Abstract

Bore holes with a large length to diameter ratio of up to l/d = 100 are typically produced using the single-tube deep hole drilling method also named BTA (Boring and Trepanning Association) deep hole drilling method. However, there are various technical applications requiring deep, complex, epitrochoid-similar and helical inner contours, such as stators used in Moineau motors and pumps. According to the current state of the art, epitrochoid-similar contours for small diameters with large drilling depths can only be produced using a special machining process which is referred to a chamber-boring process. In this paper, a developed mathematical model will be presented that describes the epitrochoid-similar contour exactly. This allows the determination of the position-dependent speed and acceleration of the tool, which are necessary for designing the joints and components of the tool system. In addition, this mathematical model can be used for a subsequent Laplace-transformation, so that could be used for a further optimization of the process dynamic in the future.

References

References
1.
Biermann
,
D.
,
Bleicher
,
F.
,
Heisel
,
U.
,
Klocke
,
F.
, and
Möhring
,
H. C.
,
2018
, “
Deep Hole Drilling
,”
CIRP Ann. Manuf. Tech.
,
67
(
2
), pp.
673
694
. 10.1016/j.cirp.2018.05.007
2.
Schnabel
,
D.
,
Oezkaya
,
E.
,
Biermann
,
D.
, and
Eberhard
,
P.
,
2018
, “
Modeling the Motion of the Cooling Lubricant in Drilling Processes Using the Finite Volume and the Smoothed Particle Hydrodynamics Methos
,”
Int. J. Comput. Methods Appl. Mech. Eng.
,
329
, pp.
369
395
. 10.1016/j.cma.2017.09.015
3.
Wilson
,
F. W.
,
1964
,
Gun Drilling and Trepanning
,
Prentice Hall
,
Englewood Cliffs, NJ
.
4.
Denkena
,
B.
,
Bergmann
,
B.
,
Kaiser
,
S.
,
Mücke
,
M.
, and
Bolle
,
D.
,
2018
, “
Process-Parallel Center Deviation Measurement of a BTA Deep-Hole Drilling Tool
,”
Procedia Manuf.
,
24
, pp.
229
234
. 10.1016/j.promfg.2018.06.034
5.
Haddag
,
B.
,
Thil
,
J.
,
Nouari
,
M.
, and
Barlier
,
C.
,
2013
, “
A Study of the BTA Deep Drilling Process Through a Quantitative and Qualitative Analysis of the Chip Formation Process
,”
Key. Eng. Mat.
,
554–557
, pp.
1992
2008
. 10.4028/www.scientific.net/KEM.554-557.1992
6.
Haddag
,
B.
,
Thil
,
J.
,
Nouari
,
M.
,
Barlier
,
C.
, and
Papillon
,
L.
,
2013
, “
Analysis of the Deep Hole Drilling With BTA System by the Characterization of the Cutting Process
,”
21ème Congrès Français de Mécanique
,
Bordeaux
,
Aug. 26–30
, pp.
1
6
.
7.
Biermann
,
D.
,
Kersting
,
M.
, and
Kessler
,
N.
,
2009
, “
Process Adapted Structure Optimization of Deep Hole Drilling Tools
,”
CIRP Ann. Manuf. Tech.
,
58
(
1
), pp.
89
92
. 10.1016/j.cirp.2009.03.102
8.
Gao
,
C. H.
,
Cheng
,
K.
, and
Kirkwood
,
D.
,
2000
, “
The Investigation on the Machining Process of BTA Deep Hole Drilling
,”
Adv. Mater. Res.
,
107
(
1–3
), pp.
222
227
. 10.1016/S0924-0136(00)00684-1
9.
Gravesen
,
J.
,
2008
, “
The Geometry of the Moineau Pump
,”
Comput. Aided Geom Des.
,
25
(
9
), pp.
792
800
. 10.1016/j.cagd.2008.06.012
10.
Thomas
,
C. E.
,
2014
, “
Process Technology Equipment and Systems
,”
Cengage Learning
.
11.
Campion
,
R. P.
,
Thomson
,
B.
, and
Harris
,
A.
,
Elastomers for Fluid Containment in Offshore Oil and Gas Production: Guidelines and Review
,
HSE Books
,
Sudbury
.
12.
DeGeare
,
J.
,
2015
,
The Guide to Oilwell Fishing Operations: Tools, Techniques, and Rules of Thumb
,
Elsevier
,
Amsterdam
.
13.
Prime Horizontal. Mud Motors
,”
2016
, http://www.primehorizontal.com/, Accessed March 13, 2019.
14.
Baker
,
H.
,
2019
,
Navi-Drill Motor Handbook
, 15th ed, Chapter 1 Technical Basics,
Baker Hughes Incorporated
,
Houston, TX
.
15.
Abbott
,
W.
,
1971
,
Practical Geometry and Engineering Graphics
,
Springer Netherlands
,
Dordrecht
.
16.
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
. 10.1016/0094-114X(88)90007-9
17.
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
18.
Hwang
,
Y. W.
, and
Hsieh
,
C. F.
,
2006
, “
Geometry Design and Analysis for Trochoidal-Type Speed Reducers: With Conjugate Envelopes
,”
Trans. Can. Soc. Mech. Eng.
,
30
(
2
), pp.
261
278
. 10.1139/tcsme-2006-0016
19.
Choi
,
T. H.
,
Kim
,
M. S.
,
Lee
,
G. S.
,
Jung
,
S. Y.
,
Bae
,
J. H.
, and
Kim
,
C.
,
2012
, “
Design of Rotor for Internal Gear Pump Using Cycloid and Circular-Arc Curves
,”
ASME J. Mech. Des.
,
134
(
1
), pp.
1
12
. 10.1115/1.4004423
20.
Patel
,
J.
,
2014
, “
Design, Development and Experimental Investigation of Epitrochoid Internal Lobe Pump
,”
Int. J. Sci. Res. Dev.
,
2
(
9
), pp.
233
236
.
21.
Ivanović
,
L.
, and
Josifović
,
D.
,
2006
, “
Specific Sliding of Trochoidal Gearing Profile in the Gerotor Pumps
,”
FME Trans.
,
34
(
3
), pp.
121
127
.
22.
Ivanović
,
L.
,
Erić
,
M. D.
,
Stojanović
,
B. Z.
, and
Ilić
,
A. B.
,
2011
, “
Determination of Tooth Clearances at Trochoidal Pump
,”
FME Trans.
,
39
(
3
), pp.
117
126
.
23.
Kostić
,
N.
,
Blagojević
,
M.
,
Petrović
,
N.
,
Matejić
,
M.
, and
Marjanović
,
N.
,
2018
, “
Determination of Real Clearances Between Cycloidal Speed Reducer Elements by the Application of Heuristic Optimization
,”
Trans FAMENA
,
42
(
1
), pp.
15
26
. 10.21278/TOF.42102
24.
Wang
,
J.
,
Wei
,
S.
,
Sha
,
R.
,
Liu
,
H.
, and
Wang
,
Z.
,
2019
, “
Design Methodology of a new Smooth Rotor Profile of the Screw Vacuum Pump
,”
Vacuum
,
159
, pp.
456
463
. 10.1016/j.vacuum.2018.10.064
25.
Nelson
,
D.
,
2008
,
The Penguin Dictionary of Mathematics
,
Penguin
,
London
.
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