The paper presents a full three-dimensional finite element model of pneumatic tyre. The inclusion of a special node to the model enabled to analyse the problem of static tyre-road contact under vertical, lateral or longitudinal external forces. The hyperelastic properties of rubber are described with the use of the elastic strain energy density function in the form of the third degree polynomial. Incompressibility is taken into account by means of the Lagrange multiplier-in the form of mean hydrostatic pressure determined within each finite element. Particular attention was paid to the directional properties of cord ply treated as monotropic linear-elastic material characterized by effective material constants. These properties were introduced into the model by overlaying the elements with monotropic material on those representing rubber. The total Lagrangian description with the Green-Lagrange strain tensor and the energetically conjugate to it the second Piola-Kirchhoff stress tensor were applied to the tyre model. The results of a truck tyre analysis concerning displacements and delamination stresses distribution show good accuracy of the pneumatic tyre modelling technique proposed in the paper.
The aim of the paper is to propose and verify an effective method for the realistic modelling of pneumatic tyres. A static, three-dimensional model of a pneumatic tyre, based on the finite element (FE) program MARC, is presented. The cord-rubber composite was modelled by overlaying the elements characterizing the cord and those representing incompressible rubber. A two-dimensional model was used to simulate the tyre mounting and inflation process. The model was then developed into a three-dimensional one. The displacements, radial stiffness and delamination stresses caused by the vertical load were determined. The shape of the tyre footprint and the pressure distribution in this zone were also predicted. Good correlation between measured and computed stiffness characteristics was observed. The proposed technique of element overlaying yields a tyre model that is numerically more stable than that using only orthotropic elements (very stiff cord merged with compliant rubber).
This paper presents a method for modeling of pneumatic bias tire axisymmetric deformation. A previously developed model of all-steel radial tire was expanded to include the non-linear stress–strain relationship for textile cord and its thermal shrinkage. Variable cord density and cord angle in the cord-rubber bias tire composite are the major challenges in pneumatic tire modeling. The variabilities result from the tire formation process, and they were taken into account in the model. Mechanical properties of the composite were described using a technique of orthotropic reinforcement overlaying onto isotropic rubber elements, treated as a hyperelastic incompressible material. Due to large displacements, the non-linear problem was solved using total Lagrangian formulation. The model uses MSC.Marc code with implemented user subroutines, allowing for the description of the tire specific properties. The efficiency of the model was verified in the simulation of mounting and inflation of an actual bias truck tire. The shrinkage negligence effect on cord forces and on displacements was examined. A method of investigating the influence of variation of cord angle in green body plies on tire apparent lateral stiffness was proposed. The created model is stabile, ensuring convergent solutions even with large deformations. Inflated tire sizes predicted by the model are consistent with the actual tire sizes. The distinguishing feature of the developed model from other ones is the exact determination of the cord angles in a vulcanized tire and the possibility of simulation with the tire mounting on the rim and with cord thermal shrinkage taken into account. The model may be an effective tool in bias tire design.
K e y w o r d s: tire, cord-rubber composite, deformation modeling, finite element method. A b s t r a c tThe existing method of a tire cord-rubber ply modeling involved the determination of effective material constants relative to ply thickness. This paper investigates the use of the same method in reference to plies with the thickness of a cord. Cord-rubber plies with orthotropic properties were separated by layers of isotropic rubber to maximize the composite susceptibility to deformation. When the improved model was applied in the simulations of tire pumping to nominal pressure, an increase was observed in the displacements of the tire characteristic points, maximum equivalent stress in rubber layers located between cord-rubber plies and the shear strain of rubber. PRÓBA DOSKONALENIA OBROTOWO-SYMETRYCZNEGO MODELU OPONY PNEUMATYCZNEJ Józef PelcKatedra Mechaniki i Podstaw Konstrukcji Maszyn Universytet Warmińsko-Mazurski w Olsztynie S ł o w a k l u c z o w e: opona, kompozyt kodowo-gumowy, modelowanie deformacji, metoda elementów skończonych.A b s t r a k t Dotychczasowy, powszechnie stosowany sposób modelowania warstwy kord-guma w oponie polegał na wyznaczaniu stałych efektywnych materiału w odniesieniu do grubości warstwy. Zbadano możliwość zastosowania tego samego sposobu, ale w odniesieniu do warstwy o grubości nici kordu. Warstwy kordu o właściwościach ortotropowych rozdzielono warstwami gumy izotropowej, co wpłynęło na zwiększenie podatności kompozytu na odkształcenia. Wykorzystując udoskonalony model do symulacji pompowania opony testowej do ciśnienia o wartości nominalnej, zaobserwowano wzrost wartości przemieszczeń jej punktów charakterystycznych, maksymalnych naprężeń zredukowanych w gumie między warstwami oraz odkształceń postaciowych w gumie.
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