Modal testing of rotating structures is complicated by difficulty of access and by the fact that, if the source of excitation is fixed in space, responses occur at frequencies other than that of the excitation. This paper demonstrates the use of, and derives output equations for, a Laser Doppler Vibrometer (LDV) for response measurement. Examples are given of measurements using the LDV beam aimed (i) at a point fixed in space, (ii) at a fixed point on the disc, and (iii) rotating at a non-synchronous speed. The third technique is perhaps the most useful, enabling the circumferential spatial disc response, expressed in terms of travelling waves or orthogonal standing modes, to be directly derived at any speed, frequency or state of disc mistuning. The same technique, applied to a non-rotating disc, provides a simple qualitative measurement of the mode shape associated with each natural frequency. An example based on a centrifugal impeller is included.

This paper describes a procedure that combines the measurement of dry-friction contact behaviour, its theoretical modelling and the analysis of structures with friction joints. The experimental part describes a friction damper test rig which is specifically designed for measuring the dynamic force-response characteristics of a joint. A hybrid mathematical model, which is a combination of the traditional macro- and micro-slip models, is proposed to represent the joint characteristics and it is shown that such a model represents the measured behaviour better than any of the traditional ones. The final part of the paper demonstrates the procedure applied to a blade-damper test structure and which includes testing, analysis and correlation of both sets of results. The non-linear response levels are predicted using a dedicated program based on the Harmonic Balance Method and it is found that the proposed analysis procedure can predict the amount of response reduction, the optimum friction damper load and the locked natural frequency quite accurately.

Experimental vibration techniques used in the characterisation of the two most common types of non-linear structure are described here. The first is used to determine friction contact hysteresis loops to provide data which can be incorporated into large, otherwise linear, structural models, to predict non-linear vibration responses. The second is a method of measuring frequency response functions (FRFs) of structures with non-linear, amplitude-dependent stiffness and damping, including the ‘unstable’, overhanging part of the FRF curve, by using a controlled-amplitude, stepped-frequency sinusoidal input. These apparently rather different test techniques are in fact connected by the fact that, in order to be effective, they both require an additional mass to be installed, on the input side of the force transducer.

The effects of random stiffness and damping variations on damped natural frequencies and response levels of turbomachinery blades are investigated by employing probabilistic approach using a single-degree-of-freedom (SDOF) model. An important feature of this study is the determination of the cumulative probability distributions for damped natural frequencies and receptance frequency response functions without having to compute their probability density distributions since it is shown that those of stiffness and damping can be used directly. The advantage of this approach is not only in the simplicity of problem formulation but also in the substantial reduction of computational requirements. Furthermore, results suggest that both stiffness and damping properties should be considered as random parameters in statistical analyses of forced response.

This paper describes a theoretical model for analysing the dynamic characteristics of wedge-shaped underplatform dampers for turbine blades, with the objective that this model can be used to minimise the need for conducting expensive experiments for optimising such dampers. The theoretical model presented in the paper has several distinct features to achieve this objective including: (i) it makes use of experimentally-measured contact characteristics (hysteresis loops) for description of the basic contact behaviour of a given material combination with representative surface finish, (ii) the damper motion between the blade platform locations is determined according to the motion of the platforms, (iii) three-dimensional damper motion is included in the model, and (iv) normal load variation across the contact surfaces during vibration is included, thereby accommodating contact opening and closing during vibration. A dedicated non-linear vibration analysis program has been developed for this study and predictions have been verified against experimental data obtained from two test rigs. Two cantilever beams were used to simulate turbine blades with real underplatform dampers in the first experiment. The second experiment comprised real turbine blades with real underplatform damper. Correlation of the predictions and the experimental results revealed that the analysis can predict (i) the optimum damping condition, (ii) the amount of response reduction and (iii) the natural frequency shift caused by friction dampers, all with acceptable accuracy. It has also been shown that the most commonly-used underplatform dampers in practice are prone to rolling motion, an effect which reduces the damping in certain modes of vibration usually described as the lower nodal diameter bladed-disc modes.

Friction dampers have been used to reduce turbine blade vibration levels for a considerable period of time. However, optimal design of these dampers has been quite difficult due both to a lack of adequate theoretical predictions and to difficulties in conducting reliable experiments. One of the difficulties of damper weight optimisation via the experimental route has been the inevitable effects of mistuning. Also, conducting separate experiments for different damper weights involves excessive cost. Therefore, current practice in the turbomachinery industry has been to conduct so-called ‘rainbow tests’ where friction dampers with different weights are placed between blades with a predefined configuration. However, it has been observed that some rainbow test results have been difficult to interpret and have been inconclusive for determining the optimum damper weight for a given bladed-disc assembly. A new method of analysis — a combination of Harmonic Balance Method and structural modification approaches — is presented in this paper for the analysis of structures with friction interfaces and the method is applied to search for qualitative answers about the so-called ‘rainbow tests’ in turbomachinery applications. A simple lumped-parameter model of a bladed-disc model was used and different damper weights were modelled using friction elements with different characteristics. Resonance response levels were obtained for bladed discs with various numbers of blades under various engine-order excitations. It was found that rainbow tests, where friction dampers with different weights are used on the same bladed-disc assembly, can be used to find the optimum damper weight if the mode of vibration concerned has weak blade-to-blade coupling (the case where the disc is almost rigid and blades vibrate almost independently from each other). Otherwise, it is very difficult to draw any reliable conclusion from such expensive experiments.

The dynamic forced response of a two-degrees-of-freedom model of an unbalanced overhung rotor with clearance and symmetric piecewise-linear stiffness is examined in the time domain. The stiffness nonlinearity is representative of the contact between the rotor and a concentric stator ring. This rubbing interaction comes as a result of the rotor transient motion initiated by the sudden application of a static unbalance, such as in a blade loss scenario. The focus of this study is on the range of rotor speeds above resonance, where the contact between rotor and stator is characterised by a “bouncing” or intermittent type of behaviour. Brute-force numerical bifurcation analysis on the long-term forced response revealed ranges of rotation frequency for which there is bi-stability between non-impacting synchronous equilibrium and impacting sub-synchronous motion. It is found that, for sufficiently high levels of transient energy in the rotor, there exists the possibility for the solution to jump into a stable limit cycle characterised by three non-harmonically related frequencies, namely the synchronous response frequency and the forward and backward whirl frequencies. A simple relationship defining the point of synchronisation between these three components is proposed as an explanation to the region of bi-stability detected. The stiffening effect induced by the contact non-linearity enables this synchronisation to be maintained over a range of forcing frequencies rather than just at the single condition determined from the nominal whirl mode frequencies.

The dynamic characteristics of a cracked rotor with an active magnetic bearing (AMB) are theoretically analyzed in this paper. The effects of using optimal controller parameters on the dynamic characteristics of the cracked rotor and the effect of the crack on the stability of the active control system are discussed. It is shown that the dynamic characteristics of the cracked rotor with AMBs are clearly more complex than that of the traditional cracked rotor system. Adaptive control with AMBs may hide the fault characteristics of the cracked rotor, rather than helping to diagnose a crack; this will depend on the controller strategy used. It is very difficult to detect a crack in the AMB-rotor system when the vibration of the rotor system is fully controlled. Only the super-harmonic components of 2X and 3X revolution in the sub-critical speed region can be used as a index to detect a crack in the rotor–AMB system. If the effect of the crack is not considered in designing the controller, then the AMB-rotor system will lose its stability in some cases when cracks appear.

It is well known that friction is really important to reduce amplitudes of vibration of rotor blades. Underplatform dampers are a common solution for introducing friction damping, but there are also other friction damping sources on blades that are produced in places with high normal loads and small relative displacements (e.g. lockplates and blade-disc joints). Several approaches based on the classical Coulomb friction law have been used in order to model the friction damping at those interfaces, but their results are not accurate enough for those cases with small displacements where high normal loads appear. This paper presents simulations of typical cases of friction on rotor blades (underplatform dampers, lockplates and blade root) using a method based on macroslip and the method developed by ‘Industria de TurboPropulsores’ (ITP) based on microslip (InTerPart MIcroslip COntact method), and their comparison with experimental results obtained with several tests performed at Imperial College London (IC). The comparison shows that, for cases with high normal loads and small displacements, the ITPMICO method obtains further more accurate results than based-on-macroslip one.

In this paper we present a methodology and results from an experimental investigation of forced vibration response for a bladed disk with fitted under-platform ‘cottage-roof’ friction dampers, together with the corresponding numerical predictions. A carefully-designed and constructed rotating test rig is used to make precise measurements which involve only the phenomena of interest. For this purpose, the measurement rig is operated under vacuum to eliminate aerodynamic effects on the rotating blisk and non-contact excitation and measurement techniques are employed so as not to modify the bladed disk dynamics. The experimental data measured are used for validation of multi-harmonic balance-based prediction tools developed at Imperial College. Predictions are carried out both with and without taking inherent mechanical mistuning into account, which is identified from measured data. Measured and predicted response curves are compared with each other and the degree of correlation is discussed.