Інженерна механіка та транспорт

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Subject: search.filters.subject.зона контакту

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    Моделювання клейового з’єднання деталей з різними пружними характеристиками
    (Видавництво Львівської політехніки, 2011) Антоненко, Ніна
    Пропонується спосіб визначення ширини зони контакту гладкої смуги, що притискається до абсолютно жорсткої півплощини нормальним зосередженим навантаженням. Отримано сингулярне інтегральне рівняння задачі, розв’язок якого знайдено методом механічних квадратур. Частково проаналізовано вплив товщини та пружних характеристик смуги наширину зони контакту. The author suggests to model the adhesive joint of two parts by means of elastic linkages. If one part is substantially more rigid than the other, while the contact region is almost flat, such structure can be modelled via the problem of one-side contact of an elastic plate with absolutely rigid half-plane. Plane deformation of a uniform isotropic smooth band pressed to absolutely rigid half-plane with the normal fixed load is considered. There is an elastic contact between the band and the half-plane: it is assumed that normal shifts in the contact region are null, while outside the contact region normal shifts of band’s lower edge points are proportional to normal loads in the points of this edge. To solve the problem, a new function of type (8) is introduced and the singular integral equation with logarithmic singularity is built under this function. The equation is reduced to the singular integral equation with Cauchy type kernel where there is additional condition. As there is no angular point in the lower edge form of a band deformed by the normal fixed pressing load, normal strains near contact region boundaries have singularity of the same type as in the contact problem of a band deformed by the stamp without angular points; this encourages seeking the solution of the equation in form of a function with root property. Mechanical quadrature method is used for solution of this equation. Conditions (5) are used to define the width of contact region. Numerical experiments result in the following conclusions: there is linear dependence of contact region width on the thickness of the band and shift module if the values of elastic linkage coefficients are fixed; increase of band’s thickness causes increase of contact region width; increase of shift module causes decrease of contact region width. The performed numerical experiments agree with what is said in [3] and are not at variance with physical meaning.
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    Статична задача про контакт пружних куль, що мають шорсткі поверхні
    (Видавництво Львівської політехніки, 2011) Грабко, Олена
    Досліджено вплив урахування шорсткості поверхонь взаємодіючих пружних куль на контактний тиск. Сформульовані умови, при виконанні яких цим впливом можна знехтувати. Taking into account surface roughness significantly complicates search of solution of a contact problem. Therefore, it is advisable to find conditions under which disregarding the roughness of the surfaces of the compressed objects does not result in a considerable change of the contact area and contact pressures. This study attempts to determine such conditions for two elastic spheres. The problem being considered is a static problem of non-friction contact between two linear-elastic spheres with rough surfaces. The equation for this problem taking into account surface roughness of the interacting objects has the form (1) and that disregarding surface roughness has the form (2). The total of 216 variants of calculation was implemented for different values of the initial parameters. The parameters considered were Poisson's ratio, Young modulus, radii of the interacting spheres, compression force and factors of the power law accounting for the effect of roughness. The distribution of contact pressures in a specific plane area covering the unknown contact area and hard approaching of the objects were found. Based on the outcomes of the numerical experiment, values of the non-dimensional parameter characterizing mutual relative deviation of the solutions to the equations (1) and (2) were established. Additionally, the dependence of this parameter on the one characterizing the relationship of the largest compression of the rough sphere to the total linear-elastic displacement of the points with the largest contact pressure was analysed. The analysis resulted in formulating the conditions fulfilment of which allows disregarding the effect exerted on contact pressure by surface roughness of the interacting objects. In order to apply these conditions practically, it is sufficient to know the hard approaching of the objects, not considering the roughness and micro-irregularities of the surface. These parameters are available in the reference literature, thereby skirting the need to solve the contact problem.