In 2015, a 45 MW vertical hydropower machine exhibited excessive vibration after refurbishment. Measurements revealed a substantial bearing clearance at the lower generator guide bearing. Consequently, the bearing was unable to generate sufficient opposing force to drive the rotor toward the bearing center, resulting in more pronounced overall system vibration. Addressing this challenge required a cost-effective and feasible solution for mitigating the vibration problem. To this end, a design modification was implemented wherein the lower generator guide bearing (originally a sleeve bearing) was modified to a four-lobe bearing by offsetting the two halves of the bearing twice in two axes. Numerical simulations and experimentations were conducted, and the dynamics of the machine before and after the design modification were investigated. Both the simulation and experimental results showed that the machine with the four-lobe bearing improved the system stability and reduced the vibration amplitudes. The numerical simulation result demonstrated that, due to the design modification, the first and second critical speeds were effectively eliminated for a speed range of up to three times the nominal speed. Furthermore, for nominal operation with unbalanced magnetic pull, the four-lobe bearing provided a stability advantage in terms of the modal parameters relative to the original sleeve bearing.

The dynamic properties of rotating machines are highly influenced by supporting elements, such as bearings, seals, damping elements or housings. They play a significant role in regulating the characteristics of the interaction between the rotating and stationary parts of machines. Over the past few years, numerous research studies have been published focusing on the dynamics of such devices across a wide range of applications. The advancement of the research has significantly contributed to enhancing their performance and ensuring the smooth operation of rotating machinery by minimizing excessive vibrations that can lead to catastrophic failure. The research work in this thesis explores the dynamics of supporting elements in vertical rotating machinery, with a particular focus on hydropower applications. In fact, some of the concepts are generic and can be applied to horizontal rotors or any other types of rotating machines. Using numerical simulation and actual measurements, their contribution to the system’s overall performance was investigated. These include the self-induced vibration in vertical application tilting pad journal bearings, and vibration issues observed on a hydropower unit attributed to large bearing clearance. Also, particular attention was given to the influence of the squeeze film damper on the rotor-stator contact dynamics of hydropower units, using tools such as Poincaré maps and bifurcation diagrams.

Moreover, achieving optimal design of such devices requires, among other key aspects, accurate and reliable simulation models to facilitate the prediction and evaluation of their characteristics at any stage in the product development process. In rotordynamic simulations, a common approach for incorporating bearing forces in the system equation is by representing them with stiffness and damping coefficients. For a small vibrational amplitude about a static position, linearized bearing coefficient assumptions can be valid. This is especially applicable for operation under a large radial static load, such as in horizontal rotors, due to the dead weight of the rotor. For vertical rotors, however, the weight of the rotor acts axially, and the radial bearing load is usually low. The bearing coefficients show nonlinearity, making them dependent on the trajectory of the rotor. Therefore, the linear bearing assumption, which is valid for horizontal rotors, does not hold true for vertical rotors. This makes the simulation of a vertical machine more complicated as it typically involves solving the fluid film lubrication model. The classical numerical models can sometimes be computationally demanding and require impractically long computational time. An efficient and fast numerical simulation method which does not significantly affect the accuracy of the result is critical to facilitating the simulation processes effectively. This thesis details the suggested simplifications employed on the bearing models and transformation matrices in the numerical integration procedure. The results from these models were validated using experiments to ensure their reliability.

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. 

Rotodynamic simulation of complex or/and large systems, for instance hydropower machines, may consist of models with many degrees of freedom and require multidisciplinary computations such as fluid-thermal-structure interactions or rotor-stator interactions due to electromagnetic forces. Simulating such systems is often computationally heavy and impractical, especially in the case of optimization or parametric study, where many iterations are required. This has, therefore, created a need for simplified dynamic models to improve computational efficiency without significantly affecting the accuracy of the simulation result. The purpose of this paper is to present simplified coordinate transformation matrices for journal bearings in vertical rotors, which require less computational effort. Matrix multiplications, which appear during coordinate transformation, were eliminated, and the bearing stiffness and damping matrices in the fixed reference frame were represented by local coefficients instead. The dynamic response of a vertical rotor with eight-shoe Tilting pad journal bearings was simulated using the proposed model for two operational conditions, i.e., when the rotor was spinning at constant and variable speeds. The results from the proposed model were compared to those from the original model and validated through experiments. The conclusion was that the presented simulation model is time efficient and can effectively be used in rotordynamic simulations and analyses.

In this paper, the dynamics of tilting pad journal bearings with four and eight pads are studied and compared experimentally and numerically. The experiments are performed on a rigid vertical rotor supported by two identical bearings. Two sets of experiments are carried out under similar test setup. One set is performed on a rigid rotor with two four-pad bearings, while the other is on a rigid rotor with two eight-pad bearings. The dynamic properties of the two bearing types are compared with each other by studying the unbalance response of the system at different rotor speeds. Numerically, the test rig is modeled as a rigid rotor and the bearing coefficients are calculated based on Navier-Stokes equation. A nonlinear bearing model is developed and used in the steady state response simulation. The measured and simulated displacement and force orbits show similar patterns for both bearing types. Compared to the measurement, the simulated mean value and range (peak-to-peak amplitude) of the bearing force deviate with a maximum of 16 % and 38 %, respectively. It is concluded that, unlike the eight-pad TPJB, the four-pad TPJB excite the system at the third and fifth-order frequencies, which are due to the number of pads, and the amplitudes of these frequencies increase with the rotor speed. 

Many dynamic simulations of a rotor with a journal bearing employ non-linear fluid-film lubrication models and calculate the bearing coefficients at each time step. However, calculating such a simulation is tedious and computationally expensive. This paper presents a simplified dynamic simulation model of a vertical rotor with tilting pad journal bearings under constant and variable (transient) rotor spin speed. The dynamics of a four-shoes tilting pad journal bearing are predefined using polynomial equations prior to the unbalance response simulations of the rotor-bearing system. The Navier–Stokes lubrication model is solved numerically, with the bearing coefficients calculated for six different rotor speeds and nine different eccentricity amplitudes. Using a MATLAB inbuilt function (poly53), the stiffness and damping coefficients are fitted by a two-dimensional polynomial regression and the model is qualitatively evaluated for goodness-of-fit. The percentage relative error (RMSE%) is less than 10%, and the adjusted R-square (R²_adj) is greater than 0.99. Prior to the unbalance response simulations, the bearing parameters are defined as a function of rotor speed and journal location. The simulation models are validated with an experiment based on the displacements of the rotor and the forces acting on the bearings. Similar patterns have been observed for both simulated and measured orbits and forces. The resultant response amplitudes increase with the rotor speed and unbalanced magnitude. Both simulation and experimental results follow a similar trend, and the amplitudes agree with slight deviations. The frequency content of the responses from the simulations is similar to those from the experiments. Amplitude peaks, which are associated with the unbalance force (1 × Ω) and the number of pads (3 × Ω and 5 × Ω), appeared in the responses from both simulations and experiments. Furthermore, the suggested simulation model is found to be at least three times faster than a classical simulation procedure that used FEM to solve the Reynolds equation at each time step.