The effect of mesh stiffness on the dynamic response of face gear transmission system combining with backlash nonlinearity is studied. First, a nonlinear time-varying (NLTV) and a nonlinear time-invariant (NLTI) dynamic models of face gear transmission system with backlash nonlinearity are formulated. The 6DOF motion equations of the face gear pair considering the mesh stiffness, backlash, contact damping and supporting stiffness are proposed. Second, the effect of mesh stiffness on the dynamic response of the face gear drive system is analyzed with the numerical method, where the mesh stiffness is expressed in two patterns as time-varying form and time-invariant form. According to the comparative study, some significant phenomena as bifurcation, chaos, tooth separation and occurrence of multijump are detected. The results show that different forms of mesh stiffness generate an obvious change on the dynamic mesh force.

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The effects of directional rotation radius and transmission error excitation on the nonlinear dynamic characteristics of face gear transmission system are analyzed. First, the accurate time-varying mesh stiffness is calculated using finite element method, and the nonlinear motion equation of the system under static transmission error excitation is proposed. The frequency response curve, time history curve, dynamic mesh force curve and dynamic factor curve are given, and the phenomena of jump, multiple solutions and tooth impact are observed. The numerical results show that the effect of amplitude variation of directional rotation radius on the dynamic characteristics of face gear pair is less conspicuous than that of transmission error but actually existing. The amplitude of the dynamic response of face gear pair reduces to some extent with the uniform distribution of the loading area through enlarging the amplitude variation of directional rotation radius. The static transmission error excitation should be reduced to perfect the transmission property. The system is in periodic motion most of the time, and tooth impact occurs only near ! ¼ 1. Since its dynamic property at low velocity and high velocity is good, the system should get through the resonant area quickly in work.

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Fault feature extraction plays a significant role in bearing fault diagnosis, especially in incipient fault period. Recently, deep neural network has been favored by many researchers due to its excellent hierarchical feature extraction capabilities. The existing diagnosis methods based on deep neural network mostly take original condition monitoring data as input and further convert fault diagnosis into pattern recognition issues. Although it improves the level of intelligent diagnosis, it is still confronted with practical problems. Since deep neural network includes many non-linear mapping layers, the extracted fault-related features show a high degree of abstraction, which reduces the practical level of this technology. Aimed at this problem, a mining method of understandably weak fault information is proposed based on deep neural network inversion estimation. From perspective of neuron response degree, this method mines the most sensitive input pattern that maximizes the neuron's activation value of network output layer in the original input feature space. It can intuitively mine the weak fault information from the original signal. Two bearing experiments verify the effectiveness and reliability of the proposed method.INDEX TERMS Deep neural network inversion estimation; fault feature extraction; mining of weak fault information.