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A weak circumferential resolution of defects in the corner part of engineering components brings great challenges to quantitative non-destructive testing. Especially for the corner of carbon fiber reinforced plastics (CFRP), the complex wave propagation behaviors caused by the elastic anisotropy, laminate structure, and curved surface make the information of defects hard to be distinguished, which finally results in a poor imaging resolution. The surface adaptive ultrasonic (SAUL) method for CFRP corner is investigated, and an improved strategy, focusing in receiving (FiR) of SAUL signals is proposed here. With an isotropic plexiglass as a comparison, the effectiveness of FiR is verified by finite element simulations and experiments. The elastic properties of CFRP corner are accurately characterized and a finite element model is established. On this basis, the wave propagation behavior in the corner is studied, and the influence of the water distance h on the maximum amplitude (MAD) and signal-to-noise ratio (SNR) at the defect is analyzed. The results show that the structural noise can be eliminated, and the imaging quality and SNR can be improved by optimizing the h. After FiR, the maximum increase of defect amplitude is about 9.5 dB and 13.2 dB for plexiglass and CFRP, respectively. Meanwhile, the maximum relative error in length is reduced by 16.7% in plexiglass, and by 13.4% for the 3-mm delamination in CFRP. The strategy would be promising to improve the detection quality of the corner in curved components. [ABSTRACT FROM AUTHOR]

Angular contact ball bearings are common basic components in rotating machinery. During the operation of the bearing, the rolling slips, resulting in contact sliding friction between it and the raceway, which in turn causes wear in the rolling element and increase in the radial clearance of the bearing. The increase in clearance also affects the stiffness of the bearing, which in turn affects the natural frequency and fatigue life of the bearing. At present, there are few studies on the influence of bearing wear (variation of clearance) on life. In this paper, the finite element model based on the theory of contact mechanics is established for the angular contact ball bearing with medium- and high-speed rotation, and the mechanical properties and fatigue life influenced by the internal action of the bearing are analyzed. The effects of radial load and deflection angle on the mechanical properties and fatigue life of the bearing are also studied. Based on the analysis results of bearing contact mechanical properties and clearance changes, the calculation method of bearing life under rolling element wear is established. The influence of the variation of clearance and preload clearance on bearing life is analyzed, and the optimal preload is obtained. The research results of this paper can provide a theoretical basis for optimizing the installation of angular contact ball bearings, reasonably determining the service conditions, and prolonging the service life of bearings, which is necessary for engineering practice. [ABSTRACT FROM AUTHOR]

Bolted joints are the major connection form to hold the aero-engine rotor system as a discontinuous entirety. What is noteworthy is that the bolt assembly process (BAP) directly relates the uniformity of preload and the symmetry of joint stiffness when the rotor comes to assembly, thereby introducing a heightened level of complexity and unpredictability to the dynamic response of the rotor system. In this paper, the effect of BAP on the stiffness softening of bolted flange joints is analyzed based on a finite element contact model. Then, a bolted joint rotor system finite element model is established to discuss the magnitude-frequency characteristic under three assembly sequences of bolts. The rotor vibration response is further compared between the three sequences considering the stiffness loss. Finally, the theoretical studies are verified by a rotor test rig. Results demonstrate that the stiffness softens to varying degrees with the increase of external load, and the softening mechanism is intricately associated with the contact state of the joint interfaces. Intriguingly, joint stiffness and its softening law are also affected by the BAP, leading to substantial discrepancies in rotor critical speed and vibration response among different assembly sequences. It is further observed that the tangential stiffness softening complicates the dynamic properties of the rotor system and enhances the nonlinear features. [ABSTRACT FROM AUTHOR]

In order to study the influence of compliance parts on spatial multibody systems, a rigid-flexible coupling dynamic equation of a spatial crank-slider mechanism is established based on the finite element method. Specifically, absolute node coordinate formulation (ANCF) is used to formulate a three-dimensional, two-node flexible cable element. The rigid-flexible coupling dynamic equation of the mechanism is derived by the Lagrange multiplier method and solved by the generalized α method and Newton–Raphson iteration method combined. Comparison of the kinematics and dynamics response between rigid-flexible coupling system and pure rigid system implies that the flexible part causes a certain degree of nonlinearity and reduces the reaction forces of joints. The elastic modulus of the flexible part is also important to the dynamics of the rigid-flexible multibody system. With smaller elastic modulus, the motion accuracy and reaction forces become lower. [ABSTRACT FROM AUTHOR]

The purpose of this article is to study the coupling effects of support stiffness on geometric scaling factor powers of the rotor-bearing system and predict vibration characteristics of a prototype by scaled models accurately. Associated to the least-squares–based similitude method, the discrete iteration method proposed evaluates the estimated scaling laws under variable (instable) powers and further broadens the restriction of boundary conditions in scaling laws, which is the main finding in this article. The discrete iteration method does not need to establish a physical model but directly uses input and output parameters to establish output scaling laws. The complete scaled model and geometric distorted model are selected as study cases to prove the effectiveness and accuracy of the discrete iteration method. The vibration characteristics of the rotor-bearing system are obtained by the finite element method with validation by experimental test for the natural characteristics. The comparison between the prediction results and those without the discrete iteration method shows that discrete iteration method can significantly improve the accuracy for predicting the prototype. [ABSTRACT FROM AUTHOR]

In this study, we investigate the dynamic scaling laws of geometrically similitude models and systems for predicting their vibration characteristics accurately. A determination method of scaling laws based on least square method for calculating weighted powers of scaling factors is proposed for the first time. Taking geometric parameters as input (design) parameters and vibration characteristics parameters as output parameters, the weighted powers of scaling factors are calculated by least squares similitude method (LSSM) with several design models, and then scaling factors of the output parameters are obtained by combining weighted powers and corresponding scaling factors. Applicability of the LSSM is verified in the following two cases with rectangular plate and rotor-bearing system that the stiffness of supports is taken into account. The vibration characteristics are calculated by using finite element method in MATLAB and compared with simulation analysis software ANSYS. As a result, stable weighted powers and good predictions are obtained for two cases. [ABSTRACT FROM AUTHOR]

As sophisticated mechanical equipment, the rotor system of aero-engine is assembled by various parts; bolted flange joints are one of the essential ways of joints. Aiming at the analysis of the nonlinear vibration characteristics of the rotor-bearing system with bolted flange joints, in this paper, a finite element modeling method for a rotor-bearing system with bolted flange joints is proposed, and an incremental harmonic balance method combined with arc length continuation is proposed to solve the dynamic solution of the rotor system. In order to solve the rotor system with rolling bearing nonlinearity, the alternating frequency/time-domain process of the rolling bearing element is deduced. Compared with the conventional harmonic balance method and the time-domain method, this method has the characteristics of fast convergence and high computational efficiency; solving the rotor system with nonlinear bearing force; overcome the shortcoming that the frequency–response curve of the system is too sharp to continue solving. By using this method, the influence of bearing clearance and stiffness on vibration characteristics of the rotor system with bolted flange joints is studied. The evolution law of the state of the rotor system with bolt flange is investigated through numerical simulation and experimental data. The results indicated that the modeling and solving method proposed in this paper could accurately solve the rotor-bearing system with bolted flange joints and analyze its vibration characteristics. [ABSTRACT FROM AUTHOR]

Scaling laws refer to the relationships of the input and output parameters between prototype and scaled models. They are usually used to predict the vibration characteristics of a large-scale structure with scaled-down models. In general, scaling laws are estimated from the dimensional analysis of concerned variables or the dimensionless governing equation of vibrating structures. However, there are still some limitations that existed in the partial similitude of complex systems. The present work is concerned with determining scaling laws to predict the vibration characteristics of a thin rectangular plate containing elastic boundary conditions and even complicated geometrical features. The Lagrange energy-least squares similitude method (LE-LSSM) is proposed in this paper, the Lagrange energy approach eliminates the coupling effect of support stiffness on powers, and the LSSM can then be used to deduce output scaling laws. In numerical verifications, a perfect rectangular thin plate is simulated by finite element analysis (FEA) to verify the scaling laws, and a perforated thin rectangular plate is further applied for standing out the highlight of the LE-LSSM. Moreover, the coupling effects on scaling laws are analyzed among geometric dimensions, support stiffness, and material parameters. The coupling effects exist if powers change over the geometric dimensions of scaled models, but the inverse is not. Powers are stable and do not change over the geometric dimensions of scaled models under the free boundary condition, illustrating no coupling effect of geometric dimensions on powers. However, the support stiffness exhibits a significant coupling effect on powers of geometric scaling factors, which leads to inaccurate scaling laws. It can be effectively eliminated no matter how large the support stiffness values when LSSM is combined with the Lagrange energy approach. It is found that the results under the uncoupled powers are more accurate than those under the coupled powers. Moreover, material parameters produce a coupling effect on powers in non-zero support stiffness. Unlike support stiffness, only the power values change, but their stability not. Finally, the simulated results and proposed method are experimentally validated using the Brüel & Kjær test system, which derives consistent results. [Display omitted] • LE-LSSM does not depend on closed-form solution or profound theoretical foundation. • LE-LSSM can be applied in plates with elastic boundaries and complicated features. • LE-LSSM is available for partial similitude even the mode orders change in models. • Coupling effect in similitude is analyzed and eliminated by LE-LSSM. • Applicability and effectiveness of the method is validated by lab experiments. [ABSTRACT FROM AUTHOR]

• A 3D clearance fit model between bearing rings and bearing pedestal is proposed. • A general analytical stiffness model of ball bearings in rotor systems is proposed. • A multi-supported rotor system is established and verified by the experiment. • The vibration and contact characteristics of bearings in the system are analyzed. Clearance fit is a common assembly method for bearings in rotor systems, which leads to a certain clearance between the outer ring of the bearing and the bearing pedestal, that is, the fit clearance. The nonlinear factors caused by the fit clearance may affect the mechanical properties of the bearing and rotor system. Considering the fillet and six-degree-of-freedom (6-DOF) motion of the outer ring, a three-dimensional (3D) clearance fit model is proposed. In addition, considering the interference fit between the inner ring and spindle, an analytical stiffness model of ball bearings is developed. By coupling the clearance fit model and the analytical bearing stiffness model with a finite element (FE) model of a spindle, a dynamic model of a multi-supported rotor system is established and verified by the experiment, which fully considers the nonlinear factors of ball-raceway contact and outer ring-bearing pedestal contact. The effects of fit clearance, radial force, and axial force on the vibration behaviors and contact characteristics of the ball bearing in the system are analyzed. The results indicate that the larger fit clearance of the unilateral bearing may lead to misalignment of the bearing and reduce the bearing force. Under radial force, the bearing clearance and fit clearance are eliminated, which improves the stability of the system. At this time, further application of axial force causes the load-bearing area to become larger and weakens the variable compliance (VC) characteristics of the bearing. This investigation can provide technical support for the assembly and design of the bearing-rotor system. [ABSTRACT FROM AUTHOR]

A semi-analytical model of a flexible varying section disk–blades (FVSDBs) system with elastic supports is proposed, where the spin softening, centrifugal stiffening, and Coriolis force effects of the system are considered. Timoshenko beams with a stagger angle are used to simulate blades, and a varying section wheel based on plate theory is used to construct the disk. Hamilton's principle and Galerkin method are utilized to derive the differential governing equations of the FVSDBs system. The proposed semi-analytical model accounts for the lateral vibration of the disk, and the longitudinal and lateral vibration of the blades. Besides, the validity of the proposed model has been verified by comparing the natural frequencies, mode shapes, and vibration responses obtained from the proposed model, finite element model (FEM), and experiment. The results indicate that the proposed semi-analytical model has high precision and computational efficiency, which can provide an alternative scheme for predicting the vibration characteristics of varying section disk–blades and overcoming the high computational cost of finite element models. [Display omitted] • A dynamic model of the FVSDBs is developed by semi-analytical method. • The varying section and elastic supports characteristics of disk–blades are considered. • The proposed model is verified by FEM and experiment. [ABSTRACT FROM AUTHOR]

• A 5-DOF bearing force model considering misalignment and cage fracture is proposed. • The effect of cage fracture on radial and axial vibration of the rotor is studied. • The effect of bearing clearance and load on cage fracture vibration is analyzed. • The experimental study on the cage fracture of rolling bearing is carried out. The rolling bearing misalignment may lead to fracture failure of the cage. However, the research on the vibration response of the rotor system caused by bearing misalignment and cage fracture has not attracted enough attention. In this paper, the vibration characteristics of cage fracture fault are studied from two aspects of simulation and experiment. Firstly, a five-degree of freedom nonlinear bearing force model with the bearing misalignment and cage fracture fault is given. Secondly, the bearing restoring force model is introduced into the rotor finite element model. Then, the dynamic model of the deep groove ball bearing-rotor system is established. The effects of key parameters such as cage fracture degree, radial load, and bearing clearance on the vibration characteristics of the system are simulated and analyzed. Thirdly, the bearing test pieces with real cage fatigue fracture fault are obtained by carrying out the bearing life cycle test. On this basis, the vibration signals of bearing with cage fracture under different loads are collected. The simulation and test results show that the system amplitude increases when cage fracture occurs. The obvious impact vibration characteristics appear in the time domain waveform. The vibration energy gradually concentrates to low-frequency vibration. The frequency components related to cage frequency, such as nf c and nf r ± mf c can be more obviously observed in the envelope spectrum. The results can provide a useful reference for the identification and diagnosis of rolling bearing misalignment and cage fracture. [ABSTRACT FROM AUTHOR]