Engineering Transactions, 63, 4, pp. 481-507, 2015

Determination of the Initial Thickness of a Tubes to Bending. Part I. Derivation of the Basic Expressions and Relationships. Part II. Discussion and Analysis of Obtained Results

Zdzisław Śloderbach
Politechnika Opolska
Poland

Abstract I. Part one of the paper presents the derived equations for calculations of the initial wall thick-ness g0 of a tube to bending for elbows, and a proper bending angle 0. The expressions for calculating g0 were presented for a suitable measure of the big actual radius Ri in the bending zone for an exact (general) solution and for three formal simplifications of the 1st, 2nd and 3rd order. At any case, a value of g0 depends on a radius and an angle of bending, an external diameter of the tube, and a per-missible elbow thickness according to the European-Polish Standards and recommendations of the European-Polish Technical Inspection Office, on the coordinates of the point where the thickness g1all was determined, and the coefficient of the bending zone range k (defined during tests). In this paper, the external or internal diameter of the tube subjected to bending is applied as a parameter.
Abstract II. In this second part of the paper, applying epressions derived in Part I, the exemplary calcu-lations of initial thickness of a metallic tube to bending at bending machines are presented. The ex-pressions for calculating of initial thickness were presented for a suitable measure of the big actual radius Ri in the bending zone for an exact (general) solution and for three formal simplifications of the 1st, 2nd and 3rd order. In calculations the external or internal diameter of the tube subjected to bend-ing is applied as a parameter. In this paper, the author shows that the calculated initial thickness of the tube (for the same parameters of bending) depending on the external diameter are lower than those calculated depending on the internal diameter. For example expression for calculation of deformations included in UE Directive [1], contain dependence on dext not on dint.The calculations results are pre-sented on the graphs and tabele enclosed.
Keywords: bending tubes; three simplifications; strains; initial wall thickness; discontinuous strain fields
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