Research On Damage Modeling And Fault Diagnosis Of The Compound Planetary Gear System

Planetary gearboxes are key components in large-scale and complex mechanical equipment,such as vehicles,wind turbines,helicopters,and construction machineries.The fault forms of the gearboxes are diverse under tough operating conditions.The undefined fault mechanics make it difficult to detect the incipient damage of planetary gearboxes.Therefore,it is essential to analyze the dynamic responses of the faulty planetary gear set to reveal the fault mechanics.Through the dynamic modeling of the faulty planetary gear set,the fault nonlinear characteristics can be analyzed.Further,the damage evolution mechanics can be revealed.Therefore,model-based dynamic analysis could be an efficient method to detect the incipient damage,which has significant theoretical and engineering values.Compound planetary gear sets are widely used in automatic transmissions.However,the dynamic modeling of the compound planetary gear set is complicated since the effects of the complex configurations,abundant nonlinear factors,and gear damages.Moreover,the fault diagnosis theory applied on the simple planetary gear set can not directly used to diagnose the compound one due to its unique configurations.Therefore,a compound and two-stage planetary gear set used in construction machinery transmission system is selected,and the corresponding theories and methods of damage modeling and fault diagnosis are studied in this research.In addition,this research is funded by the project of China(863)"Reverse Logistics Technology for Remanufacturing Objects and Application in the Construction Machinery Industry".The detailed contents of the thesis can be summarized as follows:(1)The dynamic modeling methods of the compound and two-stage planetary gear set are studied based on the dynamic theory.First,the configuration,kinematic characteristics,and meshing characteristics of the compound planetary gear set are analyzed based on the multi-body dynamic model.Further,a three-dimensional lumped-parameter dynamic model for the compound planetary gear set is established.The damping,bearing,time-varying mesh stiffness(TVMS),tooth backlash,nonlinear error excitation,and mesh phase relations are taken into consideration.The relative displacement between two components are derived,and then the overall equations of motion in matrix form for the system are established.This model is the basis of the analysis of the nonlinear dynamics of the system.(2)Based on the proposed lumped-parameter dynamic model for the compound planetary gear set,the nonlinear parameters of the model are mathematically analyzed.Further,the damage excitation is taken into consideration and the dynamic model for the faulty compound planetary gear set is proposed.Finally,the inherent characteristics of the system are studied.The TVMS and the mesh phase relations are mainly studied in this thesis.First,the gear tooth is treated as a cantilever beam on the root circle.Then,the analytical model is proposed to evaluate the TVMS of a perfect gear based on the potential energy method.Next,according to the simplified typical damages,an analytical approach is proposed to quantify the TVMS reduction due to damages.Incorporating such quantitative equation into the model,the dynamic model of the faulty compound planetary gear set can be established.This model can be used to obtain the fault properties of the compound planetary gear set.Further,the mesh phase relations between each mesh pair are derived based on the mesh mechanics.Incorporating the mesh phase relations into the TVMS functions,the TVMS of the system are analyzed.Finally,the numerical analysis method is used to solve the equation of the free motion,and the inherent characteristics of the system are obtained.The phenomenon of loci veering induced both by the TVMS and the mesh phase differences is analyzed.The proposed model is more accurate for obtaining the dynamic responses of the compound planetary gear set than the model with the simplified TVMS and mesh phases.(3)For the fault diagnosis issue of the meshed planet planetary gear set,the damage modeling method is studied.The fault properties of the planets are analyzed based on the simulation and validated by the experimental analysis.First,the time interval and period of the damaged planet tooth in meshing are derived based on the meshing characteristics of the planets.Then,the effects of damaged planet on the TVMS are studied.Next,the dynamic responses of the gear set with and without damaged planet are simulated.The fault features of planets are further extracted from the vibrations.Finally,a test rig for construction machinery transmission system is set up.Several planet damage seeded experiments are conducted on an industrial site.The fault features of planets are extracted from the experimental signals to validate the model and theoretical derivations.The results show that the proposed model of the faulty compound planetary gear set can efficiently reveal the effects of the damaged planet on the vibration properties of the system.This can guide the fault diagnosis of the meshed planet planetary gear set in practice.(4)Aiming at the fault diagnosis of multistage planetary gear set,the damage modeling method is studied.The fault properties of the sun gears in different gear stages are analyzed based on the simulation and validated by the experimental analysis.First,the TVMS model for a chipped gear is proposed and the detailed formulas of the TVMS for the chipped gear are derived.Then,the effects of the chip sizes on the TVMS reduction are studied when the defects take place on the single tooth and multiple teeth of the sun gears in different gear stages.Further,the simulated signals are analyzed to demonstrate the fault features of sun gears in different gear stages.Moreover,the theoretical derivations are validated through the experimental signals analysis.This research can guide the fault diagnosis of the multistage planetary gear set in practice.(5)Aiming at the diagnosis and fault features extraction of incipient crack damage,the crack model is proposed and the effects of the crack evolution of the sun gear on the nonlinear dynamic properties of the planetary gear set are researched.First,the TVMS model for a cracked gear is proposed and the analytical equations for the cracked gear are derived.Then,the effects of the crack propagation on the TVMS are studied.Further,the effects of the crack propagation on the natural frequencies of the system are analyzed based the inherent characteristics analysis.The dynamic responses containing the crack evolution information of the gear set are simulated.The influences of crack propagation on nonlinear dynamic properties of the system are analyzed through time history,phase trajectory,Poincare map,and order spectral analysis.The fault features of the incipient cracks are extracted.This research can guide the fault diagnosis of the incipient crack damage.