Abstract

The geometric design, meshing simulation, and stress analysis of pure rolling rack and pinion mechanisms are presented. Both the pinion and the rack are based on the active design of the meshing line to provide pure rolling for the whole cycle of meshing. The parametric equations of the contact curves on the rack and pinion tooth surfaces are determined by coordinate transformation of the meshing line equations. Three types of meshing are derived according to the motion of the generatrices along the calculated contact curves: convex-to-concave meshing, convex-to-plane meshing, and convex-to-convex meshing. Then, the basic design parameters are analyzed and formulas for calculation of the geometric size are given. Four different cases of design are considered to compare the meshing performance and mechanical behavior of the proposed gear mechanisms. The results include contact patterns, the unloaded function of transmission errors, and the evaluation of stresses along two cycles of meshing. The analysis of the results shows that the proposed method of design of pure rolling meshing reduces the relative sliding between tooth surfaces, whereas it decreases the contact strength of the tooth surfaces. However, if the design parameters are properly evaluated as a result of simulation and applied as proposed here, the mechanical behavior of the proposed rack and pinion mechanisms can be more favorable than that of the standard geometry of involute rack and pinion sets.

References

1.
Litvin
,
F. L.
, and
Fuentes-Aznar
,
A.
,
2004
,
Gear Geometry and Applied Theory
,
Cambridge University Press
,
New York
.
2.
Dooner
,
D. B.
,
2012
,
Kinematic Geometry of Gearing
,
John Wiley and Sons
,
New York
.
3.
Wu
,
X.
,
2009
,
Meshing Theory of Gears
,
China Machine Press
,
Beijing
.
4.
Onishchenko
,
V.
,
2015
, “
Investigation of Tooth Wears From Scuffing of Heavy Duty Machine Spur Gears
,”
Mech. Mach. Theory
,
83
(
1
), pp.
38
55
. 10.1016/j.mechmachtheory.2014.08.016
5.
Borba da Cunha
,
A. C.
,
Sabedot
,
S.
,
Sampaio
,
C. H.
,
Ramos
,
C. G.
, and
da Silva
,
A. R.
,
2012
, “
Salix Rubens and Salix Triandra Species As Phytoremediators of Soil Contaminated With Petroleum-Derived Hydrocarbons
,”
Water Air Soil Pollut.
,
223
(
8
), pp.
4723
4731
. 10.1007/s11270-012-1228-z
6.
Chen
,
C.
,
1995
, “
A Formula for Determining Limit Noninterference Curvature in Pure Rolling Conjugation Gears by Using Geometro-Kinematical Concepts
,”
ASME J. Mech. Des.
,
117
(
1
), pp.
180
184
. 10.1115/1.2826104
7.
Wagner
,
M. J.
,
Ng
,
W. F.
, and
Dhande
,
S. G.
,
1992
, “
Profile Synthesis and Kinematic Analysis of Pure Rolling-Contact Gears
,”
ASME J. Mech. Des.
,
114
(
2
), pp.
326
333
. 10.1115/1.2916950
8.
Song
,
Y.
,
Liao
,
Q.
,
Wei
,
S.
,
Guo
,
L.
,
Song
,
H.
, and
Lifeng
,
Z.
,
2014
, “
Modelling, Simulation and Experiment of a Novel Pure Rolling Cycloid Reducer With Involute Teeth
,”
Int. J. Model. Identif. Control
,
21
(
2
), pp.
184
192
. 10.1504/IJMIC.2014.060011
9.
Chen
,
Y.
,
Xiang
,
X.
, and
Luo
,
L.
,
2009
, “
A Corrected Equation of Space Curve Meshing
,”
Mech. Mach. Theory
,
44
(
7
), pp.
1348
1359
. 10.1016/j.mechmachtheory.2008.11.001
10.
Chen
,
Z.
,
Chen
,
Y.
, and
Ding
,
J.
,
2013
, “
A Generalized Space Curve Meshing Equation for Arbitrary Intersecting Gear
,”
Proc. Inst. Mech. Eng. Part C - J. Mech. Eng. Sci.
,
227
(
7
), pp.
1599
1607
. 10.1177/0954406212463310
11.
Chen
,
Y.
,
Lv
,
Y.
,
Ding
,
J.
, and
Chen
,
Z.
,
2013
, “
Fundamental Design Equations for Space Curve Meshing Skew Gear Mechanism
,”
Mech. Mach. Theory
,
70
(
7
), pp.
175
188
. 10.1016/j.mechmachtheory.2013.07.004
12.
Chen
,
Z.
,
Ding
,
H.
,
Li
,
B.
,
Luo
,
L.
,
Zhang
,
L.
, and
Yang
,
J.
,
2017
, “
Geometry and Parameter Design of Novel Circular Arc Helical Gears for Parallel-Axis Transmission
,”
Adv. Mech. Eng.
,
9
(
2
), pp.
1
11
.
13.
Chen
,
Z.
,
Ding
,
H.
, and
Zeng
,
M.
,
2018
, “
Nonrelative Sliding Gear Mechanism Based on Function-oriented Design of Meshing Line Functions for Parallel Axes Transmission
,”
Adv. Mech. Eng.
,
10
(
9
), pp.
1
13
.
14.
Chen
,
Z.
, and
Zeng
,
M.
,
2019
, “
Nonrelative Sliding of Spiral Bevel Gear Mechanism Based on Active Design of Meshing Line
,”
Proc. Inst. Mech. Eng. Part C, J. Mech. Eng. Sci.
,
233
(
3
), pp.
1055
1067
. 10.1177/0954406218767466
15.
Chen
,
Z.
, and
Zeng
,
M.
,
2019
, “
Design of Pure Rolling Line Gear Mechanisms for Arbitrary Intersecting Shafts
,”
Proc. Inst. Mech. Eng. Part C - J. Mech. Eng. Sci.
,
233
(
15
), pp.
5515
5531
.
16.
Fuentes-Aznar
,
A.
,
Iglesias-Victoria
,
P.
,
Eisele
,
S.
, and
Gonzalez-Perez
,
I.
,
2016
, “
Fillet Geometry Modeling for Nongenerated Gear Tooth Surfaces
,”
Proceedings of the International Conference on Power Transmissions
,
Chongqing, China
,
Oct. 27–30
, pp.
431
436
.
17.
Sheveleva
,
G. I.
,
Volkov
,
A. E.
, and
Medvedev
,
V. I.
,
2007
, “
Algorithms for Analysis of Meshing and Contact of Spiral Bevel Gears
,”
Mech. Mach. Theory
,
42
(
2
), pp.
198
215
. 10.1016/j.mechmachtheory.2006.02.009
18.
ABAQUS/Standard User’s Manual
,
2018
,
Providence, RI
.
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