Road friction coefficients are highly effective for advanced vehicle control technologies, although the estimation at four individual tires has not been practically used for ordinary vehicles. This study describes the essential relation between the tire forces and the aligning torque that can be rearranged as an estimation equation for the grip margin. The grip margin is readily convertible into the friction coefficient. The brush model is reanalyzed, beginning from the conventional simple physical model, and intrinsic expressions are derived. The grip margin, which is defined as the residual tire force normalized by the radius of friction circle, was estimated using three components of the tire forces and the aligning torque. A simple cubic equation is obtained as a grip margin equation for an isotropic brush model. Previous studies assumed an anisotropic brush model and obtained an imperfect quintic equation. In the present study, a new term is added to the algebraic equation, which was shown to be consistent with the isotropic model. The solutions to the equations are approximated by Chebyshev polynomials. The estimation methods are tested by numerical simulations using CarSim, which is a popular vehicle simulation software application. The estimated friction coefficients agree well with the values that are set during each run of the simulations, especially for the cases of smaller grip margins and lower friction conditions.

1.
Katayama
,
T.
,
Yasuno
,
Y.
,
Oida
,
T.
,
Sao
,
M.
,
Imamura
,
M.
,
Seki
,
N.
, and
Sato
,
Y.
, 2007, “
Development of 4 Wheel Active Steer
,”
JSAE Annual Congress Proceedings
, Society of Automotive Engineers of Japan, Yokohama, pp.
7
12
, No. 11-07 (in Japanese).
2.
Nishihara
,
O.
, 2007, “
Dynamic Optimizations of Tire Workload Distributions in Four-Wheel Independent Steering Vehicles
,”
Proceedings of JSME Dynamics and Design Conference 2007
, Japan Society of Mechanical Engineers, Okayama, No. 07-8 (in Japanese).
3.
Nishihara
,
O.
,
Hiraoka
,
T.
, and
Kumamoto
,
H.
, 2006, “
Exact Minimax Optimizations of Tire Workload for Independent Steering Vehicles
,”
Proceedings of FISITA World Automotive Congress
, International Federation of Automotive Engineering Societies, Yokohama, Paper No. F2006V217.
4.
Nishihara
,
O.
, and
Kumamoto
,
H.
, 2006, “
Minimax Optimizations of Tire Workload Exploiting Complementarities Between Independent Steering and Traction/Braking Force Distributions
,”
Proceedings of AVEC ‘06, International Symposium on Advanced Vehicle Control
, Taipei, pp.
713
718
.
5.
Nishihara
,
O.
,
Hiraoka
,
T.
, and
Kumamoto
,
H.
, 2006, “
Optimization of Lateral and Driving/Braking Force Distribution of Independent Steering Vehicle (Minimax Optimization of Tire Workload)
,”
Trans. JSME, Ser. C
,
72
(
714
), pp.
537
544
(in Japanese).
6.
Nishihara
,
O.
,
Noda
,
S.
,
Sakatani
,
Y.
, and
Kurishige
,
M.
, 2009, “
Protection Function for Active Four-Wheel Steering Vehicle Using Estimation Method for Road Friction Coefficient
,”
Trans. JSME, Ser. C
,
75
(
759
), pp.
3038
3046
(in Japanese).
7.
Nakano
,
S.
,
Nishizaki
,
K.
,
Nishihara
,
O.
, and
Kumamoto
,
H.
, 2002, “
Steering Control Strategies for Steer-by-Wire System (Second Report): Vehicle Attitude Control
,”
Trans. of Jap. Soc. Auto. Eng.
,
33
(
3
), pp.
121
126
(in Japanese).
8.
Kanai
,
K.
,
Kawabe
,
T.
, and
Ochi
,
T.
, 2004, Vehicle Control—Aircraft and Automobile, Maki-shoten, Tokyo, pp.
219
225
(in Japanese).
9.
Ono
,
E.
,
Hattori
,
Y.
,
Aizawa
,
H.
,
Kato
,
H.
,
Tagawa
,
S.
, and
Niwa
,
S.
, 2007, “
Clarification and Achievement of Theoretical Limitation in Vehicle Dynamics Integrated Management
,”
Trans. JSME, Ser. C
,
73
(
729
), pp.
1425
1432
(in Japanese).
10.
Ono
,
E.
,
Hattori
,
Y.
, and
Muragishi
,
Y.
, 2005 “
Estimation of Tire Friction Circle and Vehicle Dynamics Integrated Control for Four-Wheel Distributed Steering and Four-Wheel Distributed Traction/Braking Systems
,”
R&D Review of Toyota Central R&D Labs.
,
40
(
4
), pp.
7
13
. 0002-7820
11.
Ono
,
E.
,
Hattori
,
Y.
,
Muragishi
,
Y.
, and
Koibuchi
,
K.
, 2004, “
Vehicle Dynamics Control Based on Tire Grip Margin
,”
Proceedings of AVEC ‘04, International Symposium on Advanced Vehicle Control
, Arnhem, pp.
531
536
.
12.
Ono
,
E.
,
Asano
,
K.
, and
Koibuchi
,
K.
, 2003, “
Estimation of Tire Grip Margin Using Electric Power Steering System
,”
Proceedings of the 18th IAVSD Symposium
, IAVSD, Atsugi.
13.
Pacejka
,
H. B.
, 2005,
Tire and Vehicle Dynamics
,
2nd ed.
,
SAE International
,
Warrendale
, pp.
90
117
.
14.
Fujita
,
T.
,
Ohori
,
M.
,
Yoshida
,
H.
,
Suizu
,
Y.
,
Suzuki
,
S.
,
Masaki
,
N.
, and
Nakao
,
M.
, 2003, “
Fundamental Study of Smart Tire Model (2nd Report: Function for Measurement of 6 Force Components)
,”
Proceedings of Dynamics and Design Conference 2003
, Japan Society of Mechanical Engineers, No. 03-7 (in Japanese).
15.
Ishizuka
,
T.
,
Ohori
,
M.
,
Fujita
,
T.
,
Suizu
,
Y.
,
Masaki
,
N.
, and
Kato
,
A.
, 2005, “
Fundamental Study of Smart Tire System
,”
Proceedings of the Ninth Symposium on Motion and Vibration Control
, Japan Society of Mechanical Engineers, No. 05-15, pp.
120
124
(in Japanese).
16.
Press
,
W. H.
,
Flannery
,
B. P.
,
Teukolsky
,
S. A.
, and
Vetterling
,
W. T.
, 1988,
Numerical Recipes in C
,
Cambridge University Press
,
Cambridge
.
You do not currently have access to this content.