The dynamic characteristics of the combustor rotor in a turboshaft engine are inevitably affected by temperature. In this combined rotor system, complex curvic couplings interfaces are often involved, leading to discontinuous characteristics in the thermal conduction process. Previous rotor modeling methods do not account for structural discontinuities, particularly the influence of thermal contact resistance at the interface, which poses challenges in accurately constructing the temperature field of rotor model. Aiming at the issues, this paper integrates the finite element method and relies on a curvic couplings geometry model that incorporates rough conical interfaces. Innovatively, it proposes a method for analyzing the thermal contact resistance of the curvic couplings interfaces. Subsequently, a new approach considering the thermal contact resistance of the interface is established for the temperature field of the combined rotor system. And the influence of the temperature field on the natural frequency and rubbing faults of the combined rotor system is studied. Finally experimental verification confirms the rationality and effectiveness of the theoretical method. The results show that with the increase of temperature, the resonance frequency of the combustor rotor system decreases, the amplitude under the rub-impact excitation increases, and the amplitude at the gas turbine disk is the maximum. These methods and conclusions provide a reference for the design research and engineering application of combustor rotor system under temperature field influence.

To ensure the vibration safety of rotor support systems in modern aeroengines, this study develops a dynamic model of the aeroengine gas generator rotor system and analyzes its complex unbalance response characteristics. Subsequently, it investigates vibration reduction strategies based on these response patterns. This study begins by developing individual dynamic models for the disk–blade system, the circular arc end-teeth connection structure and the squeeze film damper (SFD) support system. These models are then integrated using the differential quadrature finite element method (DQFEM) to create a comprehensive dynamic model of the gas generator rotor system. The unbalance response characteristics of the rotor system are calculated and analyzed, revealing the impact of the unbalance mass distribution and the combined support system characteristics on the unbalance response of the rotor system. Drawing on the obtained unbalance response patterns, the vibration reduction procedures for the rotor support system are explored and experimentally verified. The results demonstrate that the vibration response of the modern aeroengine rotor support system can be reduced by adjusting the unbalance mass distribution, decreasing the bearing stiffness and increasing the bearing damping, thereby enhancing the vibration safety of the rotor system. This study introduces a novel integration of DQFEM with detailed component-level modeling of circular arc end-teeth connections, disk–blade interactions and SFD dynamics. This approach uniquely captures the coupled effects of unbalance distribution and support system characteristics, offering a robust framework for enhancing vibration safety in aeroengine rotor systems. The methodology provides both theoretical insights and practical guidelines for optimizing rotor dynamic performance under unbalance-induced excitations.

Aiming at the complex mechanical characteristics of the curvic coupling in the aero-engine rotor under operation condition, the contact stiffness model of the curvic coupling under the bending vibration is proposed to study the law of stiffness loss of the curvic coupling and the dynamic characteristics of the rotor with the curvic coupling under the bending vibration. Based on the Hertz contact theory and the elastic-plastic contact theory, an analytical model for the contact stiffness of the three-dimensional curvic coupling is established considering the complex geometric characteristics of the curvic coupling. And the law of stiffness loss of the curvic coupling under the bending vibration is studied. Then, a finite element model of the rotor system is proposed and the dynamic characteristics of the rotor system is analyzed. The results are tested and verified. The results show that the stiffness loss of the curvic coupling under the bending vibration is increased and the critical speed of the rotor is decreased caused by the increased stiffness loss. The contact stiffness model and research conclusions proposed in this paper provide an important theoretical basis for the design and dynamic characteristics analysis of modern aero-engine rotor systems.

For the design of advanced aero-engine rotor systems under ultra-high rotational speeds, this paper undertakes a comprehensive investigation into the contact stiffness of curvic couplings, which are the key connection mechanism of modern aero-engine rotors, and explores the dynamic variations in the contact stiffness of curvic couplings under working conditions. Firstly, the impact of dynamic loads of aero-engine rotors under working conditions on the curvic coupling is studied; Then, the contact stiffness analytical model of curvic couplings considering three-dimensional geometric features is proposed with the effects of dynamic loads; Finally, based on the established stiffness model, the dynamic loss laws of contact stiffness of curvic couplings under different dynamic loads are investigated, and the established model is experimentally validated. The results show that the dynamic loss law of contact stiffness varies with different dynamic loads. In comparison to the contact stiffness under the static condition, dynamic loads significantly reduce the contact stiffness of curvic couplings under working conditions, which in turn leads to changes in the dynamic characteristics of the rotor with curvic couplings. For the safe integration of the discontinuous rotor system under ultra-high rotational speeds, it is essential to carefully design and regulate the operating speed, transmission torque, unbalanced mass, and preload.

The curvic coupling, as one of the common connecting structures for gas turbine combined rotors, is more susceptible to various dynamic and static loads at extreme operating conditions. But, traditional combined rotor models tend to neglect the influence of the connection structure, especially failing to consider the contribution of the curvic coupling interfaces. To address this problem, this paper establishes a solid geometric model of the combined rotor with curvic couplings considering the rough three-dimensional interfaces. The effectiveness of the proposed model method is indirectly verified through the compression tests and modal tests. Subsequently, combined with finite element calculations, the mechanical properties of the rotor with curvic couplings considering the rough interface are analyzed under static and dynamic load conditions. The results indicate that the roughness of the interface significantly affects the deformation of the contact surface under static load, but its impact on the overall deformation of the rotor is relatively insignificant. The dynamic stress at the interface exhibits periodic variations at the resonance speed. At the maximum operating speed, the dynamic stress is influenced by the magnitude of imbalance. The aforementioned methods and conclusions provide a reference for the design research and engineering application of combined rotors.

In order to ensure the vibration safety of rotor systems in the next generation of aero-engines and reduce the impact of misalignment faults, the effect of support misalignment on the vibration characteristics of rotor systems under ultra-high operating speeds is investigated in this paper. Firstly, an analytical excitation model of the rotor systems under ultra-high operating speeds is established, considering the impact of the support misalignment. Then, based on the model of the misaligned combined support system, the dynamic model of the flexible discontinuous rotor support system with the support misalignment is presented. Subsequently, based on the established model, the effects of support parameters and support misalignment amounts on the vibration characteristics of the rotor support system are analyzed. Finally, experimental validation of the research findings is conducted. The research result shows that the support misalignment increases the vibration response of the rotor, reduces the vibration reduction efficiency of the combined support system, and consequently decreases the vibration safety of the rotor support system.

针对航空发动机转子复杂的结构特征及支承动力学设计问题,基于有限元(FE)、分段线性拟合和自由度(DOF)降维法,采用主子单元对复杂转子进行合理地等效,构建了航空发动机等复杂转子-支承系统的动力学模型,并对模型的有效性进行了试验验证.从转子固有特性、应变能分布、支承传递力和振动响应等方面对支承刚度进行了设计,并开展了弹性支承并联挤压油膜阻尼器(SFD)非线性减振效率分析.结果表明:动力学模型能较好地反映复杂转子的动力学特性,支承刚度合适取值范围为1.5×104～2.8×104N/mm,弹性支承并联SFD设计减振和降支承力效果显著,满足临界转速设计准则、应变能约束条件和变形要求,该研究为航空发动机支承刚度和SFD并联设计提供了定量的参考依据,具有重要的工程应用价值.

To study the contact effect of the rotor system with curvic couplings under rolling bearing supports, the combination of 3D finite element and analytical method were used to derive the curvic coupling shaft section stiffness matrix, and the dynamics model of rotor-rolling bearing system was established, which was verified by Ansys. By comparing with the continuous rotor, it was found that the curvic coupling structure reduced the first-order critical rotor speed by 5% and increased the amplitude by 3%. The results show that the nonlinear bifurcation trend of the curvic coupling rotor is nearly the same as that of the continuous rotor, however, the discontinuous characteristic of the curvic coupling structure will make the rotor access or leave the periodic motion state significantly earlier. Obviously, the contact effect needs to be considered when analyzing the rotor vibration characteristics with curvic couplings. The research can provide analysis methods and design ideas for the prediction of nonlinear vibration characteristics and the operating speed design for rotor system with curvic coupling structure.

For the aero-engine rotor system with complex vibration responses, a simplified model based dynamic similarity is proposed to study the vibration characteristics of that. On the basis of the principle of dynamic similarity, a simplified model of the combustion-driven rotor is obtained, with the criteria of the same critical speed of each order and similar vibration modes, while keeping the layout of the structure unchanged. By comparing the vibration characteristics of the actual rotor with those of the simplified model through theoretical analysis, there is less than 2.59 % error between the simplified model and the actual rotor. The rationality of the research method, which is developing the simplified model based on dynamic similarity to study the vibration response law of the original rotor, is demonstrated. Then, the unbalance response law of the rotor with a squeeze film damper is explored expanding on the produced model, and the study shows that the unbalanced excitation can significantly reduce the response. Finally, the influence law of the phase of unbalance excitation is experimentally verified on the test rotor. The results show that the simplified model of the actual rotor based on dynamic similarity can well reflect the vibration characteristics of the original rotor, and the proposed analysis method has an important reference role in studying the vibration mechanism of the aero-engine rotor system.

Hirth couplings are frequently used in the aero-engines turbine. The assembled stiffness of the Hirth couplings is significance to the design of the rotor system as it is outstandingly different from the continuous rotor structure. The decreasing of the axial pressing force to the rotor system of fifth-generation aero-engines can dramatically weaken the assembled stiffness of the Hirth coupling, which affect the rotor dynamics and even result in the rubbing faults. This paper focuses on the theoretical study on the rubbing characteristics of the noncontinuous rotor blade casing system caused by the stiffness weakening of the Hirth couplings. A novel analytical model of the Central Tie Rod Rotor-blade-Casing (CTRRBC) coupling system considering the Hirth couplings is derived through the Timoshenko theory and Hamilton variational principle. Then the no rubbing condition, the single-blade rubbing condition and four-blade rubbing condition of the non-continuous rotor system are calculated by using the Newmark-β method. The study results obtained by applying the analytical model are shown that (1) a decrease the assembled stiffness of the Hirth couplings lead to the significant amplitude amplification phenomenon of the rotor, blade and casing. (2) four-blade rubbing levels are related to the non-continuous rotor whirl, the rubbing happens on the blade located at the right end of the rotor whirl, nearest the casing, becomes more severe, vice versa. (3) Increasing the axial pressing force reaches the 60 kN, the rubbing responses of the non-continuous rotor blade system are similar to continuous structure (integral rotor). These results reveal the nonlinear rubbing faults characteristics of the central tie rod rotor blade casing coupling system with the Hirth couplings connection. Nonlinear effects are highlight and the multi-frequency components of system are contributed to diagnose the rubbing faults of noncontinuous rotating machinery.

为建立涡轮轴发动机复杂转子的动力学模型,基于有限元法和分段线性拟合,采用子结构法对复杂结构进行建模,在对系统自由度进行缩减后,推导出转子系统的运动方程.采用理论分析和试验验证了模型的有效性,分析了燃气发生器转子的振动特性.研究结果表明:建立的模型能显著降低整个系统的复杂度,在保证求解精度前提下,可大幅缩短求解时间.

In this paper, a two-dimensional spectral Tchebyshev (2D-ST) technique is developed to solve the free vibration problem of the concentric stiffened rectangular plate (CSRP) under arbitrary boundary conditions. According to this technique, the variables of the x and y axes are all selected Gauss-Lobatto sampling points for discretization, while the Tchebyshev polynomials are used to perform spectral expansion on the displacement functions of the structure. The CSRP is regarded as a coupling connection of ribs and plates of different thicknesses. By setting artificial springs to deal with the continuity and arbitrary boundary requirements, the unified fundamental differential equations of CSRP are derived from the combined framework of first-order shear deformation theory (FSDT) and Hamilton's principle. The free vibration characteristic equations in matrix form of CSRP are obtained by solving the differential equation, and the convergence of the solution is evaluated. Based on the comparison of various calculation examples with other methods and experiment, it is fully proved that the present solution has the advantages of fast convergence speed and high solution accuracy. Finally, this paper further focuses on how the geometric parameters of ribs influence the free vibration characteristics of the CSRP to implement the parametric studies. (C) 2022 Elsevier Ltd. All rights reserved.

Firstly, the random vibration characteristics of functionally graded porous (FGP) curved beams with elastically restrained ends are studied. An efficient model is presented by the Timoshenko beam theory and spectral-Chebyshev method. In this paper, three different types of porous distribution are considered, and the relationship between porosity coefficient and material parameters is determined according to the typical mechanical properties of open cell foam metal. Four types of curved beams with different curvatures are selected for the study, which are elliptical beam, parabolic beam, hyperbolic beam and circular beam. The one-dimensional admissible displacement functions of the FGP curved beam are constructed by Chebyshev polynomials of the first kind with Gauss-Lobatto sampling points discretization. Three artificial boundary springs are used to impose elastic boundary constraints at the ends of the curved beam. The pseudo excitation method is used to apply stationary and non-stationary random excitations, including point excitation and base acceleration excitation. The stationary random vibration responses of the FGP curved beam with different boundary conditions, involving the power spectral density (PSD) and root mean square (RMS) values of displacement, velocity and acceleration, are calculated and agreed well with the finite element method (FEM). At last, the RMS values of the non-stationary random vibration response of the FGP curved beam are given.

In this article, a numerical spectral-Tchebyshev (ST) technique is applied to solve the free vibration strong solution of the coupled structures of laminated composite conical, cylindrical and spherical shells under various boundary conditions. The artificial spring technique is introduced to realize the coupling connection of substructures and simulate the arbitrary boundary conditions. Considering the first-order shear deformation shell theory (FSDST), and using Hamilton variational analysis under its framework to derive the governing equations of motions of three coupled structures: coupled conical-cylindrical shells, coupled spherical-cylindrical shells and coupled spherical-cylindrical-conical shells. The solution of the governing equations of motions is obtained using the spectral-Tchebyshev technique. The variables along the generatrix direction are discretized based on the Gauss-Lobatto nodes, while the Tchebyshev polynomials are used for spectral approximation. The variables along the circumferential direction are approximated by Fourier series. The calculated free vibration characteristics of the coupled structures are compared with the numerical results based on previous references and the finite element method, which completely reflects the excellent convergence and calculation accuracy of the spectral-Tchebyshev technique. On this basis, the effect of the material properties and geometric dimensions of the substructures (conical, cylindrical and spherical shells) on the free vibration frequencies of the coupled structure is further studied.

The spectral-Chebyshev method is firstly applied to the free in-plane vibration of arbitrarily shaped plates with curvilinear geometry under different boundary conditions. With the aim of facilitating the calculation of energy, an arbitrarily shaped plate is mapped into a square plate by the one-to-one coordinate transformation. The displacement functions of the plate after transformation are then generally expressed as the two-dimensional Chebyshev polynomials. The experimental study of in-plane natural frequencies of six aluminum plates with different shapes is carried out for the first time, including free boundary conditions and cantilever support boundary conditions. The proposed spectral-Chebyshev method is applied to simulate the in-plane vibration of six aluminum plates to evaluate the precision and demonstrate the applicability of the current solution. The present calculated natural frequencies converge with the increase of Chebyshev polynomials and are in good agreement with the experimental results and the FEM solution. Thus, our conclusion is that the current spectral-Chebyshev model can accurately and quickly calculate the in-plane vibration of plates with arbitrary curvilinear geometry. Moreover, the in-plane experimental results of plates with six different curvilinear geometries can provide a reference for future theoretical research.

This article is concerned with thermal vibration behaviors of the functionally graded material–stepped cylindrical shell coupled with annular plate, including free vibration, transient response, and steady state response. The stepped cylindrical shell is divided into N s segments at locations of thickness and radius variations, which is coupled with N p annular plates. The boundary and coupling conditions are achieved by introducing the artificial virtual spring technology. Under the framework of FSDT, the displacement function of arbitrary shell segment and annular plate is expanded with Chebyshev polynomials and Fourier series for circumferential direction. Compared with results obtained by the finite element method and the references, a series of numerical examples and validations are presented to verify the convergence and accuracy of the current method. The effects of the relevant parameters containing the geometric parameters, boundary conditions, various loadings, and the thermal environment are investigated in detail.

The Hirth couplings are the basic connection structure of the central tie rod rotor-blade-bearing (CTRRBB) coupling system for turboshaft engine. Those connecting structures tend to loosen when the decrease of the pre-tightening forces, the looseness behaviors can reduce the local stiffness of the rotor system and further affect its dynamic characteristics. In this paper, a novel mechanical model of the assembled stiffness of the Hirth couplings is derived based on the force balance and deformation compatibility of each tooth; then, the dynamic model of the CTRRBB with Hirth couplings is established based on the Timoshenko beam theory and Galerkin method. Then, assembled stiffness method of the Hirth couplings is incorporated in the system. The proposed model is verified by the results of the ANSYS model. Finally, the effects of the pre-tightening forces and rotational speed on the natural frequencies, three-dimensional mode shapes of the CTRRBB with Hirth couplings are further discussed. The results show that reduction of assembled stiffness of the Hirth couplings at contact interface becomes significant as the decrease of the pre-tightening forces, which lead to the decrease of the modal frequencies in the system. The analysis of the Campbell diagram indicates that frequency veering, intersection and instability phenomena occur in the system as the decrease of the pre-tightening forces. When the pre-tightening forces reach the 60 kN, the dynamic characteristics of the system make no difference with the integral rotor. The proposed methodology makes an important contribution to the further understanding of the rotor system considering the Hirth couplings connection structure in rotating machinery.

The first order shear deformation theory (FSDT) is used to formulate a generalized model of laminated open cylindrical shell coupled with rectangular plates (LOSPS). On this basis, characteristics of free vibration and steady state response of the combination are investigated. The technique of artificial springs is used to simulate the coupling relationships between the adjacent substructures and boundary edges, and the specific coupling formulas between the adjacent substructures are presented. Then, an improved Fourier series are introduced as the displacement admissible functions of LOSPS, where the corresponding unknown coefficients of the displacement components are derived with the Rayleigh-Ritz method. Convergence and good accuracy of the proposed method are demonstrated by means of a several numerical examples. Moreover, comprehensive vibration analyses with respect to the influence mechanism of some key parameters are implemented, and corresponding new results are obtained. The present work of innovativeness can be treated as the reference for works in relative fields.

In this paper, a strong spectral Tchebychev (ST) solution is developed to investigate the free vibration behaviors of the cylindrical shell with stepped-thickness (CS-S) and cylindrical shell with internal–external stiffeners (CS-IES) subject to arbitrary boundary constraints. The spring parameter technique is used to impose combined connections and arbitrary boundaries. The potential and kinetic energy expressions of CS-S and CS-IES are derived based on the framework of the first-order shear deformation theory (FSDT). Finally, the unified governing differential equations of CS-S and CS-IES are acquired by the Hamilton’s variational principle. According to the Gauss–Lobatto point discretization process, the Tchebyshev polynomials are used to perform spectral expansion on the axial variables of admissible displacement functions. Circumferential variables are represented by sine and cosine series. In this way, the unified free vibration mathematical model of CS-S and CS-IES is obtained. On the basis of confirming that the model results have reached the state of convergence, the numerical results are compared with those calculated by the reference and the finite element method, which fully validates that the strong spectral Tchebychev model obtained in this paper is feasible for analyzing the free vibration characteristics of CS-S and CS-IES subject to arbitrary boundary constraints. Last but not least, the paper carries out the parametric analysis of how the change of the geometric parameters of the stiffeners will affect the natural frequencies of CS-IES.

Due to the wear of wheels during operation, the unbalance is induced. To study the nonlinear vibration of the arc tooth connected rotor under different loads, the motion equation was built based on Lagrange equation, considering contact property of the arc tooth and the oil-film force. From the GW rough surface model, the interface contact stiffness for the arc end-tooth was calculated. The eventual contact force was simulated by a nonlinear spring. Rich nonlinear dynamic phenomena, such as periodic doubling bifurcation phenomenon, multiperiodic motion, quasi periodic motion, oil whirl, etc., were observed. The results show distinct phenomena caused by the load variations. To reduce the nonsynchronous vibration, the relative phase is suggested to be kept at 120°.