Richard Markert

Analytically based estimation of the maximum amplitude during passage through resonance

Approximation formulae for both the maximum amplitude and the respective resonance frequencies of a linear oscillator passing resonance are derived analytically. Starting from the exact solution for run-up or run-down with constant acceleration, irrelevant terms are omitted. The analytically found results are compared to the known empirical approximation formulae.

Model based fault identification in rotor systems by least squares fitting

In the present paper a model based method for the on-line identification of malfunctions in rotor systems is proposed. The fault-induced change of the rotor system is taken into account by equivalent loads which are virtual forces and moments acting on the linear undamaged system model to generate a dynamic behaviour identical to the measured one of the damaged system.

Filter bank property of variational mode decomposition and its applications

The variational mode decomposition (VMD) was proposed recently as an alternative to the empirical mode decomposition (EMD). To shed further light on its performance, we analyze the behavior of VMD in the presence of irregular samples, impulsive response, fractional Gaussian noise as well as tones separation. Extensive numerical simulations are conducted to investigate the parameters mentioned in VMD on these filter bank properties. It is found that, unlike EMD, the statistical characterization of the obtained modes reveals a different equivalent filter bank structure, robustness with respect to the nonuniformly sampling and good resolution in spectrum analysis. Moreover, we illustrate the influences of the main parameters on these properties, which provides a guidance on tuning them. Based on these findings, three potential applications in extracting time-varying oscillations, detrending as well as detecting impacts using VMD are presented. HighlightsAn in-depth elaboration on the inherent characteristics of VMD is investigated through extensive numerical experiments.A well-controlled use of the VMD technique for specific application is addressed.Three potential applications of VMD are illustrated.

Improvements of the integration of active magnetic bearings

Functional and structural integration are tools to improve active magnetic bearing systems. In this paper two aspects of the integration of electromagnetic bearings are presented: (1) The non-linearity of the magnetic force is compensated by software integrated in the digital controller. (2) In self-sensing bearings the rotor position is identified from the electric state variables directly at the power amplifiers.

Motion patterns at rotor stator contact

The present paper discusses the various movement patterns during rotor stator contact. Both rotor and stator are assumed to be flexible damped single degree of freedom systems. The contact is described by a flexible viscoelastic model. Dry friction between rotor and stator is taken into account. Despite strong non-linearity due to contact, rotor unbalance causes purely synchronous motions. However, in some circumstances, the synchronous motion may become unstable and the rotor motion turns into a non-synchronous state, which can be very destructive. Non-synchronous motions include backward whirl, sub- and super-harmonic vibration and chaotic motion. The influence of various system parameters on the different types of motion is investigated by numerical simulation. The transients between synchronous to non-synchronous motions are exemplarily demonstrated by run-up and run-down processes. It is shown that different motion types may co-exist. Even in speed regions where the synchronous whirl is stable, non-synchronous motions with rotor stator contact are possible.Copyright

Improvements in the integration of active magnetic bearings

Abstract Functional and structural integration are tools to improve mechatronic systems that include active magnetic bearing systems. In this paper two aspects of the integration of electromagnetic bearings are presented: 1. The non-linearity of the magnetic force is compensated by software integrated in the digital controller. 2. In self-sensing bearings the rotor position is identified from the electric state variables directly at the power amplifiers without separate sensors.

Design Methodology of Application Specific Integrated Circuits for Mechatronic Systems

Abstract In this paper the implementation of the information processing element of mechatronic applications is described. First, a brief overview of a mechatronic application, an integrated active magnetic bearing system, is given. The design process for realizing a software as well as a hardware prototype of the controller is described and details of the individual modules within the design process are discussed. The controller of the magnetic bearing is implemented using a graphical high-level approach. From this specification a C as well as a VHDL description is generated automatically and transferred either as a software prototype to a DSP system or as a hardware prototype to a FPGA-based system both located at the test rig.

An analysis on the supporting structure representative model in rotating systems

Power generation systems are composed by several rotating system, which are supported by bearings, and are installed on foundation structure. For this reason, a representative model needs to take into account the components effects. Rotating systems numerical models are well known by the scientific community specialized in rotor-dynamics to predict the system dynamic behaviour. Instead, the foundation numerical model is more sensitive to uncertainties. Experimental models can be the solution to the foundation representation. In this case, some difficulty in identifying the modal parameters, mainly the damping factors, can influence the results. This work proposes a comparison between complete system response using both experimental models of mechanical impedance and mixed coordinates to represent a test-rig foundation. A classical approach is the assembly of the impedance matrix of the supporting structure directly from the flexibility matrix inversion. However, this technique can be limited by the number of degrees of freedom associated to the rotor-structure connecting elements. Therefore, a solution based on modal parameters of mass, stiffness and damping to represent the foundation is also applied and both models are associated to a rotor-bearing system model for comparison.

An extended field balancing procedure for flexible rotors fully levitated by active magnetic bearings

An extended influence coefficient matrix (EICM) is presented that enables the identification of inherent unbalances in a flexible rotor levitated by active magnetic bearings (AMBs). The traditional influence coefficient procedure for flexible rotor balancing uses measured unbalance responses to obtain residual unbalances at predefined balancing planes with the help of trial sets of unbalances. Due to partial attenuation of unbalance responses by active magnetic bearings in rotors mounted on active magnetic bearings, difficulty arises in estimating these influence coefficients since responses do not reflect the real effects of trial unbalances. The presented EICM correlates magnetic forces with unbalance forces in the form of trial sets of unbalances. This matrix is identified initially and helps in finding residual unbalances in the rotor system. The finite element method is used to model a flexible five-disc rotor system mounted on two active magnetic bearings for the numerical simulation of an experimental test rig. AMBs uses PID controller. The proposed procedure is applicable for both, discrete (constant) speeds and for run up/down measurements of magnetic forces. The developed procedure is benchmarked experimentally.

Detecting Rub-Impact Fault of Rotor System Based on Variational Mode Decomposition

Multi-component extraction is an available method for fault vibration signal analysis of rotary machinery, so a new method for rubbing fault diagnosis based on variational mode decomposition (VMD) is proposed. VMD is a newly developed technique for adaptive signal decomposition, which can non-recursively decompose a multi-component signal into a number of quasi-orthogonal intrinsic mode functions. VMD is then first applied to detect multiple rubbing-caused signatures for rotor-stator fault diagnosis via numerical simulated response. A comparison has also been conducted to investigate the effectiveness of monitoring the rubbing-caused signatures by using VMD, empirical wavelet transform (EWT), EEMD and EMD. The analysis results of the rubbing signals show that the multiple features of these signals can be efficiently extracted with the VMD.