Torque at elastic-plastic torsion of sheet-straightening machines’ steel shafts

The experiments on the torsion of the steel shaft were conducted on the machine Instron 55MT2 with a maximum torque of 220 N×m and a mass of 2500 N. The ends of the shaft clamped with collet-chucks. For the torsion we used the round cylindrical samples from a low-carbon steel with the Young’s modulus of 2×1011 Pa, the shear modulus of 7.752×1010 Pa, the Poisson’s ratio of 0.29, the yield strength of 524 MPa, the yield strength at shift of 302 MPa, the ultimate shear stress of 352 MPa, the ultimate shift of 0.18 and the plastic module at shift of 740 MPa. The torsion of the steel shafts and thick-walled pipes is widely used in the metallurgy, mechanical engineering and oilgas industry. For example, the shafts’ torsion is observed in the drive mechanisms of the sheet-straightening machines for the thin and thick steel sheets, in the rolling mills for the cold and hot steel sheets, in the drives of the rear wheels of motor transport, in the land and sea gas-oil drilling platforms and so on. Under the significant torque, the steel shafts can experience not only elastic, but also plastic deformation without the destruction. The experimental dependence of the shaft torque on the twisting angle gives researchers much more information about the mechanical properties of steel than the analogous experiments on the rupture of the steel shafts, since there is no neck formation during the torsion and the steel shaft does not collapse even at the very large twisting angles. The classical Ludwik’s and Nadai’s approximations for shear do not sufficiently accurately describe the shear deformation and are, therefore, not sufficiently effective for calculating the shaft torque. Therefore, the more accurate the straight and back Shinkin’s approximations are used below to describe the shear deformation. A special feature of calculating the dependence of the shaft torque on the shear angle is that the torque is calculated approximately as a power series, since the corresponding integrals are transcendental (cannot be calculated analytically). At the same time, the relative accuracy of the torque calculation is very high (about 10-6 %).