Nonlinear modal analysis for blisks with friction dampers

Dynamic analyses of nonlinear systems have become an important topic in the field of turbomachinery. In industrial turbomachinery, the friction damping is regarded as the major damping source compared to the aerodynamic damping and material damping. Contact with friction is a type of common non-conservative and non-smooth nonlinearities. The existence of various friction joints in industrial turbomachinery makes the dynamic analysis complicated. The definition of the damped Nonlinear Normal Modes (dNNMs) and various numerical approaches facilitate the infrastructure of nonlinear modal analysis for structures with friction dampers. However, the relations between dNNMs and resonant solutions in forced responses cannot be directly addressed. In this context, the purpose of the present thesis is (i) to evaluate the performance of the existing numerical approaches for computing the dNNMs of systems with non-conservative nonlinearities; (ii) to develop a new method to directly relate the dNNMs to the resonant solutions in forced response for such system; and (iii) to study the geometric influence of the friction ring dampers on their dynamic responses and damping performances. The first contribution of the present thesis is to provide a comprehensive comparison of the existing numerical approaches, including Complex Nonlinear Mode (CNM) and Extended Periodic Motion Concept (EPMC). EPMC with artificial hysteretic damping is firstly attempted and compared with the original EPMC and CNM. The advantages and limitations of each method are critically discussed. The second contribution is the development of the Extended Energy Balance Method (E-EBM), which is a numerical method used to efficiently predict the resonances using the dNNMs of a non-conservative nonlinear system. This E-EBM can be simply applied to both CNM and EPMC approaches. The third contribution is the investigation the damping performance of friction ring dampers for blisk structures, especially the geometric effects of the ring dampers. The geometric design of the ring dampers is achieved by using kriging meta-modelling to predict the dNNMs. Useful advice is proposed for the future design of friction ring dampers.Open Acces

Nonlinear modal analysis of frictional ring damper for compressor blisk

The use of integrally blisk is becoming popular because of the advantages in aerodynamic efficiency and mass reduction. However, in an integrally blisk, the lack of the contact interface leads to a low structural damping compared to an assembled bladed-disk. One emerging damping technique for the integrally blisk is based on the use of friction ring damper which exploits the contact interfaces at the underneath of the disk. In this paper, three different geometries of the ring dampers are investigated for damping enhancement of a blisk. A full-scale compressor blisk is considered as a case study where a node to node contact model is used to compute the contact forces. The dynamic behaviour of the blisk with the ring damper is investigated by using nonlinear modal analysis which allows a direct estimation of the damping generated by the friction interface. The damping performance for the different ring dampers are evaluated and compared. It appears that the damping efficiency as well as the shift in the resonant frequency for the different geometries are highly related to the nodal diameter and contact pressure/gap distributed within contact interface. The geometry of the ring damper has significant impact on the damping performance

Computation of damped nonlinear normal modes for large scale nonlinear systems in a self-adaptive modal subspace

The concept of nonlinear modes has been proved useful to interpret a wide class of nonlinear phenomena in mechanical systems such as energy dependent vibrations and internal resonance. Although this concept was successfully applied to some small scale structures, the computational cost for large-scale nonlinear models remains an important issue that prevents the wider spread of this nonlinear analysis tool in industry. To address this challenge, in this paper, we describe an advanced adaptive reduced order modelling (ROM) technique to compute the damped nonlinear modes for a large scale nonlinear system with frictional interfaces. The principle of this new ROM technique is that it enables the nonlinear modes to be computed in a reduced self-adaptive modal subspace while maintaining similar accuracy to classical reduction techniques. The size of such self-adaptive subspace is only proportional to the number of active slipping nodes in friction interfaces leading to a significant reduction of computing time especially when the friction interface is in a micro-slip motion. The procedure of implementing this adaptive ROM into the computation of steady state damped nonlinear mode is presented. The case of an industrial-scale fan blade system with dovetail joints in aero-engines is studied. Damped nonlinear normal modes based on the concept of extended periodic motion is successfully calculated using the proposed adaptive ROM technique. A comparison between adaptive ROM with the classical Craig-Bampton method highlights the capability of the adaptive ROM to accurately capture the resonant frequency and modal damping ratio while achieving a speedup up to 120. The obtained nonlinear modes from adaptive ROM are also validated by comparing its synthesized forced response against the directly computed ones using Craig-Bampton (CB) method. The study further shows the reconstructed forced frequency response from damped nonlinear modes are able to accurately capture reference forced response over a wide range of excitation levels with the maximum error less than 1% at nearly zero computational cost

Flutter analysis of blisks with friction ring dampers

Aeroelastic flutter is a phenomenon when blades experience an aeroelastic self-excitation from the surrounding air resulting in the full destruction of aero-engines. It poses a big challenge for aero-engine bladed-disks design, especially for integrally bladed-disks (blisks). The lack of friction interfaces in blisks drastically reduces structural damping making them more likely to experience aeroelastic flutter. One of the most effective approaches to improve the damping in a blisk is the use of friction ring dampers. This paper presents a numerical study to investigate the effects of friction ring dampers on the aeroelastic stability of blisks. A lumped parameter model is used to represent the blisk with a ring damper. Aeroelastic self-excitations are simply represented by Van der Pol oscillators. The frictional contact between the blisk and ring damper is modelled by using Jenkins elements. Nonlinear modal analysis is used to compute the nonlinear dynamic response of the system. The results show that the friction ring damper can significantly reduce the risk of flutter and the amplitude of flutter induced limit cycle oscillations for a blisk by increasing the structural damping, especially at a high modal amplitude. The study also shows that the nonlinear modal analysis can efficiently identify the flutter boundary of such a strongly dissipated nonlinear system

Nonlinear vibrational analysis for integrally bladed disk using frictional ring damper

The use of integrally bladed-disk is now very popular in turbomachinery industry since they feature significant aerodynamic and structural improvements along with a significant mass reduction. However, these integrated single structures can arise a major high cycle fatigue issue due to the lack of sufficient damping for dissipating the vibrational energy. This work describes a numerical investigation of the nonlinear dynamic behaviour and nonlinear normal mode for such a bladed-disk with frictional ring damper using the Harmonic Balanced Method (HBM) with alternating Fourier transformation. Jenkins element is used to model the nonlinear contact friction between the disc and ring damper. Using such a modeling strategy, the modal damping and resonance amplitude are directly and efficiently computed through nonlinear normal mode analysis. The initial results show the vibrational level on the blades can be effectively controlled by the parameters of the ring damper model. The effectiveness of ring damper and damping performance is evaluated. This study also indicates the nonlinear normal mode analysis based HBM may be an effective method to analyse the dynamic behaviour of the integrated bladed-disk with frictional ring damper

A study of the contact interface for compressor blisks with ring dampers using nonlinear modal analysis

The integrally bladed disks, also known as blisks, have been widely used in industrial turbomachinery because of their benefits in aerodynamic performance and mass reduction. Friction damping is considered as the major damping sources in turbomachinery. However, in blisks, the friction damping is negligible due to the lack of the contact interfaces. The friction ring dampers are one of the emerging external damping sources for blisks. In this paper, a full-scale blisk with a friction ring damper is studied, where a 3D contact element is used to compute the contact frictions. The blisk and ring damper is investigated using their damped nonlinear normal modes. The modal damping can be directly calculated and used to quantify the friction damping generated by the ring damper. The contact behaviour within the contact interface is further analysed. The nodes with initial gap show less damping ability. The separations within the contact interface are expected to be avoided to achieve a better damping performance

Recent Advances in Regioselective C–H Bond Functionalization of Free Phenols

Phenols are important readily available synthetic building blocks and starting materials for organic synthetic transformations, which are widely found in agrochemicals, pharmaceuticals, and functional materials. The C–H functionalization of free phenols has proven to be an extremely useful tool in organic synthesis, which provides efficient increases in phenol molecular complexity. Therefore, approaches to functionalizing existing C–H bonds of free phenols have continuously attracted the attention of organic chemists. In this review, we summarize the current knowledge and recent advances in ortho-, meta-, and para-selective C–H functionalization of free phenols in the last five years

Comparison of different methodologies for the computation of damped nonlinear normal modes and resonance prediction of systems with non-conservative nonlinearities

The nonlinear modes of a non-conservative nonlinear system are sometimes referred to as damped Nonlinear Normal Modes (dNNMs). Because of the non-conservative characteristics, the dNNMs are no longer periodic. To compute non-periodic dNNMs using classic methods for periodic problems, two concepts have been developed in the last two decades: Complex Nonlinear Mode (CNM) and Extended Periodic Motion Concept (EPMC). A critical assessment of these two concepts applied to different types of non-conservative nonlinearities and industrial full-scale structures has not been thoroughly investigated yet. Furthermore, there exist two emerging techniques which aim at predicting the resonant solutions of a nonlinear forced response using the dNNMs: Extended Energy Balance Method (EEBM) and Nonlinear Modal Synthesis (NMS). A detailed assessment between these two techniques has been rarely attempted in the literature. Therefore, in this work, a comprehensive comparison between CNM and EPMC is provided through two illustrative systems and one engineering application. The EPMC with an alternative damping assumption is also derived and compared with the original EPMC and CNM. The advantages and limitations of the CNM and EPMC are critically discussed. In addition, the resonant solutions are predicted based on the dNNMs using both E-EBM and NMS. The accuracies of the predicted resonances are also discussed in detail

Nonlinear modal analysis of frictional ring damper for compressor blisk

The use of integrally blisk is becoming popular because of the advantages in aerodynamic efficiency and mass reduction. However, in an integrally blisk, the lack of the contact interface leads to a low structural damping compared to an assembled bladed-disk. One emerging damping technique for the integrally blisk is based on the use of friction ring damper which exploits the contact interfaces at the underneath of the disk. In this paper, three different geometries of the ring dampers are investigated for damping enhancement of a blisk. A full-scale compressor blisk is considered as a case study where a node to node contact model is used to compute the contact forces. The dynamic behaviour of the blisk with the ring damper is investigated by using nonlinear modal analysis which allows a direct estimation of the damping generated by the friction interface. The damping performance for the different ring dampers are evaluated and compared. It appears that the damping efficiency as well as the shift in the resonant frequency for the different geometries are highly related to the nodal diameter and contact pressure/gap distributed within contact interface. The geometry of the ring damper has significant impact on the damping performance.</p

Computation of damped nonlinear normal modes for large scale nonlinear systems in a self-adaptive modal subspace

The concept of nonlinear modes has been proved useful to interpret a wide class of nonlinear phenomena in mechanical systems such as energy dependent vibrations and internal resonance. Although this concept was successfully applied to some small scale structures, the computational cost for large-scale nonlinear models remains an important issue that prevents the wider spread of this nonlinear analysis tool in industry. To address this challenge, in this paper, we describe an advanced adaptive reduced order modelling (ROM) technique to compute the damped nonlinear modes for a large scale nonlinear system with frictional interfaces. The principle of this new ROM technique is that it enables the nonlinear modes to be computed in a reduced self-adaptive modal subspace while maintaining similar accuracy to classical reduction techniques. The size of such self-adaptive subspace is only proportional to the number of active slipping nodes in friction interfaces leading to a significant reduction of computing time especially when the friction interface is in a micro-slip motion. The procedure of implementing this adaptive ROM into the computation of steady state damped nonlinear mode is presented. The case of an industrial-scale fan blade system with dovetail joints in aero-engines is studied. Damped nonlinear normal modes based on the concept of extended periodic motion is successfully calculated using the proposed adaptive ROM technique. A comparison between adaptive ROM with the classical Craig-Bampton method highlights the capability of the adaptive ROM to accurately capture the resonant frequency and modal damping ratio while achieving a speedup up to 120. The obtained nonlinear modes from adaptive ROM are also validated by comparing its synthesized forced response against the directly computed ones using Craig-Bampton (CB) method. The study further shows the reconstructed forced frequency response from damped nonlinear modes are able to accurately capture reference forced response over a wide range of excitation levels with the maximum error less than 1% at nearly zero computational cost