Julio César Gomez-Mancilla

The influence of crack-imbalance orientation and orbital evolution for an extended cracked Jeffcott rotor

Vibration peaks occurring at rational fractions of the fundamental rotating critical speed, here named Local Resonances, facilitate cracked shaft detection during machine shut-down. A modified Jeffcott-rotor on journal bearings accounting for gravity effects and oscillating around nontrivial equilibrium points is employed. Modal parameter selection allows this linear model to represent first mode characteristics of real machines. Orbit evolution and vibration patterns are analyzed, yielding useful results. Crack detection results indicate that, instead of 1x and 2x components, analysis of the remaining local resonances should have priority; this is due to crack-residual imbalance interaction and to 2x multiple induced origins. Therefore, local resonances and orbital evolution around 1/2, 1/3 and 1/4 of the critical speed are emphasized for various crack-imbalance orientations. To cite this article: J. Gomez-Mancilla et al., C. R. Mecanique 332 (2004).

Exact Output Regulation for Nonlinear Systems Described by Takagi–Sugeno Fuzzy Models

The exact output regulation for Takagi-Sugeno (T-S) fuzzy models depends on two conditions: 1) The local steady-state zero-error manifolds have to be the same for every local subsystem, and 2) the local input matrices have to be the same for every local subsystem included in the T-S fuzzy model. These conditions are difficult to satisfy in general. In this paper, those conditions are relaxed by solving the fuzzy regulation problem directly on the overall T-S fuzzy model, instead of constructing the fuzzy regulator on the basis of linear local controllers. By considering the fuzzy model as a special class of linear time-varying systems, existence conditions are rigorously derived. These new conditions, which can be solved by means of any mathematical software, depend on the solution of a set of symbolic simultaneous linear equations depending on the membership values of the plant and/or the exosystem. Two examples are given to illustrate the construction of the proposed regulator and to validate the improvement that is achieved with the proposed approach.

Flow-Excited Turbine Rotor Instability

The problem of steam whirl is one of the technological limits that now prohibit the development of power-generating turbomachinery substantially above GW. Due to steam flow, self-excited vibrations develop at high loads in the form of stable limit cycles that, at even higher loads, deteriorate to chaotic vibration of high amplitude.

Rotor-Bearing System Stability Performance Comparing Hybrid versus Conventional Bearings

New closed-form expressions for calculating the linear stability thresholds for rigid and flexible Jeffcott systems and the imbalance response for a rotor supported on a hybrid bearing are presented. For typical bearings characteristics, expressions yield stability thresholds practically equal to those reported by Lund (1966). The hybrid bearing design has a single injection port whose location is so chosen to stabilize the bearing performance and to reduce the steady equilibrium attitude angle. Rotordynamics coefficients graphs for conventional and pressurized bearings, as functions of bearing equilibrium eccentricity and/or Sommerfeld number, are presented. Using the rotordynamics coefficients into the expressions for the corresponding velocity thresholds and the imbalance response, the system stability and vibration performances are estimated and analyzed. When comparing the Jeffcott flexible shaft supported on two journal bearings of the conventional type with the hybrid type, the results show a clear superiority of the pressurized design as far as stability behavior is concerned. Specifically for cases of flexible shafts with similar characteristics to those used in industry, the analysis shows that this design yields velocity thresholds 25%–40% higher compared to the conventional circular ones. Also this bearing displays nonlinear feeding pressure behavior, and it is capable of reducing the synchronous vibration amplitude in most speed ranges, except around the critical speed; moreover, for certain Jeffcott configurations the amplitude reduction can be substantial.

On the exact output regulation for Takagi-Sugeno fuzzy systems

In this paper, the Takagi-Sugeno (TS) fuzzy modelling and the fuzzy regulation theory are considered in order to design a fuzzy controller capable of taking the output of a fuzzy plant to the reference signal generated by an external system. It is well-known that TS fuzzy modelling allows the stabilizer to be obtained by means of numerical techniques. As a result, stability region defined by the fuzzy stabilizer is larger than the one obtained when a simple linear stabilizer is considered. On the other hand, a fuzzy regulator constructed from linear controllers does not solve the exact regulation problem in general [6], [12], [13], [15]. Therefore, a fully nonlinear regulator, defined on the overall TS fuzzy model, is considered in this work. The results are applied on a simple fuzzy model in order to illustrate the improvement achieved with the proposed approach.

Model Derivation and Numerical Simulation for a Pivoted Rigid Rotor-Bearing System

This work addresses the obtainment of a mathematical model for a rotor-bearing system with orbital movement pivoted on a lubricated bushing. This kind of model allows the rotodynamic system to be analyzed using its angular displacement. Nonlinear dimensionless model is developed in order to present an approach capable of being used in general situations. Both numeric simulations and experimental results, which show the vibration response of the system and the angular orbits, illustrate the validity of the proposed approach.

Experimental and Numerical Analysis of Transversal Open Cracked Shafts Considering Beam Slenderness and Crack Depth

Stiffness variation due to cracks in rotors is a well-known problem; plenty of studies to prevent/avoid catastrophic accidents and rotor bursts exist. FEM numerical results calculating natural modal frequencies for open cracked beams at different notch depths and slenderness ratios, are compared versus experimental laboratory measurements. Shaft beams under simply supported and free-free boundary conditions, focusing on solids and Timoshenko beam finite elements, are studied. Timoshenko beams employ the Mayes and Davies equivalent-length concept for crack modeling. Notched shafts provide useful upper bound frequency reductions values (breathing cracks display up to, and smaller decrements). Modal frequency splitting for each natural frequency are confirmed and validated by numerical simulation and tests. Modal frequencies splitting functions are given, obtained by simulation and experiments which reflect strong crack depth and slenderness ratio influences. Vibrational coupling energy of the frequency splitting reaches a maximum when the excitation is orthogonal to the crack orientation, conclusions are given.

Crack Detection in Shafts of Rotating Machinery Using Active Sensing With an External Excitation on a Bearing

Because several power plants have undergone burst shafts with catastrophic consequences, methods for detecting cracks in the shafts of rotating machinery are of great interest to the research community. Cracked shafts represent a very small percentage of the vibration issues in machinery (less than 2%) compared with other faults such as misalignment and mass imbalance, which are responsible for 85% of these issues. However, if a cracked shaft is not detected early enough, it can jeopardize the safety of operators and result in high costs for replacement. A method sensitive enough to detect cracks in the shafts of rotating machinery is investigated in this paper. It is shown that changes in the natural frequencies and/or mode shapes are not sensitive enough indicators to detect transverse cracks at the mid-span of shafts in rotating machinery. An exhaustive numerical analysis using a finite element model of a simple machine is conducted to consider many different measurements of the machinery vibratory responses that most clearly detect cracking. It is shown that external excitations applied on a bearing enhance the sensitivity of vibration measurements to cracking. Experimental tests are also used to validate several of the numerical simulation findings.Copyright

On the Appearance of Lubricant Film Rupture in Cylindrical Journal Bearings

Based on energy and mass balances in conjunction with the classical Reynolds equation in the film region, expressions for cavitation phenomenon are developed. They determine the circumferential location angle where cavitation might start, and the potential number of bifurcating fluid streamer surfaces (boundaries between gas-liquid flow) can be estimated. The expressions depend on the journal angular velocity, equilibrium eccentricity ratio, and bearing and fluid characteristics; they strongly influence cavitation and have not been considered in previous studies. Conditions under which the cavitation phenomenon does not occur are also given. Finally, a comparison to previous research results showing a very close agreement is presented.

A Simple Method for Geometry Definition of Radial Compressors

During the pre-design stage of radial flow compressors for gas turbine or industrial applications, it is necessary to carry out an aero-thermodynamic analysis to define flow properties and from those to define the compressor geometry, i.e. inlet and outlet areas, volute, impeller profiles, etc.. It is well known, that there is no unique design process or method for this kind of turbomachine, so several assumptions have to be made according to the task or application that the compressor is going to carry out. Then, based on those assumptions, the compressors geometry will be defined. Unfortunately, there is not any method fully explained published in the open literature for designing. In this work, a simple method is presented and applied to calculate the geometry of a radial compressor (volute, impeller, etc.) based on the aerothermodynamic analysis.