Tyres are a vital vehicle component forming an interface between a vehicle and the road, enabling the generation of braking, steering and traction forces. However, they also generate rolling resistance which researchers have tried to minimise through the years for environmental and economic reasons. Despite numerous attempts to model rolling resistance of tyres there still does not seem to exist a simple, flexible and accepted way of modelling rolling resistance in the time domain as well as parametrising models in an easy and accessible way. This study explores a simple and intuitive way of parametrising a hyperviscoplastic parallel rheological framework. In the experimental part of this study, rubber samples with various amounts of carbon black filler are extracted from a truck tyre section and tested using dynamic mechanical analysis. The test data was used to parametrise the material model. The model consists of Mooney-Rivlin hyperelasticity, 40 Prony elements and 8 perfectly plastic elements with Ogden hyperelasticity. The paper introduces a method to obtain a large number of parameters using only six tuneable parameters, which simplifies the tuning of the model drastically. The parametrised model is suitable for tyre rolling resistance simulations with frequency and strain amplitude dependency of the storage and loss modulus. A wide range of strain amplitudes and frequencies can be covered with the proposed method and it is possible to achieve a good fit for the storage and loss modulus values with the benefit of only a few tuneable parameters. Additional Prony or plastic networks do not increase the amount of tuneable parameters. Moreover, the method can be used to parametrise the material using manual iterations which is generally not possible for a parallel rheological framework with such a large amount of parameters. 

Tyres are a vital component for handling and load carrying while also contributing to the operating cost and environmental impact. The innovations in tyre design are driven by the need to reduce greenhouse gases and to make a better compromise between conflicting tyre properties. To accurately simulate tyres and to make these compromises a representative rubber model needs to be incorporated with strain amplitude dependency for the storage and loss modulus (the Fletcher-Gent effect). Prony series is a commonly used viscoelastic model in tyre simulations but it does not take into account the Fletcher-Gent effect and e.g. possible nonlinearities due to axle load variations are not feasible to simulate. The Fletcher-Gent effect can be modelled using parallel rheological framework (PRF), which can consist of any combination of parallel material models. Nonlinear viscoelastic models have strain amplitude dependency for the storage modulus but single nonlinear parameters lose their clarity in a PRF. Another approach is to combine a linear viscoelastic model with plasticity as is done in this article. Here, an FE truck tyre is developed and used with a viscoplastic PRF model that utilises Prony series with Mooney-Rivlin hyperelasticity and multiple plastic networks. The benefit of this combination is that the strain amplitude and frequency dependency of the storage and loss modulus are separated, which makes parameter studies simpler. The article shows that an FE truck tyre with a viscoplastic PRF model can be used in different simulations to study e.g. steady-state rolling, footprint, vertical stiffness and longitudinal tyre forces.

Rolling resistance is consuming a large portion of the generated powertrain torque and thus have a substantial effect on truck energy consumption and greenhouse gas emissions. EU labelling of tyres mandates the manufacturers to measure rolling resistance at +25 degrees C ambient temperature after stabilised rolling resistance has been established. This is a convenient way of comparing rolling resistance but disregards aspects such as transient rolling resistance and influence of the ambient temperature. For many purposes, such as dimensioning batteries for electric vehicles, this value is not representative enough to give a good understanding of the rolling resistance. In this article, the rolling resistance of a truck tyre was measured at different ambient temperatures (-30 to +25 degrees C) in a climate wind tunnel and a considerable tyre and ambient temperature dependency on rolling resistance was found. The investigation shows that the temperature inside the tyre shoulder has a good correlation with rolling resistance. Measurements with spraying water on tyres were conducted showing a considerable increase in rolling resistance due to higher cooling effect. Driving range simulations of a long haulage battery-electric truck have been conducted with temperature-dependent rolling and aerodynamic resistance, showing a significant decrease in driving range at decreasing temperature.

Rolling resistance is causing a significant part of the energy consumption in truck applications, especially at lowspeed levels. To be able to better estimate the energy consumption or remaining driving range, the truck tyre rolling resistance must be understood well. Temperature is a vital parameter for rolling resistance estimations. This article shows truck tyre rolling resistance and temperature measurements in a climate wind tunnel and simulations of tyre temperature and rolling resistance. During the climate wind tunnel tests, tyre temperature at the shoulder and tread was measured. In addition, on-road driving was conducted with inner-liner infrared temperature measurements. Tyre temperature simulations were conducted using a thermal tyre model with speed-variable thermal inertia. The comparison of tyre temperature simulations with measured inner-liner and shoulder temperatures showed good agreement with the test data. The rolling resistance was simulated using the principle of time-temperature superposition, and a master curve for rolling resistance and a curve for tyre temperature shift were constructed. These curves were used to simulate rolling resistance at a wide range of speed levels with good agreement to the experimental results. The investigation showed that the tyre shoulder temperature is a better indicator of rolling resistance than infrared measurements from the tyre tread.

Knowing the tyre pressure during driving is essential since it affects multiple tyre properties such as rolling resistance, uneven wear, and how prone the tyre is to tyre bursts. Tyre temperature and cavity pressure are closely tied to each other; a change in tyre temperature will cause an alteration in tyre cavity pressure. This article gives insights into which tyre temperature measurement position is representative enough to estimate pressure changes inside the tyre, and whether the pressure changes can be assumed to be nearly isochoric. Climate wind tunnel and road measurements were conducted where tyre pressure and temperature at the tyre inner-liner, the tyre shoulder, and the tread surface were monitored. The measurements show that tyres do not have a uniform temperature distribution. The ideal gas law is used to estimate the tyre pressure from the measured temperatures. The results indicate that of the compared temperature points, the inner-liner temperature is the most accurate for estimating tyre pressure changes (average error 0.63 %), and the pressure changes during driving are nearly isochoric. This conclusion can be drawn because the ratio between inner-liner temperature and tyre pressure is nearly constant, and the pressure can be simulated well using the isochoric gas law.

Rolling resistance dictates a large part of the energy consumption of trucks. Therefore, it is necessary to have a sound understanding of the parameters affecting rolling resistance. This article proposes a semi-physical thermodynamic tyre rolling resistance model, which captures the essential properties of rolling resistance, such as non-stationary changes due to temperature effects and the strain amplitude dependency of the viscous properties. In addition, the model includes cooling effects from the surroundings. Both tyre temperature and rolling resistance are obtained simultaneously in the simulation model for each time step. The nonlinear viscoelasticity in rubber is modelled using a Bergström-Boyce model, where the viscous creep function is scaled with temperature changes. The cooling of the tyre is considered with both convective and radiative cooling. Finally, the article explains different material parameters and their physical meaning. Additionally, examples of how the model could be used in parameter studies are presented.

A vehicle’s energy consumption is significantly affected by a resisting force created by the tyres. This resisting force, called rolling resistance, is an essential factor in the energy consumption of trucks, not only in terms of operational costs but also in terms of the range of electric trucks or other vehicles that run on sustainable energy sources. This article presents a method for calculating truck tyre rolling resistance in finite element software (MSC Marc). With the help of X-ray, 3D, and CT scanning, a representative tyre model is obtained. A viscoplastic model with separate viscoelastic and plastic parts is used to model rubber. The rolling resistance coefficient is obtained using two different methods: calculating it from the nodal contact forces at the contact patch and from contact body forces. Both methods produced comparable results, showing that the constitutive model produces realistic simulation results and, therefore, is suitable for rolling resistance simulations.

Background: Rolling resistance and aerodynamic losses cause a significant part of a truck's energy consumption. Therefore there is an interest from both vehicle manufacturers and regulators to measure these losses to understand, quantify and reduce the energy consumption of vehicles. On-road measurements are particularly interesting because it enables testing in various ambient conditions and road surfaces with vehicles in service.

Objective: Common driving loss measurement devices require unique instrumented measurement wheels, which hinders effective measurements of multiple tyre sets or measurements of vehicles in service. For this purpose, the objective is to develop a novel load-sensing device for measuring braking or driving torque.

Methods: The strength of the measurement device is calculated using finite element methods, and the output signal is simulated using virtual strain gauge simulations. In addition to the signal simulation, the device is calibrated using a torsional test rig.

Results: The simulation results confirm that the device fulfils the strength requirements and is able to resolve low torque levels. The output signal is simulated for the novel cascaded multi-Wheatstone bridge using the strains extracted from the finite element analysis. The simulations and measurements show that the measurement signal is linear and not sensitive to other load directions. The device is tested on a truck, and the effort of mounting the device is comparable to a regular tyre change.

Conclusions: A novel driving loss measurement device design is presented with an innovative positioning of strain gauges decoupling the parasitic loads from the driving loss measurements. The design allows on-road testing using conventional wheels without requiring special measurement wheels or instrumentation of drive shafts, enabling more affordable and accurate measurements.

Due to legislations introduced to prevent global warming, vehicle manufacturers must find new ways to reduce CO2 emissions. This paper explores a way to reduce rolling resistance by heat insulating and covering a truck's wheelhouse. The rolling resistance of a truck tyre was measured at +5 °C ambient temperature for consecutive speed steps in a climate wind tunnel with and without heat insulation. The study showed that by encapsulating and insulating the wheelhouse, already generated strain-induced heat could be kept in the tyre, consequently producing a lower rolling resistance. During the tests, the tyre shoulder temperature was monitored along with the tyre pressure. When the wheelhouses were encapsulated, a significant reduction in rolling resistance and an increase in tyre pressure and temperature were measured at all evaluated speed levels.