Relevance of magnetostriction and forces for the generation of audible noise of transformer cores

Recently, the two most significant characteristics of power transformer cores, i.e., loss and noise, have been reduced considerably because of improved material and improved core design. An undisputed base value of noise results from magnetostriction (MS) due to the global magnetization of limbs and yokes, whereas excess values are attributed to different mechanisms, such as excess MS and magnetic forces (MF), in a controversial way. However, a multistep lap (MSL; number of overlap steps N>1) yields considerably lower noise than a single-step lap (SSL; N=1), indicating a specific role of joint design. The present work was aimed at a deeper understanding as a tool for further improvements. For a large number of differently built-up single-phase model cores, local distributions of surface displacements d_x, d_y, d_z and velocities v_x, v_y, v_z as well as the corresponding noise n were determined. As a major finding, MSL yielded weak reductions of in-plane vibrations v_x and V_y, considerable reductions of v _z, and strong reductions of n. Interpretations of results were based on numerical Spice modeling of linearized joint vibrations, which were also established experimentally. The results indicate high values of off-plane flux density B_z and the corresponding Maxwell stress arising at the outermost sheet ends for SSL, and considerably lower values for MSL, provided that B is below its critical value B_c. MSL yielded reductions of d_z, v_z , and n in 80% of all cases. Three additional core parameters-small air gap lengths, high overlap lengths, and high lamination factors A-all lead to reduced n; the use of oil yielded strong reductions. It is concluded that joint designs actually play a predominant role in noise generation. Apart from some contribution from attractive in-plane forces due to B_z, in air gaps, interlaminar flux B_z yields primary sources of vibrations that propagate to the entire core surface. In core regions of reduced Λ, B_z yields vibrations of sheet ends due to MF according to an experimentally determined effective Young´s modulus that considers practical conditions like waviness, burrs, and thickness variations of laminations. For high h, oscillations of the whole core thickness due to B_z-caused MS will arise close to joints. For MSL, all of these mechanisms become less relevant: Gap regions show much lower B_x and, provided B<B_c, also lower B_z , apart from being regionally distributed. Further, imperfections of joint assembling are less critical. As a consequence, the noise level of modern MSL power transformer cores, as commercially assembled with homogeneous compression and high N, can be well predicted by mere consideration of MS resulting from global magnetization