System-level Identification and Analysis of Gear Dynamics

This study presents an effort in system level identification and gear dynamics analysis. The mechanical system usually includes several parts with different mechanisms to achieve a particular job. To simulate the motion of the parts, evaluate the performance, and analyze the vibration of the system, a system level modeling is needed. However, the modeling is challenging because of unknown parameters, nonlinearities, and uncertainties. System identification is one of the key techniques to obtain a reliable dynamic model by appropriately choosing the mathematical model, identifying the unknowns, and reducing the uncertainties. This study illustrates approaches and procedures in building system-level model for an electric impact wrench. Electric impact wrench, whose operation involves dynamic events occurring at vastly different time scales, is an important tool used in manufacturing and maintenance services where high torque is required. A first-principle-based, system-level model is built by incorporating the dynamics of gear transmission, spindle, and impacting components. The nonlinear impact and kinematic constraints are explicitly analyzed, and systematic parametric identification is performed based on a multi-objective optimization approach, i.e. archived multi-objective simulated annealing. The predictions from the model with system identification correlate well with the experimental results. In the system level modeling, it is found that gear transmission is one of the most popular and important sub-system whose dynamics and health conditions affect the system performance significantly. Therefore, this study also presents the effort in the gear dynamics analysis and fault diagnosis. It is well known that the nonlinear characteristics of the gearbox are mainly induced by time-varying mesh stiffness and backlash. To solve this nonlinear system, numeric method is usually employed whose time step has to be carefully controlled and the accuracy suffers from cumulative errors. To overcome the limitations of the numeric method, an approach, integrating Floquet theory with harmonic balance method, is proposed to analytically analyze the dynamics of the gearbox that subjects to parameter excitation and backlash nonlinearity. This approach can not only solve the steady-state system response, as traditional harmonic balance method, but also the transient response of the system. Case study verifies the accuracy of the proposed approach and its efficiency in calculating the frequency response of the system. The proposed method also accurately predicts the nonlinear jump of the gearbox. In the gear fault diagnosis, a fault signature enhancement method, i.e. angle-frequency domain synchronous averaging, is developed. This method is capable of highlighting the fault related features from the nonstationary and noisy vibration signal. Rather than being averaged in time-domain as traditional method, the vibration signal is averaged in angle-frequency domain after being resampled from time domain into angle domain and analyzed by the joint angle-frequency technique so as to solve the phase shift problem. The enhanced results are then analyzed through feature extraction algorithms, i.e. Kernel Principal Component Analysis, Multilinear Principal Component Analysis, and Locally Linear Embedding, to extract the most distinct features for fault classification and identification. Experimental study demonstrates that the proposed method significantly enhances the fault related features and improves the identification rate of support vector machine in identifying multi gear faults