A new method for calculating rolling resistance is developed. This method includes a simplified structural model of a wheel in the form of a rigid cylinder with a thin viscoelastic rim. The wheel loading mode is considered in the absence of shearing (horizontal) force. In the entire contact area, it is assumed that the wheel is gripped with a non-deformable support surface. Deformation of the viscoelastic layer is analyzed on the basis of the Winkle model. In contrast to the previously known ones, the proposed method implies a description of the symmetry breaking in the distribution of contact pressure when a small torque is applied to the wheel, not exceeding the rolling resistance at rest. Contact pressure diagrams are obtained at different values of the torque applied to the wheel. It is shown that as the torque increases, the maximum value of the contact pressure increases, and the position of this maximum shifts in the direction of possible rolling. From the condition of violating the contact area dimensions at the beginning of rolling, an analytical expression is derived for the moment of rolling resistance at rest. The calculated dependence of this moment on the wheel draft is compared with known experimental data. When describing stationary free rolling, the asymmetry of the contact pressure corresponding to the beginning of rolling and the loss of energy during deformation of the viscoelastic material of the wheel rim are taken into account. The dependences of the coefficient of rolling resistance and wheel draft on the speed of the wheel center of mass at a fixed value of the vertical load are obtained. It is shown that taking into account the initial asymmetry of the contact pressure leads to a more intensive increase in the calculated estimates of the resistance coefficient and a less marked decrease in the wheel draft with an increase in rolling speed.

Viscoelastic and thermomechanical properties of tire rubbers have been studied to predict hysteresis losses during rolling of automobile tires. The temperature dependences of the elasticity modulus and the tangent of mechanical losses obtained by dynamic mechanical analysis and combined tests in the mode of quasi-static cyclic stretching with subsequent relaxation were used for the calculated determination of the deformation and dissipative parameters of 20 rubber compositions. As a basic theoretical description of rubber as a thermorheologically simple material, a linear viscoelastic Prony model is used, for the identification of which the Willams–Landel–Ferry (WLF) temperature-time analogy is used. The advantage of the computational and experimental approach used is the ability to determine the parameters of the WLF equation regardless of the values of other material characteristics. A fairly simple Mooney–Rivlin potential function for an incompressible material is used to describe large elastic deformations of the elastomer under study. The relaxation curve obtained by means of quasi-static tests is applied to assess the adequacy of the constructed mechanical and mathematical model. In particular, the comparison of the experimental relaxation curve with the results of calculations for tread rubber showed a discrepancy not exceeding 15 %. The performed analysis of viscoelastic and thermomechanical parameters of tire rubbers covers (and significantly exceeds in frequencies) the range of operating temperatures and loads of automobile tires. The results obtained can be used in the computational optimization of the composition of materials and the design of automobile tires according to the criterion of rolling resistance and minimizing heat generation in the tire during movement.

Strength and strain sensitivity of a thin polymer-ceramic coating in the form of a nanoporous anodic aluminum oxide impregnated with a piezoelectric polymer are studied. The coating is considered as a unidirectionally reinforced composite containing cylindrical polymer fibers oriented perpendicular to the coating surface. A three-phase micromechanical model of the specified material is proposed and the stress-strain state of the coating under the influence of uniformly distributed pressure is analyzed. As a result of solving the related problem of electroelasticity, calculated estimates of the specific piezoelectric sensitivity of the coating used as a pressure sensor and the maximum allowable pressure were obtained according to the strength criteria of the ceramic matrix and the plastic flow of the polymer filler. The article shows dependences of the indicated parameters on the volumetric content of the polymer for the coating, adhesively bonded to a non-deformable foundation and freely (without friction) lying on the foundation. At low volume content of polymer, the strength loss of coating is caused by local failure of matrix. At high filler content the transition of polymer into plastic state precedes to the beginning of matrix failure. After increasing the filler content above 80 % the value of maximal pressure according to yield criteria for polymer filler scarcely changes.

The application of highly ordered thin ceramic coatings with nano-dimensional pores obtained by metal anodic oxidation in pressure sensors of a matrix type is promising. For this purpose the pores of a ceramic base are impregnated with polymer realizing a direct piezoelectric effect. There is developed a procedure for the calculated definition of piezoelectric pressure sensor sensitivity which is a thin coating made of nano-porous aluminum anodic oxide the pores of which are filled with polyvinylidene fluoride. The procedure is based on a three-phase model of fiber-reinforced composite and a simplified problem setting of electroelasticity. The sensor is modeled by a thin two-layer coating located on a conditionally non-deformable base. It is defined that for a coating lying freely on a rigid foundation the sensitivity is directly proportional to volume fraction of the polymer filler. For a coating con-nected in an adhesion way with the base the sensitivity dependence upon a filler share is close to a quadratic one. The estimated assessments of sensor characteristics under analysis at different ways of fastening coincide at 58% volume content of polymer piezoelectric.