For the lightweight design of the wheel rim of motorcycles, the knowledge of the way in which contact forces are transmitted by the tire is of crucial importance. In this paper, an analytical model of the tire is developed and explicit formulae giving the distribution of the radial and axial forces acting on the wheel rim for a given vertical load are derived. The analytical model is validated by means of a finite element method (FEM) model and experimental tests. The proposed analytical model is able to predict the radial deflection of both a front and a rear tire for a racing motorbike with very good accuracy over a wide range of inflating pressures and vertical loads. The force distributions are in very good agreement with the results of the FEM model. Experimental tests show that the force distribution at the interface between the tire and rim can be used to predict the stress distribution in the rim with a good accuracy.

References

References
1.
Stearns
,
J.
,
Srivatsan
,
T.
,
Gao
,
X.
, and
Lam
,
P.
,
2006
, “
Understanding the Influence of Pressure and Radial Loads on Stress and Displacement Response of a Rotating Body: The Automobile Wheel
,”
Int. J. Rotating Mach.
,
2006
, p.
60193
.
2.
Das
,
S.
,
2014
, “
Design and Weight Optimization of Aluminum Alloy Wheel
,”
Int. J. Sci. Res. Publ.
,
4
(
6
).
3.
Wang
,
L.
,
Chen
,
Y.
,
Wang
,
C.
, and
Wang
,
Q.
,
2011
, “
Fatigue Life Analysis of Aluminium Wheels by Simulation of Rotary Fatigue Test
,”
J. Mech. Eng.
,
57
(
1
), pp.
31
39
.
4.
Raju
,
P. R.
,
Satyanarayana
,
B.
,
Ramji
,
K.
, and
Babu
,
K. S.
,
2007
, “
Evaluation of Fatigue Life of Aluminium Alloy Wheels Under Radial Loads
,”
Eng. Failure Anal.
,
14
(
5
), pp.
791
800
.
5.
Stearns
,
J.
,
Srivatsan
,
T.
,
Prakash
,
A.
, and
Lam
,
P.
,
2004
, “
Modeling the Mechanical Response of an Aluminium Alloy Automotive Rim
,”
Mater. Sci. Eng.
,
A366
, pp.
262
268
.
6.
Lot
,
R.
,
2004
, “
A Motorcycle Tire Model for Dynamic Simulations
,”
Meccanica
,
39
(
3
), pp.
207
220
.
7.
Cossalter
,
V.
,
Doria
,
A.
,
Lot
,
R.
,
Ruffo
,
N.
, and
Salvador
,
M.
,
2003
, “
Dynamic Properties of Motorcycle and Scooter Tires: Measurement and Comparison
,”
Veh. Syst. Dyn.
,
39
(
5
), pp.
329
352
.
8.
Lu
,
C.
, and
Shih
,
M.
,
2005
, “
An Experimental Study on the Longitudinal and Lateral Adhesive Coefficients Between the Tyre and the Road for a Light Motorcycle
,”
Veh. Syst. Dyn.
,
43
, pp.
168
178
.
9.
Pauwelussen
,
J.
,
Gootjes
,
L.
,
Schröder
,
C.
,
Köhne
,
K.-U.
,
Jansen
,
S.
, and
Schmeitz
,
A.
,
2003
, “
Full Vehicle ABS Braking Using the Swift Rigid Ring Tyre Model
,”
Control Eng. Pract.
,
11
(
2
), pp.
199
207
.
10.
Jansen
,
S.
,
Zegelaar
,
P.
, and
Pacejka
,
H.
,
1999
, “
The Influence of In-Plane Tyre Dynamics on ABS Braking of a Quarter Vehicle Model
,”
Veh. Syst. Dyn.
,
32
(2--3), pp.
249
261
.
11.
Mastinu
,
G.
, and
Fainello
,
M.
,
1992
, “
Study of the Pneumatic Tyre Behaviour on Dry and Rigid Road by Finite Element Method
,”
Veh. Syst. Dyn.
,
21
(
1
), pp.
143
165
.
12.
Pacejka
,
H. B.
,
1972
, “
Analysis of the Dynamic Response of a Rolling String-Type Tire Model to Lateral Wheel-Plane Vibrations
,”
Veh. Syst. Dyn.
,
1
(
1
), pp.
37
66
.
13.
Clover
,
C.
, and
Bernard
,
J. E.
,
1998
, “
Longitudinal Tire Dynamics
,”
Veh. Syst. Dyn.
,
29
(
4
), pp.
231
260
.
14.
Kim
,
S.
,
Nikravesh
,
P.
, and
Gim
,
G.
,
2008
, “
A Two-Dimensional Tire Model on Uneven Roads for Vehicle Dynamic Simulation
,”
Veh. Syst. Dyn.
,
46
(
10
), pp.
913
930
.
15.
Kindt
,
P.
,
Sas
,
P.
, and
Desmet
,
W.
,
2009
, “
Development and Validation of a Three-Dimensional Ring-Based Structural Tyre Model
,”
J. Sound Vib.
,
326
(3–5), pp.
852
869
.
16.
Kung
,
L.
,
Soedel
,
W.
, and
Yang
,
T.
,
1986
, “
Free Vibration of a Pneumatic Tire-Wheel Unit Using a Ring on an Elastic Foundation and a Finite Element Model
,”
J. Sound Vib.
,
107
(
2
), pp.
181
194
.
17.
Pinnington
,
R. J.
, and
Briscoe
,
A. R.
,
2002
, “
A Wave Model for a Pneumatic Tyre Belt
,”
J. Sound Vib.
,
253
(
5
), pp.
941
959
.
18.
Pinnington
,
R. J.
,
2002
, “
Radial Force Transmission to the Hub From an Unloaded Stationary Tyre
,”
J. Sound Vib.
,
253
(
5
), pp.
961
983
.
19.
Larsson
,
K.
, and
Kropp
,
W.
,
2002
, “
A High-Frequency Three-Dimensional Tyre Model Based on Two Coupled Elastic Layers
,”
J. Sound Vib.
,
253
(
4
), pp.
889
908
.
20.
Mastinu
,
G.
,
Gaiazzi
,
S.
,
Montanaro
,
F.
, and
Pirola
,
D.
,
1997
, “
A Semi-Analytical Tyre Model for Steady and Transient-State Simulations
,”
Veh. Syst. Dyn.
,
27
, pp.
2
21
.
21.
Mastinu
,
G.
,
Previati
,
G.
, and
Gobbi
,
M.
,
2011
, “
Analytical Computation of the Radial Stiffness of Pneumatic Tyres
,”
22nd IAVSD Symposium on Dynamics of Vehicles on Roads and Tracks
,
Manchester, UK
.
22.
Hall
,
W.
,
Mottram
,
J.
, and
Jones
,
R.
,
2004
, “
Tire Modeling Methodology With the Explicit Finite Element Code LS-DYNA
,”
Tire Sci. Technol., TSTCA
,
32
(
4
), pp.
236
261
.
23.
Meschke
,
G.
,
Prayer
,
H.
, and
Mang
,
H.
,
1997
, “
3D Simulations of Automobile Tires, Mesh Generation and Solution Strategies: Material Modeling
,”
Tire Sci. Technol., TSTCA
,
25
(
3
), pp.
154
176
.
24.
Yang
,
X.
,
2011
, “
Finite Element Analysis and Experimental Investigation of Tyre Characteristics for Developing Strain-Based Intelligent Tyre Systems
,” Ph.D. dissertation, University of Birmingham, Edgbaston, UK.
25.
Yan
,
X.
,
2001
, “
Non-Linear Three-Dimensional Finite Element Modeling of Radial Tires
,”
Math. Comput. Simul.
,
58
(
1
), pp.
51
70
.
26.
Tönük
,
E.
, and
Ünlüsoy
,
Y.
,
2001
, “
Prediction of Automobile Tire Cornering Force Characteristics by Finite Element Modeling and Analysis
,”
Comput. Struct.
,
79
(
13
), pp.
1219
1232
.
27.
Korunović
,
N.
,
Trajanović
,
M.
, and
Stojković
,
M.
,
2007
, “
FEA Tires Subjected to Static Loading
,”
J. Serb. Soc. Comput. Mech.
,
1
, pp.
87
98
.
28.
Ghoreisky
,
M.
,
2006
, “
Finite Element Analysis of the Steel-Belted Radial Tyre With Tread Pattern Under Contact Load
,”
Iran. Polym. J.
,
15
, pp.
667
674
.
29.
Korunović
,
N.
,
Trajanović
,
M.
,
Stojković
,
M.
,
Mišić
,
D.
, and
Milovanović
,
J.
,
2011
, “
Finite Element Analysis of a Tire Steady Rolling on the Drum and Comparison With Experiment
,”
J. Mech. Eng.
,
57
(
12
), pp.
888
897
.
30.
Pelle
,
R. G.
,
1994
, “
FEM Simulation of the Tire/Rim Seating Process
,”
Tire Sci. Technol.
,
22
(
2
), pp.
76
98
.
31.
Faria
,
L. O.
,
Oden
,
J. T.
,
Yavari
,
B.
,
Tworzydlo
,
W. W.
,
Bass
,
J. M.
, and
Becker
,
E. B.
,
1992
, “
Tire Modeling by Finite Elements
,”
Tire Sci. Technol.
,
20
(
1
), pp.
33
56
.
32.
Jeusette
,
J. P.
, and
Theves
,
M.
,
1992
, “
Finite Element Analysis of Tire/Rim Interface Forces Under Braking and Cornering Loads
,”
Tire Sci. Technol.
,
20
(
2
), pp.
83
105
.
33.
Lee
,
C.
,
2006
, “
Rim Slip and Bead Fitment of Tires: Analysis and Design
,”
Tire Sci. Technol.
,
34
(
1
), pp.
38
63
.
34.
Ballo
,
F.
,
Gobbi
,
M.
,
Mastinu
,
G.
,
Previati
,
G.
, and
Zerboni
,
R.
,
2015
, “
Motorcycle Tire Modeling
,” ASME Paper No. DETC2015-46607.
35.
Holzapfel
,
G.
,
2000
,
Nonlinear Solid Mechanics: A Continuum Approach for Engineering
,
Wiley
,
Hoboken, NJ
.
36.
Alkan
,
V.
,
Karamihas
,
S. M.
, and
Anlas
,
G.
,
2011
, “
Finite Element Modeling of Static Tire Enveloping Characteristics
,”
Int. J. Automot. Technol.
,
12
(
4
), pp.
529
535
.
37.
Lei
,
L.
,
Zuo
,
S.
,
Yang
,
X.
,
Wu
,
X.
, and
Li
,
Y.
,
2010
, “
Finite Element Analysis of Radial Tires Based on the Software of MARC
,”
3rd International Conference on Advanced Computer Theory and Engineering (ICACTE)
, Vol.
1
.
38.
Previati
,
G.
, and
Kaliske
,
M.
,
2012
, “
Crack Propagation in Pneumatic Tires: Continuum Mechanics and Fracture Mechanics Approaches
,”
Int. J. Fatigue
,
37
, pp.
69
78
.
39.
Simulia
,
2012
,
Abaqus 6.12 Analysis User's Manual 28.1.5
,
Dassault Systèmes Simulia Corp.
,
Providence, RI
.
40.
Mastinu
,
G.
,
Gobbi
,
M.
, and
Previati
,
G.
,
2011
, “
A New Six-Axis Load Cell—Part I: Design
,”
Exp. Mech.
,
51
(
3
), pp.
373
388
.
41.
Gobbi
,
M.
,
Previati
,
G.
,
Guarnieri
,
P.
, and
Mastinu
,
G.
,
2011
, “
A New Six-Axis Load Cell—Part II: Error Analysis, Construction and Experimental Assessment of Performances
,”
Exp. Mech.
,
51
(
3
), pp.
389
399
.
42.
Ballo
,
F.
,
Gobbi
,
M.
,
Mastinu
,
G.
, and
Previati
,
G.
,
2014
, “
Advances in Force and Moments Measurements by an Innovative Six-Axis Load Cell
,”
Exp. Mech.
,
54
(
4
), pp.
571
592
.
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