Modelling and experimental validation of active and passive eddy current sensors for blade tip timing

To monitor the vibration of blades in rotating machinery, the contactless method called Blade Tip Timing (BTT) is widely used. blade vibration and clearance are important diagnostic features for condition monitoring, including the detection of blade cracks. To perform the BTT technique, optical sensors were widely used by industry due to their high accuracy, but the main drawback of these systems is their low tolerance to the presence of contaminants. To overcome this downside, eddy current sensors are a good alternative for health monitoring applications in gas turbines due to their insensitivity to contaminants and debris. This type of sensor has been used by many researchers, predominantly on the experimental side to investigate BTT systems and there is a lack of modelling to support the measurement system design. This paper fills the gap between experiments and modelling for the particular case of a blade rotating past eddy current sensors. Hence the novelty of this paper is the simulation of the BTT application using detailed quasi-static finite element models of the electro-magnetic field to estimate the outputs from active and passive eddy current sensors. A test rig composed of a bladed disk with 12 blades clamped to a rotating shaft was designed and manufactured in order to validate the proposed models with experimental measurements. Finally, a parametric study is presented to show the effect of the blade tip clearance and the rotational speed on the accuracy of the BTT measurement. This leads to better understanding of the sources of error in the time of arrival of the blades passing the sensor and hence insight into the blade vibration measurement accuracy

Coupled mech nical and electromagnetic modeling of eddy current sensors

To effectively monitor the vibration of blades in a rotating machine, a non-contacting method called blade tip-timing (BTT) has been used. The method is based on the analysis of the differential arrival times of the blades at sensors mounted on the stator to characterize the vibration amplitude and frequency of the blades. These sensors can also provide blade tip clearance measurement. A combination of these data can provide a robust condition monitoring approach for the early detection of blade cracks. Eddy current sensors (ECS) have shown great potential to assess the health of an engine without any need for direct access to the blade and therefore they are insensitive to the presence of any type of contaminant. Also, both tip timing and tip clearance of each blade could be measured by these sensors in real time and at high resolution. ECSs measure the magnetic field caused by eddy currents during the blade motion, and hence are a coupled mechanical and electromagnetic problem. An ECS on the casing of a machine has been modeled to fully understand how the dynamic response of the blade is measured by the sensors. Detailed 2-D and 3-D modeling and simulation of a rotating simplified bladed disk passing an ECS is presented. The effect of the variation of the rotation speed and the gap between the sensor and the blade tip on the accuracy of the measurement is investigated. Such an analysis will enable the reliable monitoring of blade damage during engine operation

Harmonic-Balance-Based parameter estimation of nonlinear structures in the presence of Multi-Harmonic response and force

Testing nonlinear structures to characterise their internal nonlinear forces is challenging. Often nonlinear structures are excited by harmonic forces and yield a multi-harmonic response. In many systems, particularly ones with strong nonlinearities, the effect of higher harmonics in the force and responses cannot be ignored. Even if the intended excitation is a single frequency sinusoidal force, the interaction of the shaker and the nonlinear structure can lead to harmonics in the applied force. The effects of these higher harmonics of the input force on nonlinear model identification in structural dynamics are often neglected. The objective of this study is to introduce an identification method, motivated by the alternating frequency/time approach using harmonic balance (AFTHB), which is able to consider both multi-harmonic forces and multi-harmonic responses of the system. The proposed AFTHB method can include all significant harmonics by selecting an appropriate time step and sampling frequency to guarantee the accuracy of the results. An analytical harmonic-balance-based (AHB) approach is also considered for comparison. However, the inclusion of all significant harmonics of the response in the analytical expansion of the nonlinear functions is often cumbersome. Furthermore, the AFTHB method can easily cope with complex nonlinearities such as Coulomb friction and with multi-degree of freedom nonlinear systems. Including the effect of higher harmonics in the identification process reduces the approximation error due to truncation and very accurate approximation of the balanced equations of each harmonic is obtained. The proposed identification method requires prior knowledge or an appropriate estimation of the type of system nonlinearities. However, the method of model selection may be used for a set of candidate models, and avoiding a dictionary of arbitrary candidate basis functions significantly reduces the computational costs. This paper highlights the important features of the AFTHB method to ensure accurate estimation using four simulated and two experimental examples. The effects of the number of harmonics considered, the modelling error, measurement noise and the frequency range on the quality of the estimated model are demonstrated

On the sensitivity of the equivalent dynamic stiffness mapping technique to measurement noise and modelling error

The objective of this study is to investigate the sensitivity of the Equivalent Dynamic Stiffness Mapping (EDSM) identification method to typical types of inaccuracy that are often present during the identification process. These sources of inaccuracy may include the presence of noise in the simulated/measured data, expansion error in the estimation of unmeasured coordinates, modelling error in the updated underlying linear model, and the error due to neglecting the higher harmonics in the nonlinear response of the system. An analytical study is performed to identify the structural nonlinearities of two nonlinear systems, a discrete three-DOF Duffing system and a cantilever beam with a nonlinear restoring force applied to the tip of the beam, considering the presence of all the aforementioned sources of inaccuracy. First, the EDSM technique is utilized to identify the nonlinear elements of two example systems to verify the accuracy of the EDSM technique. Finite Element modelling, the Modified Complex Averaging Technique (MCXA), and arc-length continuation are exploited in this study to obtain the steady state dynamics of the nonlinear systems. Numerical models of the two systems are then simulated in MATLAB and the numerical results of the simulation are used to identify the unknown nonlinear elements using the EDSM technique and investigate the effect of different sources of error on the outcome of the identification process. The nonlinear response of the system has been regenerated using the identified parameters with the sources of error present and the generated response has been compared to the simulated response in the absence of any noise or error. The EDSM technique is capable of identifying accurately the nonlinear elements in the absence of any source of inaccuracy although, based on the results, this method is highly sensitive to the aforementioned sources of inaccuracy that results in significant error in the identified model of the nonlinear system. Finally, an optimization-based framework, developed by the authors, is utilized to identify the nonlinear cantilever beam and the results are compared with the results of the EDSM technique. It is shown that by using the optimization method, the inaccuracy due to different sources of noise and error is significantly reduced. Indeed, by using the optimization method, the necessity to use an expansion method and consider the higher harmonics of the response is eliminated

Simulating eddy current sensor outputs for blade tip timing

Blade tip timing is a contactless method used to monitor the vibration of blades in rotating machinery. Blade vibration and clearance are important diagnostic features for condition monitoring, including the detection of blade cracks. Eddy current sensors are a practical choice for blade tip timing and have been used extensively. As the data requirements from the timing measurement become more stringent and the systems become more complicated, including the use of multiple sensors, the ability to fully understand and optimize the measurement system becomes more important. This requires detailed modeling of eddy current sensors in the blade tip timing application; the current approaches often rely on experimental trials. Existing simulations for eddy current sensors have not considered the particular case of a blade rotating past the sensor. Hence, the novel aspect of this article is the development of a detailed quasi-static finite element model of the electro-magnetic field to simulate the integrated measured output of the sensor. This model is demonstrated by simulating the effect of tip clearance, blade geometry, and blade velocity on the output of the eddy current sensor. This allows an understanding of the sources of error in the blade time of arrival estimate and hence insight into the accuracy of the blade vibration measurement

Development of a digital twin operational platform using Python Flask

The digital twin concept has developed as a method for extracting value from data, and is being developed as a new technique for the design and asset management of high-value engineering systems such as aircraft, energy generating plant, and wind turbines. In terms of implementation, many proprietary digital twin software solutions have been marketed in this domain. In contrast, this paper describes a recently released open-source software framework for digital twins, which provides a browser-based operational platform using Python and Flask. The new platform is intended to maximize connectivity between users and data obtained from the physical twin. This paper describes how this type of digital twin operational platform (DTOP) can be used to connect the physical twin and other Internet-of-Things devices to both users and cloud computing services. The current release of the software—DTOP-Cristallo—uses the example of a three-storey structure as the engineering asset to be managed. Within DTOP-Cristallo, specific engineering software tools have been developed for use in the digital twin, and these are used to demonstrate the concept. At this stage, the framework presented is a prototype. However, the potential for open-source digital twin software using network connectivity is a very large area for future research and development