Mathematical modelling of thermal behaviour of cylindrical roller bearing for towed railway vehicles

U radu je prikazan matematički model za predviđanje toplinskog ponašanja valjnog ležaja s valjčićima za uležištenje vučenih željezničkih vozila. Matematički model omogućava izračunavanje generirane topline uslijed podmazivanja, radijalnog i aksijalnog opterećenja za različite brzine gibanja vlaka. U radu je također prikazan način izračunavanja koeficijenata provođenja i prevođenja topline u ležaju. Uporabom programskog sustava opće namjene na bazi metode konačnih elemenata analizirano je toplinsko ponašanje valjnog ležaja s valjčićima za vučena željeznička vozila. Metodom konačnih elemenata određene su vrijednosti temperature ležaja u ovisnosti o brzini gibanja vlaka (v = 20 km/h, v = 40 km/h, v = 60 km/h, v = 80 km/h i v = 100 km/h), polumjera zakrivljenosti zavoja (R = 500 m), ambijentalne temperature od 20 °C i visine nadvišenja pruge u krivini (h = 110 mm, h = 140 mm, h = 180 mm).This paper presents a mathematical model for the prediction of the thermal behaviour of a cylindrical roller bearing for axle assembly of the wheel set of the towed railway vehicles. The mathematical model allows for the heat generated due to lubrication, radial and axial loads at different speeds of the train to be calculated. The method of calculating of the heat conducting and converting coefficients in the bearing is also shown. By using the general purpose software system based on the finite elements method, the thermal behaviour of the above mentioned cylindrical roller bearings was analysed. Temperature values of the bearings are determined by the finite elements method values depending on the speed of the train movement on a straight-line section and the curve (v = 20 km/h, v = 40 km/h, v = 60 km/h, v = 80 km/h and v = 100 km/h), the curve radius (R = 500 m), the ambient temperature of 20 °C and the cant height (h = 110 mm, h = 140 mm, h = 180 mm)

Flexural-Torsional Buckling of Cantilever Strip Beam-Columns with Linearly Varying Depth

International audienceIn this paper, one investigates the elastic flexural-torsional buckling of linearly tapered cantilever strip beam-columns acted by axial and transversal point loads applied at the tip. For prismatic and wedge-shaped members, the governing differential equation is integrated in closed form by means of confluent hypergeometric functions. For general tapered members (0 <(h(max)-h(min))/h(max)< 1), the solution to the boundary value problem is obtained in the form of a Frobenius' series, which is shown to converge in the interior of the domain and at the boundary if and only if 0 <(h(max)-h(min))/h(max)< 1/2. Therefore, for 1/2 <=(h(max)-h(min))/h(max)< 1 the Frobenius' series solution cannot be used to establish the characteristic equation for the cantilever beam-columns; the problem is then solved numerically by means of a collocation procedure. Some of the analytical solutions (buckling loads) were compared with the results of shell finite-element analyses and an excellent agreement was found in all cases, thus validating the mathematical model and confirming the correctness of the analytical results. The paper closes with a discussion on the convexity of the stability domain (in the load parameter space) and the accuracy of approximations based on Dunkerley-type theorems