To address the challenges of poor performance in traditional diagnosis methods and two-dimensional (2-D) feature based approaches, this paper proposes a novel fault diagnosis approach based on multi-scale spectrum feature images and deep learning. Firstly, the vibration signal is preprocessed through mean removal processing and then converted to multi-length spectrum with fast Fourier transform (FFT). Secondly, a novel 2-D feature called multi-scale spectral image (MSSI) is constructed by multi-length spectrum paving scheme. Finally, a deep learning framework, convolutional neural network (CNN), is formulated to diagnose the bearing faults. Two experimental cases are utilized to verify the effectiveness of the proposed method. Experimental results demonstrate that the proposed method significantly improves the accuracy of fault diagnosis.

Optimization with edge contact avoidance and contact stress minimization is essential for gear design. Due to the complex geometry of modified helical face gear drives, it is complicated to find the optimal design parameters with the consideration of issues including loading, assembly errors, and edge contact. As the finite element method is tedious and time-consuming, an optimization model with a simplified algorithm of the loaded tooth contact analysis with errors (ELTCA) for modified helical face gears is presented, and it can programmatically optimize the contact stress with edge contact avoidance. Firstly, a simplified ETCA algorithm is introduced, which reduces the five unknowns in the traditional contact equations to three. Secondly, the LTCA is analytically implemented according to the Hertz theory. Subsequently, an optimization model with the objective function of avoiding edge contact and reducing maximum contact stress is proposed. Furthermore, the proposed model is applied to reveal the effects of design parameters and assembly errors on the optimized contact path and stress. The results show that the optimization model is accurate and efficient; the design parameters and assembly errors have great effects on the meshing of modified helical face gears.