Vibration signals acquired by accelerometers are commonly used in the field of bearing fault diagnosis. The measured vibration signals contain a series of impulse responses when localized bearing faults occur. These impulses are often viewed as fault features and exhibit nonlocal self-similarity in terms of morphological characteristics. However, the impulses are generally contaminated by background noise. In this paper, a group-based K-SVD denoising algorithm, which exploits the nonlocal self-similarity property, is presented to extract bearing fault features. In contrast to regular K-SVD denoising, this denoising algorithm forms groups by clustering similar signal segments and regards each group rather than each segment as the basic unit of sparse representation. To group similar segments, we further propose a particular grouping method that exploits bearing prior knowledge (i.e., possible impulse spacings). The new grouping method could form groups in a targeted manner, thereby achieving more accurate grouping. Group-based K-SVD denoising is able to extract fault features better as similar segments collaboratively provide a large amount of shared feature information, especially in the presence of strong noise (such as signal-to-noise ratios lower than -10 dB). The numerical and experimental results demonstrate the superior performance of group-based K-SVD denoising over regular K-SVD denoising and other two benchmark algorithms (i.e., wavelet shrinkage and spectral kurtosis).

The geometric design, meshing performance, and mechanical behavior of pure rolling helical gear drives are presented. Parametric equations for contact curves on the pinion and gear are determined by coordinate transformation of the active designed pure rolling meshing line for the whole cycle of meshing. Moreover, parametric equations for the tooth surfaces of helical gears with convex-to-convex meshing type are derived according to the motion of generatrices in the transverse section along the calculated contact curves. Then, the basic design parameters are analyzed and formulas for calculation of the geometric size are given. The meshing performance and mechanical behavior, including contact patterns, loaded function of transmission errors, and variation of stresses for two pitch angles of meshing are compared with those of a reference design of micro-geometry modified involute helical gears. Besides, the influence of basic design parameters on tooth contact analysis and stress analysis is studied. The analysis of the results shows that the proposed pure rolling helical gears have the advantage of reducing the relative sliding between tooth surfaces and the possibility of designing pure rolling helical gears with a small number of teeth, though the contact strength of the surfaces is impaired. However, if the appropriate design parameters and Hermite curve parameters for the fillets are properly evaluated as proposed here, the mechanical behavior of the proposed pure rolling helical gear drive, in terms of contact patterns and variation of bending stresses can be superior to that of the micro-geometry modified involute helical gear drives.