Influence of the Load-Dependent Shift of the Center Distance of Cylindrical Gears on the Calculated Load Capacity and Noise Excitation Using an Analytical Mesh Stiffness Approach

摘要

The nominal center distance in cylindrical gears is defined for the non-loaded state. The center distance changes under load conditions, which leads to a reduction of the plane of contact and respectively of the length of the effective path of contact. The effective total contact ratio is also shortened. This affects the load and pressure distribution on the flank and thus the load capacity of the gears. The transmission error is also mutated, which affects the noise excitation of the gear pair. For the analysis of these effects, we are using an analytical approach for the calculation of the local mesh stiffness. It is based on the Schmidt plate theory and the local gear tooth deformation approach according to Weber-Banaschek. We are evaluating the load capacity using the calculated pressure distribution on the flanks based on the static deformation analysis of the gear system. Shafts are modelled analytically as Timoshenko beams and bearings are considered as non-linear elements depending on the internal contact situation. In addition, the tooth root stresses are taken into consideration using a boundary element method (BEM). The noise excitation is evaluated using transmission error, force excitation, and other resulting characteristic values. These are formed using a Fourier transformation and level formation. This analytical approach allows excellent calculating precision while achieving high calculation performance. In our paper, we show the importance of considering the load-dependent change of the center distance for the calculation and layout of cylindrical gears. Furthermore, we show the advantages of using an analytical approach for calculating mesh stiffness.