Search

The rotor systems are the critical components of many rotational machines. The dynamic stiffness of the supporting structure affects the dynamic characteristics of the rotor system significantly. The effect can't be overlooked for obtaining accurate dynamic characteristics. The judgment index of dynamic stiffness influence (DSI) is proposed in this paper to evaluate the degree of dynamic stiffness influence on the dynamic characteristics. The dynamic model of the rotor system considering the dynamic stiffness of supports is established, and the expression of DSI is given. Then the Campbell diagrams and corresponding DSI values for different system parameters under the influence of dynamic stiffness are discussed and analyzed. The effectiveness of DSI is verified by the literature. Besides, an experiment is carried out to verify the effectiveness of the DSI. The results indicate that the effectiveness of DSI can be confirmed by both numerical and experimental cases, and that the DSI can evaluate the degree of dynamic stiffness influence well. [ABSTRACT FROM AUTHOR]

In this study, we developed a data-driven frequency domain analysis method for rotor systems using the NARX (Nonlinear Auto-Regressive with eXternal input) model established by system vibration signals. We propose a model-based index of fault features calculated in a multi-frequency range to facilitate condition monitoring of rotor systems. Four steps are included in the proposed method. Firstly, displacement vibration signals are collected at multiple monitored rotating speeds. Secondly, the collected signals are processed as output data and the corresponding input data is generated. Then, NARX models are developed with input and output data to characterize the rotor system. Finally, the NRSF (Nonlinear Response Spectrum Function)-based nonlinear fault index is calculated and compared to the healthy condition. An experimental application to the misaligned rotor system is also demonstrated to verify its effectiveness. Our results indicate that the value of the index directly reflects the severity of the misaligned fault. [ABSTRACT FROM AUTHOR]

• This paper presents a solution methodology for the rotor system with bolted joint. • The presented solution methodology is verified by the Newmark method. • The 3X and 5X of the rotating frequency are found in the spectrum. • The rotating speed corresponding to 5X's peak precedes the critical speed. • The findings of spectral characteristics are verfied by the experimental test. The bolted joint is commonly used to connect several parts of aero-engine rotor system. Several papers have studied the nonlinear vibration responses of bolted rotor systems. However, the frequency spectrum characteristics of bolted rotor systems are not fully revealed. Aiming at this issue, this study develops a dynamic model of the bolted rotor system, where the piecewise stiffness characteristic is considered. A solution methodology is presented by incorporating the piecewise stiffness into the incremental harmonic balance method. The effects of unbalance and preload on the dynamic characteristics are discussed. Moreover, the stiffness and damping of the support structure and bolted joint are identified based on the particle swarm optimization algorithm and experimental results. Furthermore, the experimental study on a bolted rotor test rig is conducted to verify the accuracy of the identified parameters and the model. The simulation and experimental results indicate that 3X and 5X of the rotating frequency can be observed. Besides, the rotating speed corresponding to 5X's peak is different from the critical speed, and the peak of 5X precedes the primary resonance peak. [ABSTRACT FROM AUTHOR]

Rotor system with bolted joints is widely used in aero-engine, and has the features of large axial span, high-degrees of freedom, and nonlinearity. There exist several researches on similitude of rotor systems, but these studies mainly focus on the simple and linear systems. The similitude investigation for the rotor system considering bolted joints has not been conducted. To fill this gap, a method to obtain the scaling laws for low-pressure (LP) compressor are presented based on the generalized and fundamental equations of substructures (bolted joint, shaft, and disk), which considers the nonlinearity of bolted joints and different materials. The dynamic model of the LP compressor considering the nonlinearity produced by bolted joints is established. Moreover, the effect of bolted joints on the LP compressor is investigated to illustrate the necessity for considering bolted joints in similitude procedure. In order to ensure the similitude of nonlinear dynamic characteristics, the scaling factors are divided into the linear and nonlinear scaling factors, where the nonlinear scaling factors are used to put the bolted joint into similitude. The results show that the natural frequencies, vibration responses, frequency components, and stability can be predicted accurately by scaled models, even the models are made of relatively cheap materials. [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]

• This paper presents a similitude method considering the vibration consistency. • The proposed method can improve the prediction accuracy of vibration responses. • The accuracy of proposed method is validated by comparing with existing methods. • The comparison results are verified by numerical and experimental studies. Similitude theory can be utilized to perform scaled experiments and facilitate the understanding of physical behaviors of large structures. However, the prediction accuracy in partial similitude is still needed to be improved. To address the problem, a partial similitude method is presented to improve the prediction accuracy. The vibration consistency is satisfied by developing the scaling laws of critical speed. In addition, the scaling laws of vibration response are developed after ensuring consistency. The ability and performance of the presented method are demonstrated using a simulation case study and an experiment case study. In both case studies, the presented method is utilized to reproduce the vibration responses of the prototype, which includes the predictions of resonant and non-resonant responses. Besides, the prediction results of the existing methods are also provided for comparison. In the numerical case, the errors of the proposed method are less than 3% in predicting the vibration amplitude. In the experimental case, the minimum and maximum errors are 0.1% and 14.4%, respectively. Moreover, the proposed method can achieve better performance than the current methods. [Display omitted] [ABSTRACT FROM AUTHOR]

• This paper proposes an unbalance identification method for full-size rotor system. • The unbalance value is identified by using the scaling laws and scaled model. • The unbalance phase is identified by the proposed method. • The distortion in geometrical dimension is taken into account. • Testing for both prototype and model is carried out. • The proposed method is verified by numerical and experimental cases. Perfect balance of rotor systems is difficult to achieved in practical engineering and some amount of unbalance is unavoidable. However, identifying the unbalance value of full-size rotor system is difficult, time-consuming and sometimes dangerous. Aiming at this issue, this paper proposes an unbalance identification method for full-size rotor systems. The unbalance value can be identified through the scaling laws and scaled model, where the scaling laws are developed by incorporating the least squares method and sensitivity analysis. The effectiveness of the proposed method is verified by the numerical and experimental case studies, where the distortion in geometrical dimension is taken into account. The numerical case identifies the unbalance value of a rotor system and evaluate the identification errors. Furthermore, the experimental testing for the prototype and model test rigs is carried out. The results show that the unbalance values can be accurately identified by the proposed method. This allows one to identify the unbalance value of full-size rotor system through a small scaled model. [Display omitted] [ABSTRACT FROM AUTHOR]

[Display omitted] • This paper proposes a method to obtain scaling laws for rotor systems. • The power in scaling laws is represented by a function related to scaling factor. • The proposed method can predict the dynamic characteristic in partial similitude. • Testing for both prototype and model is carried out to verify the proposed method. • The proposed method can improve prediction accuracy compared with existing methods. Similitude theory is widely used to predict the structural responses of the full-size prototype through scaled models and is categorized into complete and partial similitude according to the way of scaling parameters. Partial similitude is more flexible in practical design engineering, but its accuracy still needs to be improved. This study presents an improved partial similitude approach, which can be used to establish the scaling laws and understand the scaling behaviors of rotor systems. The aim is to overcome the insufficient accuracy of the existing methods in predicting the dynamic characteristic of rotor systems. The power in scaling laws is represented by a function, which is related to the scaling factor of the prototype to be predicted. In this work, the power function is developed by incorporating the Levenberg–Marquardt method and sensitivity analysis. The accuracy and effectiveness of the proposed partial similitude method are validated through numerical and experimental case studies, where the distortion in geometrical dimension is considered. The dynamic characteristic of prototypes is predicted through the scaled model. Furthermore, the accuracy of the proposed method is evaluated by using the existing methods. Both the numerical and experimental case studies indicate that the proposed method achieves higher accuracy than the existing methods in predicting the dynamic characteristic of rotor systems. [ABSTRACT FROM AUTHOR]

• This paper proposes a method to obtain scaling laws for rotor systems. • This paper proposes frequency adjustment laws for predicting responses in non-resonant state. • The proposed method provides several scaling laws in whole range of rotating speed. • Experimental testing for vibration responses of prototype and model is carried out. • The proposed method can improve prediction accuracy compared with existing methods. Similitude theory provides the necessary conditions to predict the structural responses of the full-scale prototype through the scaled model, and is widely used in full-scale experiments of large structures. However, the prediction accuracy is insufficient in partial similitude. Aiming at this issue, this paper proposes the frequency adjustment laws to predict vibration responses of full-scale rotor in non-resonant state, since the rotating machinery usually works in non-resonant state. On this basis, a partial similitude method is presented by combining the frequency adjustment laws with the current method. The proposed method provides several scaling laws in the whole range of rotating speed, while only one scaling factor is used to predict the vibration responses in existing methods. The accuracy of the proposed method is verified by the numerical and experimental case studies, where the geometrical distortion is considered. In the numerical case study, the scaling laws of a rotor system are obtained by the proposed method and existing methods. The predicted results of the proposed method are compared with those of the existing methods. It is found the proposed method accurately predicts the displacements and accelerations of prototypes through those of scaled model. Moreover, the proposed method achieves a higher accuracy. The experimental study carries out the testing for the prototype and model test rigs. The experimental results show that the proposed method provides better results in predicting the displacement and acceleration compared with the existing methods. The proposed method allows designers to design a scaled model and to reproduce the vibratory behavior of the full-size prototype, which reduces the difficulty, costs and time of experimental test. Moreover, the proposed partial similitude method has a better performance than the existing methods. [Display omitted] [ABSTRACT FROM AUTHOR]

• This paper proposes a method to obtain scaling laws for rotor systems. • The derived scaling laws consider the gravity, geometric and material distortion. • A method to design models that can reduce the costs of model test is presented. • Neglecting gravity leads to an error in predicting the vertical vibration response. • Considering gravity results in a contradiction in the derivation of scaling laws. In practical engineering, gravitational acceleration cannot be scaled (λ g = 1), which is not considered in the existing similitude studies of rotor systems. In this paper, a restriction in scaling procedure caused by λ g = 1 is first demonstrated analytically. Aiming at this issue, a method to derive the scaling laws of rotor systems is proposed based on the generalized equations of subsystems, where gravitational acceleration, geometric and material distortion are considered. The derived scaling law for the vibration response is different from that of previous literatures because λ g = 1 is considered. On this basis, this paper presents a method for designing scaled models that can reduce the difficulty and costs of the model test. The accuracy and effectiveness of the proposed methods are verified by predicting the dynamic characteristics of a rotor system. Moreover, the effect of gravitational acceleration is discussed and the predicted results are compared with the previous literature. The results show that neglecting the gravitational acceleration leads to a certain error when predicting the vibration responses in the vertical direction. [ABSTRACT FROM AUTHOR]

• A dynamic model of bolted joint rotor system was established by considering bolted joints and pedestals. • The effect of the pedestal looseness fault on the bending stiffness of bolted joint structure was evaluated. • The feature of the pedestal looseness fault that happens in a bolted joint rotor system was investigated. • A rotor-bearing test rig with bolted joint and pedestal was set up to verify the numerical simulation results. Pedestal looseness is a common fault in rotating machines. To enhance the economy and convenience of the assembly of the aero-engine rotor system, the bolted joint structures are a useful tool for fastening multiple parts of different materials into an integrated system. To our knowledge, the time-varying bending stiffness and looseness fault at the pedestal significantly influence rotor dynamics. The present work aims to gain insight into the dynamic behaviors and mechanical behaviors of a rotor-bearing system with a bolted joint structure subjected to a pedestal looseness fault. Firstly, the dynamic model of a bolted joint rotor-bearing system supported by pedestals was set up taking into account the time-varying bending stiffness of bolted joint and the pedestal looseness fault. The feature of the pedestal looseness fault that occurs in a bolted joint rotor system was investigated by comparing the variation ranges of bending stiffness and dynamic responses. An experimental study was then performed using a rotor-bearing test rig equipped with a bolted joint and pedestals. Finally, dynamic phenomena such as offset of the equilibrium position of the vibration waveform, appearance of continuous frequency spectra, and irregular shaft orbits can be known as the dynamic features for the pedestal looseness fault. [ABSTRACT FROM AUTHOR]

• A data-driven idea is proposed to improve phase-based motion estimation method. • Optimal filter parameter by synthetic video and improved particle swarm optimisation. • Log-Gabor filter improves illumination robustness and extends filter parameter range. • Several influential factors were analysed using simulation videos. • Comparative experiments prove superior measurement accuracy in this study. Phase-based motion estimation has gained popularity due to its sub-pixel accuracy and high-spatial resolution. Recently, various phase extraction techniques were incorporated to improve its motion extraction performance. However, existing methods cannot directly determine the filter parameters based on the motion estimation accuracy, instead relying on the local amplitude magnitude as the selection index, which may not directly prove that such a filter can give the best motion extraction results. This study proposes a data-driven approach to automatically select optimal filter parameters based on the accuracy of motion extraction. An optimisation algorithm and a synthetic video with predefined motion are combined to find the optimal filter parameters. Log-Gabor filter is introduced to extend the range of parameters. Simulation results demonstrate the feasibility and analyse the impact of various factors. The superiority is validated by a vibration experiment, which demonstrated a significantly higher level of motion extraction accuracy compared to other algorithms. [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]