Keywords

1 Introduction

Nowadays, the standard process to assess the wear performance of a tyre involves outdoor tests, during which a convoy of vehicles travels along predefined road courses. Although well consolidated, this testing methodology has several limitations: long duration, high costs and subjected to uncontrollable variables such road conditions, weather and traffic; nonetheless, it is responsible for environmental pollution. Indoor wear testing is emerging as a viable alternative to road testing, with the advantage of being performed in an environment where boundary conditions are controlled and with the possibility of rigorous monitoring of key performance indicators. In addition to that, the development of an indoor methodology can enhance the understanding of the underlying mechanisms to wear phenomena; similarly, smart systems for monitoring tyre conditions could undoubtedly benefit from data of indoor testing process. Nevertheless, to drive indoor tests that are representative of on-road conditions, several issues must be addressed: a) definition of the machine-input time histories of forces, slip ratio, inclination angle and speed able to reproduce the wear induced by a given track and vehicle combination; b) identification of indoor testing conditions such as abrasiveness of sandpaper.

This paper focuses on the first aspect, aiming to identify the manoeuvres to be performed on the indoor testing machine in order to replicate the wear rate/shape achieved outdoor. Telemetry data acquired on outdoor sessions are processed and clustered in terms of accelerations and speed, with the aim of extrapolating from the whole time history a reduced number of significant conditions, which can be representative of the full outdoor wear session.

2 Objective and Methodology

The indoor wear machine considered for this study is a new facility by ZF (Fig. 1), composed of two testing stations and a 3 m diameter drum with a width of 600 mm, actuated by an AC electric motor. The tyres, mounted on the rim, are fixed to a load carriage that features four degrees of freedom: the three rotations, and the axial translation with respect to the drum. The machine is able to provide radial and lateral forces, driving and braking torque and camber angle to the wheel. Each testing station has a powder feeding system to prevent gumming of the drum surface, typically covered in abrasive sandpaper; in addition, a laser monitors the tread wear evolution during the test.

Fig. 1.
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ZF indoor wear tester

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The wear machine input file required to run a wear test is typically derived from telemetry data acquired during outdoor testing campaigns. The main steps in the generation of the input file to the wear machine (Drive-File), which include the time history of forces, speed, angles and slips to apply to the tyre, are:

  1. 1.

    Processing of acquired outdoor data: the data coming from outdoor sessions are processed through a properly designed routine, with the aim of removing outliers and filter unwanted disturbances.

  2. 2.

    Clustering: accelerations and speed time histories are clustered in order to extrapolate from the whole dataset a reduced number of significant manoeuvres, able to describe the chosen outdoor wear course. This is a key step when building the indoor wear machine input since it allows to rationalize and simplify a complex time history in a reduced set of manoeuvres with increased control and insight capability; same procedure could be applied for virtual track replicas via FEA simulations as well. The description of the procedure followed in this work will be addressed later on.

  3. 3.

    manoeuvres simulation and Drive-File composition: the representative manoeuvres obtained by means of clustering contain only kinematics information about the global motion of the vehicle, i.e. speed and accelerations in the CoG. These data must be simulated by means of an inverse dynamics model, in order to obtain forces, torques and inclination angles acting on each car corner. During typical outdoor wear courses, the vehicle experiences soft handling manoeuvres with accelerations up to 0.5 g, in which the behaviour of the car can be assumed as linear; this enables a validated dynamics model that accounts for some simplification to be chosen. This vehicle dynamics model has been validated by comparing its output to those obtained either via VI-Grade CarRealTime or directly to outdoor data. After the vehicle dynamics simulation phase, the significant manoeuvres are re-arranged to build a suitable Drive-File for the indoor test.

The present paper focuses on the clustering process, which is crucial in the Drive-File definition.

Indeed, the proposed procedure (Fig. 2) is not the only one when dealing with indoor tyre testing. A similar approach was described in [1], but with no specific mention to clustering. Another viable procedure consists of defining a set of standardised manoeuvres by default. These do not represent any real course, but are able to summarise the typical working conditions of a tyre. Alternatively, the indoor load history can be derived from direct measurements on the car wheels [2].

Fig. 2.
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Drive-File generation workflow

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3 Clustering

Clustering is a crucial step in the generation of the input file for the indoor wear machine. This procedure allows to reduce the number of conditions to be replicated from the thousands of samples acquired outdoor to few significant manoeuvres, able to fully reproduce a complete wear course.

The extrapolation of such manoeuvres has to combine two different principles. In fact, the number of conditions to be replicated indoor must be sufficient to avoid the loss of significant information from the original acquisition. At the same time, it has to include the fewest manoeuvres possible, in order to keep the test simple and not over-complicated. In this work, a statistical clustering procedure has been adopted. The k - medoids data mining algorithm is used to achieve a reduction in the number of conditions from the thousands of samples acquired outdoor to few hundreds of manoeuvres, based on vehicle longitudinal and lateral acceleration (\(a_x\), \(a_y\)), speed (v) and travelled distance. The resulting set of conditions can be effectively visualised in Fig. 3. It is a bubble plot in which each point represents a cluster center defined by longitudinal and lateral accelerations and speed. The size of the bubbles identifies the time spent in each condition. A cluster identified by a larger dot is highly representative of the outdoor acquisition, therefore a longer time must be spent in such manoeuvre.

Fig. 3.
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Bubble plot of clustered manoeuvres. The size of each point refers to the time spent in a certain condition, i.e. the frequency of occurrence of such manoeuvre. The colors refer to the speed level.

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As said, the choice of the number of cluster (i.e. manoeuvres) is not trivial. In this work, a sensitivity analysis to clusters number has been performed through FEA with a model defined on a chosen tyre specification and on a selected wear route. The aim was to find the minimum manoeuvres number providing a sufficient fidelity level to the original course. To do that, the energy dissipated on each tyre groove in the contact patch was computed after the clustering procedure. Then, that values compared to those obtained with the full outdoor acquisition. The acceptance threshold was set to \(\pm \,5\%\) of relative percentage error. Figure 4 shows the trend of such error on dissipated energy for each tyre groove. As can be evinced, about 150 clusters are sufficient to achieve an error within the imposed threshold. Increasing the manoeuvres number even more, such discrepancy tends to zero, while in case of decreasing them an accuracy reduction can be assessed anyhow. Nevertheless, choosing larger sets of conditions (for instance 600) would not be beneficial since leading to over complicated indoor tests. Same considerations would apply if same approach were used for virtual track replica by means of FE analyses.

This sensitivity analysis, here only briefly reported, showed that this clustering approach is able to fulfil the previously mentioned requirements: adequate similarity to the unclustered time history of speed and accelerations by using a small number of extrapolated conditions. Extensions to multiple cases confirmed the considerations hereby reported.

Fig. 4.
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Relative percentage error on dissipated energy computed with respect to the full outdoor acquisition, as function of increasing clusters number. Each line refers to a single tyre groove (GRV).

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4 Results and Conclusions

In this section, results of indoor and outdoor tests are compared. The indoor test was driven by an input file obtained using the proposed clustering approach. The correlation between outdoor and indoor tests was assessed comparing the weight loss rate [mg/km], the abrasion rate [mm/1000 km] and wear shape.

Fig. 5.
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Wear profile indoor vs outdoor

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Figure 5 shows the wear profile evolution (tread height vs. tread width) over travelled distance both for indoor and outdoor test (data are presented in a non-dimensional way for industrial privacy reasons). As it can be seen, the indoor tests result to be an accelerated version of the outdoor ones: a comparable wear amount can be reached in around half travelled distance. This aspect is primarily related to the higher abrasiveness of the sandpaper used for indoor testing. Compared to road asphalt, it exhibits higher levels of micro-roughness and lower of macro-roughness. This can be considered as beneficial, since indoor tests take shorter time than outdoor ones. Coming to the wear profiles, a good agreement between indoor and outdoor can be appreciated. Main differences are concerned with a higher material loss on the inner shoulder, which is likely to be induced by the different tyre footprint on a curved surface compared to a flat road and the difference between the kinematics of vehicle suspension and the wear machine load carriage.

Concluding, the main results obtained in this work are related to the implementation of a validated clustering procedure. This is able to extract from large dataset only few significant manoeuvres, helping in saving time and resources both in FEA and experimental tests. Then, concerning the latter, the indoor procedure exhibited a larger wear rate compared to the outdoor one. As said, this was expected and can be attributed to the different abrasiveness of the two contact surfaces. Also the wear shape obtained indoor showed good similarities to that outdoor.