This paper explains development of the general mathematical model of trochoidal gearing that can be applied for gerotor pumps and cyclo reducers. The model analyzes geometry and physics of the gearing pair in trochoidal pump where the outer gear has one tooth more than the inner gear. The inner gear profile is described by peritrochoid equidistance and the outer gear profile by circular arc. Mathematical model of gearing with clearances is based on the principle of an ideal profile development. Minimum clearance height between teeth profiles in relation to instantaneous gear ratio is determined. The influence of gear profile geometrical parameters on gearing process, clearance height change, and pulsation of drive moment is analyzed and presented in numerical examples. Obtained results can be used for the design of the trochoidal gearing where accurate and silent operation is required.

References

References
1.
Ansdale
,
R. F.
, and
Lockley
,
D. J.
, 1970,
The Wankel RC Engine
,
Iliffe Books Ltd
,
London
.
2.
Wutz
,
V. M.
, 1975, “
Vakuumpumpen nach dem Kreiskolbenprinzip
,”
VDI Z.
,
117
(
6
), pp.
271
281
.
3.
Lehman
,
M.
, 1979, “
Sonderformen der Zykloidenverzahnung
,”
Konstruktion
,
31
, pp.
429
433
.
4.
Colbourne
,
J. R.
, 1974, “
The Geometry of Trochoid Envelopes and Their Application in Rotary Pumps
,”
Mech. Mach. Theory
,
9
, pp.
421
435
.
5.
Colbourne
,
J. R.
, 1976, “
Reduction of the Contact Stress in Internal Gear Pumps
,”
J. Eng. Ind., Trans. ASME, Series B
,
98
(4)
, pp.
1296
1300
.
6.
Robinson
,
F. J.
, and
Lyon
,
J. R.
, 1976, “
An Analysis of Epitrochoidal Profiles With Constant Difference Modification Suitable for Rotary Expanders and Pumps
,”
J. Eng. Ind., Trans. ASME, Series B
,
98
(1)
, pp.
161
165
.
7.
Maiti
,
R.
, and
Sinha
,
G. L.
, 1988, “
Kinematics of Active Contact in Modified Epitrochoid Generated Rotary Piston Machines
,”
Mech. Mach. Theory
,
23
(
1
), pp.
39
45
.
8.
Maiti
,
R.
, and
Sinha
,
G. L.
, 1990, “
Limits on Modification of Epitrochoid Used in Rotary Piston Machines and the Effects of Modification on Geometric Volume Displacement and Ripple
,”
Ing.-Arch.
,
60
, pp.
183
194
.
9.
Blanche
,
J. G.
, and
Yang
,
C. H.
, 1989, “
Cycloid Drives With Machining Tolerances
,”
ASME J. Mech., Transm., Autom. Des.
,
111
, pp.
337
344
.
10.
Sensinger
,
J. W.
, 2010, “
Unified Approach to Cycloid Drive Profile, Stress, and Efficiency Optimization
,”
ASME J. Mech. Des.
,
132
(
2
), p.
024503
.
11.
Blagojevic
,
M.
,
Marjanovic
,
N.
,
Djordjevic
,
Z.
,
Stojanovic
,
B.
, and
Disic
,
A.
, 2011, “
A New Design of a Two-Stage Cycloidal Speed Reducer
,”
ASME J. Mech. Des.
,
133
(
8
), p.
085001
.
12.
Beard
,
J. E.
,
Yannitell
,
D. W.
, and
Pennock
,
G. R.
, 1992, “
The Effects of the Generating Pin Size and Placement on the Curvature and Displacement of Epitrochoidal Gerotors
,”
Mech. Mach. Theory
,
27
(
4
), pp.
373
389
.
13.
Shung
,
J. B.
, and
Pennock
,
G. R.
, 1994, “
Geometry for Trochoidal-Type Machines With Conjugate Envelopes
,”
Mech. Mach. Theory
,
29
(
1
), pp.
25
42
.
14.
Shung
,
J. B.
, and
Pennock
,
G. R.
, 1994, “
The Direct Contact Problem in a Trochoidal-Type Machines
,”
Mech. Mach. Theory
,
29
(
5
), pp.
673
689
.
15.
Litvin
,
F. L.
, and
Feng
,
P.
, 1996, “
Computerized Design and Generation of Cycloidal Gearings
,”
Mech. Mach. Theory
,
31
(
7
), pp.
891
911
.
16.
Mimmi
,
G.
, and
Pennacchi
,
P.
, 2000, “
Non-Undercutting Conditions in Internal Gears
,”
Mech. Mach. Theory
,
35
, pp.
477
490
.
17.
Mancò
,
S.
,
Nervegna
,
N.
,
Rundo
,
M.
,
Armenio
,
G.
,
Pachetti
,
C.
, and
Trichilo
,
R.
, 1998, “
Gerotor Lubricating Oil Pump for IC Engines
,”
International Fall Fuels and Lubricants Meeting and Exposition
,
San Francisco
, SAE Paper No. 982689.
18.
Mancò
,
G.
,
Mancò
,
S.
,
Rundo
,
M.
, and
Nervegna
,
N.
, 2000, “
Computerized Generation of Novel Gearings for Internal Combustion Engines Lubricating Pumps
,”
Int. J. Fluid Power
,
1
(
1
), pp.
49
58
.
19.
Vecchiato
,
D.
,
Demenego
,
A.
,
Argyris
,
J.
, and
Litvin
,
F. L.
, 2001, “
Geometry of a Cycloidal Pump
,”
Comput. Methods Appl. Mech. Eng.
,
190
, pp.
2309
2330
.
20.
Demenego
,
A.
,
Vecchiato
,
D.
,
Litvin
,
F. L.
,
Nervegna
,
N.
, and
Mancò
,
S.
, 2002, “
Design and Simulation of Meshing of a Cycloidal Pump
,”
Mech. Mach. Theory
,
37
, pp.
311
332
.
21.
Paffoni
,
B.
, 2003, “
Pressure and Film Thickness in a Trochoidal Hydrostatic Gear Pump
,”
Proc. Inst. Mech. Eng., Part G: J. Aerosp. Eng.
,
217
, pp.
179
187
.
22.
Paffoni
,
B.
,
Progri
,
R.
, and
Gras
,
R.
, 2004, “
Teeth Clearance Effects Upon Pressure and Film Thickness in a Trochoidal Hidrostatic Gear Pump
,”
Proc. Inst. Mech. Eng., Part G: J. Aerosp. Eng.
,
218
, pp.
247
256
.
23.
Gamez-Montero
,
P. J.
,
Castilla
,
R.
,
Khamashta
,
M.
, and
Codina
,
E.
, 2006, “
Contact Problems of a Trochoidal-Gear Pump
,”
Int. J. Mech. Sci.
,
48
(
12
), pp.
1471
1480
.
24.
Gamez-Montero
,
P. J.
, and
Codina
,
E.
, 2007, “
Flow Characteristics of a Trochoidal-Gear Pump Using Bond Graphs and Experimental Measurement—Part 1
,”
Proc. Inst. Mech. Eng., Part I: J. Syst. Control Eng.
,
221
, pp.
331
346
.
25.
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: J. Syst. Control Eng.
,
221
, pp.
347
363
.
26.
Hwang
,
Y. W.
, and
Hsieh
,
C. F.
, 2007, “
Determination of Surface Singularities of a Cycloidal Gear Drive With Inner Meshing
,”
Math. Comput. Modell.
,
45
(
4
), pp.
340
354
.
27.
Hsieh
,
C. F.
, 2009, “
Influence of Gerotor Performance in Varied Geometrical Design Parameters
,”
ASME J. Mech. Des.
,
131
(
12
), p.
121008
.
28.
Yan
,
J.
,
Yang
,
D. C. H.
, and
Tong
,
S.-H.
, 2009, “
A New Gerotor Design Method With Switch Angle Assignability
,”
ASME J. Mech. Des.
,
131
(
1
), p.
011006
.
29.
Yang
,
D. C. H.
,
Yan
,
J.
, and
Tong
,
S.-H.
, 2010, “
Flowrate Formulation of Deviation Function Based Gerotor Pumps
,”
ASME J. Mech. Des.
,
132
(
6
), p.
064503
.
30.
Ivanović
,
L.
, 2007, “
Identification of the Optimal Form of the Trochoidal Tooth Profile of the Rotary Pumps Elements
,” Ph.D. thesis, University of Kragujevac, Faculty of Mechanical Engineering in Kragujevac, Kragujevac, Serbia (in Serbian).
31.
Ivanović
,
L.
,
Devedžić
,
G.
,
Mirić
,
N.
, and
Ćukovic
,
S.
, 2010, “
Analysis of Forces and Moments in the Gerotor Pumps
,”
Proc. Inst. Mech. Eng., Part C: J. Mec. Eng. Sci.
,
224
(
10
), pp.
2257
2269
.
You do not currently have access to this content.