# Finite Element Modeling of an Aircraft Tire Rolling on a Steel Drum: Experimental Investigations and Numerical Simulations

^{*}

## Abstract

**:**

## 1. Introduction

#### Drum Testing Machine

## 2. Measurement Methods and Equipment: Laboratory Drum

- Acceleration step, from s
_{1}= 0 km/h up to s_{2}km/h during t_{1}seconds at preliminary constant loading l_{1}= l_{2}kN and a given skidding angle β. - Loading step, vertical loading increases up to l
_{3}kN during t_{2}seconds, at constant velocity s_{3}= s_{2}km/h. - Rolling step at constant velocity s
_{3}= s_{2}km/h, at constant loading l_{3}kN during t_{3}seconds. - Unloading step from l
_{4}= l_{3}kN down to l_{5}= 0 kN within t_{4}seconds.

#### 2.1. The Influence of Skidding Angle, Velocity and Loading on the Thermal Evolution of the Tire Tread, Experimental Data

_{1}, β

_{2}, β

_{3}and β

_{4}represent the same angle values in all the tests). The velocity varies from 110 Km/h up to 190 km/h. In the same way, nominal loadings start at 200 kN and end up at 330 kN. The inflation pressure is maintained at its nominal value (about 1700 kPa). All figures here after represent the mean temperature distribution along the interface line between the tread and the drum during the stabilized velocity and loading period.

#### 2.1.1. The Effect of Skidding Angle

- The variation of skidding angles in the case of loading l
_{3}= 200 kN at velocity lower than 120 km/h.

_{3}= 200 kN and a velocity of s

_{3}lower than 120 km/h were chosen.

_{1}, the heat amount is about 10 °C. Increasing the skidding angle from β

_{1}to −β

_{2}, leads to a significant heating, more than 50 °C. The amount of heat decreases for higher β

_{3}and −β

_{4}angles. All these temperature profiles present a rising or descending slope of heating depending directly on the sideslip angle orientation.

- The variation of skidding angles in the case of loading l
_{3}= 260 kN at velocity lower than 120 km/h.

_{3}= 260 kN. The thermal evolution presents a higher temperature compared to the first case were the loading value was only l

_{3}= 200 kN (Figure 5). It can be noted that in the case of high loading (Figure 6), the effect of the skidding angle is still significant. The same considerable heating could be seen passing from β

_{1}to β

_{2}. The next changes in β produce the same effects, with almost the same mean temperatures, but the temperature distributions change from ascending-descending slopes to plateau-like shapes.

- The variation skidding angles in the case of loading l
_{3}= 200 kN at velocity up to 190 km/h.

_{3}=200 kN and rolling at velocity s

_{3}up to 190 km/h. As it can be seen, there is a considerable influence of the skidding angle on the thermal evolution. The high velocity leads to a somewhat homogeneous thermal distribution on the left and right sides of the tire tread. Mean temperature distributions present the same plateau shapes, but the maximum values increase by at least 20 °C.

#### 2.1.2. The Effect of Velocity

_{3}, s

_{4}), the temperature rise rate seems to saturate, tire tread profiles became flat and most temperatures in the contact zone are close to those of the center of the tread.

#### 2.1.3. The Effect of Loading

_{1}, l

_{2}= l.5 × l

_{1}, l

_{3}= 2 × l

_{2}, l

_{4}= 1.3 × l

_{3}, l

_{5}= 1.3 × l

_{4}, for a fixed velocity s

_{3}lower than 120 km/h and a constant skidding angle of 6°.

_{1}, l

_{2}), the vertical load seems to be not high enough to influence the whole contact patch; it could be related to the tire structure, which is designed to operate at high loading. For loadings beyond 260 kN (l

_{4}, l

_{5}), no major influence of the vertical loading is noticeable. The amount of heat induced by loadings l

_{4}or l

_{5}over the heat level of loading l

_{3}is lower than 10 °C.

#### 2.2. Which Test Should Be Used: Rolling on a Flat Runway or on a Steel Drum?

#### 2.3. Remarks on the Experimental Results

- -
- The skidding angle influences directly the temperature evolution; higher temperatures are recorded for higher skidding angle values.
- -
- The vertical loading has less effect on the thermal evolution in the center of the tire tread, but a higher effect on the borders.
- -
- The heat rate as a function of velocity seems to have an asymptotic behavior.
- -
- The mean temperature presents sloping or flat profiles depending on charging parameters.

## 3. Numerical Simulations of an Aircraft Tire Rolling on a Steel Drum

^{−6}× 1/°C for 20 °C and 150e

^{−6}× 1/°C for 200 °C.

_{0}. The contact pressure transmitted between the two surfaces increases exponentially as the clearance continues to diminish. Figure 13 illustrates this behavior. The value of the clearance C

_{0}and the contact pressure P

_{0}were determined after a numerical sensitivity analysis, C

_{0}= 0.002 m and P

_{0}= 2000 kPa.

_{1}kN. The numerical simulations are done taking into account the high geometrical deformations of the tire and its hyper-elastic materials. The next Figure 14 shows the tire position on the drum at slip angles at 0° and 6°. The skidding angle is imposed before the drum starts rotating.

#### 3.1. Mesh Sensitivity and Computational Time (CPU)

_{1}kN, Figure 17c shows the tire loaded with l

_{2}= 10 × l

_{1}kN and Figure 17d illustrates the tire section loaded with l

_{3}= 25 × l

_{1}kN. The model realized with 51 circumferential elements seems to be convenient for loading less than 300 kN. It is clear that in the case of a loading greater than 300 kN, the option of 101 or 181 elements seems to be necessary, knowing that the computational time is still a considerable factor to take into account.

#### 3.2. Numerical Simulation of an Aircraft Tire Rolling on a Steel Drum, Loading with 200 kN, Velocity up to 114 km/h, Skidding Angle = 6°

#### 3.3. Numerical Simulation of an Aircraft Tire Rolling on a Steel Drum, Loading with 200 kN, Velocity up to 190 km/h, Skidding Angle = 6°

## 4. Conclusions

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Typical drum testing machine/external surface test [12].

**Figure 2.**(

**a**) Experimental set-up (

**b**) tire position, view camera/before loading, (

**c**) tire position, view camera/after loading, (

**d**) mirror and infrared camera positions.

**Figure 4.**Experimental set-up: (

**a**) tire/drum configuration (

**b**) temperature distribution in the contact zone, (

**c**) the thermal evolution of contact zone.

**Figure 5.**The variation of skidding angles for loading l

_{3}= 200 kN and velocity lower than 120 km/h.

**Figure 6.**The variation of skidding angles for constant loading l

_{3}= 260 kN at velocity lower than 120 km/h.

**Figure 7.**The variation of skidding angles for a constant loading l

_{3}= 200 kN at velocity up to 190 km/h.

**Figure 8.**Temperature variation of tire tread for a constant loading of 200 kN, at a given skidding angle of 8° and for four different velocities: s

_{1}, s

_{2}= 3 × s

_{1}, s

_{3}= 1.6 × s

_{2}, s

_{4}= 1.4 × s

_{3}.

**Figure 9.**Temperature variation of the tire tread for a given velocity s

_{3}lower than 120 km/h, at a given skidding angle of 6° and for five different loadings: l

_{1}, l

_{2}= l.5 × l

_{1}, l

_{3}= 2 × l

_{2}, l

_{4}= 1.3 × l

_{3}, l

_{5}= 1.3 × l

_{4}.

**Figure 10.**Experimental measurements: (

**a**) thermal evolution of an aircraft tire tread rolling on a standard runway, (

**b**) image of contact zone, infrared camera acquisition, (

**c**) typical S-profile of thermal evolution of tire tread rolling on a flat runway.

**Figure 11.**Experimental test: (

**a**) thermal evolution of the tire tread rolling on a drum, (

**b**) image of the contact zone.

**Figure 14.**(

**a**) The tire position on the drum at skidding angles at 0° and 6°, (

**b**) numerical simulation, tire/drum set-up.

**Figure 15.**Different mesh options: Tire modeled using: (

**a**) 51 elements, (

**b**) 101 elements, (

**c**) 181 elements.

**Figure 16.**(

**a**) Variation of contact area as a function of the number of elements, (

**b**) computational time (CPU) as a function of the number of elements.

**Figure 17.**Numerical simulation, tire modeled with 51 elements (

**a**) 2-D, deflated and inflated tire, (

**b**) 3-D inflated tire pre-loaded with l

_{1}kN, (

**c**) inflated tire loaded with l

_{2}= 10 × l

_{1}kN, (

**d**) inflated tire loaded with l

_{3}= 25 × l

_{1}kN.

**Figure 18.**Experimental data, tire rolling on a steel drum, loading with 200 kN, velocity up to 114 km/h, skidding angle = 6°, (

**a**) global temperature evolution of tire tread during the four steps of testing (Figure 3), (

**b**) temperature of the contact zone, infrared camera recorded during 1.5 s of the step 3.

**Figure 19.**Numerical simulation, thermal evolution of the tire tread, numerical simulation, for a tire loading with 200 kN, rolling velocity up to 114 km/h, skidding angle of 6°.

**Figure 20.**Temperature distribution on the cross-section of the tire tread loading with 200 kN rolling up to 114 km/h, with a skidding angle of 6, (

**a**) experimental data, (

**b**) numerical simulation.

**Figure 21.**Thermal evolution of the tire tread, numerical simulation, for a tire loading with 200 kN, rolling velocity up to 190 km/h, skidding angle of 6°, (

**a**) experimental data, (

**b**) numerical simulation.

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**MDPI and ACS Style**

Rosu, I.; Elias-Birembaux, H.L.; Lebon, F.
Finite Element Modeling of an Aircraft Tire Rolling on a Steel Drum: Experimental Investigations and Numerical Simulations. *Appl. Sci.* **2018**, *8*, 593.
https://doi.org/10.3390/app8040593

**AMA Style**

Rosu I, Elias-Birembaux HL, Lebon F.
Finite Element Modeling of an Aircraft Tire Rolling on a Steel Drum: Experimental Investigations and Numerical Simulations. *Applied Sciences*. 2018; 8(4):593.
https://doi.org/10.3390/app8040593

**Chicago/Turabian Style**

Rosu, Iulian, Hélène L. Elias-Birembaux, and Frédéric Lebon.
2018. "Finite Element Modeling of an Aircraft Tire Rolling on a Steel Drum: Experimental Investigations and Numerical Simulations" *Applied Sciences* 8, no. 4: 593.
https://doi.org/10.3390/app8040593