Research Of Vibration AM-FM Mechanisim Of Gear Fault And Decomposition Method

Gear transmission system is widely used in the significant machineries such as the automobile,wind turbine generator and ships,whose reliable service benefits the economic gain and the safety of life and property.Thus,the object of this research focuses on the fixed-shaft and planetary gear system.Aiming to the difficulties of the compound gear fault features extraction and the accurate separation of the modulation components,the vibration AM-FM mechanism of gear fault is further investigated.Based on the fault modulation mechanism,the extraction method of fault features induced by the compound-fault gear and the separation method of modulation components are proposed,which are employed to fault diagnosis and possess the practical engineering values.(1)The formula of FM component in the meshing stiffness attributed to the fault-induced periodic speed fluctuation is deduced,whose effects on the vibration response are researched.A series of phenomenon models of gear-pair are established,which consider the FM generated by the fault-induced speed fluctuation.The models are able to analyze the mapping relation of AM-FM features and gear fault modes.The mathematic models of vibration signal caused by the gear fault are built.The vibration signal caused by the steady-type gear fault includes the asymmetrical AM-FM sidebands around harmonics of the meshing frequency and the harminics of fault feature frequency of fault gear in the low frequency range.The vibration response induced by the impact-type gear fault contains the modulation sidebands around harmonics of the meshing frequency that are similar to those caused by the steady-type gear fault,as well as the harmonics of the fault feature frequency distributing in the whole frequency range.Moreover,the spurious are caused by the nonlinear excitation.The product of two groups of FM compnents in the meshing stiffness and the vibration resposnse is proved to bring in AM-FM components.The lumped parameter model of fault fixed-shaft gear-pair is built to acquire the vibration AM-FM sidebands,which are similar to those obtained from the phenomenon models of fault gear-pair.The AM-FM sidebands features of vibration response in experimental gearbox fault are coincide with the results of theoretical analysis.(2)The influences of fault-induced periodic speed fluctuation in the planetary gear-train on the time-varying transfer path function and measured-direction projection function of meshing force are studied.Based on the vibration AM-FM research of fault fixed-shaft gear-pair,a groups of phenomenon models are established,which contain the sun gear,single planet gear and ring with distributed or localized fault,respectively.These models are utilized to analyze the causes and the distribution features of AM-FM sidebands.The lumped parameter models that include the speed fluctuation induced by the faulty sun gear or ring gear in planetary gear,are used to obtain the modulation sidebands of vibration response.The modulation sideband features of vibration responses respectively acquired from the lumped parameter models and the field planetary gearbox in the wind turbine and the experimental single stage planetary gearbox agree highly with the sideband distributions obtained from the phenomenon models.Compared with the vibration AM response regardless of the speed fluctuation induced by the gear fault,the frequency distribution research of vibration AM-FM response has largly perfected the exsiting modulation mechanism research of gear fault.(3)Based on the fault modulation mechanism of fault gear and the sparse decomposition theory,an extraction method of compound gear faults is proposed.The double dictionary including steady-type fault and impact-type fault is designed,which can represent the fault modulation feature of compound gear faults.The split augmented Lagrangian shrinkage algorithm(SALSA)is combined with hard threshold de-noising to simultaneously obtain the optimal sparse coefficients of steady modulation and impact modulation components.Key parameters including Lagrange multipliers,penalty factor of SALSA and hard threshold are studied to determine their optimal value ranges.The effectiveness of the proposed method is verified by the simulation and experiments.Comparative analyses with methods respectively based on matching pursuit and tunable Q-factor wavelet transform indicate that the proposed method is superior to other two methods in calculation efficiency and anti-noise performance,especially when these two kinds of modulation components are completely coupled in some resonance bands.(4)According to the mathematic model of vibration modulation caused by the faulty fixed-shaft gear pair,the separation method of AM and FM is developed,which consists of the squared amplitude demodulation and phase demodulation based on Bessel function of the first kind.Discrete spectrum correction technique is employed to correct the modulation frequency and amplitudes in amplitude spectrum,which are utilized to establish system of nonlinear equations of AM and PM parameters.Trust-region reflective least square algorithm is then applied to solve these parameters and extract AM and PM components in sequence.The simulations indicate the superiority of the proposed method in anti-noise performance than the Hilbert transform demodulation and energy-operator-based demodulation.The proposed method is used to separate the AM and FM components around the meshing frequency in the experimental gearbox.The separation results manifest that the visible differences of separated PM components under steady-type or impact-type gear fault condition,which can be used as an accordance of broken-tooth fault diagnosis.A novel diagnosis method for gear broken-tooth fault is finally generated.The relationship of the size of broken-tooth and modulation intensity is researched by the proposed method,which indicates that more serious broken-tooth degree behaves stronger modulation.