A model for nonfrictional power loss in derailleur-type, bicycle chain drives is developed to identify factors that influence transmission efficiency. Existing treatments of chain drive efficiency consider frictional losses but these do not explain the measured tension dependence of power losses and efficiencies for derailleur-type systems. Based on a nonlinear, spring-mass, mechanical transmission line, the model developed in this work shows that losses can be related to harmonic generation and dispersion in the chain. The nonlinear response leading to harmonic generation results from elastic contact at pin-bushing interfaces while dispersion is related to the periodic nature of the chain construction. Using this approach, the tension-dependence of power loss and efficiency are modeled and the influences of various chain-related characteristics on efficiency are assessed. If Hertzian contact descriptions are used, then the dependence of loss and efficiency on pin-bushing clearance, contact length and modulus can be estimated. Modeled results agree with experiment and show that power loss decreases with increasing chain tension and that efficiency varies nearly linearly with the reciprocal of the chain tension under operational conditions that are typical for bicycle chain drives. Significant increases to the power transmission efficiency of bicycle chain drives in derailleur-based systems could be achieved by altering the geometries and materials of current chain components.

References

References
1.
Keller
,
J.
,
1983
, “
Der Wirkunsgrad im Fahrradantrieb
,”
Radmarkt
,
12
, pp.
71
75
.
2.
Hollingworth
,
N. E.
, and
Hills
,
D. A.
,
1986
, “
Forces in a Heavy-Duty Drive Chain During Articulation
,”
Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
,
200
(
C5
), pp.
367
374
.10.1243/PIME_PROC_1986_200_140_02
3.
Hollingworth
,
N. E.
, and
Hills
,
D. A.
,
1986
, “
Theoretical Efficiency of a Cranked Link Chain Drive
,”
Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
,
200
(
C5
), pp.
375
377
.10.1243/PIME_PROC_1986_200_141_02
4.
Kidd
,
M. D.
,
Loch
,
N. E.
, and
Reuben
,
R. L.
,
1999
, “
Experimental Examination of Bicycle Chain Forces
,”
Exp. Mech.
,
39
(
4
), pp.
278
283
.10.1007/BF02329805
5.
Lodge
,
C. J.
, and
Burgess
,
S. C.
,
2002
, “
A Model of the Tension and Transmission Efficiency of a Bush Roller Chain
,”
Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
,
216
, pp.
385
394
.10.1243/0954406021525179
6.
Lodge
,
C. J.
, and
Burgess
,
S. C.
,
2004
, “
An Investigation into the Selection of Optimum Chain and Sprocket Size
,”
J. Eng. Design
,
15
(
6
), pp.
563
580
.10.1080/09544820410001731128
7.
Spicer
,
J. B.
,
Richardson
,
C. J. K.
,
Ehrlich
,
M. J.
,
Bernstein
,
J. R.
,
Fukuda
,
M.
, and
Terada
,
M.
,
2001
, “
Effects of Frictional Loss on Bicycle Chain Drive Efficiency
,”
Trans. ASME, J Mech. Des.
,
123
, pp.
598
605
.10.1115/1.1412848
8.
Ariaratnam
,
S. T.
, and
Asokanthan
,
S. F.
,
1987
, “
Dynamic Stability of Chain Drives
,”
ASME, J. Mech. Transm., Autom. Des.
,
109
, pp.
412
418
.10.1115/1.3258811
9.
Liu
,
S. P.
,
Wang
,
K. W.
,
Hayek
,
S. I.
, and
Trethewey
,
M. W.
,
1997
, “
A Global-Local Integrated Study of Roller Chain Meshing Dynamics
,”
J. Sound Vib.
,
203
(
1
), pp.
41
62
.10.1006/jsvi.1996.0792
10.
Shimizu
,
H.
, and
Sueoka
,
A.
,
1975
, “
Nonlinear Forced Vibrations of Roller Chain
,”
Bull. JSME
,
18
(
124
), pp.
1090
1100
.10.1299/jsme1958.18.1090
11.
Coste
,
C.
, and
Gilles
,
B.
,
1999
, “
On the Validity of Hertz Contact Law for Granular Material Acoustics
,”
Eur. Phys. J. B
,
7
, pp.
155
168
.10.1007/s100510050598
12.
Coste
,
C.
, and
Gilles
,
B.
,
2003
, “
Low-Frequency Behavior of Beads Constrained on a Lattice
,”
Phys. Rev. Lett.
,
90
(
7
), p.
174302(4)
.10.1103/PhysRevLett.90.174302
13.
Coste
,
C.
, and
Gilles
,
B.
,
2008
, “
Sound Propagation in a Constrained Lattice of Beads: High-Frequency Behavior and Dispersion Relation
,”
Phys. Rev. E
,
77
, p.
021302(13)
.10.1103/PhysRevE.77.021302
14.
Job
,
S.
,
Santibanez
,
F.
,
Tapia
,
F.
, and
Melo
,
F.
,
2008
, “
Nonlinear Waves in Dry and Wet Hertzian Granular Chains
,”
Ultrasonics
,
48
(
6–7
), pp.
506
514
.10.1016/j.ultras.2008.03.006
15.
Sopouch
,
M.
,
Hellinger
,
W.
, and
Priebsch
,
H. H.
,
2003
, “
Prediction of Vibroacoustic Excitation Due to the Timing Chains of Reciprocating Engines
,”
Proc. Inst. Mech. Eng., Part K, J. Multi-Body Dynamics
,
217
, pp.
225
240
.10.1243/14644190360713579
16.
Noguchi
,
S.
,
Nagasaki
,
K.
,
Nakayama
,
S.
,
Kanada
,
T.
,
Nishino
,
T.
, and
Ohtani
,
T.
,
2009
, “
Static Stress Analysis of Link Plate of Roller Chain Using Finite Element Method and Some Design Proposals for Weight Saving
,”
J. Adv. Mech. Des., Systems and Manufacturing
3
(
2
), pp.
159
170
.10.1299/jamdsm.3.159
17.
Norden
,
B. N.
,
1973
, “
On the Compression of a Cylinder in Contact With a Plane Surface
,” Technical Report No. NBSIR 73-243, U.S. Department of Commerce,
National Bureau of Standards
,
Washington, DC.
18.
Puttock
,
M. J.
, and
Thwaite
,
E. G.
,
1969
, “
Elastic Compression of Spheres and Cylinders at Point and Line Contact
,” National Standards Laboratory Technical Paper No. 25,
Commonwealth Scientific and Industrial Research Organization (CSIRO)
,
Melbourne, Australia
.
19.
Castillo
,
J.
, and
Barber
,
J. R.
,
1997
, “
Lateral Contact of Slender Prismatic Bodies
,”
Proc. R. Soc. London, Ser. A
,
453
, pp.
2397
2412
.10.1098/rspa.1997.0128
20.
Persson
,
A.
,
1964
, “
On the Stress Distribution of Cylindrical Elastic Bodies in Contact
,” Ph.D. dissertation,
Chalmers University of Technology
,
Göteborg, Sweden
.
21.
Ciavarella
,
M.
, and
Decuzzi
,
P.
,
2001
, “
The State of Stress Induced by the Plane Frictionless Contact. I. The Case of Elastic Similarity
,”
Int. J. Solids Struct.
,
38
, pp.
4507
4523
.10.1016/S0020-7683(00)00289-4
22.
Wilson
,
H. B.
, and
Hill
,
J. L.
,
1972
, “
Non-Hertzian Contact Stresses in a Smoothly Cradled Heavy Cylinder
,”
J. Elast.
,
2
(
2
), pp.
143
151
.10.1007/BF00046064
23.
Woodward
,
W.
, and
Paul
,
B.
,
1976
, “
Contact Stresses for Closely Conforming Bodies—Application to Cylinders and Spheres
,” Technical Report No. DOT-TST-77-48,
U.S. Department of Transportation, Office of the Secretary, Office of University Research
,
Washington, DC.
24.
Nowell
,
D.
,
Hills
,
D. A.
, and
Sackfield
,
A.
,
1988
, “
Contact of Dissimilar Elastic Cylinders Under Normal and Tangential Loading
,”
J. Mech. Phys. Solids
,
36
(
1
), pp.
59
75
.10.1016/0022-5096(88)90020-8
25.
Tsubakimoto Chain Company
,
2006
, “
The Complete Guide to Chain
,”
Reference Handbook
,
Osaka, Japan
, http://chain-guide.com/toc.html
26.
Standards Committee Meeting
,
1921
, “
Chain Division Report, Roller Chain Sprockets
,”
J. Soc. Automotive Eng.
,
9
(
1
), pp.
55
57
.
You do not currently have access to this content.