This paper studies the dynamics of a 150 MW hydropower rotor system, in whichan elastic structure supports the generator guide bearing. A non-linear large-displacement force-deflection relationship for the bearing support is derived withinthe elastic range under quasi-static conditions, which is incorporated into theequations of motion for a rotor dynamic model. The proposed model includestwo tilting pad journal bearings, along with nonlinear magnetic interaction andunbalance forcing acting on the generator. The equation of motion is solved bytime-integrating procedures to study the system’s dynamics. A drastic softeningeffect is observed for the bracket within the elastic range, in which the nominalvalue represents merely 10% of the bearing stiffness. It is concluded that theexcessive support flexibility significantly reduces the lowest pair of frequencies,diminishes the damping ratios and alters the orbit characteristics during operation.Furthermore, the amplified eccentricity increases the risk of instability due to theradial magnetic pull.

Hydropower generators are normally considered rigid in rotordynamic studies; nevertheless, according to previous studies, they should be regarded as elastic, and this will affect the system's dynamics. The interaction between the magnetic flux of the stator and rotor creates attractive forces between the parts that would balance to zero at the centered position. However, asymmetries in the magnetic flux create an uneven distribution of forces that threaten the machine's life; these forces are non-linearly dependent on the gap between the rotation and stationary part of the generators, although it has been considered linear for simplification. This study focuses on how the dynamics of the rotor are affected by static eccentricity and unbalanced masses while considering nonlinear electromagnetic forces. The rotor has been modeled using curved beams and attached to the rotor-spider by connecting plates, allowing the expansion of the ring due to centrifugal and thermal loads. The electromagnetic forces are modeled as a sum of exponential functions. Bifurcation diagrams and Poincaré maps are employed to analyze the stability of the generator. 

Rotating machines may encounter rubbing due to contact between stationary and rotating structures, leading to large mechanical vibrations that can cause catastrophic failure. In hydropower machines, rubbing contact could occur for many reasons, such as mass imbalance or mechanical/electrical misalignments. This paper investigates whether squeeze film dampers can improve the contact dynamics of a 45 MW hydropower unit. The squeeze film dampers were installed in series with the upper and lower generator guide bearings, and the reaction forces were predicted based on short bearing approximation. A finite element model was established, and the equation of motion of the rotor–stator system was solved numerically using a MATLAB inbuilt function (ode23tb), taking the rotor speed, the retainer spring stiffness, and damper clearance as control parameters. The simulation results are presented using a bifurcation diagram, Poincaré map, orbit, frequency spectrum and maximum contact force. The results indicated that squeeze film dampers improved the damping characteristics of the hydropower machine and reduced the vibration amplitudes. Consequently, it curtailed the risk of rubbing contact at a critical speed for larger range of load cases, ensuring safe operations. Besides, retainer spring stiffness and damper clearance play an important role in the contact dynamics of the hydropower machine with squeeze film damper. 

In 2005 a vertical 42 MW hydropower unit was upgraded in Sweden. The upgrade included the fitting of a new turbine guide bearing, a modified runner, a modified turbine regulator and a new brushless exciter. One of the requirements was that the dynamic behaviour of the machine should not be affected. In spite of the requirements, resonance problems became apparent after the hydropower unit was re-commissioned. Measurements from the re-ommissioning showed poor alignment of the shaft system and shape deviations in the generator. The exchange of the turbine guide bearing from a sleeve bearing to a block bearing also caused changes in the machines dynamic behaviour. Measurements on the unit were conducted at normal operation and resonance. These show that at normal operation, the machine has dominant frequencies at the nominal speed and at twice the nominal speed. When the machine goes into resonance, the dominant frequencies increase to approx. 2.4 times the nominal speed.The machine will undergo a major overhaul in ten years. The objective is to find a solution of the resonance problem that is both inexpensive and possible to implement. The conclusion was drawn that the low damped eigenmode at 2.4 times the nominal speed had been excited and caused the machine to go into resonance. The unit's dynamic sensitivity to different bearing settings was investigated numerically and with tests on site, i.e. bearing clearances were varied. The calculated result was verified against measured resonance frequencies. Agreement between the estimated and measured result was good. Other possible measures to rectify the resonance problems were also analyzed numerically. The effect of making the surrounding structures more rigid, the installation of additional guide bearings, making the shaft system more rigid, etc. were examined. A temporary solution, used for the last six months, is to operate the machine with larger bearing clearances on all bearings. Increased bearing clearance of the turbine guide bearing cause increased damping of the natural frequency at 2.4 times the nominal speed. No problems related to resonance have occurred at the hydropower unit during the last six months.

In almost all production of electricity the rotating machines serves as an important part of the energy transformation system. In hydropower units, a hydraulic turbine connected to a generator converts the potential energy stored in the water reservoir into electrical energy in the generator. An essential part of this energy conversion is the rotating system of which the turbine and the generator are crucial parts. During the last century the machines for production of electricity have been developed from a few megawatts per unit, up to several hundreds megawatts per unit. The development and increased size of the hydropower machines has also brought a need for new techniques. The most important developments are the increased efficiency of the turbines and generators, new types of bearings and the introduction of new materials. Vibration measurement is still the most reliable and commonly used method for avoiding failure during commissioning, for periodic maintenance, and for protection of the systems. Knowledge of the bearing forces at different operational modes is essential in order to estimate the degeneration of components and to avoid failures. In the appended Paper A, a method has been described for measurement of bearing load by use of strain gauges installed on the guide bearing bracket. This technique can determine the magnitude and direction of both static and dynamic loads acting on the bearing. This method also makes it possible to find the cause of the radial bearing force among the various eccentricities and disturbances in the system. This method was used in Paper C to investigate bearing stiffness and damping. A principal cause of many failures in large electrical machines is the occurrence of high radial forces due to misalignment between rotor and stator, rotor imbalance or disturbance from the turbine. In this thesis, two rotor models are suggested for calculation of forces and moments acting on the generator shaft due to misalignment between stator and rotor. These two methods are described in appended papers B and D. In Paper B, a linear model is proposed for an eccentric generator rotor subjected to a radial magnetic force. Both the radial force and the bending moment affecting the generator shaft are considered when the centre of the rotor spider hub deviates from the centre of the rotor rim. The magnetic force acting on the rotor is assumed to be proportional to the rotor displacement. In Paper D, a non-linear model is proposed for analysis of an eccentric rotor subjected to radial magnetic forces. Both the radial and bending moments affecting the generator shaft are considered when the centre of the generator spider hub deviates from the centre of the generator rim. The magnetic forces acting on the rotor are assumed to be a non-linear function of the air-gap between the rotor and stator. The stability analysis shows that the rotor can become unstable for small initial eccentricities if the position of the rotor rim relative to the rotor hub is included in the analysis. The analysis also shows that natural frequencies can decrease and the rotor response can increase if the position of the rotor rim in relation to the rotor spider is considered. In Paper E, the effect of damping rods was included in the analysis of the magnetic pull force. The resulting force was found to be reduced significantly when the damper rods were taken into account. An interesting effect of the rotor damper rods was that they reduced the eccentricity forces and introduced a force component perpendicular to the direction of eccentricity. The results from the finite-element simulations were used to determine how the forces affect the stability of the generator rotor. Damped natural eigenfrequencies and the damping ratio for load and no-load conditions were investigated. When applying the forces computed in the time- dependent model, the damped natural eigenfrequencies were found to increase and the stability of the generator rotor was found to be reduced, compared with when the forces were computed in a stationary model. Damage due to contact between the runner and the discharge ring have been observed in several hydroelectric power units. The damage can cause high repair costs to the runner and the discharge ring as well as considerable production losses. In Paper F a rotor model of a 45 MW hydropower unit is used for the analysis of the rotor dynamical phenomena occurring due to contact between the runner and the discharge ring for different grades of lateral force on the turbine and bearing damping. The rotor model consists of a generator rotor and a turbine, which are connected to an elastic shaft supported by three isotropic bearings. The discrete representation of the rotor model consist of 32 degrees of freedom. To increase the speed of the analysis, the size of the model has been reduced with the IRS method to a system with 8 degrees of freedom. The results show that a small gap between the turbine and discharge ring can be dangerous, due to the risk of contact with high contact forces as a consequence. It has also been observed that backward whirl can occur and in some cases the turbine motion becomes quasi-periodic or chaotic. The endurance of hydropower rotor components is often associated with the dynamic loads acting on the rotating system and the number of start-stop cycles of the unit. Measurements, together with analysis of the rotor dynamics, are often the most powerful methods available to improve understanding of the cause of the dynamic load. The method for measurement of the bearing load presented in this thesis makes it possible to investigate the dynamic as well as the static loads acting on the bearing brackets. This can be done using the suggested method with high accuracy and without re-designing the bearings. During commissioning of a hydropower unit, measurement of shaft vibrations and forces is the most reliable methods for investigating the status of the rotating system. Generator rotor models suggested in this work will increase the precision of the calculated behaviour of the rotor. Calculation of the rotor behaviour is important before a generator is put in operation, after overhaul or when a new machine is to be installed.

Asymmetry of the magnetic field in a synchronous generator will induce a magnetic unbalance pull. In this paper, a hydropower rotor system is modelled and the influence of electro-mechanical forces due to different amounts of real power is analysed. The electromagnetic field is solved with the finite element method and coupled with mechanical system as a magnetic stiffness. The mechanical model of the generator consists of a four degree of freedom rigid disc connected to an elastic shaft supported by two bearings with linear properties. It has been found that the unbalance magnetic pull increases for a lover amount of real power leading to a decrease of natural frequencies and an increase of unbalance response. Since many hydropower units are used for both part and full load it becomes important to model the electro-mechanical interaction when developing new generators, in order to improve the mechanical design.

In hydropower generators, the measurement of bearing load, vibration and shaft displacement are wildly used methods for indication of maintenance demand and troubleshooting. When measurement of bearing load and shaft displacement is performed the collected data make it possible to determine the bearing properties, such as stiffness and damping. In this paper a method to determine the bearing stiffness and damping properties for generator journal bearing in hydropower units is presented. The majority of hydropower generators are, however, not equipped with facilities for measurements of bearing loads. To provide the bearings with load sensors it is necessary to reconstruct the bearings, which is associated with heavy expenditures. In this paper an alternative method to obtain the bearing load is utilize, in which strain gauges installed on the generator bearing brackets is used. The collected data in the experiment were obtained from measurements on a 238 MW hydropower generator connected to a Francis type runner. The bracket that holds the generator bearing consists of 18 spokes and each of these spokes has been provided with strain gauges for load measurements. The displacement of the shaft has been measured relative to the generator-bearing casing. The generator-bearing model has been described as a system with two degrees of freedom containing both bearing stiffness and damping matrix as well as displacement and displacement velocity vector. When the calculation of the bearing properties are based on measured data, the irregularity in the calculated stiffness and damping has to be eliminated. To eliminate the unrealistic values of the calculated damping and stiffness, the samples that cause high condition numbers of the displacement - velocity matrix are neglected. The results of the calculation of bearing stiffness and damping are presented in polar plots. This method determines the bearing properties for the generator bearing in a certain point, the point where the generator shaft has its stationary position. The stationary position for the generator shaft depends on the static magnetic pull force acting on the generator rotor and the influence from the turbine. The influence on the bearing characteristics of non-stationary loads as acting on the bearing can be investigated. The non-stationary loads can for instance be rotor unbalance force, influence of thermal expansion and dynamical magnetic pull force. It is thereby possible to evaluate different loads effect on the generator bearing and in which way the bearing properties are affected. Copyright

In almost all production of electricity the rotating machines serves as an important part of the energy transformation system. In hydropower units, a hydraulic turbine connected to a generator converts the potential energy stored in the water reservoir into electrical energy in the generator. An essential part of this energy conversion is the rotating system of which the turbine and the generator are part. During the last century the machines for electricity production have been developed from a few mega watts per unit up to several hundreds mega watts per unit. The development and increasing of size of the hydropower machines have also brought a need for new techniques. The most important developments are the increased efficiency of the turbines and generators, new types of bearings and the introduction of new materials. Vibration measurements are still the most reliable and commonly used method to avoid failure during commissioning, for periodic maintenance, and as protection of the systems. Knowledge of the bearing forces in different operational modes is essential in order to estimate the degeneration of components and to avoid failures. In the appended Paper A, a method has been described for measurement of bearing load by use of strain gauges installed on the guide bearing bracket. This technique can determine the magnitude and direction of both static and dynamic loads acting on the bearing. This method also makes it possible to find the cause of the radial bearing force among the various eccentricities and disturbances in the system. A principal cause of many failures in large electrical machines is the occurrence of high radial forces due to misalignment between rotor and stator, rotor imbalance or disturbance from the turbine. In this thesis, two rotor models are suggested for calculation of forces and moments acting on the generator shaft depending on misalignment between stator and rotor. These two methods are described in appended papers B and C. In Paper B, a linear model is proposed for an eccentric generator rotor subjected to a radial magnetic force. Both the radial force and the bending moment affecting the generator shaft are considered when the centre of the rotor spider hub deviates from the centre of the rotor rim. The magnetic pull force acting on the rotor is assumed to be proportional to the rotor displacement. In Paper C, a non-linear model is proposed for analysis of an eccentric rotor subjected to radial magnetic force. Both the radial and bending moments affecting the generator shaft are considered when the centre of the generator spider hub deviates from the centre of the generator rim. The magnetic forces acting on the rotor are assumed to be a non-linear function of the air-gap between the rotor and stator. The stability analysis shows that the rotor can become unstable for small initial eccentricities if the rotor rim position relative to the rotor hub is included in the analysis. The analysis also shows that the natural frequencies can decrease and the rotor response can increase if the rotor rim position in relation to the rotor spider is considered. The endurance of hydropower rotor components is often associated with the dynamic loads acting on the rotating system and the number of start-stop cycles of the unit. Measurements together with analysis of the rotordynamics are often the most powerful methods available to improve understanding of the cause of the dynamic load. The method for measurement of bearing load presented in this thesis makes it possible to investigate the dynamic as well as the static loads as acting on the bearing brackets. This can be done using the suggested method with high accuracy and without redesign of the bearings. During commissioning of hydropower unit, measurements of shaft vibrations and forces are the most reliable method to investigate the status of the rotating system. Generator rotor models suggested in this work will increase the precision of the calculated behavior of the rotor. Calculation of the rotor behavior is important before the generator is put in operation, after rehabilitation or when new machines will be installed.