# ECOTIRE: A New Concept of a Smart and Sustainable Tire Based on a Removable Tread
## 3 Design Requirements for Casing-Tread Mechanical Connections
### Study Based on Dynamic Boundary Conditions  
The first step to design the appropriate joint geometry to optimally transmit the forces from the tire to the pavement was to carry out simulations of a vehicle in complex maneuvers and analyze the evolution of the transmitted forces. For this, a standard D-segment car was selected, with a mass of 1600 kg, a total length of 4500, and a wheelbase of 2800 mm. The test maneuver selected was the double lane change (DLC) [46].  
This maneuver was performed at various speeds, all of which exceeded the grip limit at some point during the maneuver, as illustrated in Figure 2, where the vehicle passes the test at 50 km/h, but at 55 km/h it no longer passes, thus determining the limit of the vehicle in this test and distinguishing between controlled and uncontrolled sliding conditions. The pavement selected for the tests is a conventional asphalt surface, dry and well-maintained, with longitudinal grip values ranging between 0.8 and 1.  
Figure 2: Target trajectory and trajectories calculated by simulation of a segment D vehicle during a DLC maneuver at 50 km/h (passing the test) and 55 km/h (failing the test).  
The analysis of the longitudinal and lateral forces achieved in these simulations allows the calculation of the resulting tangential force, \(\mathrm{F_{t}}\), the total requested grip, \(\mathrm{\mu_{t}}\), and the angle, \(\mathrm{\theta}\), between the resulting tangential force and the longitudinal direction of displacement, or direction of advance, OX, as indicated by Equation (1). Figure 3 illustrates these three parameters for the left front tire (where the maximum forces are registered) under the previously mentioned simulation conditions. From these curves, a more accurate analysis of the forces that the tire must transmit can be carried out, studying their evolution both in magnitude and direction. This dynamic analysis will allow the identification of the maximum force vectors that the joint between casing and tread must support and transmit, allowing the establishment of an appropriate initial geometry to effectively transmit these mechanical stresses.  
\[\mathrm{F_{t}}=\sqrt{\mathrm{F_{x}}^{2}+\mathrm{F_{y}}^{2}}\Rightarrow\mathrm{ \mu_{t}}=\frac{\mathrm{F_{t}}}{\mathrm{F_{z}}}\Rightarrow\mathrm{\theta}= \arcsin\frac{\mathrm{F_{y}}}{\mathrm{F_{t}}} \tag{1}\]  
Although this is a dynamic reference test with the possibility of numerous other tests to enhance the study, the analysis leads to the following conclusions:  
* For a general-purpose tire, there is no preferred direction in which the tangential force is transmitted. There is an equal probability of transmitting force in any direction contained in the contact plane.  
Figure 3: Evolution of the values of tangential force, total requested grip, and angle of the tangential force during the DLC test at 50 km/h (**a**) and 55 km/h (**b**).  
* The grip constrains the maximum transmitted force, and in the same way, the force that the casing-tread mechanical joint must withstand is determined by the maximum tire-pavement grip.
* As is well known, the tire-pavement grip is different for the OX and OY directions, with the usual values in conventional tires being close to 1 and 0.8, respectively. In the case of combined efforts, the total combined grip approaches the greater of both values.
* Based on the vertical force that a tire must withstand in dynamic conditions, Fz, and the maximum available grip based on that load, it is possible to estimate the maximum force that can be transmitted for each type of tire and, therefore, it must withstand any geometric connection that is designed between casing and tread.