A dynamic model of a tenoned rotating blade considering the pressure distribution characteristics of the contact interface is established and the degree of freedom of the model is reduced by the double coordination free-interface modal synthesis method in this paper. Firstly, the finite element model of the blade is established by ANSYS and the finite element matrix is extracted. Subsequently, multiple contact pairs were established on the contact surface of the tenon to capture the micro-slip characteristics of the contact interface. The normal pressure of the contact pair is obtained by the ANSYS blade-disk contact prediction and load equivalence to take the pressure distribution characteristics into account in the blade dynamics analysis. Then, non-uniform aerodynamic excitation is applied to the blade to simulate the load on the blade under real working conditions. Finally, the double coordination free-interface modal synthesis method is used to reduce the degree of freedom. Due to the coordination condition of the force and displacement of the substructure connection interface, the degree of freedom of the substructure interface is directly reduced. The final reduced degree of freedom is only the sum of the retained modes of the substructure, which greatly improves the computational efficiency. The dynamic equation is solved by the time integration method, and the effects of the tenon angle, rounded corner, and friction coefficient are discussed. The results show that the double coordination free -interface modal synthesis method can greatly reduce the degree of freedom of the tenon -connected blade model under the premise of ensuring accuracy while retaining the local con-tact characteristics of the contact interface. The structural parameters of the dovetail structure have a great influence on the vibration reduction characteristics of the blade. When designing the tenon structure, it is necessary to pay attention to these parameters.

In this paper, a contact slip mechanics model based on pressure distribution is developed, it is formed from multiple contact pairs and can define the contact behavior between contact interfaces. First, we establish the jointed structure's finite element model to calculate the contact interface's nodal pressure. Following this calculation, applying the cubic spline interpolation to the nodal pressure data, we obtain the contact surface pressure. Then using the theory of load equivalence, the contact surface pressure is converted into an equivalent load. The equivalent load is used as the normal pressure of the contact pairs place on the contact surface nodes. Subsequently, to verify the developed modeling approach, we establish a simplified blade model with the tenon-mortise structure for trial calculation. Finally, the nonlinear frictional force is linearized to solve the nonlinear differential equation by the incremental harmonic balance method (IHBM). The results show that the tenon-mortise contact surface exhibits micro-slip characteristics, which means that the pressure distribution characteristics of the contact surface are retained. The contact slip mechanics model developed in this paper is general which can be applied in modeling the contact surfaces of other joints.

The vibration reduction characteristics of the flexible blade with a dovetail joint and underplatform damper are studied in this paper. Considering the influence of the platform mass on the inherent characteristics of the blade, this paper regards the underplatform as a particle with mass. Moreover, two types of friction models are introduced on the contact interfaces of the blade. Meanwhile, the normal pressure of the contact interfaces will change with the rotating speed of the blade. Also, the dynamical equation for the rotating blade is established based on the finite element method. The nonlinear friction force on the contact interface is brought into the dynamical equation, and the vibration response of the blade is solved. The effects of the rotating speed, the initial preload, and the contact angle of the underplatform on the vibration reduction characteristic of the blade are investigated.

A nonlinear dynamic model of a rotating beam with dry friction support boundary conditions is developed, and the effectiveness of this model is verified by comparing it with the relevant literature. In the proposed model, a macro-slip friction model of the contact interfaces at the root of the beam with a dovetail tenon is established to characterize the friction on the beam. Furthermore, a time-domain solution and a linearization method of nonlinear friction force are proposed. The dynamic differential equations of the rotating beam are obtained conveniently by means of Chebyshev polynomials theory. Based on the developed model, the effect of the harmonic number on calculations is discussed by incremental harmonic balance method (IHBM). Moreover, the influences of friction coefficient, excitation amplitude, and rotational speed on the amplitude-frequency response of the system are analyzed. The results indicate that the higher-order harmonic components have significant influence on the nonlinear dynamic response of the tenon-mortise connected beam, which must be considered in the frequency-domain computation. When the contact interface slips, the contact stiffness decreases and the contact damping increases. With the rise of friction coefficient, rotational speed or the decreases of excitation amplitude, the range of slip zone narrows. The variation of amplitude-frequency curves is well explained from the perspective of contact stiffness and contact damping. (c) 2021 Elsevier Ltd. All rights reserved.

The vibration dissipation mechanism of the rotating blade with a dovetail joint is studied in this paper. Dry friction damping plays an indispensable role in the direction of vibration reduction. The vibration level is reduced by consuming the total energy of the turbine blade with the dry friction device on the blade-root in the paper. The mechanism of the vibration reduction is revealed by the variation of the friction force and the energy dissipation ratio of dry friction. In this paper, the flexible blade with a dovetail interface feature is discretized by using the spatial beam element based on the finite element theory. Then the classical Coulomb-spring friction model is introduced to obtain the dry friction model on the contact interfaces of the tenon-mortise structure. What is more, the effects of the system parameters (such as the rotating speed, the friction coefficient, the installation angle of the tenon) and the excitation level on blade damping characteristics are discussed, respectively. The results show that the variation of the system parameters leads to a significant change of damping characteristics of the blade. The variation of the tangential stiffness and the position of the external excitation will affect the nonlinear characteristics and vibration damping characteristics.