| The concentric face-gear split-torque transmission system(CFGSTTS)integrates the advantages and structural characteristics of face gear drives,split-torque transmissions,and concentric transmissions.Face gear drives are characterized by high speed,heavy load and without axial force of pinion.The power capacity of a split-torque transmission can be expanded throuth multiple branches.The overall size of a concentric transmission can be reduced as much as possible with overlapping components.As a result,the CFGSTTS has the properties of high speed,heavy load,and large power density,which helps its application in extreme working conditions such as helicopter transmissions.Dynamics affects the vibration and noise of gear systems.Load sharing relates to unbalance loading and local failure in a transmission.Thus,this work focuses on the characteriscs of vibration and load sharing of CFGSTTS.Unfortunately,the vibration of CFGSTTS involves the factors of parametric excitations and nonlinear characteristics,as well as the issues of space gear meshing,power split and converge,statically indeterminate structures,and rigid-flexible coupling,etc.The load sharing analysis depends on the power transmission path in such a complex spatial system with closed loops.The assembly condition,the finite element simulation,and the power flow direction are firstly investigated in this work.Then,a bending-torsional-axial-pendulum lumped parameter dynamic model and a gear-rotor flexible multibody dynamic model are established.Furthermore,the relationship between the main design parameters and the performance of vibration and load sharing is studied based on the flexible multibody model.The main contents and conclusions are:1)The assembly conditions,the finite element simulation technology of system level,the face gear modification,the power flow direction,and the static load sharing of CFGSTTS are researched.Firstly,the assembly conditons are deduced and verified by the method of virtual assembly.Then,the key techniques of finite element simulation modeling for 3D closed-loop gear systems with multiple input-output ports are studied,and the face gear surface is modified because of the edge contact.Furthermore,based on the finite element simulation techonology,the power flow direction of the system is judged and analized,and the static load shaing coefficients are worked out.Additionally,the influence of main parameters including distribution structures,distribution angles,number of pinions and load condition parameters on static load sharing is researched by the finite element simulation.As researches indicate,the performance of static load sharing between two face gears is worse than that between two input gears or that between two idler gears.Reasonable system parameters can effectively improve the performance of static load sharing up to 70%.2)A bending-torsional-axial-pendulum lumped parameter dynamic model with 44 degrees of freedom(DOF)is established,based on which the natural characteristcs is anaylized,so as the dynamic performance of vibration and dynamic load sharing of both single speed and speed sweep.At first,the lumped parameter model is established based on the force analysis with the consideration of the parameter excitations and the structure characteristics.The parameter excitations include time-varying meshing stiffness,static transmission error(TE),meshing damping,support stiffness,meshing backlash,and the tortional stiffness of shafts.Then,the natural frequencies and modes are figured out with the characteristic equations,and the dynamic equations are solved by the numerical integration method of Runge-Kutta.Finally,under an extreme working condition,the characteristics of vibration and dynamic load sharing of both single speed and speed sweep are focused on,and the following conclusions are obtained.i)The vibration modes are mainly translation-torsion coupling ones,and a small number of high-order torsional modes and low-order translational modes.ii)The dynamic load sharing of single speed and speed sweep between two input gears or between two idler gears is acceptable,while that between two face gears is unacceptable.iii)The frequency spectrum of dynamic transmission error(DTE)mainly contains large magnitudes of meshing frequency 2913.3 Hz,and small magnitudes of other frequencies.iv)The time history diagram,bifurcation diagram,phase diagram,Poincare diagram show that the whole system enters a stable vibration state without bifurcation or chaos.3)The gear-rotor flexible multibody dynamic model is established based on the theory of rotor dynamics.The vibration and load sharing of single speed and speed sweep,as well as the natural characteristics,are investigated and compared with the results of lumped parameter dynamic model.The flexible multibody model is established according to the theories of rotor dynamics,Timoshenko beam,and finite element method,as well as the structural characteristics of face gear meshing and bearing support.Secondly,with the consideration of gyroscopic effect,the natural frequencies and modes are figured out with Campbell diagrams and characterictic equations.The established dynamic model is sovled with the numerical integration method of Newmark,and the dynamic responses and load sharing under the extreme working condition are worked out.Results show that,the natural frequencies,modes,frequency spectra,and dynamic load sharing obtained with the flexible multibody model are basically in accordance with that of the lumped parameter model.The flexible multibody model has the advantages over the lumped parameter model as follows.i)The former reflects more characteristics of the system such as natural frequencies,modes,and vibration responses of nodes than the latter.ii)The shaft frequency components in DTE spectrum are observed in the former,but not in the latter.iii)Both the hysteresis at 10618 rpm and the chaos at14091 rpm are observed in the former,but not in the latter.4)The effects of the factors including distribution structure,distribution angle,meshing backlash,meshing stiffness and support stiffness on the vibration and load sharing of CFGSTTS are studied by applying the flexible multibody dynamic model.As showed in the results,small distribution angles of right input and right idler and small gear backlash are beneficial to the performance of both vibration and dynamic load sharing of the system.Reasonable values of meshing stiffness and support stiffness improve the dynamic performance of the system.The external symmetrical structure is helpful to the system vibration and dynamic load sharing,in which the dynamic load sharing coefficient can be reduced as much as 60% than that of the internal symmetrical structure and the intersect structure,and the peak vibration can be reduced 25%.5)The theoretical methods including the flexible multibody dynamic modeling and the system-level finite element simulation are verified by compaired with the rolling test,modal test and vibration test based on a reduced CFGSTTS.Firstly,the system-level method of finite element simulation is verified by the distribution of contact area in the rolling test based on the reduced CFGSTTS.Then,the flexible multibody modeling is validated from the following aspects.i)The natural frequencies and modes of the face gear and spur gear parts are measured by the hammer method,and compared with partial of the natural characteristics of the face gear drive in theoretical calculation.ii)The single-speed and speed-sweep vibration acceleration of the reduced CFGSTTS is measured,and compared with the results in theoretical calculation.In short,the difference between the theoretical calculations and the experiments are less than 15%,which basically verifies the correctness of the theoretical methods in this work.The methods of transmission dynamic modeling and analysis in this thesis provide important reference for the research of similar gear systems,and the correlation law between the main parameters and the performance of vibration and load sharing is valuable for engineering design. |
