Control system design for flexible rotors supported by actively lubricated bearings

This article presents a methodology for calculating the gains of an output feedback controller for active vibration control of flexible rotors. The methodology is based on modal reduction. The proportional and derivative gains are obtained by adjusting the first two damping factors of the system and keeping the lengths of the two eigenvalues constant in the real-imaginary plane. The methodology is applied to an industrial gas compressor supported by active tilting-pad journal bearings. The unbalance response functions and mode shapes of the flexible rotor with and without active control are presented, showing significative improvement in damping reserve with the control. The importance of sensor location is emphasized, on the basis of the energy necessary to operate the active system over the entire frequency range studied. The best results are obtained by a decentralized controller, observing displacement and velocity of the shaft at the bearing positions.

Axial wedge effect in tilted hydrodynamic journal bearings

Hydrodynamic journal bearings are susceptible to static angular misalignment, resulting from improper assemblage, elastic and thermal distortion of the shaft and bearing housing, and also manufacturing errors. Several previous works on the theme, both theoretical and experimental, focused on the determination of the static properties of angular misaligned bearings. Although some reports show agreement between theoretical and experimental results, the increasingly severe operating conditions of hydrodynamic bearings (heavy loads and high rotational speeds) require more reliable theoretical formulations for the evaluation of the journal performance during the design process. The consideration of the angular misalignment in the derivation of the Reynolds equation is presented here in detail, showing that properly conducted geometric and magnitude-order analyses lead to the inclusion of an axial wedge effect term that influences the velocity and pressure fields in the lubricant film. Numerical results evidence that this axial wedge effect more significantly affects the hydrodynamic forces and static operational properties of tilted short journal bearings.

Influence of grease rheology on thrust ball bearings friction torque

The friction torque and the operating temperatures in a thrust ball bearing were measured for seven different types of greases, including three biodegradable greases having low toxicity. These friction torque tests were performed using a modified Four-Ball machine. Rheological evaluations of the lubricating greases were made using a rheometer. Bleed oils were extracted from the greases and the dynamic viscosities were measured. In order to compare the performance of the lubricant greases in terms of friction, the grease characteristics were related to experimental results, showing that the interaction between thickener and base oil have strong influences in the bearing friction torque.

Experimental measuring procedure for the friction torque in rolling bearings

The reduction of the power loss generated in mechanical transmissions and the use of low friction biodegradable lubricants has been attracting considerable attention in recent times. Therefore, it is necessary to develop methods to test and evaluate the performance of such lubricants and compare them with conventional ones. In this sense, a Four-Ball Machine was modified allowing the test of rolling bearings. A 51107 thrust ball bearing was used to test two different greases and the corresponding base oils. Friction torque and operating temperatures were continuously monitored to quantify the power loss and the heat evacuation for each lubricant tested. Copyright © 2010 John Wiley & Sons, Ltd.

Friction and wear in thrust ball bearings lubricated with biodegradable greases

Thrust ball bearings lubricated with several different types of grease, including three biodegradable low-toxicity greases, were tested in a modified four-ball machine in order to evaluate the bearing friction torque. At the end of each test, grease samples were obtained and analysed through ferrography, allowing the quantification and evaluation of the bearing wear. In order to compare the grease performance in terms of friction and wear, a correlation between the grease characteristics (base oil, bleed oil, thickener structure, and rheological parameters) and the experimental results was established.

Friction torque in grease lubricated thrust ball bearings

Thrust ball bearings lubricated with several different greases were tested on a modified Four-Ball Machine, where the Four-Ball arrangement was replaced by a bearing assembly. The friction torque and operating temperatures in a thrust ball bearing were measured during the tests. At the end of each test a grease sample was analyzed through ferrographic techniques in order to quantify and evaluate bearing wear. A rolling bearing friction torque model was used and the coefficient of friction in full film lubrication was determined for each grease, depending on the operating conditions. The experimental results obtained showed that grease formulation had a very significant influence on friction torque and operating temperature. The friction torque depends on the viscosity of the grease base oil, on its nature (mineral, ester, PAO, etc.), on the coefficient of friction in full film conditions, but also on the interaction between grease thickener and base oil, which affected contact replenishment and contact starvation, and thus influenced the friction torque.

Influence of grease formulation on thrust bearings power loss

The minimization of the power loss and the use of the biodegradable greases have attracting considerable attention. To compare the energetic performance of biodegradable lubricant greases, power loss tests were performed on a modified four-ball machine. A correlation between the grease formulation and rheology was established with its energetic performance

How to Get Your Bearings - How to Get A Job: A Guide for Women who are Unemployed, Underemployed, or Underpaid

A guide for women who are preparing to enter the workforce. Produced by the Iowa Commission on the Status of Women.

Problems of Bridge Supporting and Expansion Devices and an Experimental Comparison of the Dynamic Behavior of Rigid and Elastomeric Bearings, HR-105, 1965

The design of satisfactory supporting and expansion devices for highway bridges is a problem which has concerned bridge design engineers for many years. The problems associated with these devices have been emphasized by the large number of short span bridges required by the current expanded highway program of expressways and interstate highways. The initial objectives of this investigation were: (1) To review and make a field study of devices used for the support of bridge superstructures and for provision of floor expansion; (2) To analyze the forces or factors which influence the design and behavior of supporting devices and floor expansion systems; and (3) To ascertain the need for future research particularly on the problems of obtaining more economical and efficient supporting and expansion devices, and determining maximum allowable distance between such devices. The experimental portion was conducted to evaluate one of the possible simple and economical solutions to the problems observed in the initial portion. The investigation reported herein is divided into four major parts or phases as follows: (1) A review of literature; (2) A survey by questionnaire of design practice of a number of state highway departments and consulting firms; (3) Field observation of existing bridges; and, (4) An experimental comparison of the dynamic behavior of rigid and elastomeric bearings.

SIMULATION OF AMB SUPPORTED ROTOR DURING DROP ON RETAINER BEARINGS

The active magnetic bearings present a new technology which has many advantages compared to traditional bearing designs. Active magnetic bearings, however, require retainer bearings order to prevent damages in the event of a component, power or a control loop failure. In the dropdown situation, when the rotor drops from the magnetic bearings to the retainer bearings, the design parameters of the retainer bearings have a significant influence on the behaviour of the rotor. In this study, the dynamics of an active magnetic bearings supported electric motor during rotor drop on retainer bearings is studied using a multibody simulation approach. Various design parameters of retainer bearings are studied using a simulation model while results are compared with those found in literature. The retainer bearings are modelled using a detailed ball bearing model, which accounts damping and stiffness properties, oil film and friction between races and rolling elements. The model of the ball bearings includes inertia description of rollingelements. The model of the magnetic bearing system contains unbalances of the rotor and stiffness and damping properties of support. In this study, a computationally efficient contact model between the rotor and the retainer bearings is proposed. In addition, this work introduces information for the design of physicalprototype and its retainer bearings.

Dynamic Simulations of Rotors during Drop on Retainer Bearings

The active magnetic bearings have recently been intensively developed because of noncontact support having several advantages compared to conventional bearings. Due to improved materials, strategies of control, and electrical components, the performance and reliability of the active magnetic bearings are improving. However, additional bearings, retainer bearings, still have a vital role in the applications of the active magnetic bearings. The most crucial moment when the retainer bearings are needed is when the rotor drops from the active magnetic bearings on the retainer bearings due to component or power failure. Without appropriate knowledge of the retainer bearings, there is a chance that an active magnetic bearing supported rotor system will be fatal in a drop-down situation. This study introduces a detailed simulation model of a rotor system in order to describe a rotor drop-down situation on the retainer bearings. The introduced simulation model couples a finite element model with component mode synthesis and detailed bearing models. In this study, electrical components and electromechanical forces are not in the focus. The research looks at the theoretical background of the finite element method with component mode synthesis that can be used in the dynamic analysis of flexible rotors. The retainer bearings are described by using two ball bearing models, which include damping and stiffness properties, oil film, inertia of rolling elements and friction between races and rolling elements. Thefirst bearing model assumes that the cage of the bearing is ideal and that the cage holds the balls in their predefined positions precisely. The second bearing model is an extension of the first model and describes the behavior of the cageless bearing. In the bearing model, each ball is described by using two degrees of freedom. The models introduced in this study are verified with a corresponding actual structure. By using verified bearing models, the effects of the parameters of the rotor system onits dynamics during emergency stops are examined. As shown in this study, the misalignment of the retainer bearings has a significant influence on the behavior of the rotor system in a drop-down situation. In this study, a stability map of the rotor system as a function of rotational speed of the rotor and the misalignment of the retainer bearings is presented. In addition, the effects of parameters of the simulation procedure and the rotor system on the dynamics of system are studied.

Modeling dynamic behavior in tilting pad gas journal bearings

Thisresearch deals with the dynamic modeling of gas lubricated tilting pad journal bearings provided with spring supported pads, including experimental verification of the computation. On the basis of a mathematical model of a film bearing, a computer program has been developed, which can be used for the simulation of a special type of tilting pad gas journal bearing supported by a rotary spring under different loading conditions time dependently (transient running conditions due to geometry variations in time externally imposed). On the basis of literature, different transformations have been used in the model to achieve simpler calculation. The numerical simulation is used to solve a non-stationary case of a gasfilm. The simulation results were compared with literature results in a stationary case (steady running conditions) and they were found to be equal. In addition to this, comparisons were made with a number of stationary and non-stationary bearing tests, which were performed at Lappeenranta University of Technology using bearings designed with the simulation program. A study was also made using numerical simulation and literature to establish the influence of the different bearing parameters on the stability of the bearing. Comparison work was done with literature on tilting pad gas bearings. This bearing type is rarely used. One literature reference has studied the same bearing type as that used in LUT. A new design of tilting pad gas bearing is introduced. It is based on a stainless steel body and electron beam welding of the bearing parts. It has good operation characteristics and is easier to tune and faster to manufacture than traditional constructions. It is also suitable for large serial production.

Design and implementation of FPGA-based LQ control of active magnetic bearings

The need for high performance, high precision, and energy saving in rotating machinery demands an alternative solution to traditional bearings. Because of the contactless operation principle, the rotating machines employing active magnetic bearings (AMBs) provide many advantages over the traditional ones. The advantages such as contamination-free operation, low maintenance costs, high rotational speeds, low parasitic losses, programmable stiffness and damping, and vibration insulation come at expense of high cost, and complex technical solution. All these properties make the use of AMBs appropriate primarily for specific and highly demanding applications. High performance and high precision control requires model-based control methods and accurate models of the flexible rotor. In turn, complex models lead to high-order controllers and feature considerable computational burden. Fortunately, in the last few years the advancements in signal processing devices provide new perspective on the real-time control of AMBs. The design and the real-time digital implementation of the high-order LQ controllers, which focus on fast execution times, are the subjects of this work. In particular, the control design and implementation in the field programmable gate array (FPGA) circuits are investigated. The optimal design is guided by the physical constraints of the system for selecting the optimal weighting matrices. The plant model is complemented by augmenting appropriate disturbance models. The compensation of the force-field nonlinearities is proposed for decreasing the uncertainty of the actuator. A disturbance-observer-based unbalance compensation for canceling the magnetic force vibrations or vibrations in the measured positions is presented. The theoretical studies are verified by the practical experiments utilizing a custom-built laboratory test rig. The test rig uses a prototyping control platform developed in the scope of this work. To sum up, the work makes a step in the direction of an embedded single-chip FPGA-based controller of AMBs.

Numerical Simulation of the Cavitation in the Hydrodynamic Lubrication of Journal Bearings: a Parallel Algorithm

In this paper we present an algorithm for the numerical simulation of the cavitation in the hydrodynamic lubrication of journal bearings. Despite the fact that this physical process is usually modelled as a free boundary problem, we adopted the equivalent variational inequality formulation. We propose a two-level iterative algorithm, where the outer iteration is associated to the penalty method, used to transform the variational inequality into a variational equation, and the inner iteration is associated to the conjugate gradient method, used to solve the linear system generated by applying the finite element method to the variational equation. This inner part was implemented using the element by element strategy, which is easily parallelized. We analyse the behavior of two physical parameters and discuss some numerical results. Also, we analyse some results related to the performance of a parallel implementation of the algorithm.