#### 539.3 Mathematical modeling of massive tire stationary rolling on the chassis dynamometer with regard to energy dissipation in rubber

##### Belkin A. E. (Bauman Moscow State Technical University), Semenov V. K. (Bauman Moscow State Technical University)

doi: 10.18698/2309-3684-2016-1-1737

The article examines the problem of mathematical modeling tests of massive tire bench run with the chassis dynamometer. Conducted tests enable to define the characteristics of resistance to the tire rolling. The article contains the main stages of model building. We give a formulation for the contact problem of tire stationary free rolling on the test drum considering the energy dissipation in the rubber during cyclic deformation. We also describe a rubber viscoelastic behavior by the model Bergstrom – Boyce and ascertain its numerical parameters according to the samples tests results. The contact conditions for normal and tangential directions are formulated on basis of the penetration function. For the contact restrictions implementation we use the penalty method and obtain the numerical solution of the three-dimensional viscoelasticity problem by the finite element method. To estimate the adequacy of the built model, we compare the calculation results with the test data received for massive tire on Hasbach test equipment. For this purpose rolling resistance forces under different loads were collated. The pressure distribution in the contact area obtained from calculations and experiments by using XSENSOR Technology Corporation equipment are also juxtaposed.

Belkin A., Semenov V. Mathematical modeling of massive tire stationary rolling on the chassis dynamometer with regard to energy dissipation in rubber. Маthematical Modeling and Coтputational Methods, 2016, №1 (9), pp. 17-37

#### 539.3 Modeling polyurethane viscoelasticity at moderately high strain rates

##### Belkin A. E. (Bauman Moscow State Technical University), Dashtiev I. Z. (TSNIISM), Lonkin B. V. (Bauman Moscow State Technical University)

doi: 10.18698/2309-3684-2014-3-3954

The article presents a mathematical model of the viscoelastic behavior of polyurethane SKU-PFL-100 for strain range of 0...30 % and moderately high strain rates up to 10–1. To determine the viscous component of the deformation Bergstrom – Boyce rheological model has been applied. Relationship between stress and the elastic component of deformation is described by an Arruda – Boyce potential. We determined the model parameters using experimental compression diagrams of polyurethane obtained from Instron Electropuls 1000 machine at different strain rates. The model parameter values obtained by minimizing a function of the calculated value deviations from the experimental results are given. It is shown that in the considered range of deformations and strain rates model allows describing the polyurethane behavior with sufficient accuracy for practical purposes. The model is designed for calculating polyurethane shock-absorber parts, cushions, buffers and other structures subjected to dynamic loading.

Belkin A., Dashtiev I., Lonkin B. Modeling polyurethane viscoelasticity at moderately high strain rates. Маthematical Modeling and Coтputational Methods, 2014, №3 (3), pp. 39-54