| The main gear transmission of the helicopter drive system is generally considered to be the key part in transmission which performed to transfer and turn the power to propeller,the dynamical characteristics of the gear transmission has a significance influence on the flight performance as well as safety performance to the helicopters.In the advanced configuration of current transmission system of helicopters,the split torque-combining gear transmission has been getting more and more attentions,the reasion is that the configuration of split torquecombining gear transmission can bring many advantages to the transmissions,such as small volume,light weight,large transmission ratio,high reliability and so forth,which can satisfy the design requirements for the contemporary helicopter transmission.The nonlinear dynamical characteristics are also need to be taken into account while designing or investigating the split torque-combining gear transmission,meanwhile,it is also essential to examine the vibration reduction mechanism,resonance suppression method and vibration control strategy.In this dissertation,the Lyapunov exponent spectrum,Poincaré section as well as correlation dimension is employed to analyze the nonlinear vibration behaviors,such as the global bifurcation and chaos,for split torque-combining gear transmission.The parametric domain decomposition technique is established to explore the global features of nonlinear vibration behaviors,consequently,the structure of parametric solution domain and the state space domain are profoundly investigated and monitored for split torque-combining gear drive system from both the micro-and macro-perspectives.Eventually,the multi-step chaos control technique is proposed to conduct the control work which is to make the chaotic attractor reached on the target periodic orbit,and the control effect is evaluated with some numerical comparisons as well.The main works and innovation points are listed as follows:(1)The purely torsional nonlinear dynamical model of a split torque-combining gear transmission is established,and two types of functional formula of time-varying meshing stiffness are derived for driving gears,based on the system equations which without rigid body displacement,the gaussian elimination technique is proposed to solve the dynamic equations that with singular stiffness matrix.The natural characteristic is analyzed by comparing two types of modal shape of the transmission system,the dynamic load characteristic of split torque gears and split combining gears under a couple of nonlinear excitations are investigated through numerical analyzation,respectively.(2)The nonlinear global bifurcation behavior is investigated for the gear transmission with respect to the parameters of meshing frequency,backlash,synthetical transmission error and damping ratio.Meanwhile,the phase portrait,Poincaré section,Lyapunov exponent spectra and FFT spectrum analysis techniques etc.,are also employed to analyze the global bifurcation route and chaotic features,the characteristics of attractor are depicted by means of quantitative calculation,and the nonlinear phenomena,for instance,discontinuity jumping,boundary crisis,are all detected too.(3)A bending-torsion-shaft coupled vibration model of the combining spiral bevel gear transmission is created,the decomposed algorithm for solution domain structure in parameter space is developed based on the Cell mapping method(CMM).Several parametric solution domains are constructed,the global dynamical characteristic is mainly examined with respect to synthetical transmission error and damping ratio,and the sudden switching behavior of attractors which near the domain border is explored.The predicted dynamical behavior inside the parametric solution domain is double verified effectively with the help of bifurcation diagram and the largest Lyapunov exponent in one-dimensional parameter domain.(4)The correlation dimension is introduced and used to quantify the fractal dimension of attractors,and the development process of strange attractor in phase space is examined while the damping ratio alters,the changes about the transformation of attractor trajectory in time history is also depicted by the Lyapunov exponent.The global solution in state space is implemented employing Cell mapping method,the global solutions,such as periodic attractor basin of attraction,chaotic attractor basin of attraction as well as the domain boundary cells are obtained,furthermore,the global evolution feature is explored under the changes of damping ratio,the attractor collision,boundary crisis,and the shrinking and extension relationship between the basin of attractions are investigated as well.(5)The Multi-step chaos control technique is implemented to realize the stabilization of chaotic trajectory for a high-dimensional non-hyperbolic gear system,By means of NewtonRaphson iterative algorithm,the fixed point of unstable period orbit(UPO)embedded in strange attractor is obtained.Based on the analysis of eigenvalue subspace of local Jacobi matrix,the non-hyperbolic fixed point is driven to be stabilized on the local stable manifold,consequently,the problem of unstable dimension variability caused by imaginary eigenvalue of the systematic Jacobi matrix is solved.The control technique of several different periodic orbits connected in sequence in phase space is carried out successfully.The deviation of controlled trajectory and the fluctuation of perturbation parameter are both analyzed while the chaotic attractor is stabilized on the road towards continuous periodic double orbits,in addition,the influence and effect of the perturbation region of control parameter on controlling different periodic orbit is also investigated.(6)The testing platform of split torque-combining gear transmission is built,and the experimental studies on the vibration characteristics of a split torque-combining cylindrical gear system is carried out.By analyzing and comparing the result between experimental test and theoretical calculation,it is verified that the dynamic model and analyzing method are both correct and effective. |
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