Abstract

The noise generated by the rolling tyre contributes significantly to the car's interior noise. This is caused by the tyre-road contact, and at low frequencies (0–500 Hz) is mostly transmitted inside the cockpit through the structure-borne transmission path. In support of the studies in this research field, an interpretative model of the tyre-wheel system accounting for the effects induced by the angular speed represents a useful tool. To this aim, we implemented an analytical model based on a flexible ring on an elastic foundation to analyze the dynamics of the tyre-wheel system, in both static and rotating configurations. We fine-tuned the parameters of the tyre based on data coming from experimental modal analysis of the static tyre. Particular attention has been paid to the system's free and forced responses, commonly analyzed with the so-called cleat test. The results are discussed interpreting the behavior in different reference systems.

References

1.
Bernard
,
R.
, and
Wayson
,
R. L.
, Haddock, J., Neithalath, N., El-Aassar, A., Olek, J., and Weiss, W. J,
2005
, “
An Introduction to Tire/Pavement Noise of Asphalt Pavement
,”
Institute for Safe, Quiet and Durable Highways
,
Purdue University
.
2.
Iversen
,
L.
,
Marbjerg
,
G.
, and
Bendtsen
,
H
.,
2013
, “
Noise From Electric Vehicles - ‘state-of-the-art' A Literature Survey,” Proceedings of Inter-Noise, Innsbruck, Austria, Sept. 15–18
.
3.
Harrison
,
M.
,
2004
,
Vehicle Refinement: Controlling Noise and Vibration in Road Vehicles
,
SAE International
,
Oxford, UK
.
4.
Pang
,
J.
,
2018
,
Noise and Vibration Control in Automotive Bodies Chine Machine Press
,
Wiley
, Hoboken, NJ.
5.
Mohamed, Z., and Wang
,
X.
,
2016
, “
A Deterministic and Statistical Energy Analysis of Tyre Cavity Resonance Noise
,”
Mech. Syst. Signal Process.
,
70–71
, pp.
947
957
.10.1016/j.ymssp.2015.09.012
6.
Mohamed Z., and Wang
,
X.
,
2015
, “
A Study of Tyre Cavity Resonance and Noise Reduction Using Inner Trim
,”
Mech. Syst. Signal Process.
,
50–51
, pp.
498
509
.10.1016/j.ymssp.2014.05.044
7.
Cao, R., and Bolton
,
J. S.
,
2015
, “
Improved Model for Coupled Structural-Acoustic Modes of Tires
,”
SAE Int. J. Passenger Cars Mech. Syst.
,
8
(
3
), pp.
845
854
.10.4271/2015-01-2199
8.
Jessop, A. M., and Bolton
,
J. S.
,
2011
, “
Tire Surface Vibration and Sound Radiation Resulting From the Tire Cavity Mode
,”
Tire Sci. Technol.
,
39
(
4
), pp.
245
255
.10.2346/1.3670037
9.
Baro
,
S.
,
Corradi
,
R.
,
Abom
,
M.
,
Caracino
,
P.
, and
Fioravanti
,
A. P.
,
2019
, “
Modelling of a Lined Tyre for Predicting Cavity Noise Mitigation
,”
Appl. Acoust.
,
155
, pp.
391
400
.10.1016/j.apacoust.2019.05.033
10.
Périsse
,
J.
,
2002
, “
A Study of Radial Vibrations of a Rolling Tyre for Tyre-Road Noise Characterization
,”
Mech. Syst. Signal Process.
,
16
(
6
), pp.
1043
1058
.10.1006/mssp.2001.1432
11.
Diaz
,
C. G.
,
Kindt
,
P.
,
Middelberg
,
L.
,
Vercammen
,
S.
,
Thiry
,
C.
,
Close
,
R.
, and
Leyssens
,
J.
,
2016
, “
Dynamic Behaviour of a Rolling Tyre: Experimental and Numerical Analyses
,”
J. Sound Vib.
,
364
, pp.
147
164
.10.1016/j.jsv.2015.11.025
12.
Gong
,
S.
,
1993
, “
A Study of In-Plane Dynamics of Tires
,” Ph.D. thesis,
Delft University of Technology, Delft, The Netherlands
.
13.
Lopez
,
I.
,
Blom
,
R. E. A.
,
Roozen
,
N. B.
, and
Nijmeijer
,
H.
,
2007
, “
Modeling the Vibrations of a Rotating Tyre: A Modal Approach
,”
J. Sound Vib.
,
307
(
3–5
), pp.
481
494
.10.1016/j.jsv.2007.05.056
14.
Nackenhorst
,
U.
,
2004
, “
The ALE-Formulation of Bodies in Rolling contact-Theoretical Foundations and Finite Element Approach
,”
Comput. Methods Appl. Mech. Eng.
,
193
(
39–41
), pp.
4299
4322
.10.1016/j.cma.2004.01.033
15.
Endo
,
M.
,
Hatamura
,
K.
,
Sakata
,
M.
, and
Taniguchi
,
O.
,
1984
, “
Flexural Vibration of a Thin Rotating Ring
,”
J. Sound Vib.
,
92
(
2
), pp.
261
272
.10.1016/0022-460X(84)90560-1
16.
Pinnington
,
R. J.
, and
Briscoe
,
A. R.
,
2002
, “
A Wave Model for a Pneumatic Tyre Belt
,”
J. Sound Vib.
,
253
(
5
), pp.
941
959
.10.1006/jsvi.2001.3944
17.
Soedel
,
W.
,
1975
, “
On the Dynamic Response of Rolling Tires According to Thin Shell Approximation
,”
J. Sound Vib.
,
41
(
2
), pp.
233
246
.10.1016/S0022-460X(75)80099-X
18.
Soedel
,
W.
,
2004
, “
Vibrations of Shells and Plates-Third Edition
,”
Revised and Explained
,
Marcel Dekker
,
New York
, Chapter 4,6,16.
19.
Huang
,
S. C.
, and
Soedel
,
W.
,
1987
, “
Effect of Coriolis Acceleration on the Free and Forced In-Plane Vibrations of Rotating Rings on Elastic Foundation
,”
J. Sound Vib.
,
115
(
2
), pp.
253
274
.10.1016/0022-460X(87)90471-8
20.
Lu
,
T.
,
Tsouvalas
,
A.
, and
Metrikine
,
A. V.
,
2017
, “
The In-Plane Free Vibration of an Elastically Supported Thin Ring Rotating at High Speeds Revisited
,”
J. Sound Vib.
,
402
, pp.
203
218
.10.1016/j.jsv.2017.05.013
21.
Lin
,
J.
, and
Soedel
,
W.
,
1988
, “
On General In-Plane Vibrations of Rotating Thick and Thin Rings
,”
J. Sound Vib.
,
122
(
3
), pp.
547
570
.10.1016/S0022-460X(88)80101-9
22.
Lin
,
J.
, and
Soedel
,
W.
,
1988
, “
On the Critical Speeds of Rotating Thick or Thin Rings
,”
Mech. Struct. Mach.
,
16
(
4
), pp.
439
483
.10.1080/08905458808960272
23.
Gong
,
S.
,
Savkoor
,
A.
, and
Pacejka
,
H.
,
1993
, The Influence of Boundary Conditions on the Vibration Transmission Properties of Tires,
SAE
Paper No. 931280.10.4271/931280
24.
Cooley
,
C. G.
, and
Parker
,
R. G.
,
2014
, “
Vibration of High-Speed Rotating Rings Coupled to Space-Fixed Stiffnesses
,”
J. Sound Vib.
,
333
(
12
), pp.
2631
2648
.10.1016/j.jsv.2014.01.005
25.
Lu
,
T.
,
Tsouvalas
,
A.
, and
Metrikine
,
A. V.
,
2019
, “
A High-Order Model for In-Plane Vibrations of Rotating Rings on Elastic Foundation
,”
J. Sound Vib.
,
455
, pp.
118
135
.10.1016/j.jsv.2019.04.037
26.
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
868
.10.1016/j.jsv.2009.05.019
27.
Nilsson
,
A.
, and
Liu
,
B.
,
2016
,
Vibro-Acoustics
,
Science Press
,
Beijing and Springer-Verlag Berlin Heidelberg, Germany
.
28.
Heylen
,
W.
,
Lammens
,
S.
, and
Sas
,
P.
,
1998
, “
Modal Analysis Theory and Testing
,”
Faculty of Engineering, Department of Mechanical Engineering, Division of Production Engineering, Machine Design and Automation
,
Katholieke Universiteit Leuven, 907380261X, 9789073802612
.
29.
Van der Auweraer
,
H.
,
Guillaume
,
P.
,
Verboven
,
P.
, and
Vanlanduit
,
S.
,
2001
, “
Application of a Fast-Stabilizing Frequency Domain Parameter Estimation Method
,”
ASME. J. Dyn. Sys., Meas., Control
,.
123
(
4
), pp.
651
658
.10.1115/1.1410369
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