Research On Dynamic Characteristics Of Vehicle Compound Planetary Gear Train Sets

With the promotion of the vehicles performance requirements, compound planetarygear train sets (CPGT) have been used in vehicle. Compared to simple planet gear train sets,more range shift, larger loads and transmission ratios can be achieved by CPGT. However,there are many factors affecting its dynamic characteristics because of its complexstructures. Thus, more serious problems of vibration and noise are avaliable. The researchesat home and abroad on CPGT are in initial states with the lack of complete design criteria.Most engineers only continue to use conventional static method when they design theCPGT. The dynamic characteristics and the impact of parameters are usually obtained byexperience and estimation. It will exert harmful effect in practice as well as its inefficiency.With higher performance requirements of gear transmission system, dynamic design hasbecome a development trend of transmission system design, which knowledge of thedynamic characteristics of the system is the foundation of dynamic design. Therefore, Ithave great significance on building the dynamic model and researching the dynamiccharacteristics of CPGT.This dissertation is supported by the National Natural Science Foundation of China(Project name:Research on Dynamic Design Theory of Vehicle Compound Planetary GearTransmission System.Grant No.:50875189) and national defense project of China NorthVehicle Research Institute (Project name:Research on torsional vibration characteristics ofXXX special type of transmission system. Grant No.:9140C340101101). Based onbuilding the dynamic model of CPGT, by means of nonlinear dynamic and chaos theory, aswell as experimental observations and signal analysis, the dynamic characteristics ofvehicle CPGT are studied in this dissertation systematically and penetratingly. The maincontents and conclusions are as follows:1. A Ravigneaux CPGT in practical vehicle automatic gearbox is used for the researchsubject in this dissertation. In case of some reasonable assumptions, the system purelytosional and translational-torsional coupled dynamic models are established by lumpedmass method. Considering the gear backlashes, time-varying meshing stiffness andsynthetical meshing errors, the mathematical description is applied. Based on deducing therelative displacements between the components, the corresponding kinematic differentialequations of the two kinds of models are established by means of Lagrange equation. The differential equations are adequate for iterative solving instance, any group number, spacelength and relative position of the planet gears.2. Based on the pure torsional model of CPGT, Harmonic Balance Method (HBM) isapplied for studying the nonlinear frequency response characteristics. In the first place,coordinate transformation and nondimensional treatment are operated on the model toeliminate rigid body displacement and solve conveniently. The pocess of solving CPGT'sdynamic response by Harmonic Balance Method (HBM) is studied in detail. The steadystate response of the system is expanded as a form of average component together withfundamental frequency component. The backlash nonlinear function is expanded as thesame form by using Describing Function, which convert the differential equations intononlinear algebraic equations. To solve the algebraic equations, single rank inverseBroyden quasi Newton method is applied iteratively for obtaining the fundamentalfrequency steady state response of the CPGT. It shows from the study that the typicalnonlinear feature of jumping and multivalue in the frequency response curves has arisen forthe existence of gear backlashes. This feature is affected by gear backlashes, time-varyingmeshing stiffness and synthetical mesh errors, which the detail calculation and explanationare processed by changing the above parameters in this dissertation.3. Based on the translational-torsonal coupled model of CPGT, numerical method isused for studying the nonlinear dynamic responses of the system under different excitationfrequency, meshing damping ratio and backlashes, which the qualitative methods areapplied to discuss the different movment forms. The translational-torsonal coupleddifferential equation of Ravigneaux CPGT, which the complex nonlinear multi-variablefunction and linear variable are coextensive, is written as matrix form through lineartransform to overcome the difficulty of solving inconvenience. Based on analyzing theprinciple of steplength-varying Gill integral method, the global bifurcation diagrams of theCPGT's dynamic response are obtained by changing the excitation frequency, gearbacklashes and damping ratio, which the different motion states impacted by aboveparameters are achieved. The CPGT's periodic, quasi-periodic and chaotic motions areanalyzed through using time history curve, phase-plane diagram, Poincáre section andpower spectrum synthetically. The analysis shows that rich and varied dynamic behavioursare included in CPGT because of the existence of nonlinear factors as gear backlashes,time-varying meshing stiffness and synthetical mesh errors.4. Direct method of dynamic response sensitivity analysis is derived and the calculation flow graph is given. Based on the Ravigneaux CPGT's translational-torsionaldynamic model, the dynamic response sensitivities on mass, supporting stiffness of centercomponents, meshing stiffness and meshing damping are calculated by direct methodtogether with Runge-Kutta numerical methods of integration. It shows that the dynamicresponse sensitivities on the parameters above are non-zero totally. The same parameter hasdifferent contribution on different engagement pairs and different parameters have differentcontribution on the same engagement pairs. Among the four kinds of parameters, thesupporting stiffness of center component has minimal influence on the CPGT's dynamicresponse and the meshing damping has the maximum.5. Experimental platform of CPGT is built to test the dynamic characteristic and therationality of the theoretical analysis is affirmed. Frequency response function is achievedby means of hammer blow. The primary natural frequency of torsional vibration is proved,which certify the rationality of purely torsional model built by mass lumped method. Thenthe CPGT's dynamic responses under three different input rotationl speeds are measured. Itshows from spectrum analysis that the response signals include fundamental frequency andits octave parts in the section of low frequency away from CPGT's resonance frequency.The fundamental frequency is predominant in the signals and nonlinear vibrations likesubharmonic or ultraharmonic vibration are not appeared. The rationality of the method andconlusion made by the theoretical study in the dissertation is proved by physical test.The dynamic characteristics of compound planetary gear train sets are came out andthe influences of design parameters on dynamic characteristics are possessed, whichprovide theoretical foundation on dynamic design of compound planetary gear train sets.