| The gear train is one of the most important transmission mechanisms in the automotive transmission system.Due to the harsh working environment,it is prone to fatigue damage and crack,which affects the driver's comfort and even safety.Study on the vibration characteristics of gear train under normal and tooth crack conditions and establishing the mapping mechanism between vibration response and fault type are essential for theoretical research and engineering application.Based on the energy method and geometrical property of involute,the calculation formula of the time-varying meshing stiffness under normal and tooth crack is derived which is used to research the characteristics of meshing stiffness under different state.Under healthy condition,the meshing stiffness only contains the meshing frequency and its harmonics.When the tooth crack emerges(without considering speed fluctuation),there are rotational frequency harmonics of fault gear covering all the frequency range and meshing frequency harmonics existing in meshing stiffness of healthy gear pair.When considering the speed fluctuation,frequency modulation sidebands appear in the vicinity of meshing frequency harmonics.The frequency-modulation components of rotation frequency of cracked gear are also generated.Meshing stiffness decreases with the crack propagation extent and the crack growth angleTaking a single-stage fixed-shaft gear system as the object of study,lumped parameter method is used to establish dynamic model of gear system.The vibration response characteristics of system under normal and tooth crack state are studied by numerical simulation and theoretical analysis.Under healthy condition,the vibration signal only contains the meshing frequency and its harmonics.When gear has tooth crack and neglecting the effects of speed fluctuation on vibration response,natural frequencies are modulated by rotational frequency of crack gear,which cover all the frequency range.In addition,the frequency components caused by healthy gear are also exist in the vibration signal.When considering the speed fluctuation caused by crack,frequency modulation sidebands of rotational frequency of crack gear emerge around meshing frequency harmonics,which are superimposed with the original resonance sideband to change only the amplitudes of sidebands.The correctness of numerical simulation and theoretical analysis is verified by experiments of single-stage fixedshaft reducer.Taking a single-stage planetary gear system as the object of study,lumped parameter method is used to establish dynamic model of planetary system.Taking the time-varying effects of transmission paths into account,numerical simulation is applied to study the vibration response characteristics of healthy gear/crack sun gear/crack ring/crack planet.Response spectra are normalized by frequency of the planet carrier.In normal state,the vibration signal contains order components that are divisible by 3(the number of planets)and their aymmetrical modulation sidebands with interval of 3 times the rotating frequency of carrier.The resonant sidebands near the meshing frequency harmonics may also be evoked.When there is a tooth crack on sun gear,resonant bands contain two groups of modulation sidebands whose intervals are the feature frequency of faulty sun gear and therefore forms a special interval between the two adjacent orders.When there is a tooth crack on ring gear,resonant bands only contain one group of modulation sidebands with interval of 3 times rotating frequency of planet carrier.When there is a tooth crack on planet gear,resonant bands involve two groups of modulation sidebands whose intervals are rotational orders of the planet gear relative to that of plant carrier.The coupling of these two groups of sidebands forms a special frequency interval.The conclusion of numerical simulation analysis is verified by the experimental results of singlestage planetary gearbox. |
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