Abstract — This paper deals with tyre enveloping behaviour
on uneven road surface. To build realistic and reliable vehicle
dynamics models it is of fundamental importance to study the
influence of road obstacles and irregularities on forces and
displacements involving a rolling tyre. After a brief review
about early studies concerning this phenomenon, the tandem
model with elliptical cams is introduced and described,
highlighting its hypothesis and the parameters on which it is
based, the most important of which are the cams profiles and
the distance between them. The main aim of this paper is the
executive project of a test rig aimed to carry out an
experimental campaign for the identification of the parameters
of the tandem cam model and for its validation.
The idea is to experimentally acquire the path of the patch
centre of a tyre rolling over an obstacle, to define the
parameters of the curves employed for the cam profiles and the
distance between them in the tandem model. It is important to
highlight that these parameters are strictly connected to tyre
properties and need tests to be investigated and identified.
The design started from a test bench for motorcycles
already available at DII’s Tyre Lab, introducing proper
changes without compromising original test bench destination.
Index Terms — Tyre envelope model, Tyre experimental test
rig, Tyre ride quality
URING its real working life a tyre rolls over uneven
road and the presence of irregularities generates sudden
variations both in tyre position and in interaction forces
direction and modulus. This aspect concerns transient
performances and is usually not taken into account in
vehicle dynamics modelling and simulation , , , ,
, , , , , ,  despite it has not a negligible
influence on tyre dynamics and then on vehicle behaviour.
Moreover, vehicle dynamics control systems , ,
, , ,  are usually based on the hypothesis
that the tyre is always in contact with the road and this not
always verified assumption can cause their improper
intervention. Also tyre friction , , , , ,
,  and thermal modelling  are influenced by the
effects of this phenomenon.
For this reasons the development of reliable models able
to take into account tyre enveloping behaviour on road
Manuscript received July 16, 2015; revised February 01, 2016.
Flavio Farroni is with Dipartimento di Ingegneria Industriale, Università
degli Studi di Napoli Federico II, via Claudio n. 21 80125 Napoli Italy (e-
Francesco Timpone is with Dipartimento di Ingegneria Industriale,
Università degli Studi di Napoli Federico II, via Claudio n. 21 80125
irregularities is necessary to better understand and simulate
the vehicle real performance.
Research on the excitation of pneumatic tyres caused by
uneven road surfaces started in the 1960s. Since then,
several models have been developed in order to describe the
tyre enveloping behaviour, which consists in the capability
of the tyre to deform when rolling over small road
irregularities. Although many of these models are used as
components in dynamic vehicle models, the development of
these last started from the late 1980s. Many dynamic tyre
models were developed during the last decade as results of
growing interest in virtual prototyping with regard to ride
comfort and durability simulations.
The research in the 1960s was mainly experimental:
Hey  stated that little was known about the forces
generated between tyre and road when rolling over
obstacles. Important observations considering the
enveloping behaviour on short obstacle were made by
Gough , who indicated that a tyre rolling quasi-statically
at constant velocity and axle height  over an obstacle
with characteristic length much smaller than the tyre contact
length, shows three distinct responses: (1) variations in the
vertical force, (2) variations in the longitudinal force and (3)
variations in the spin velocity of the wheel. These responses
are shown in Fig. 1.
Gough's test results showed that the duration of the
three responses is much longer than the time employed to
cross the obstacle. This is due to the visco-elastic properties
and geometry of the tyre : because of its curvature in the
contact zone, the tyre gets in contact with the obstacle
before than the wheel centre overtakes it; vice versa, the
tyre is still in contact with the obstacle after that the wheel
centre has overtaken it.
In the sketched situation, two contact patches exist: this
phenomenon results in a response of the tyre that is much
smoother than the obstacle shape, often described as an
Lippmann et al.  studied the responses of both truck and
passenger car tyres rolling over short sharp unevennesses
like cleats and steps of several heights. From their
experiments, they concluded that an almost linear relation
exists between tyre longitudinal and vertical force variations
and step height. Therefore, they proposed that the
superposition principle could be used to calculate the
response of a tyre to any obstacle shape described as the
sum of elementary steps.
Napoli Italy (corresponding author: Francesco Timpone; phone: +39 081 76
83263; fax: +39 081 2394165; e-mail: firstname.lastname@example.org).
A Test Rig for Tyre Envelope Model
F. Farroni, F. Timpone, Member, IAENG
Later researches have been mainly focused on the
development of techniques to model tyre behaviour on road
unevennesses. Bandel and Monguzzi  discovered that
the variations of vertical and longitudinal forces for a tyre
rolling quasi-statically over an obstacle could be
transformed into the convolution of two identical basic
functions by means of empirical relations. They showed that
the basic function for a specific obstacle represents a
characteristic of the tyre and is independent on inflation
pressure and deflection (or vertical load). They also showed
the influence of obstacle length and height on the basic
functions. This concept was adopted by Zegelaar , who
used half and quarter sine waves for the basic functions of a
cleat and step obstacle. He also introduced an alternative
technique for obtaining the effective road surface using a
single basic curve and a two-point follower. After having
worked with the two-point follower model on quarter sine
waves (Fig. 2) and after having understood its limitations,
the idea was hit upon to generate the elementary basic curve
that holds for a step in road profile with an elliptical cam.
II. THE TANDEM MODEL WITH ELLIPTICAL CAMS
In order to reproduce the experimental double-bump
shaped curve , it is necessary to adopt the results
provided by the two-point follower solution. It is however
more convenient to use a full geometrical model that can
move directly over the actual road profile. Since a single
elliptical cam moving over the actual road profile is able to
describe the basis curve, the effective height and slope can
be obtained by moving with two cams in "tandem"
configuration over the actual road surface, as is illustrated in
The distance between the two elliptical cams ls is equal to
the length of the two-point follower. The effective height w
of the contact patch centre is equal to the height of the
midpoint of the lower tandem rod (fig. 5). Thus, the
equation for the effective height is:
where X is the global wheel centre longitudinal position
and Zf and Zr are the global heights of the front and rear
ellipse centres, respectively. The inclination angle of the
tandem rod corresponds to the effective slope tan(βy):
The main goal of the presented activity is to study the
behaviour of a tyre rolling over an obstacle. In order to
reproduce analytically the experimental shapes, a first stage
of the work concerned with the design of the test bench for
the data collection presented in this paper. Further
developments will consist in the parametrical identification
Fig. 1. Variations in the vertical force, variations in the longitudinal
force, variations in the spin velocity of the wheel .
Fig. 2. Representation of the basic function
and two-point follower models .
Fig. 3. Generation of the elementary basic curve
with an elliptical cam .
Fig. 4. Two elliptical cams in "tandem" configuration
used to generate the effective road surface .
Fig. 5. The tandem model with elliptical cams .
used to generate the effective road surface.
of the tandem cam model and in its validation on the basis
of experimental results.
III. TYRE ENVELOPE TEST BENCH
The idea to assess experimentally the centre’s path of a
tyre rolling over an obstacle represents in the described
activity a preliminary step, useful to define the parameters
of the ellipse employed for the cam profile and the distance
between them in the tandem model.
It is important to highlight that these parameters are
strictly connected to tyre properties, that need tests to be
investigated and identified. In order to carry out these
experiments, it has been necessary to realize a dedicated test
Since in DII’s Tyre Lab a test bench for motorcycles
was already available , ,  it has been decided to
modify and to use it to test car tyres. The pre-existing test
bench is shown in Fig. 6. This framework allows to simulate
a motorcycle going on an even road surface. Essentially it is
composed of a driver belt moved by an electrical motor and
of a portal that shores up part of the motorcycle that has to
be tested. The idea is to use the other side of the driver belt
without interfering with the motorcycle experiments, so that
it has been fundamental to build another portal that could
shore up car tyre.
The new test bench (Fig. 7) is composed of a portal, of
a tyre supporting system and of a device able to apply a load
equivalent to the one due to vehicle mass and to load
transfers observable in common working conditions. New
portal is composed of an upper and two lateral crossbars in
Fe510B steel, section bars 60mm x 40mm, fixed to the pre-
existing one with bolted connections.
Simulating tyre motion needs a system that allows the
replication of its real working conditions: in order to make
this possible, the tyre has to be able to rotate around its axis
and to move vertically. For this reason tyre supporting
system is composed by a shaft onto which it is fitted a
flange to fasten the rim of the wheel (Fig. 8a), fixed to the
portal through two linear guideways (Fig. 8b).
To mount different kinds of rims onto the shaft it has
been necessary to realize a proper fitting system, allowing
the flange to be interchangeable. The fitting system is
composed of two adapter sleeves for shafts, two spherical
roller bearings for cylindrical and tapered bore and an axle
box fastened on them. Finally, the mounting flange is bolted
onto the axle box. It is important to point out that the shaft
does not rotate, while the axle box and the flange do. The
system just described is depicted in Fig. 8a.
Shaft has been built in a 39NiCrMo3, surface hardened
(HRC 55-60, hardening depth 2.00 – 5.00 mm), grinded and
chromium plated steel of circular section (Ø 40 mm), for
which a stress verification calculation has been done. In
order to avoid shaft rotation, its ends have been machined in
a square shape (Fig. 9).
The device for load application is composed of two
double hoists depicted in Fig. 10, installed at the shaft ends.
The lower part of the hoist, composed of two pulleys
mounted on a support, is fixed to the base of the structure.
The upper part is composed of two pulleys mounted on a
support and a welding eyebolt hooked on an element fitted
on the shaft.
Since maximum applied load is equal to 6000N on each
side of the shaft, a verification of the strength of the hoist’s
components has been performed.
IV. EMPLOYED SENSORS AND TESTING PROCEDURE
In order to characterize experimentally the tyre
Fig. 6. Pre existing motorcycle test bench.
Fig. 7. New car tyre test bench.
Fig. 8a. Tyre supporting system.
Fig. 8b. Portal guideways detail.
Fig. 9. View of the shaft square end.
Fig. 10. Double hoist loading system.
enveloping model, it is necessary to estimate the trajectory
of the wheel center and the interaction forces Fx and Fz of
the tyre rolling over an obstacle. For this reason the test
bench has been equipped with a displacement sensor and
eight load cells.
It has been chosen to employ a non-contact laser
displacement sensor. Since the idea is to perform
experiments at high speed, a contact displacement sensor
would have been inaccurate because of the delay related to
the inertia of the sensor’s mobile components at high speed.
Basing on optical triangulation principle, the laser ray has to
point in perpendicular direction to an even surface; for this
reason the best mounting solution is to fix the sensor to one
of the lateral crossbars of the portal and to point the laser
ray to the flange bolted to the guideway’s block.
It has been defined that the optimal procedure to measure
the interaction forces Fx and Fz, according to the position of
all components of the structure, is to insert eight
compression mini-load cells between the square section
faces of the shaft and the square section faces of the flange.
The load cells, sensitive to compression loads, must be
positioned in perpendicular direction so that four cell can
measure the vertical load and the other four the longitudinal
Once defined and tested the optimal rig setup, the system
has been employed with the aim to carry out a wide
experimental campaign, able to investigate the dependence
of tyre enveloping behaviour on several variables, such as
obstacles length and height, load and speed at which the tyre
approaches to the obstacle and tyre structure and dimension.
Standard test procedure consists in: (1) sticking the
testing obstacle (typically, a kerb for motorsport
applications and a step or a rail piece for passenger ones) on
the driver belt, (2) putting tyre in contact with the belt and
applying load by means of the described device, choosing
the proper force on the basis of the nominal load acting on
the tyre in common working conditions employing
calibrated weights, (3) activating the driver belt, selecting
the proper speed, (4) starting data acquisition.
In figure 11 a first experimental result of the wheel centre
vertical displacement as a function of the longitudinal
displacement is reported. The test has been carried out using
a slick high performance tyre with an inflation pressure of
1,85 bar and a vertical load of 4800 N rolling along a flat
surface with a cleat 0,03 m high.
In the figure it is possible to observe the typical
experimental double-bump shaped curve . The profile of
each single bump is linked to tyre stiffness characteristics,
as to inflation pressure. Variations in such quantities
reproduce an immediately visible change in the trend of
each bump, generally quite linear for high stiffness and high
pressure, more curved at lower ones. Curves like the shown
one can be used to identify the parameters of the tandem
It has to be highlighted that rig users are able to act on the
test conditions controlling the working variables from a PC
located behind a protective glass shield, built in order to
respect the safety standards adopted in the laboratory.
In this paper the final design and the first experimental
results of an experimental test rig aimed to characterize the
behaviour of a tyre rolling on road obstacles has been
presented together with the description of the adopted
sensors and of the testing methodology. In particular the test
bench is aimed to identify the parameters of tyre envelope
models, among which the tandem model with elliptical cams
has been preferred, being the most reliable and realistic in
this field. Tests are carried out making the tyres roll on a
belt on which different obstacles are applied. The obstacles
produce changes in tyre center position and in its normal
interaction forces, measured by means of displacement and
load sensors and sent to a PC. The acquired data are
employed as an input for an identification procedure aimed
to find out the proper cams profile and distance to reproduce
the experimental results. In this way it is possible to
understand the influence of tyre constructive properties and
of obstacle geometrical dimensions  on enveloping
model parameters. Future developments of the study will
deal with the definition of a specific analytical formulation
able to express such influences.
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F. Farroni (Naples, 7th of March 1985) received his
M.Sc. degree in Mechanical Engineering in 2010
and Ph.D. in Mechanical System Engineering in
2014 at University of Naples “Federico II”. He is
technical consultant for vehicle dynamics at Ferrari
S.p.A. and tyre modeler at GES racing department.
Dr. Farroni's recent work has focused on the
development of interaction models accounting
friction and thermodynamics phenomena and on
experimental activities in the field of contact
mechanics for the optimization of dry and wet grip performances. In
February 2015 he has been awarded as Young Scientist of the Year at Tire
Technology International Conference 2015 in Cologne.
F. Timpone (Naples, 5th of September 1974)
received the M.Sc. degree in Mechanical
Engineering in 1999 and the Ph.D. degree in
Thermomechanical System Engineering in 2004
both from the University of Naples “Federico II”.
He is Assistant Professor at the University of
Naples “Federico II” and his research interests
include the dynamics and the control of
Dr. Timpone became a Member (M) of IAENG in