A semi-analytical multi-harmonic balance method on full-3D contact model for dynamic analysis of dry friction systems

Dry friction damping structures are widely-used in aero-engines to mitigate vibration.The nonlinear nature of friction and the two-dimensional in-plane motion on the contact interface bring challenges to accurately and efficiently predict the forced response of frictionally damped structures.The state-of-the-art Multi-Harmonic Balance Method(MHBM)on quasi-3D contact model in engineering cannot precisely capture the kinematics on the friction interface although the efficiency is high.The full-3D contact model can describe the constitutive relationship of the interface in a more accurate manner;however,the efficiency and convergence are not guaranteed for large-scale models.In this paper,a semi-analytical MHBM on full-3D contact model is proposed.The original Trajectory Tracking Method(TTM)for evaluating the contact force is reformulated to make the calculation more concise and the derivation of the Analytical Jacobian Matrix(AJM)feasible.Based on the chain rule of derivation,the AJM which is the core to upgrade the performance is deduced.Through a shrouded blade finite element model,the accuracy and efficiency of the proposed method are compared with both the MHBM on full-3D contact model with numerical Jacobian matrix and the MHBM on quasi-3D contact model with AJM.The results show that the AJM improves significantly the efficiency of the MHBM on full-3D contact model.The time cost of the proposed method is in the same order of magnitude as that of the MHBM on quasi-3D contact model.We also confirm that the full-3D contact model is necessary for the dynamic analyses of shrouded blades.If one uses the quasi-3D model,the estimation relative error of damping can even reach 31.8%in some cases.In addition,the AJM also brings benefits for stability analysis.It is highly recommended that engineers use the MHBM on full-3D contact model for the dynamic analysis and design of shrouded blades.

Mechanism of interconnected synchronized switch damping for vibration control of blades

The Synchronized Switch Damping(SSD)is regarded as a promising alternative to mitigate the vibration of thin-walled structures in aero-engines,especially for blades or bladed disks.The common manner is to shunt the switch circuit independently to a single piezoelectric structure.This paper is aimed at exploring a novel way of using the SSD,i.e.,the SSD is interconnected between two piezoelectric structures or substructures.The damping mechanism,performance,and effective range of the interconnected SSD are studied numerically and experimentally.First,based on a dual cantilever beam finite element model,the time domain and frequency domain modeling and solving methods of the interconnected SSD are deduced and validated.Then,the influence of the amplitude and phase relationship on the damping effect of the interconnected SSD is numerically studied and compared with the shunted SSD.A self-sensing SSD control board is developed,and experimental studies are carried out.The results show that the interconnected SSD establishes an additional energy channel between the corresponding piezoelectric structures.When the amplitudes of the two cantilever beams are different,the interconnected SSD balances the vibration level of each beam.When the amplitudes of the two cantilever beams are the same,if the appropriate interconnection manner is selected according to the phase,the resonance peak can be reduced by more than 30%.When the vibration is in-phase/out-of-phase,the damping generated by the interconnected SSD in a cross/parallel manner is even more significant than the shunted SSD.Furthermore,this novel connection scheme reduces the number of SSD circuits in half.Finally,for engineering applications,we implement the proposed damping technology to the finite element model of a typical dummy bladed disk.A piezoelectric damping ratio of 13.7%is achieved when the amount of piezo material is only 10%of blade mass.Compared with traditional friction dampers,the major advancements of the interconnected SSD are:(A)it can reduce the vibration level of blades without friction interface;(B)the space constraint is overcome,i.e.,the vibration energy is not necessarily dissipated independently in one sector or through physically adjacent blades,and instead,the dissipation and transfer of vibrational energy can be realized between any blade pair.If a specific gating circuit is adopted to adjust the interconnection manner of the SSD,vibration mitigation under variable working conditions with different engine orders will be expected;(C)designers do not need to worry about the annoying nonlinearities related to working conditions anymore.