E.
, and
Ginsberg
,
B.
,
2016
, “
A Lumped Parameter Approach for GEROTOR Pumps: Model Formulation and Experimental Validation
,”
Tenth International Fluid Power Conference
, Dresden, Germany, Mar. 8–10.https://pdfs.semanticscholar.org/2588/8fb13178c9401375e3d6a6f5fe1f179c6c32.pdf
8.
Pellegri
,
M.
,
Vacca
,
A.
,
Frosina
,
E.
,
Buono
,
D.
, and
Senatore
,
A.
,
2016
, “
Numerical Analysis and Experimental Validation of Gerotor Pumps: A Comparison Between a Lumped Parameter and a Computational Fluid Dynamics-Based Approach
,”
Inst. Mech. Eng., Part C
,
231
(
23
), pp.
4413
4430
.
9.
OpenCFD
, 2020, “
OpenFOAM Programmer's Guide
,” OpenCFD.
10.
ANSYS
, 2020, “
ANSYS® Fluent
,” Release 19.1, ANSYS Inc., Canonsburg, PA.
11.
ANSYS
, 2020, “
ANSYS® CFX, Release 15.0
,” ANSYS Inc., Canonsburg, PA.
12.
Simerics
, 2020, “
PumpLinx | Simerics [Online]
,” Bellevue, WA, accessed Feb. 18, 2020, http://www.simerics.com/pumplinx/
13.
Gamez-Montero
,
P. J.
,
Castilla
,
R.
,
Del Campo
,
D.
,
Ertürk
,
N.
,
Raush
,
G.
, and
Codina
,
E.
,
2012
, “
Influence of the Interteeth Clearances on the Flow Ripple in a Gerotor Pump for Engine Lubrication
,”
Proc. Inst. Mech. Eng., Part D
,
226
(
7
), pp.
930
942
.10.1177/0954407011431545
14.
Castilla
,
R.
,
Gamez-Montero
,
P. J.
,
Raush
,
G.
, and
Codina
,
E.
,
2017
, “
Method for Fluid Flow Simulation of a Gerotor Pump Using OpenFOAM
,”
ASME J. Fluids Eng.
,
139
(
11
), p.
111101
.10.1115/1.4037060
15.
Altare
,
G.
, and
Rundo
,
M.
,
2016
, “
Computational Fluid Dynamics Analysis of Gerotor Lubricating Pumps at High-Speed: Geometric Features Influencing the Filling Capability
,”
ASME J. Fluids Eng.
,
138
(
11
), p.
111101
.10.1115/1.4033675
16.
Bae
,
J. H.
,
Kwak
,
H. S.
,
San
,
S.
, and
Kim
,
C.
,
2016
, “
Design and CFD Analysis of Gerotor With Multiple Profiles (Ellipse–Involute–Ellipse Type and 3-Ellipses Type) Using Rotation and Translation Algorithm
,”
Proc. Inst. Mech. Eng., Part C
,
230
(
5
), pp.
804
823
.10.1177/0954406215583888
17.
Pellegri
,
M.
,
2018
, “
A Study on the Operation of Gerotor Type Units Considering Fluid Structure and Mechanical Interaction Effects
,” Ph.D. thesis, Purdue University, West Lafayette, IN.
18.
Hamrock
,
B. J.
,
Schmid
,
S. R.
, and
Jacobson
,
B. O.
,
2004
,
Fundamentals of Fluid Film Lubrication
,
CRC Press
, Boca Raton, FL.
19.
Kudish
,
I. I.
,
1999
, “
On Formulation of a Non-Steady Lubrication Problem for a Non-Conformal Contact©
,”
Tribol. Trans.
,
42
(
1
), pp.
53
57
.10.1080/10402009908982189
20.
Kuhr
,
M.
,
Cornell
,
T.
, and
Pelz
,
P.
,
2018
, “
Reduction of Bearing Load Capacity and Increase in Volume Flow Due to Wall Slip
,”
20th International Sealing Conference
, Stuttgart, Germany, Oct. 10–11, pp.
569
579
.http://wl.fst.tu-darmstadt.de/wl/publications/paper_181020_ReductionOfBearingLoadCapacityIncreaseVolumeFlowWallSlip_corneli_kuhr_pelz.pdf
21.
Kwon
,
S.-M.
,
Kim
,
M. S.
, and
Shin
,
J.-H.
,
2008
, “
Analytical Wear Model of a Gerotor Pump Without Hydrodynamic Effect
,”
J. Adv. Mech. Des., Syst., Manuf.
,
2
(
2
), pp.
230
237
.10.1299/jamdsm.2.230
22.
Kwon
,
S.
,
Kim
,
C.-H.
, and
Shin
,
J.
,
2011
, “
Optimal Rotor Wear Design in Hypotrochoidal Gear Pump Using Genetic Algorithm
,”
J. Central South Univ. Technol.
,
18
(
3
), pp.
718
725
.10.1007/s11771-011-0753-z
23.
Biernacki
,
K.
, and
Stryczek
,
J.
,
2010
, “
Analysis of Stress and Deformation in Plastic Gears Used in Gerotor Pumps
,”
J. Strain Anal. Eng. Des.
,
45
(
7
), pp.
465
479
.10.1243/03093247JSA630
24.
ANSYS
, 2020, “
ANSYS® Structural, Release 19.1
,” ANSYS Inc., Canonsburg, PA.
25.
Vacca
,
A.
, and
Guidetti
,
M.
,
2011
, “
Modelling and Experimental Validation of External Spur Gear Machines for Fluid Power Applications
,”
Simul. Modell. Pract. Theory
,
19
(
9
), pp.
2007
2031
.10.1016/j.simpat.2011.05.009
26.
Zhou
,
J.
,
Vacca
,
A.
, and
Casoli
,
P.
,
2014
, “
A Novel Approach for Predicting the Operation of External Gear Pumps Under Cavitating Conditions
,”
Simul. Modell. Pract. Theory
,
45
, pp.
35
49
.10.1016/j.simpat.2014.03.009
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