In this study, a new lattice structure ARCH is proposed, ARCH lattice structure and traditional lattice structures BCT were fabricated from 316 L stainless steel by SLM. Mechanical properties and deformation behavior of the lattice structures were experimentally investigated. The results show that the ARCH lattice structures have better mechanical property and energy absorption capability than BCT lattice structures. Under the same relative density, the compressive strength and elastic modulus of the ARCH lattice structure is 121.27% and 60.48% higher than the BCT lattice structure, and the ARCH lattice structures have better energy absorption properties than the BCT lattice structures.

Due to the generally strong non-linear characteristics of bearing failure, leading to overall mechanical system failure, fault state feature extraction is difficult. In this paper, a fault feature extraction method based on the Volterra series kernel under multi-pulse excitation is proposed. To avoid reliance on simplified models based on traditional mechanics, a nonlinear Volterra series model was constructed by introducing the input and output signals of the system, and using a low-order Volterra series kernel from the time domain and frequency domain, which was then solved using a multi-pulse excitation method. Furthermore, the state of the rolling bearing was determined using different characteristics of the corresponding generalized frequency response, and the current fault stage was inferred. The rolling bearing failure was validated experimentally, and it was shown that the Volterra series model can be more easily used to extract fault characteristics and trends of a rolling bearing in comparison to the traditional wavelet algorithm, therefore serving as a better method for fault prediction.

In this paper, relying on the Volterra series nonlinear system model and the high-order kernel Hilbert’s reconstructed kernel fast solved algorithm, a fault feature frequency domain identification method based on Volterra high-order kernel generalized frequency response graph analysis is proposed. Firstly, the method uses the system input and output vibration signals to determine the Volterra model. Then, the Volterra high-order kernel function is solved quickly by reproducing kernel Hilbert space method, and the generalized frequency response function is used to identify the model. Finally, multidimensional high-order spectral pattern analysis is used to separate and extract the fault and degree characteristic information implied by frequency and phase coupling in the third-order kernel function. Following the theoretical approach, in the experimental part, this paper uses the planetary gearbox fault loading test rig to complete the data collection and establishes the Volterra experimental model through the measured data. The generalized frequency responses of each order kernel function are compared and analyzed and the capability of distinguishing and the adaptability of different order kernel functions for the degree of crack failure are discussed. The effects of changing the memory length of the Volterra model and the order of the kernel function on the recognition result are verified. The final experimental results show that the use of reproducing kernel Hilbert space can effectively avoid the dimension disaster problem that occurs in the high-order kernel solution process. Moreover, the third-order kernel can describe more intuitively the nonlinear system model under multifactor coupling than the second-order kernel. Finally, Volterra series model the third-order kernel’s generalized frequency response can effectively distinguish between nondefective and faulty gears, and its resolution is enough to distinguish the degree of failure of gear cracks.

This study presented a method for modeling the nonlinear system of a planetary gearbox and the fault diagnosis of a crack in a planetary gear based on the Volterra series theory. First, the exponential Hilbert reproducing kernel and its fast optimization algorithm was proposed and deduced in theory, and the fast solution of the fourth-order kernel of the Volterra series was successfully solved. Second, the Volterra series model estimation was compared with the least squares estimation of the actual collected signals from the planetary gearbox and the time-domain output signal was estimated using a neural network. The accuracy and the superiority of the Volterra series model of the planetary gearbox were then verified. At the same time, the convergence and the memory length of the Volterra series were discussed. In order to further mine and extract fault feature information, coupling relationship between the generalized frequency response of higher order spectrum of the Volterra series model and fault frequency was also studied. This study attempted to reflect the fault state and fault degree of a crack in a planetary gear from different observation angles and dimensions. Finally, the real condition loading test of a gearbox's comprehensive fault test platform was carried out. The validity of the method of nonlinear system modeling and fault diagnosis of the planetary gearbox, based on the Volterra series theory, was verified, and a new solution has been provided for related research in this field.