Stiffness properties characterization of pneumatic tire by methods of computer-aided 3D modeling

В роботі побудовано тривимірну геометричну та скінчено-елементну моделі пневматичної шини легкового автомобіля, що враховують особливості її геометрії, багатошарову структуру, ортотропію механічних властивостей у гумово-кордних шарах. Запропоновано систему фінітно-тороїдальних систем координат для завдання криволінійної ортотропії відповідним шарам. Наведено результати розрахунків пружної контактної взаємодії шини з дорожнім покриттям при різних типах навантажень: вертикальному, боковому та поздовжньому та за різних значень внутрішнього тиску. Отримано закономірності зміни переміщень (прогину чи зсуву) ободу колеса в залежності від прикладеного навантаження тобто визначені навантажувальні характеристики шини. Із отриманих результатів розраховані коефіцієнти жорсткості пневматичної шини по різним напрямам та закономірності їх зміни за різних значень внутрішнього тиску. Наведено порівняльну оцінку зміни характеру деформацій у внутрішніх шарах шини за різних типів навантажень.The purpose. The paper deals with the computer finite-elements 3D modelling of the pneumatic tires in a contact interaction with the almost rigid road surface that allowed to find the different types of tires operational stiffnesses (vertical, lateral and longitudinal). Design/methodology/approach. In the paper, it is developed a three-dimensional geometry and finite element model of the pneumatic tire, which takes into account the peculiarities of its geometry, multilayer structure and orthotropy of a mechanical properties in the rubber-cord layers. The system of piecewise-toroidal coordinates is proposed to specify the curvilinear orthotropy of the corresponding layers in the model. The calculations of the elastic contact of the tire with the road have been carried out at the different types of load: vertical, lateral and longitudinal with the different values of the internal pressure. Findings. The dependencies of the displacement (vertical compression or lateral shear) of the wheel rim on the applied loads are defined. From the obtained results, the stiffness factors in different directions were calculated and their dependence on the internal pressure value have been analyzed. Originality/value. The results can be used in the development of new tires design parameters, as well as in a computerized systems of the car movement control and stability (ABS, ESP, StabiliTrak).В работе построены трехмерные геометрическая и конечно-элементная модели пневматической шины легкового автомобиля, которые учитывает особенности ее геометрии, многослойную структуру, ортотропию механических свойств в резиново-кордных слоях. Предложена система финитно-тороидальных систем координат для задания криволинейной ортотропии соответствующим слоям. Приведены результаты расчетов упругого контактного взаимодействия шины с дорожным покрытием при различных типах нагрузок: вертикальной, боковой и продольной и при различных значениях внутреннего давления. Получены закономерности изменения перемещений (прогиба или смещения) обода колеса в зависимости от приложенной нагрузки, то есть, определены нагрузочные характеристики шины. Из полученных результатов рассчитаны коэффициенты жесткости пневматической шины по разным направлениям и закономерности их изменения при различных значениях внутреннего давления

Stochastic Dynamics of the Specialized Vehicle with Nonlinear Suspension

This work deals with the theoretical modelling of the vertical dynamics of the vehicle which has an additional level of suspension for a cargo platform with the nonlinear stiffness. The paper presents the design scheme of the additional level of cushioning having a quasi-zero stiffness in the equilibrium position. The mathematical model of the dynamic behavior of specialized vehicles is developed as a nonlinear discrete system. The results of numeric calculations of the vehicle dynamic response on the stochastic load is represented based on the developed model. Vertical vibrations of the cargo platform caused by the kinematics random influence applied to the axels of the vehicle are analyzed. The load is applied to the axels of the vehicle with a time delay. The results of the comparative analysis are displayed for the frequencies and amplitudes of the vehicle vertical vibrations within two different suspensions: in the linear and nonlinear statements

Nonperturbative ghost dynamics in the maximal Abelian gauge

We construct the effective potential for the ghost condensate in the maximal Abelian gauge. This condensate is an order parameter for a global continuous symmetry, which is spontaneously broken since a nonvanishing value of lowers the vacuum energy. The associated Goldstone mode turns out to be unphysical.Comment: 16 pages. v2: version accepted for publication in JHE

Relating Physical Observables in QCD without Scale-Scheme Ambiguity

We discuss the St\"uckelberg-Peterman extended renormalization group equations in perturbative QCD, which express the invariance of physical observables under renormalization-scale and scheme-parameter transformations. We introduce a universal coupling function that covers all possible choices of scale and scheme. Any perturbative series in QCD is shown to be equivalent to a particular point in this function. This function can be computed from a set of first-order differential equations involving the extended beta functions. We propose the use of these evolution equations instead of perturbative series for numerical evaluation of physical observables. This formalism is free of scale-scheme ambiguity and allows a reliable error analysis of higher-order corrections. It also provides a precise definition for $\Lambda_{\overline{\rm MS}}$ as the pole in the associated 't Hooft scheme. A concrete application to $R(e^+e^- \to {\rm hadrons})$ is presented.Comment: Plain TEX, 4 figures (available upon request), 22 pages, DOE/ER/40322-17

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The nu_mu -> nu_tau oscillation hypothesis will be tested through nu_tau production of tau in underground neutrino telescopes as well as long-baseline experiments. We provide the full QCD framework for the evaluation of tau neutrino deep inelastic charged current (CC) cross sections, including next-leading-order (NLO) corrections, charm production, tau threshold, and target mass effects in the collinear approximation. We investigate the violation of the Albright-Jarlskog relations for the structure functions F_4,5 which occur only in heavy lepton (tau) scattering. Integrated CC cross sections are evaluated naively over the full phase space and with the inclusion of DIS kinematic cuts. Uncertainties in our evaluation based on scale dependence, PDF errors and the interplay between kinematic and dynamical power corrections are discussed and/or quantified.Comment: 28 pages, 10 figure

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The third moment $d_2$ of the twist-3 part of the nucleon spin structure function $g_2$ is generalized to arbitrary momentum transfer $Q^2$ and is evaluated in heavy baryon chiral perturbation theory (HBChPT) up to order ${\mathcal{O}}(p^4)$ and in a unitary isobar model (MAID). We show how to link $d_2$ as well as higher moments of the nucleon spin structure functions $g_1$ and $g_2$ to nucleon spin polarizabilities. We compare our results with the most recent experimental data, and find a good description of these available data within the unitary isobar model. We proceed to extract the twist-4 matrix element $f_2$ which appears in the $1/Q^2$ suppressed term in the twist expansion of the spin structure function $g_1$ for proton and neutron.Comment: 30 pages, 7 figure

Strong Coupling Constant with Flavour Thresholds at Four Loops in the MS-bar Scheme

We present in analytic form the matching conditions for the strong coupling constant alpha_s^(n_f)(mu) at the flavour thresholds to three loops in the modified minimal-subtraction scheme. Taking into account the recently calculated coefficient beta_3 of the Callan-Symanzik beta function of quantum chromodynamics, we thus derive a four-loop formula for alpha_s^(n_f)(mu) together with appropriate relationships between the asymptotic scale parameters Lambda^(n_f) for different numbers of flavours n_f.Comment: 10 pages (Latex), 3 figures (Postscript

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An evidence for nontriviality of asymptotically non-free (ANF) Yang-Mills theories is found on the basis of optimized perturbation theory. It is argued that these theories with matter couplings can be made nontrivial by means of the reduction of couplings, leading to the idea of dynamical unification of couplings (DUC) The second-order reduction of couplings in the ANF $SU(3)$-gauged Higgs-Yukawa theory, which is assumed to be nontrivial here, is carried out to motivate independent investigations on its nontriviality and DUC

Notes on Operator Equations of Supercurrent Multiplets and the Anomaly Puzzle in Supersymmetric Field Theories

Recently, Komargodski and Seiberg have proposed a new type of supercurrent multiplet which contains the energy-momentum tensor and the supersymmetry current consistently. In this paper we study quantum properties of the supercurrent in renormalizable field theories. We point out that the new supercurrent gives a quite simple resolution to the classic problem, called the anomaly puzzle, that the Adler-Bardeen theorem applied to an R-symmetry current is inconsistent with all order corrections to $\beta$ functions. We propose an operator equation for the supercurrent in all orders of perturbation theory, and then perform several consistency checks of the equation. The operator equation we propose is consisitent with the one proposed by Shifman and Vainshtein, if we take some care in interpreting the meaning of non-conserved currents.Comment: 28 pages; v2:clarifications and references added, some minor change

New perturbation theory representation of the conformal symmetry breaking effects in gauge quantum field theory models

We propose a hypothesis on the detailed structure for the representation of the conformal symmetry breaking term in the basic Crewther relation generalized in the perturbation theory framework in QCD renormalized in the ${\rm \bar{MS}}$ scheme. We establish the validity of this representation in the $O(\alpha_s^4)$ approximation. Using the variant of the generalized Crewther relation formulated here allows finding relations between specific contributions to the QCD perturbation series coefficients for the flavor nonsinglet part of the Adler function $D^{ns}_A$ for the electron-positron annihilation in hadrons and to the perturbation series coefficients for the Bjorken sum rule $S_\text{Bjp}$ for the polarized deep-inelastic lepton-nucleon scattering. We find new relations between the $\alpha_s^4$ coefficients of $D^{ns}_A$ and $S_\text{Bjp}$. Satisfaction of one of them serves as an additional theoretical verification of the recent computer analytic calculations of the terms of order $\alpha_s^4$ in the expressions for these two quantities.Comment: 12 pages, Title modified, abstract modified, improved and extended variant of the talks, presented at Int. Seminar "Quarks-2010" (6-12 June, 2010, Kolomna) and Int. Workshop Hadron Structure and QCD: From Low to High Energies (5-9 July 2010, Gatchina