To satisfy the requirements of the end-to-end fault diagnosis of rolling bearings, a hybrid model, based on optimal SWD and 1D-CNN, with the layer of multi-sensor data fusion, is proposed in this paper. Firstly, the BAS optimal algorithm is adopted to obtain the optimal parameters of SWD. After that, the raw signals from different channels of sensors are segmented and preprocessed by the optimal SWD, whose name is BAS-SWD. By which, the sensitive OCs with higher values of spectrum kurtosis are extracted from the raw signals. Subsequently, the improved 1D-CNN model based on VGG-16 is constructed, and the decomposed signals from different channels are fed into the independent convolutional blocks in the model; then, the features extracted from the input signals are fused in the fusion layer. Finally, the fused features are processed by the fully connected layers, and the probability of classification is calculated by the cross-entropy loss function. The result of comparative experiments, based on different datasets, indicates that the proposed model is accurate, effective, and has a good generalization ability.

Gear system is characterized by high efficiency, compact structure, and transmission ratio stability, and it has been extensively applied in various industrial equipment. This paper presents a novel preliminary estimate method for gear reducer noise radiation and vibration characteristics, and systematic researches on radiation characteristics of gear reducer are made. In the noise analysis process, the influence of time-varying mesh stiffness, error excitation, and tooth flank contact feature are comprehensively considered, the linear vibration model and nonlinear vibro-impact model for transmission system is set up, and then the dynamic load of the gearbox is obtained by solving the model. The dynamic load of bearing is taken as an excitation, the finite element method/boundary element method is adopted to analyze vibration and noise radiation characteristics of the gear reducer. The time domain response and field point noise spectrum at sound field are obtained, and the influence of harmonic components in excitation on vibration noise radiation of gearbox are discussed. The dynamic characteristics and sound radiation characteristics of gear reducer under different operating conditions are calculated, the change pattern of frequency component of the bearing dynamic load and noise radiation based on operating condition are obtained, and some interesting conclusions are observed from research that the gearbox produce the linear vibration and noise under the heavy load condition. Meanwhile, the nonlinear vibro-impact and noise is appeared under light load condition. The distribution of the gearbox radiated nose is uniform in various conditions, but noise takes sub-harmonic components as fundamental frequency and more peaks in the noise spectrum are observed. With the increase of the rotary speed, the noise tallies with the trend described by Kato formula except that under the gear system resonance speed. The impact force between teeth flanks shall be on the increase with the increase of rotary speed, and gear pair vibration experiencing a course from irregular vibration to regular periodic rattle vibration. With the increase of load, the noise of reducer changes with load as the variation of logarithmic function. For the noise in the process with load on the increase from no-load (the load is 0), the gear reducer vibration condition experienced both sides collision, single-side collision, and normal meshing in three stages. The radiated nose is increased gradually, but the abrupt change happened in critical positions between both sides collision and single-side collision as well as single-side collision and normal meshing in the process. The conclusions of this paper will offer theoretical basis for reducer to reduce vibration and noise.

This paper presents a comprehensive procedure to calculate steady dynamic response and noise radiation generated by a gear reducer. In this process, the bearing force is obtained by solving the transmission system dynamic model, which is taken as the excitation of the gearbox, the noise generated by the gearbox vibration is researched by using FEM/BEM, so the dynamic characteristics of gear transmission and gearbox structure are demonstrated. Then the time history of node dynamic response and noise spectrum of the gearbox are obtained, and the effect of the excitation of frequency doubling of mesh frequency on the gearbox vibration and noise radiation is illustrated. The changes in radiated noise of gear reducers with load are calculated respectively by using both simulation and Kato's formulae, and results agree well with each other. The frequency range of the gearbox resonance is obtained by analyzing the spectral maps of the vibration and noise under the case of engine speed steadily increased. The study provides useful theoretical guideline to the design of the gearbox.

Aiming at noise problem of two-stage gearbox, this paper uses the panel acoustic contribution analysis (PACA) and response surface methodology to conduct structural-borne acoustics analysis and multi-objective optimization of gearbox. Using this optimization, optimal layout and parameters of the added ribs can be determined. The dynamic model of a spur gear-shaft-bearing system is built in consideration of the time-varying mesh stiffness, the time-varying bearing stiffness, and the flexibility of the shaft, while dynamic load of the bearing is obtained through solving the model. The dynamic load of bearings is considered as excitation to analyze the vibration and noise radiation characteristics of housing. Furthermore, acoustic transfer vector, modal acoustic contribution and PACA are used to select the region with the most acoustic contribution. The variable ribs structure model (VRSM) is established in this region. Finally, the VRSM are adopted to optimize the housing. The optimization model based on the peak sound pressure level (PSPL) and the ribs mass (R_m) is established by using response surface method. Through multi-objective optimization, the variable in VRSM can be modified or deleted to reduce the radiated noise of the gearbox. The optimization results demonstrate that the PSPL after optimization is decreased by 4.88 dB at frequency of 3130 Hz. At the same mass, the noise reduction effect of VRSM is 12% higher than that of standard rib. Therefore, the optimization effect of the housing structure is obvious. PACA-VRSM-RSM- NSGA-II technology provides a new research scheme for reducing the vibration and noise of the gearbox.

In this work, an improved computational method for the prediction of the vibration and noise of a gearbox that considers the flexibility of the shaft is developed. Based on the finite element method (FEM), a coupled dynamic model of a spur gear-shaft-bearing system is established, and the time-varying mesh stiffness (TVMS), the time-varying bearing stiffness (TVBS), and the flexibility of the shaft are considered. The Newmark integration method (NIM) is utilized to obtain the dynamic load of the bearing. Furthermore, the proposed model is validated by experiments. The bearing load is then considered to be the excitation of the housing, and the radiated noise is calculated via the finite element method/boundary element method (FEM/BEM). The effects of the shaft flexibility on the bearing response and radiated noise are discussed based on the proposed method. The results demonstrate that, when the shaft flexibility is considered, the system undergoes the bending vibration of the shaft, and the vibration amplitude and excitation frequency components of the bearing load decrease significantly. Additionally, the main resonance mode of the gearbox is changed, and the radiated noise is enhanced. The effects of the input speed and shaft stiffness on the bearing response and radiated noise are also investigated. The results provide a theoretical basis for the further development of the vibration and noise reduction of gearboxes.