Research On Load Sharing And Dynamics Characteristics Of Encased Differential Herringbone Train

The load sharing is particularly important for improving the life of planetary gear train, increasingreliability and reducing vibration. The theory of nonlinear dynamics is required to study the vibrationmechanism of the strong nonlinear planetary gear train. So the load sharing and nonlinear dynamicscharacteristics of the planetary gear train have become the current hotspots and difficult issues. Thepaper mainly studies the load sharing and nonlinear dynamics characteristics of encased differentialherringbone train (main reducer of large ships) to provide theoretical and technical support for thedesign of this train.In the research on the meshing and tangential stiffness, the phase relationships of the meshinggears are determined in the train, and the mesh stiffness formula of the helical gear which is derivedbased on the instantaneous total length of the contact line for the gear pair is introduced to calculatethe time-varying mesh stiffness of the herringbone on the stiffness parallel. So the cause of the smallfluctuation of the herringbone meshing stiffness is analyzed. In the meantime the materials mechanicsprinciple is applied to calculate the tooth displacement which is also called as flexibility caused by theunit load. And then the herringbone tangential stiffness of the intermediate floating component for thistrain is calculated.The equivalent displacement formulas of the run-out and meshing-frequency errors along themeshing line are deduced by using harmonic function. An equivalent displacement calculation methodof the geometric errors for the gear transmission is proposed and the equivalent displacement formulaof the gear installation error along the meshing line is deduced based on this method. So the completeequivalent displacement formula system of the gear errors along the meshing line is set up in thistrain.The static model which includes the intermediate floating component of this train is set up. Thestatic formulas of load sharing coefficients for this train are defined. The static load sharingcoefficients are calculated and the impact of the main parameters on the static load sharing isanalyzed.The impact of the gear weight, the time-varying mesh stiffness, the gear errors on this train hasbeen considered, and the dynamics model which include the intermediate floating component of thistrain is set up. The dynamic equation is linearized and the Fourier series method is used to solve thisequation. The dynamics formulas of load sharing coefficients for this train are defined. The dynamics load sharing coefficients are calculated and the influence of the main parameters on the dynamics loadsharing for this train is analyzed. The dynamics load sharing characteristics for the encaseddifferential herringbone train are obtained.The calculating method of the dynamics floating displacements for this train is established.Thedynamics floating displacements of the gears for the train are calculated, and the impact of the mainparameters on dynamics floating displacements of the train are analyzed. The dynamics floatingcharacteristics for the encased differential herringbone train are obtained.A nonlinear torsional dynamic equation with multi-backlash, time-varying mesh stiffness,multi-degree of freedom is set up. The Newmark numerical integration method is used to solve thenonlinear dynamics differential equations from which the result of the nonlinear dynamic response isgot. The influences of the backlash, time-varying mesh stiffness, meshing ratio of damping, integrateerror on nonlinear dynamics characteristics for the encased differential herringbone train are analyzedby using time process diagram of displacement response, time process diagram of meshing forceresponse, phase diagram, Poincaré section. This impact on the gear meshing force, motion state is got.