Chapter 1
Introduction
1.1
Objectives
The automotive field is an active engineering sector in which the development
of new components is constantly improving under increasingly strict regulations
and requirements. Developing new components must consider styling, durability,
manufacturing cost reduction, lightweight, and carbon footprint.
One of the fundamental components for overall vehicle safety and performance
is the wheel. Since tyres and wheels are recognised as significant contributor to
road safety, European and worldwide organisations promote a common approach
for dimensioning, tyre-wheel coupling, operative conditions and usage recommendations [1]–[3]. The regulations mentioned above also introduce a reduced amount
of performance parameters to be taken under control during experimental test procedures in order to increase the repeatability of results. Usually, only fatigue life in
terms of the number of cycles, maximum stress, and failure location is considered.
Since experimental test procedures are time and cost-demanding [4], [5], numerical modelling has been introduced in the automotive field for decades. Specifically,
many authors [6]–[14] proposed different procedures based on the finite element
method to numerically reproduce experimental fatigue tests. Nevertheless, the increase in complexity in experimental procedures, i.e. biaxial fatigue test [15], is
still not aligned with corresponding numerical results. It is necessary to fill the gap
between tyre technology and wheel manufacturers’ knowledge, which is the most
significant contribution to simulation reliability.
Available simulation schemes are limited to a conservative estimation of main
performance parameters, e.g. residual stress sources in the wheel manufacturing
process. Therefore, the current state-of-the-art is a support diagnostic tool to the
design, not the leading actor. Hence, parameter sensitivity is not considered in the
simulation process since the implementations cannot depict the effect.
Since the design period is, on average, three months or more, the iterative optimisation process has to be intensely exploited during the design phase to minimise
1
Introduction
the experimental test phase. It is necessary to reach a sufficiently reliable modelling
level to describe the detailed performance parameter sensitivity to design variables.
Therefore, the project’s primary goal is to establish a high confidence level in
automotive steel wheels’ dynamic and static behaviour simulation process. The
methodology results could introduce alternative manufacturing techniques for improving wheel design and manufacturing processes.
1.2
Main contributions
Consequently the project development, five main original contributions have
been obtained during this Ph.D. research period and are hereby presented:
• Indirect estimation of interference fit properties by monitoring the corresponding stress-stiffening effect on system dynamics Through the application of
the concept of Design for Modal Assembly (DMA) [16], [17], the correlation
between variation in structural properties such as the stiffness and natural
frequencies, it is obtained an estimation of the interference fit level and pressfit force based on polynomial chaos expansion models. The methodology is
used to fill the gap between consolidated interference fit analytical models as
thick and thin theories [18]–[20], developing a generalised technique to characterise the interference between components non-invasively. Moreover, an
experimental-only procedure is proposed to train the meta-model.
• Robust methodology for steel wheel subject to residual stress and linear mean
stress variation fatigue assessment A systematic finite element method modelling approach is defined to consider main residual stress contributions and
the reduction of mean load level during fatigue test cases. The disc-rim interference fit, the bolt tightening torque loss, and principal geometry variability
such as the scallop feature are considered. The methodology is validated
against massive experimental data with geometry, loading condition, and operative condition variability for the current state-of-the-art fatigue test procedures.
• Strain-geometrical selection criterion for efficient strain gauge sensor positioning A procedure for optimal strain gauge sensor placement for validation
of stress analysis is defined. The methodology is based on the consolidated
Modal-Geometrical Selection Criterion (MoGeSeC) [21], modified for strain
field data. It is effectively used for experimental-numerical comparison by
minimising the number of sensors describing the significant strain field.
• Tyre-rim interfaces for different scale simulations The tyre-rim interaction
issue is approached to reduce the limitations in connecting tyre models, often
over-detailed for the wheel fatigue assessment, by defining a set of crescent
2
1.3 – Thesis structure
complexity interface models capable of describing main non-linearities acting
on the rim flanges. The methodology allows depicting the pressure field on the
rim induced by the combined effects of inflation pressure, tyre bead tension,
side-wall large deformations and bead contact.
• Optimisation algorithm for improvement of strain gauge experimental-numerical
correlation when sensor location is uncertain An algorithm to improve the
experimental-numerical correlation based on strain gauge measurements is
developed. The methodology is applied in critical experimental setups where
the sensor position and orientation are almost unknown.
1.3
Thesis structure
This dissertation is organised into seven main parts:
• Chapter 2 presents a brief introduction to different experimental methodologies to accomplish steel wheel fatigue assessment. Moreover, the tyre and
wheel dynamic behaviour simulation state-of-the-art show the limitations and
the challenges.
• Chapter 3 describes the development of a non-linear finite element method
strategy to simulate automotive steel wheel fatigue assessment. The methodology includes the failure criterion selection based on experimental evidence.
The approach is validated against the experimental fatigue test database supplied by MW Italia S.p.A.
• Chapter 4 : a methodology to indirectly estimate interference fit between bodies based on variability in structural properties is developed. The methodology is numerically studied against a simple shaft-hub press-fit setup, showing
the limitations of consolidated analytical methodologies such as Lamé [18]
and Young-Laplace [19], [20] theories. Then, an industrial case study based
on steel wheel disc-rim interference fit is studied, showing the efficiency of the
developed technique.
• Chapter 5 : the tyre-rim interface is characterised by modelling the load contributions. The formulation is separated into three models, namely rigid, stiff
lumped and stiff distributed interfaces in which linearisation hypotheses are
gradually removed, obtaining a compact, reliable approach to depict stress
and contact pressure field among the rim flanges, crucial in fatigue assessment occasions.
• Chapter 6 : a methodology to estimate the experimental position of strain
gauges on an instrumented structure is developed and applied to improve the
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