A theoretical method is proposed in this paper to calculate the unit curve of gear integrated error (GIE). The calculated GIE unit curve includes the quasi-static transmission error (TE) curves of the approach stage, the involute stage, and the recession stage of the ZI worm and helical gear transmission. The misalignments between the two axes of the worm and gear, as well as the modifications or errors of the tooth flanks of the gear, are considered in the procedure of calculation. Optimization algorithm is introduced to replace the solving of implicit differential equations of the conventional tooth contact analysis (TCA) method. It is proved that the proposed method is clearer and more convenient than the conventional TCA methods in calculating the GIE unit curve. The correctness and merits of the proposed method are verified by two experiments.

References

References
1.
Shi
,
Z.
, and
Tang
,
J.
,
2008
, “
Research on a Measurement Principle of the Double-Flank Gear Rolling Test With Many Degrees of Freedom for Fast Inspection
,”
Proc. SPIE
,
7127
, p.
71271C
.
2.
Shi
,
Z.
,
Tang
,
J.
,
Wei
,
H.
,
Gao
,
Y.
, and
Liu
,
C.
,
2009
, “
Gear In-Line Measuring Machine Based on Double-Flank Gear Rolling Test With Multi-Degrees of Freedom
,”
Yi Qi Yi Biao Xue Bao/Chin. J. Sci. Instrum.
,
30
(
2
), pp.
303
307
(in Chinese).
3.
Xie
,
H.
,
Ying
,
F.
,
Feng
,
G.
,
Yong
,
Y.
, and
Huang
,
W.
,
2011
, “
New Way for Accuracy Measurement of Fine-Pitch Gears in Batch Production
,”
Proc. SPIE
,
7997
, p.
79971A
.
4.
Wu
,
B.
, and
Bai
,
Y.
,
1993
, “
Determination of the Start Point of Profile in the Measurement of Gear Integrated Error
,”
Meas. Tech.
,
10
, pp.
3
6
(in Chinese).
5.
Zhao
,
Y.
,
Kong
,
J.
,
Li
,
G.
,
Wu
,
T.
, and
Shi
,
S.
,
2012
, “
Computerized Simulation of Tooth Contact and Error Sensitivity Investigation for Ease-Off Hourglass Worm Drives
,”
Comput.-Aided Des.
,
44
(
8
), pp.
778
790
.
6.
Dong
,
L.
,
Liu
,
P.
,
Wei
,
W.
,
Dong
,
X.
, and
Li
,
H.
,
2014
, “
Study on ZI Worm and Helical Gear Drive With Large Transmission Ratio
,”
Mech. Mach. Theory
,
74
, pp.
299
309
.
7.
Velex
,
P.
, and
Ajmi
,
M.
,
2007
, “
Dynamic Tooth Loads and Quasi-Static Transmission Errors in Helical Gears—Approximate Dynamic factor Formulae
,”
Mech. Mach. Theory
,
42
(
11
), pp.
1512
1526
.
8.
Spitas
,
C.
, and
Spitas
,
V.
,
2008
, “
Direct Analytical Solution of a Modified Form of the Meshing Equations in Two Dimensions for Non-Conjugate Gear Contact
,”
Appl. Math. Modell.
,
32
(
10
), pp.
2162
2171
.
9.
Litvin
,
F. L.
,
Lu
,
J.
,
Townsend
,
D. P.
, and
Howkins
,
M.
,
1999
, “
Computerized Simulation of Meshing of Conventional Helical Involute Gears and Modification of Geometry
,”
Mech. Mach. Theory
,
34
(
1
), pp.
123
147
.
10.
Argyris
,
J.
,
De Donno
,
M.
, and
Litvin
,
F. L.
,
2000
, “
Computer Program in Visual Basic language for Simulation of Meshing and Contact of Gear Drives and Its Application for Design of Worm Gear Drive
,”
Comput. Methods Appl. Mech. Eng.
,
189
(
2
), pp.
595
612
.
11.
Seol
,
I. H.
, and
Litvin
,
F. L.
,
1996
, “
Computerized Design, Generation and Simulation of Meshing and Contact of Worm-Gear Drives With Improved Geometry
,”
Comput. Methods Appl. Mech. Eng.
,
138
(
1–4
), pp.
73
103
.
12.
Tran
,
V.-T.
,
Hsu
,
R.-H.
, and
Tsay
,
C.-B.
,
2014
, “
Tooth Contact Analysis of Double-Crowned Involute Helical Pairs Shaved by a Crowning Mechanism With Parallel Shaving Cutters
,”
Mech. Mach. Theory
,
79
, pp.
198
216
.
13.
Shu
,
Z.
,
Shi
,
Z.
,
Chen
,
H.
,
Lin
,
J.
, and
Kang
,
Y.
,
2014
, “
Research on Gear Integrated Error Curves
,”
International Gear Conference
,
P.
Velex
, ed.,
Lyon, France
, Aug. 26–28,
Chandos Publishing
,
Oxford, UK
, pp.
418
426
.
14.
Shi
,
Z.
, and
Kang
,
Y.
,
2012
, “
Gear Pair Integrated Error and Its Measurement Method
,”
Tianjin Daxue Xuebao (Ziran Kexue yu Gongcheng Jishu Ban)/J. Tianjin Univ., Sci. Technol.
,
45
(
2
), pp.
128
134
(in Chinese).
15.
Huang
,
L.
, and
Zhong
,
X.
,
1973
, “
Gear Dynamic Whole Error Curve and the Methodology of the Measurement
,”
Sci. China, Ser. A: Math., Phys., Astron.
, pp.
434
453
(in Chinese).
16.
Smith
,
R. E.
,
1984
, “
What Single Flank Measurement Can Do for You
,” Fall Technical Meeting of the American Gear Manufacturers Association, Technical Paper No. 84FTM2.
17.
VDI/VDE Gesellschaft Mess- und Automatisierungstechnik (GMA)
,
2001
,
VDI/VDE 2608: Tangential Composite and Radial Composite Inspection of Cylindrical Gears, Bevel Gears, Worms and Worm Wheels
,
Beuth-Verlag
,
Berlin
.
18.
ISO 1328-1
,
2013
,
Cylindrical Gears—ISO System of Accuracy—Part 1: Definitions and Allowable Values of Deviations Relevant to Corresponding Flanks of Gear Teeth
,
International Organization for Standardization (ISO)
,
Geneva, Switzerland
.
19.
ISO/TR 10064-1
,
1992
,
Cylindrical Gears—Code of Inspection Practice—Part 1: Inspections of Corresponding Flanks of Gear Teeth
,
International Organization for Standardization (ISO)
,
Geneva, Switzerland
.
20.
Goch
,
G.
,
2003
, “
Gear Metrology
,”
CIRP Ann.
,
52
(
2
), pp.
659
695
.
21.
Huang
,
T.
,
1979
, “
Gear Dynamic Integrated Error Measurement New Technology
,”
Machinery
,
1979
(
1
), pp.
1
26
(in Chinese).
22.
Zhang
,
Z.
,
Huang
,
S.
, and
Huang
,
T.
,
1995
, “
Review of Gear Measurement Using Single Flank Meshing Movement Method
,”
Mod. Meas. Test
,
1995
(
6
), pp.
2
7
(in Chinese).
23.
Lotze
,
W.
, and
Haertig
,
F.
,
2001
,“
3D Gear Measurement by CMM
,”
5th International Conference on Laser Metrology, Machine Tool, CMM and Robot Performance, LAMDAMP 2001
,
Birmingham, UK
, July 17–20,
WIT Press
,
Southampton, UK
, pp.
333
344
.
24.
Kawalec
,
A.
, and
Magdziak
,
M.
,
2012
, “
Usability Assessment of Selected Methods of Optimization for Some Measurement Task in Coordinate Measurement Technique
,”
Measurement
,
45
(
10
), pp.
2330
2338
.
25.
Wang
,
X.
,
Shi
,
Z.
,
Lin
,
J.
, and
Liu
,
J.
,
2015
, “
Design of a Rapid Inspection Machine for Automotive Gears Based on Gear Integrated Error
,”
ASME
Paper No. DETC2015-46744.
You do not currently have access to this content.