Mobile Interface CMS Method for Vibration Characteristics Prediction of Mistuned Bladed Disk with Different Coupling Degrees

The prediction of vibration characteristics was studied in the mistuned bladed disk by the mobile interface prestressed component mode synthesis (CMS) superelement method. When the strongly, generally, and weakly coupling in the mistuned bladed disk, according to the results of the direct FEM method, the prediction accuracy of this method was verified and compared with the fixed-interface CMS method by using the relative error of dynamic frequency, vibration mode matching function, and dimensionless root mean square error of vibration amplitudes. It is pointed that for mistuned bladed disk in the strong coupling, the prediction accuracy of dynamic frequency and vibration amplitudes are higher by the mobile interface CMS method and the vibration modes are matched with the direct method. In weak coupling, the results of dynamic frequency and vibration modes predicted by the mobile interface CMS method and the fixed-interface CMS method are consistent with the direct method, but the vibration amplitudes’ prediction error of the mobile interface CMS method is lower than that of the fixed-interface CMS method. In general coupling, the mobile interface CMS method has higher dynamic frequency prediction accuracy at low order, and the two methods have comparable dynamic frequency prediction accuracy at high order. The vibration modes predicted by the two methods are matched with the direct FEM method, and the prediction accuracy of vibration amplitude by the mobile interface CMS method is better than that of the fixed-interface CMS method. The results indicate that the mobile interface CMS method could more accurately predict vibration characteristics of the mistuned bladed disk with different coupling degrees and could be an effective measurement for studying the vibration characteristics of the mistuned bladed disk system.

Study on the Coupled Vibration Characteristics of a Two-Stage Bladed Disk Rotor System

This paper conducts a coupled vibration analysis of a two-stage bladed disk rotor system. According to the finite element method, the bladed disk rotor system is established. The substructure modal synthesis super-element method (SMSM) with a fixed interface and free interface is presented to obtain the vibration behaviors of the rotor system. Then, the free vibration results are compared with the ones calculated by the cyclic symmetry analysis method to validate the analysis in this paper. The results show that the modes of the two-stage bladed disk not only include the modes of the first- and second-stage bladed disk, but also the coupled modes of the two-stage bladed disk.

Numerical Methods for Calculating Component Modes for Geometric Mistuning Reduced-order Models

Geometric mistuning models formulated from a component mode synthesis methods often require the calculation of component modes, particularly constraint and fixed interface normal modes, during substructuring. For Integrally Bladed Rotors, these calculations are required for each sector. This paper proposes methods that reuse information garnered from solving the constraint modes of a single sector on the remaining sectors to reduce memory requirements and solution times. A mesh metamorphosis tool is used to ensure finite element models match geometry obtained from a 3D optical scanner. This tool also produces a common mesh pattern from sector-to-sector. This is exploited to produce common permutation matrices and symbolic factorizations of sector stiffness matrices that are proposed for reuse in solving subsequent constraint modes. Furthermore, a drop tolerance is introduced to remove small values during constraint mode calculation to reduce memory requirements. It is proposed to reuse this dropping pattern produced from a single sector on the remaining sectors. Approaches are then extended to a parallel processing scheme to propose effective matrix partitioning methods. Finally, information gathered during the constraint mode calculations are reused during the solution of the fixed interface normal modes to improve solution time. Results show reusing permutation matrices and symbolic factorizations from sector-to-sector improves solution time and introduces no error. Using a drop tolerance is shown to reduce storage requirements of a constraint mode matrix, while reusing the dropping pattern introduces minimal error. Similarly, reusing constraint mode information in calculating normal modes greatly improves the performance.

A Multiple and Multi-Level Substructure Method for the Dynamics of Complex Structures

Based on the fixed interface component mode synthesis, a multiple and multi-level substructure method for the modeling of complex structures is proposed in this paper. Firstly, the residual structure is selected according to the structural characteristics of the assembled complex structure. Secondly, according to the assembly relationship, the parts assembled with the residual structure are divided into a group of substructures, which are named the first-level substructure, the parts assembled with the first-level substructure are divided into a second-level substructure, and consequently the multi-level substructure model is established. Next, the substructures are dynamically condensed and assembled on the boundary of the residual structure. Finally, the substructure system matrix, which is replicated from the matrix of repeated physical geometry, is obtained by preserving the main modes and the constrained modes and the system matrix of the last level of the substructure is assembled to the upper level of the substructure, one level up, until it is assembled in the residual structure. In this paper, an assembly structure with three panels and a gear box is adopted to verify the method by simulation and a rotor is used to experimentally verify the method. The results show that the proposed multiple and multi-level substructure modeling method is not unique to the selection of residual structures, and different classification methods do not affect the calculation accuracy. The selection of 50% external nodes can further improve the analysis efficiency while ensuring the calculation accuracy.

Numerical Methods for Calculating Component Modes for Geometric Mistuning Reduced-Order Models

Geometric mistuning models formulated from a component mode synthesis methods often require the calculation of component modes, particularly constraint and fixed interface normal modes, during substructuring. For Integrally Bladed Rotors, these calculations are required for each sector. This paper proposes methods that reuse information garnered from solving the constraint modes of a single sector on the remaining sectors to reduce memory requirements and solution times. A mesh metamorphosis tool is used to ensure finite element models match geometry obtained from a 3D optical scanner. This tool also produces a common mesh pattern from sector-to-sector. This is exploited to produce common permutation matrices and symbolic factorizations of sector stiffness matrices that are proposed for reuse in solving subsequent constraint modes. Furthermore, a drop tolerance is introduced to remove small values during constraint mode calculation to reduce memory requirements. It is proposed to reuse this dropping pattern produced from a single sector on the remaining sectors. Approaches are then extended to a parallel processing scheme to propose effective matrix partitioning methods. Finally, information gathered during the constraint mode calculations are reused during the solution of the fixed interface normal modes to improve solution time. Results show reusing permutation matrices and symbolic factorizations from sector-to-sector improves solution time and introduces no error. Using a drop tolerance is shown to reduce storage requirements of a constraint mode matrix. Additionally, it is shown that reusing the same dropping pattern introduces minimal error without degradation in solution times. Similarly, reusing the information from constraint modes for calculating fixed interface normal modes greatly improves the performance in a shift-and-invert technique for solving eigenvalue problems.

Fast structural dynamic modeling and analysis for horizontally folding wing

To investigate the structural dynamic characteristics of a folding wing effectively, a fast structural dynamic modeling approach is proposed. Firstly, the interface compatible relationship of the traditional fixed interface component modal synthesis method is modified, and the internal force of the interface is completely expressed in the structural dynamic equation, so that the influence of the connection stiffness on the wing structure dynamics can be considered. Then, on the basis of the fixed interface component modal synthesis method, the main mode of fixed-loaded interface is introduced to establish the mixed-loaded interface component modal synthesis method, which makes it feasible to accurately reflect the influence of elasticity and inertia of fuselage and outer wing on inner wing. The structural dynamics modeling method based on two different kinds of component modal synthesis method analyzed and deduced in detail. The application of component modal synthesis method in the fast structural dynamics modeling of folding wing is achieved. The whole program is compiled in MATLAB. At the same time, the dynamic characteristics of the folding wing with different folding angles, different connections and different connection positions is investigated. The results of the method proposed in this paper are compared with the results of the repeated finite model established in MSC.NASTRAN to verify the effectiveness from the aspects of natural frequency and vibration mode.

Model Dimension Reduction and Nonlinear Analysis of the Sprag Clutch-flexible Rotor System Considering Local Nonlinearity

In order to study the influence of local nonlinear factors such as bearing clearance and Hertzian contact on the nonlinear behavior of the sprag clutch-rotor system during high-speed steady-state engaging, a nonlinear force model of rolling bearing considering radial clearance and Hertzian contact is established. Regarding the inner and outer rotors as substructures, the fixed interface modal synthesis method is used to reduce the dimension of the substructure model, and the nonlinear dimension reduction model of the sprag clutch-flexible rotor system (SC-FRS) is obtained. To improve computational efficiency, the Newmark method combined with the fixed interface synthesis method is presented to calculate the system response. The response results of the reduced model with a different number of dominant modes and the unreduced model are compared, and the number of reserved dominant modes of the inner and outer rotors is selected based on the calculation efficiency and accuracy. The effect of the radial clearance of different bearings on the nonlinear vibration response and the dynamic load of the inter-shaft bearing is discussed. It is found that the sensitivity of different radial clearances to the system's amplitude-frequency response is different, and the amplitude jump and the frequency hysteresis appear at the resonance peak.

THE EFFECT OF TIME PRESSURE ON THE PERFORMANCE OF DEXTEROUS OPERATIONS

This study explores the effects of time pressure in dexterous operations on two types of interface: the fixed interface and the moving interface. Results show that the accuracy of finger movement is decreased, the information processing on the sense of sequence, position and direction is worsened by the psychological disturbance. The findings indicate that a fixed interface is more robust to performance and participants can learn and perform tasks quicker than a moving interface. Finally, the researchers give some practices on both fixed and moving interface design.