Query: Tilting pad radial restrictor experiment

title: Towards Model Based Control Design for Flexible Rotors Supported by Active Tilting Pad Bearings Theory Experiment
abstract: deal with the targeted systems from a theoretical and experimental perspective simultaneously. Contrarily, rigid rotor systems are more profusely covered [13,14,34,23,20,21] In this framework, the main contribution of this work is fundamentally theoretical by presenting the modelling of flexible rotors when supported by active TPJBs. This modelling is based on the standard beam finite element formulation for the rotor and by including the full bearing matrices derived from an ETHD approach for the active TPJBs. This further includes the pad degrees of freedom (dofs) tilt, bending and radial movement and an extra dof the servovalve spool driven flow which makes the link between the mechanical and hydraulic systems. Special emphasis is given to the modelling of the different lubrication regimes by analysing the influence of the fluid film forces on the journal equilibrium and the bearing dynamic properties, leading to appropriated models for the passive, hybrid and active lubrication regimes. These models can be used for assisting the journal position changes under the hybrid lubrication regime or for designing modelbased state feedback controllers to develop the active lubrication, as presented next in part II. In this part, the hybrid lubrication is thoroughly covered and an integral controller derived using modelbased tools is used to aid the journal equilibrium position changes. This study on flexible rotor active bearing systems offers a more complete analysis that includes the flexible rotor dynamics and also serves to supplement the shortage identified previously. 2. The test rig facilities The rotor bearing test rig, shown in Fig. 1(a) resembles an industrial overhung centrifugal compressor. The driven torque is delivered through a flexible coupling connected to a layshaft, which is belt driven by an AC motor. The rotor is supported by a ball and an active TPJB at the driven and free end respectively. Discs can be overhung at the shaft free end to resemble impellers and to increase the gyroscopic effect. None, one and up to two discs can be suspended. Without discs the rotor behaves as a rigid rotor at frequencies below 150 Hz, whereas any extra disc means analysing it as a flexible one. The system can be excited either through an electromagnetic shaker connected to the excitation bearing at the shaft end or through the active magnetic bearing placed between bearings. The main design and operational characteristics of the test rig are summarized in Table 1. 2.1. The active TPJB and lubrication regimes The controllable bearing, schematized in Fig. 1(b) is a tilting pad journal bearing with 4 bronze pads in a load between pads configuration. The pad is centrally pivoted with a rocker type pivot. The active or controllable feature of the bearing is rendered by an electronic radial oil injection system as proposed by Santos  This injection system combines a hydrostatic with the hydrodynamic pressure distribution by injecting pressurized oil in the journal pad clearance through, in this case, a single centred nozzle aligned with the pivot line. The high pressure oil flow is injected by two high frequency response servovalves, where each one couples to a pairwise of counter pads. Such pad sets are orthogonally installed. This servovalve pad configuration enables us to freely exert controllable forces within the bearing plane so that any external force, such as imbalance, can be counteracted. One of the main components of the servovalve is the spool, whose position is driven by an input control signal which if set to positive, connects the supply port with one pad or if set to negative with the counter pad. With a zero input control signal, the servovalve's spool is centred to keep both ports closed, hence blocking the flow to the pads. However, due to tight fabrication tolerances between spool lands and ports being difficult to produce, the spool lands underlap the ports and a small leakage flow is always injected [39] Further design parameters are presented in Table 2. Fig. 2 depicts the layout of the hydraulic units connected to the active TPJB. This includes a flooding system for the conventional lubrication and the electronic radial oil injection system for developing the hybrid and active lubrication when enabled. These regimes, which are mathematically approached in the next section, can be further described as follows: The Passive Lubrication Regime: provides the main bearing dynamic properties and its load carrying capacity due to the hydrodynamic lubrication. There is no controller implemented. It also acts as backup in case of failure of the radial oil injection system. This regime is utilized for benchmarking. The Hybrid Lubrication Regime: in this regime, which is one of the research objectives of this work, the high pressure unit is turned on and the hydrostatic contribution to the pressure build up is enabled. Depending on the servovalve's spool position, the high pressurized oil can be permanently injected by different pad combinations, leading to a change of the journal equilibrium position within the "x y" plane and hence on the bearing dynamic properties. For horizontal machines, injecting from bottom pads has shown to produce a vertical bearing softening [40] and to reduce the system response amplitude  In general terms, the higher the supply pressure the easier it is to change the journal equilibrium position. By using feedback signals, this regime can be aided by integral controllers to attain or maintain a predefined equilibrium, especially when servovalve dynamics are unequal  The Active Lubrication Regime: if the control signals driving the servovalves are defined by a control law, then the hydrostatic fluid film force exerted over the journal can be actively controlled. This is achieved by using the system lateral movements or their estimates as feedback signals to synthesize classical or model based control laws. This was carried out in [26] based on proportional derivative controllers, which have been also used to demonstrate the bearing properties modification by control laws in [17,19] Provided a reliable rotor bearing system model, system states can be estimated so that model based state feedback controllers can be designed and implemented. 3. The rotor active TPJB modelling The framework for the modelling of flexible rotor supported by active TPJBs when featuring the three lubrication regimes is set. Firstly, the generalized governing equations are obtained upon the linearisation of the equation of motion subjected to the fluid film nonlinear forces. Then, the modelling of the active TPJB through the ETHD approach is briefly addressed. Full bearing dynamic coefficients, which includes the pads and hydraulic dynamics, are reviewed for the three regimes. Lastly, the coupling of the active TPJB properties with a beam based finite element model of the rotor is covered. Table 3 summarizes the contribution of dofs from each subsystem, which will be used throughout this section. The rotor subsystem introduces 4 dofs per node, two translational and two rotational. The pads introduce three dofs per pad: the pad tilt, bending and radial translation (due to the pivot flexibility) Finally, two extra dofs are introduced because of the hydraulic system, one per servovalve. 3.1. Linking the rotor bearing with the hydraulic dynamics for the different lubrication regimes Fig. 3 presents the mechanical model of the integrated rotor active 1 Other configurations may also be developed, such as multi orifice pads [16,35 37] or shifted nozzle pads [38] J.G. Salazar, I.F. Santos Tribology International 107 (2017) 94 105

title: Running Performance of a Squeeze Film Air Bearing with Flexure Pivot Tilting Pad
abstract: A novel flexure pivot tilting pad squeeze film air bearing (FPTP SFAB) based on near field acoustic levitation (NFAL) for a rotor is proposed in this article. The most important advantage of this structure is the suitability of the bearing for high speed and light load conditions because the FPTP can adapt well to squeeze action during operation. The rotating orbit of the rotor can be adjusted according to the machining conditions. A theoretical model is employed to analyze the running characteristics of the rotor by using the coupled NFAL and FPTP model. Experiments were conducted to investigate the running performance of the rotor bearing system. Moreover, the effects of input voltage, rotational speed, eccentricity ratio, radial clearance, vibration amplitude, and installation method on bearing performance were analyzed. Numerical and experimental results show that a rotor supported by the FPTP SFAB with a reasonable input excitation magnitude can effectively adjust the rotating orbit of the rotor and inhibit the divergence of the rotor vibration amplitude, thus improving the stability of the rotor bearing system under complicated and alternating machining conditions.

title: Model based nonlinear control of active tilting pad bearings
abstract: A promising mechanical bearing candidate for active operation is the tilting pad bearing. The proposed active tilting pad bearing has linear actuators that radially translate each pad. The use of feedback control in determining the actuator forces allows for the automatic, continuous adjustment of the pad position during the operation of the rotating machine. In the first part of the dissertation, we develop a nonlinear dynamic model of the active bearing system. The hydrodynamic force produced by the fluid film is modeled as a nonlinear, squeeze film damper plus repellent spring. A model based nonlinear controller is then designed to exponentially regulate the rotor position to the origin. A proof of concept experiment shows that the active strategy improves the bearing performance relative to its traditional passive operation. Further, the experiment demonstrates that the model based nonlinear control regulates the rotor comparably to a linear PID control, but requires significantly less control energy. The second part of the dissertation introduces a new type of active fluid film bearing which actively adjusts the angular velocity of the pads of a tilting pad bearing. This is motivated by the observation that there is more control authority in the pad tilting motion than in its radial translation. To this end, a dynamic model for the bearing system is developed, inclusive of the nonlinear hydrodynamic force for the infinitely short bearing case. A model based controller is then constructed, based on measurements of the journal position and velocity and pad tilting angles, to ensure that the journal is asymptotically regulated to the bearing center. Numerical simulations illustrate the performance of the active bearing under the proposed control in comparison with the bearing's standard passive mode of operation.

title: Model based nonlinear control of active tilting pad bearings
abstract: A promising mechanical bearing candidate for active operation is the tilting pad bearing. The proposed active tilting pad bearing has linear actuators that radially translate each pad. The use of feedback control in determining the actuator forces allows for the automatic, continuous adjustment of the pad position during the operation of the rotating machine. In the first part of the dissertation, we develop a nonlinear dynamic model of the active bearing system. The hydrodynamic force produced by the fluid film is modeled as a nonlinear, squeeze film damper plus repellent spring. A model based nonlinear controller is then designed to exponentially regulate the rotor position to the origin. A proof of concept experiment shows that the active strategy improves the bearing performance relative to its traditional passive operation. Further, the experiment demonstrates that the model based nonlinear control regulates the rotor comparably to a linear PID control, but requires significantly less control energy. The second part of the dissertation introduces a new type of active fluid film bearing which actively adjusts the angular velocity of the pads of a tilting pad bearing. This is motivated by the observation that there is more control authority in the pad tilting motion than in its radial translation. To this end, a dynamic model for the bearing system is developed, inclusive of the nonlinear hydrodynamic force for the infinitely short bearing case. A model based controller is then constructed, based on measurements of the journal position and velocity and pad tilting angles, to ensure that the journal is asymptotically regulated to the bearing center. Numerical simulations illustrate the performance of the active bearing under the proposed control in comparison with the bearing's standard passive mode of operation.

title: Influence of cross coupling stiffness in tilting pad journal bearings for vertical machines
abstract: This paper evaluates how cross coupling coefficients affects the dynamics of a vertical rotor with tilting pad journal bearings. For vertical machines, the bearing properties are dependent on the bearing load and direction. As a result, it generally requires that bearing properties are calculated at each time step using the governing fluid dynamic equations. This method gives a good representation of the bearing but computational time increases and can cause stability problems. In this study the bearing properties are instead modelled as a function of eccentricity and its direction. Hence, the bearing properties can be evaluated at each time step without solving Navier Stokes or Reynold's equation. The main advantage of using this method is to decrease the computational time. The cross coupling stiffness and damping coefficients are usually neglected since they are small compared to the radial stiffness and damping coefficients. In this paper, the simulated unbalanced response is compared to experimental results and it is seen that the cross coupling stiffness for vertical machines can influence the dynamics. It is shown that the cross coupling can be of the same order of magnitude as the radial stiffness component depending on the shaft angular position in the bearing. Including cross coupling increases higher frequency components and the experiments show similar behaviour. Hence the cross coupling stiffness and damping coefficients should be included when simulating vertical machines subjected to high loads or when the detailed dynamical behaviour is important to investigate.

title: Steady state characteristics of a tilting pad journal bearing with controllable lubrication: Comparison between theoretical and experimental results
abstract: This paper is aimed at presenting results regarding the static and thermal behavior of a tilting pad journal bearing operating under controllable regime. The bearing is rendered controllable by injecting high pressure oil into the clearance using holes drilled across the bearing pads in the radial direction. The modification of the injection pressure enables to modify the bearing static and dynamic properties according to the operational needs. The results presented are obtained using a theoretical model, which considers all the effects that determine the bearing behavior (controllable elastothermohydrodynamic lubrication regime) as well as using a test rig designed and built to this effect. The comparison between experimental and theoretical results provides solid ground to determine the accuracy of the available model for the the prediction of the steady state behavior of the tilting pad bearing with controllable lubrication. Among the parameters considered for the study are: oil film temperature field, resulting forces over rotor and pads, and rotor equilibrium position. The results obtained show good agreement between theory and experiment, as long as the assumptions on which the model is based are respected. Also, it is shown that some improvements are possible when it comes to model the steady state behavior of the controllable bearing with the injection system turned off.

title: Increase of Operational Safety of Tilting Pad Journal Bearings by Extraction of Hot Oil at the Trailing Edge
abstract: A theoretical study is presented with the main objective on the operational safety parameters (minimum film thickness and maximum pad temperature) and thermomechanical deformations of a o500 mm rocker pad tilting pad journal bearing (TPJB) for application in large turbo machinery. It can be described by the following specifications: Five pads, 0.23 nominal preload, 60% offset, 56deg pad arc angle, 350 mm pad length and 1.28%0 relative bearing clearance. Theoretical investigations are carried out for circumferential speeds up to 78 m/s and static loads up to 3.60 MPa.The simulation tool simultaneously solves both Reynolds and energy equations for the oil film (3D temperature distribution) on the one hand and computes thermomechanical deformations of the pad on the other hand. The simulations are conducted for a single pad and are supported by boundary conditions taken from experiments. The results with regard to static bearing characteristics and pad deformation show good agreement with experiments.The impact of axial pad arching on operational safety parameters and load carrying capacity are shown and compared to experimental results. It is shown that the axial deviation in film thickness Dh can be even higher than the minimum film thickness hmin. This leads to reduced hydrodynamic pressure build up towards the axial edges and therefore significantly decreased safety parameters or load carrying capacity.In order to reduce pad crowning, radial bores through the pad body are modelled to simulate the extraction of hot oil from the trailing edge. In the simulation, the hot oil is used to heat up the back of the pad for a decrease of radial temperature gradients and thus pad arching. It is shown that by extracting 0.4 l/s of hot oil, a decrease in axial pad crowning from Dh 47mm to Dh 26mm can be achieved and that this leads to a decrease of 7.8 K in maximum temperature and an increase of 5 mm in minimum film thickness respectively a gain of load carrying capacity of 0.4 0.6 MPa.

title: Constrained Optimization of Gas Turbine Tilting Pad Bearing Designs
abstract: This paper presents the constrained optimization of the tilting pad bearing design on a gas turbine rotor system. A real coded genetic algorithm with a robust constraint handling technique is used as the optimization method. The objective is to develop a formulation of the optimization problem for the late bearing design of a complex rotor bearing system. Furthermore, the usefulness of the search method is evaluated on a difficult problem. The effects considered are power loss and limiting temperatures in the bearings as well as the dynamics at the system level, i.e. stability and unbalance responses. The design variables are the bearing widths and radial clearances. A nominal design is the basis for comparison of the optimal solution found. An initial numerical experiment shows that finding a solution that fulfills all the constraints for the system design is likely impossible. Still, the optimization shows the possibility of finding a solution resulting in a reduced power loss while not violating any of the constraints more than the nominal design. Furthermore, the result also shows that the used search method and constraint handling technique works on this difficult problem.

title: Computational Fluid Dynamics Based Mixing Prediction for Tilt Pad Journal Bearing TEHD Modeling Part II: Implementation With Machine Learning
abstract: Reynolds based thermo elasto hydrodynamic (TEHD) simulations of tilting pad journal bearings (TPJBs) generally provide accurate results; however, the uncertainty of the pad's leading edge thermal boundary conditions causes uncertainty of the results. The highly complex thermal flow mixing action between pads (BPs) results from the oil supply nozzle jets and geometric features. The conventional Reynolds approach employs mixing coefficients (MCs) estimated from experience, to approximate a uniform inlet temperature for each pad. Part I utilized complex computational fluid dynamics (CFD) flow modeling to illustrate that temperature distributions at the pad inlets may deviate strongly from being uniform. The present work retains the uniform MC model but obtains the MC from detailed three dimensional CFD modeling and machine learning, which could be extended to the radially and axially varying MC case. The steps for implementing an artificial neural network (ANN) approach for MC regression are provided as follows: (1) utilize a design of experiment step for obtaining an adaptable training set, (2) conduct CFD simulations on the BP to obtain the outputs of the training set, (3) apply an ANN learning process by Levenverg Mardquart backpropagation with the Bayesian regularization, and (4) couple the ANN MC results with conventional TEHD Reynolds models. An approximate log fitting method provides a simplified approach for MC regression. The effectiveness of the Reynolds TEHD TPJB model with ANN regression based MC distributions is confirmed by comparison with CFD based TEHD TPJB model results. The method obtains an accuracy nearly the same as the complete CFD model, but with the computational economy of a Reynolds approach.

title: Experimental and Analytical Studies on Flexure Pivot Tilting Pad Gas Bearings With Dampers Applied to Radially Compliant Pads
abstract: Hydrodynamic flexure pivot tilting pad gas bearings (FPTPGBs) can enable successful operation of oil free microturbomachinery and FPTPGBs with radially compliant pads permit rotor centrifugal and/or thermal growth to exceed original bearing clearances and achieve higher speeds. This work presents the experimental and analytical study of such bearings and the application of dampers behind the pad radial compliance structure. A time domain orbit simulation method was implemented as the primary analysis tool to predict the rotor bearing response to imbalance, the presence and location of critical speeds, etc. and to compare with test results. Experiments demonstrate the stable hydrodynamic operation of FPTPGBs with an ~28.6 mm, 0.8 kg rotor above 120 krpm, for the first time. The rotor bearing system was intentionally destabilized in tests by increasing bearing clearances and the viscoelastic dampers added behind the FPTPGB pads delayed the onset of subsynchronous vibrations (from 43 krpm without damper to above 50 krpm with damper) Midrange subsynchronous vibrations of the destabilized system initiated at ~20 krpm were suppressed by ~25 krpm due to the stabilizing effect of rotor centrifugal growth. The viscoelastic dampers had a negligible effect on suppressing these midrange subsynchronous vibrations in experiments, but this was not demonstrated in simulations, presumed to be due to much lower stiffness contribution of the damper at lower frequencies.