Different components of a typical radial tire are shown in Figure 1. Each component has been designed to comply with the rubber and cord composite in addition to several specific factors for driving performance. These take an important role in maintaining the stiffness and strength required in a tire. The roles of each part are well described in a book by Lindenmuth [17]. The components are composed of several rubber components and fiber-reinforced components such as radial carcass plies, belt plies, bead wires, and so on. A great portion of the tire structure consists of vulcanized rubber. The rubber has a nonlinear and incompressible behavior towards loading which is independent of the strain rate. The nonlinear elastic material response is formulated by a strain energy density function accounting for large strain components. The strain energy density function is defined according to the penalized first-order Mooney-Rivlin model in which the strain density function is defined by

W ( J 1 , J 2 , J 3 : K ) = C 10 ( J 1 − 3 ) + C 01 ( J 2 − 3 ) + K 2 ( J 3 − 3 ) 2 (1)

where J i is the invariants of the Green-Lagrangian strain tensor and C 10 and C 01 are the rubber material constants determined from the experiment. On the other hand, K is a sort of penalty parameter controlling the rubber incompressibility. The shear modulus τ and the bulk modulus κ of rubber are related as 2 ( C 10 + C 01 ) = τ and K = 2 κ , from which one can easily obtain the following relation for Poisson’s relation:

ν = [ 3 K / 4 ( C 10 + C 01 ) − 2 ] / [ 3 K / 2 ( C 10 + C 01 ) + 2 ] [16]. It is clear that the incompressibility of rubber is asymptotically enforced as the penalty parameter approaches infinity, but the choice of K near 100 is usually recommended for the stable transient dynamic response with the reasonable time step size. The fiber reinforced components are the predominant load carrying members of the cord-rubber composite. They provide strength and stability to the sidewall and tread as well as contain the air pressure. Since the fiber reinforced components parts are in the highly complex structure, the material models are chosen by the objective of the numerical simulation. In the tire analysis, the fiber reinforcement components in the model were modeled using special purpose rebar shell

elements. The rebar layers were embedded in the 3D solid by defining the nodes for rebar element. The embedded rebar elements were constrained to move relative host elements by a kinematic coupling which enforces the position of the host nodes and embedded rebar elements nodes to have a mutually linear dependency. In this study, two belt layers and carcass with embedded rebar elements are modeled. Meanwhile, steel cord and rubber matrix of the bead area is modeled as a homogeneous solid. Figure 2 shows a two-dimensional section mesh constructed according to the above-mentioned material modeling such that pure rubber solid, composite shell and homogenized solid elements are mixed.

The CFD package from Capvidia [15] was developed as wide application tool for study of complex gas/fluid flows. And FE software from SIMULIA [16] provides many functions of tire simulation such as embedded element technique for composite and enables steady state simulations in order to reduce the analysis time and so on. To solve hydroplaning simulation, CFD code Flowvision and FE code ABAQUS which are strongly coupled for bidirectional fluid structure interaction (FSI) co-simulation are implemented. An axisymmetric structural part and a non-symmetrical tread part are consisted in the tire model. Tread geometry is obtained by assembling a sequence of pitches. A vertical load is then applied, and using steady state transport analysis, the tire will reach a stationary rolling condition at travelling speed. When the tire FE model is completed, tread surface geometry of tire FE model is imported into CFD code as shown in Figure 3. CFD code uses the interactive interface to create computational fluid domain for hydroplaning simulation, and specify appropriate boundary conditions such as flow velocity and flow inlet/outlet etc.

After then Abaqus/explicit analysis will start to co-simulate with CFD software, to simulate the tire rolling over water films and investigate the performance of tire wet-grip capabilities. The whole analysis procedure is shown in Figure 4.

The link between FE and CFD meshes is built automatically via Flowvision Sub-Grid Geometry Resolution (SGGR) technique [18] [19]. The SGGR technology allows to import the CAD file to the computational domain without any feature loss, thus both saving man hour for meshing and letting the engineering focus on the physics of the problem to be solved. Theoretically, common CAD systems can generate the description of object surface by a set of plane facets. Using this representation allows for CFD code to perceive geometry information from CAD through FEM coupling. In this case, the CFD code becomes compatible with other CAE systems based on finite element analysis. Let the adaptive locally refined grid (ALGR) has given in computational domain. At first stage of algorithm the facets intersecting the grid cell are being found. Then the grid cell is disjoined into a set of finite volumes bounded by facets and cell faces. If the cell does not intersect any facet, the finite volume coincides with cell as shown in Figure 5. With the help of this technology, it can make program deal with the tire with complex tread pattern rolling in computational domain without problem of distortion of computational grid.

In this paper, water flow assumes that it is governed by system of equations for incompressible fluid which includes continuity and Navier-Stokes equations [19]. To consider the algorithm of the equations solving again write ones in Lagrange integral form for volume moved with fluid during intermitted time duration is:

∂ p ∂ t + ∇ ⋅ ( ρ V ) = 0 (2)

∂ p V ∂ t + ∇ ⋅ ( ρ V ⊗ V ) = − ∇ P + ∇ ⋅ τ ^ e f f + ρ F (3)

Equations (2) and (3) were used to solve the velocity and pressure of fluid with a decouple process called as pressure and velocity split process [9]. Here, τ ^ e f f is the effective shear stress tensor caused by viscosity of fluid. The turbulence of water flow around the rolling tire is also considered. The standard K-ε model, expressed as (4) and (5) is used to solve the turbulent energy and dissipation of fluid.

∂ ( p k ) ∂ t + ∇ ⋅ ( ρ V k ) = ∇ ( ( μ + μ t σ k ) ∇ k ) + μ t ( G + β P r t g ⋅ ∇ T ) − ρ ε (4)

∂ ( p ε ) ∂ t + ∇ ⋅ ( ρ V ε ) = ∇ ( ( μ + μ t σ k ) ∇ ε ) + C 1 ε k μ t ( G + β P r t g ⋅ ∇ T ) − C 2 ρ ε 2 k (5)

The model parameters and the expression for generating term G can be rewritten as (6), (7), and (8):

G = D i j ∂ V i ∂ x j (6)

D i j = S i j − 2 3 ( ∇ ⋅ V + ρ k μ t ) δ i j (7)

S i j = ∂ V i ∂ x j + ∂ V j ∂ x i (8)

The object of this study is to investigate the resistance force of a rolling tires caused by fluid-dynamic, we will be introduced the similarity approach to experimentally measure the resistance of a tire rolling in a basin instead of wind tunnel for the validation of simulation. Therefore, the working fluid in this simulation is water, and heat transfer can be neglected reasonably. The units and numerical settings are listed in Table 1. Equation (9) was used to solve the total pressure of fluid, and the total resistance force of a rolling tire is calculated by Equation (10)

P t o t = P + P h s t + 1 2 ρ | V a b s | 2 (9)

F fluid = ∮ s ( P + P h s t ) n d S − ∮ s ( μ + μ t ) ∂ V ∂ n d S (10)

The free surface flow is modeled by the “Advanced VOF model” in Flowvision [15]. Transfer of the water phase boundary is described by the equation for the volume fraction of this (continuous) phase in a computational cell (“Volume Of Fluid” = VOF). Variable VOF takes values from 0 (Gas) to 1 (Liquid). A cell, where 0 < VOF < 1, contains a contact surface. In the solver, this surface is represented by a set of polygons. Propagation of the volume fraction of water is solved by the transport Equation (11).

∂ F ∂ T + V ⋅ ∇ F = 0 (11)

A representative tire model of passenger car is implemented to evaluate performance of hydroplaning. The size of tire is 205/55 R16 with simple tread pattern. Figure 6 and Figure 7 show the results of hydroplaning simulation. In Figure 6, velocity contour describes how the water flows through the channels of the treads. Also contact pressure plot indicates significant loss of contact force which is consistent with the buoyancy force as shown in Figure 7. The reason why the buoyancy increases rapidly and stabilizes at the start of the analysis is due to the initial speed and damping of the fluid and tire, and does not have any special meaning. As described above, the simulation results of hydroplaning were analyzed through buoyancy of FVM and contact force of FEM. Buoyancy is value caused by water pressure, large value means that hydroplaning performance is not good. But, contact force means force between tire and road, high value means good performance. The oscillations in the buoyancy force as shown in Figure 7 are due to the tread pattern surface and water flow. Despite the co-simulation of two different softwares, the tendency of buoyancy and contact pressure seems to be very well.

Four different test tires with simplified tread patterns were produced and experiments evaluating of longitudinal hydroplaning test were carried out. Figure 8 shows the tire shape which actually manufactured and was designed considering the pattern design factor. In order to confirm a difference in the results of hydroplaning analysis of the tire, each version of tire is considered to give 3% - 7% design changes such as longitudinal/lateral groove, location/orientation of void and angle of tread block. Figure 9 shows a test of hydroplaning at the proving ground. Longitudinal hydroplaning test is for evaluating tire’s hydroplaning performance during straight line driving on wet surface.

The measurement of hydroplaning performance by test tire is carried out on hydroplaning trailer. The hydroplaning trailer should be connected to a tow vehicle and drive left side of trailer to the wet test road. Then, measures speed of the test tire of left side of trailer and the tow vehicle. After that, calculate the hydroplaning occurred speed by compare speed of between the test tire and the vehicle. Specific test conditions are listed in Table 2. In the experiment, the relationships between vehicle velocity and slip ratio of each tire were measured for a vehicle running on a pool of water whose water depth is 10 mm. Tire slip ratio in the experiment is defined as follows.

Slip   ratio = 1 − Velocityofatire Velocityofatrailor (12)

The experimental rating indicates the trailer velocity, when the slip ratio is 10%. This is the way to obtain result in general experimental methods. The computational results used the contact force, when the simulation result is in stable.

Figure 10 shows the buoyancy result images between tires during rotates at high speed and water. Since PTN01 is receiving more buoyancy than PTN04, it can be expected that the performance will be inferior from the pressure distribution range. The buoyancy of PTN02 and PTN03 is shown similar performance in hydroplaning simulation. The result comparison between the contact force of simulation and the experimental test is shown in Figure 11. The hydroplaning simulation using 3D patterned tires has similar results with the proving ground test. The tendency of proving ground test can be interpreted in the same with hydroplaning simulation, PTN04 > PTN03 > PTN02 > PTN01. Little difference of the value among each version is likely to be a common error in proving ground testing, so the results of the hydroplaning simulation have a high reliability with experimental test.

To find out how the hydroplaning characteristics change at different speed, the same passenger car tire model is used to carry out the simulations at different speeds. Figure 12 shows contact pressure results at different vehicle speeds 50 km/h - 90 km/h, and Figure 13 shows the buoyancy and contact pressure plots. Hydroplaning performance based on speed was verified to produce reasonable results. At lower speeds, the hydroplaning performance was better, but hydroplaning at higher speeds was worse in buoyancy and contact force. The results indicate that as speed increased, the tire completely loses contact force with the road surface at 90 km/h. This result is meaningful in various aspects, and it can be considered to be similar to the results of Guo et al. [14] that it is necessary to drive below 90 km/h on wet surface road in a rainy day.

In a tire pattern design, the width of the longitudinal groove is one of the most

important factors to tire. It is necessary to increase the width of the groove to improve wet performance. In this section, hydroplaning simulation according to change groove width was conducted as shown in Figure 14. From Ver1 to Ver3, the width of tread groove is increased by 1 mm. Figure 15 and Figure 16 show the contact pressure results, buoyancy and road reaction force. In the contact pressure, there were no significant changes in water pressure. However, in buoyancy and contact force, we identified logical results that improved performance as the width of the grooves increased.

Since the V-shape grooved tire has different hydroplaning velocities according to the normal and reverse rotational directions a closer look will be taken at this tread pattern design as shown in Figure 17. Generally, these tires show better performance in forward rotation than reverse direction. As shown in Figure 18, the tire rotating in reverse direction quickly loses contact force between tire and road. And, tire that rotates in reverse direction showed an early increase in buoyancy. Vorticity, which indicates turbulence, is recommended to develop from the groove of tread to the outside because it affects water drainage. The vorticity of the forward direction tire occurs much more in the tire rotation direction, while the reverse tire can be seen to occur a lot in front of rolling direction as shown in Figure 19. It can be expected that the interference of the fluid flow will eventually lead to an increase in pressure and eventually the performance of the tire will deteriorate.