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Strategies are required to reduce vibrations in machines that use rotor systems, as these disturbances reduce the life and quality of the machine. A novel low-frequency on-board counter-bend actuator topology has been designed in order to control high frequency vibrations by taking advantage of synchronous forces from the rotating frame of a rotor supported by Active Magnetic Bearings (AMBs). The AMBs ensure in return stable contact-free levitation of the rotor. A complete model of the rotor system is established, based on a finite element representation of the rotor. The feedback control forces of the AMBs are described to account for the non-collocation of the sensor and actuation, and the PD controller gains are chosen using the sensitivity function. The lowest frequency mode of the operating range is located at 2,700 RPM, and time domain analysis shows that the application of symmetric 80 N.m counter-bend moments on the rotor coupling flanges can reduce the vibration amplitude by 88% at this rotation speed.

Passive rotors are often limited in rotational speed due to bearing constraints, stability and excessive vibration levels. To address the vibration issue, Active Magnetic Bearings (AMBs) levitating the rotor with a magnetic field can be used. They offer a clearance and variable stiffness and damping to the rotor support, which help to mitigate greatly the vibration issue. However, they are also limited at large rotational speed because of the high frequency control force required to levitate the rotor safely. To overcome the frequency limitation, a dual AMBs/internal bending control concept is investigated with associated modelling and control algorithms. This approach is examined in simulation with a 19 kg rotor running up to 10,000 RPM, where three resonance frequencies are present at 2700, 5300, and 9300 RPM, with the first resonant frequency being the most strongly excited. Using internal rotor bending control, a maximum radial displacement of 15 μm for the rotor mid-point is achieved, which gives a reduction in vibration amplitude of 45% compared to the case of no control. Variations of the algorithm are presented and discussed, showing the potential of the proposed approach.

The actuation and energy-harvesting performance of dielectric elastomers are strongly related to their intrinsic electrical and mechanical properties. For future resilient smart transducers, a fast actuation response, efficient energy-harvesting performance, and mechanical robustness are key requirements. In this work, we demonstrate that poly(styrene-butadiene-styrene) (SBS) can be converted into a self-healing dielectric elastomer with high permittivity and low dielectric loss, which can be deformed to large mechanical strains; these are key requirements for actuation and energy-harvesting applications. Using a one-step click reaction at room temperature for 20 min, methyl-3-mercaptopropionate (M3M) was grafted to SBS and reached 95.2% of grafting ratios. The resultant M3M-SBS can be deformed to a high mechanical strain of 1000%, with a relative permittivity of ϵr = 7.5 and a low tan δ= 0.03. When used in a dielectric actuator, it can provide 9.2% strain at an electric field of 39.5 MV m-1 and can also generate an energy density of 11 mJ g-1 from energy harvesting. After being subjected to mechanical damage, the self-healed elastomer can recover 44% of its breakdown strength during energy harvesting. This work demonstrates a facile route to produce self-healing, high permittivity, and low dielectric loss elastomers for both actuation and energy harvesting, which is applicable to a wide range of diene elastomer systems.

Active magnetic bearing systems provide contact-free rotor levitation, which allows near frictionless rotation and high rotational speeds when they operate normally. Under certain operational conditions, a transient fault, overload condition, or disturbance may occur. Touchdown bearings or bushings are therefore implemented in such systems to prevent contact between rotor and stator laminations. If the rotor makes contact with a touchdown bearing, the rotor dynamics may become transient or persistent in contact. Appropriate control strategies through the magnetic bearings to restore contact-free rotor operation may extend the life of touchdown bearings, and minimise operational downtime. To achieve this, an understanding of the contact dynamics is required, together with the relationship between contact and magnetic bearing forces. In this paper, rotor/touchdown bearing contact conditions are investigated experimentally using an active magnetic bearing system with a flexible rotor. Design methodology is presented for a measurement system capable of providing rotor/touchdown bearing contact related data, based on strain measurement. Strain induced contact signals are calibrated against applied magnetic bearing forces. The frequency dependent behaviour of the active magnetic bearing system is considered using evaluated force and phase measurements. The measurement data represent system identification for the potential of active magnetic bearing force-based contact control.

The introduction of active magnetic bearings (AMBs) has enabled turbomachinery to increase power density, controllability, and general resilience to external disturbances. However, because of the limited load capacity of AMBs, the base shock condition that "on-board" machines often encounter may result in contact between the rotor and the touchdown bearings (TDBs), which can seriously damage the machine. A challenge in AMB applications is to alleviate this problem. This study presents a dynamic analysis of a rotor-AMB-TDB system under strong base shocks while the AMBs are operating. Detailed TDB and contact models are presented using Hertzian contact theory. A PD controller was then designed considering system saturation and friction, based on the Coulomb model and the effect of lubrication. The dynamic equations were solved for the dynamic trajectory and FFT spectra, STFT spectra, Poincaré maps and bifurcation diagrams were used for the parametric analysis. The results show that the rotor had three motion modes. System parameters, including unbalance eccentricity, magnetic gap clearance and equivalent stiffness and damping ratio, may lead to complex nonlinear dynamic behavior including periodic, KT-periodic, and quasi-periodic responses and jump phenomenon. Suitable designs that consider these parameters may avoid undesirable rotor dynamic behavior. This study reveals the mechanism for nonlinear response, providing a method for its prediction, and core controller parameter designs for rotor re-levitation.

Active magnetic bearings (AMBs) have limited dynamic load capacity due to magnetic saturation. Hence, large external disturbances (such as shock loads) may cause contact between the rotor and touchdown bearings (TDBs), which may evolve into complex dynamic behaviour and damage the machine. This paper considers the shock responses of a rotor and viable re-levitation control options when the AMB is still functional. Bi-stable responses and shock-induced persistent forward rubbing were observed in an experimental AMB-flexible rotor facility and its numerical model. The analytical solution for steady synchronous motions with rubbing of a general AMB-flexible rotor system was proposed. The standard control action for a contact-free rotor state would not be appropriate due to phase changes and the displacement amplitude differences in the frequency responses. To destabilise the persistent contact responses and restore contact-free levitation, open-loop phase search based synchronous compensation (PSSC) control and synchronous motion compensation (SMC) control are designed, which are activated when a persistent contact is detected. Stability of the control system and the effectiveness of these two re-levitation control methods are verified by simulation and experimental results. It is also found by comparison that the efficiency of PSSC depends on the phase difference (incorrect phases may degrade rotor response), while the SMC consumes more computing effort.

A new approach for the recovery of contact-free levitation of a rotor supported by active magnetic bearings (AMB) is assessed through control strategy design, system modelling and experimental verification. The rotor is considered to make contact with a touchdown bearing (TDB), which may lead to entrapment in a bi-stable nonlinear response. A linear matrix inequality (LMI) based gain-scheduling H ∞ control technique is introduced to recover the rotor to a contact-free state. The controller formulation involves a time-varying effective stiffness parameter, which can be evaluated in terms of forces transmitted through the TDB. Rather than measuring these forces directly, an observer is introduced with a model of the base structure to transform base acceleration signals using polytopic coordinates for controller adjustment. Force transmission to the supporting base structure will occur either through an AMB alone without contact, or through the AMB and TDB with contact and this must be accounted for in the observer design. The controller is verified experimentally in terms of (a) non-contact robust stability and vibration suppression performance; (b) control action for contact-free recovery at typical running speeds with various unbalance and TDB misalignment conditions; and (c) coast-down experimental tests. The results demonstrate the effectiveness of the AMB control action whenever it operates within its dynamic load capacity.

Purpose The purpose of this paper is to present an optimal posture evaluation model to control the assembly gaps in aircraft wing assembly. The gaps between two mating surfaces should be strictly controlled in precision manufacturing. Oversizing of gaps will decrease the dimensional accuracy and may reduce the fatigue life of a mechanical product. To reduce the gaps and keep them within tolerance, the relative posture (orientation and position) of two components should be optimized in the assembly process. Design/methodology/approach Based on the step alignment strategy, i.e. preliminary alignment and refined alignment, the concept of a small posture transformation (SPT) is introduced. In the preliminary alignment, an initial posture is estimated by a set of auxiliary locating points, with which the components can be quickly aligned near each other. In the refined alignment, the assembly gaps are calculated and the formulation of the gaps with component posture is derived by the SPT. A comprehensive weighted minimization model with gap tolerance constraints is established for redistributing the gaps in multi-regions. Powell-Hestenes-Rockafellar optimization, Singular Value Decomposition and K-Dimensional tree searching are introduced for the solution of the optimal posture for localization. Findings Using the SPT, the trigonometric posture transformation is linearized, which benefits the iterative solution process. Through the constrained model, overall gaps are minimized and excess gaps are controlled within tolerance. Practical implications This method has been tested with simulated model data and real product data, the results of which have shown efficient coordination of mating components. Originality/value This paper proposed an optimal posture evaluation method for minimizing the gaps between mating surfaces through component adjustments. This will promote the assembly automation and variation control in aircraft wing assembly.

This paper deals with optimal controller design for active magnetic bearing (AMB) systems for which nonlinear rotordynamic behavior is evident, and so vibration predicted by operating point linearization differs from that which occurs in actuality. Nonlinear H-infinity control theory is applied with a rotordynamic model involving nonlinear stiffness and/or damping terms. The associated Hamilton-Jacobi-Isaacs (HJI) equation is formulated and solved to obtain a state feedback control law achieving specified vibration attenuation performance in terms of the peak L2 gain of the nonlinear system. The method is applied in case study to a flexible rotor/AMB system that exhibits nonlinear stiffness properties owing to rotor interaction with a clearance bearing. Simulations are performed to quantify RMS vibration due to harmonic disturbances and the results compared with the norm-bound values embedded in the HJI equations. A feedback controller design method is then presented that is similar in approach to the standard loop-shaping/mixed-sensitivity methods used for linear systems, and involves augmenting the system model with weighting transfer functions. Experiments are undertaken to compare controller performance for designs based on nonlinear and linearized models. The results highlight the shortcomings of applying linear optimal control methods with rotor systems exhibiting nonlinear stiffness properties as large amplitude vibration and loss of rotordynamic stability can occur. Application of the described nonlinear H-infinity control method is shown to overcome these problems, albeit at the expense of vibration attenuation performance for operation in linear regimes.

This paper presents a new ceiling-mounted workshop Measurement Positioning System (C-wMPS) compensating for many deficiencies shown by conventional metrology systems, especially on the possibility of task-oriented designing for coverage ability, measurement accuracy and efficiency. A hybrid calibration system consisting of a high-precision coordinate control field and standard lengths is developed and implemented for the C-wMPS, which can be designed concretely to provide both traceability and the ability of local accuracy enhancement. Layout optimization using a genetic algorithm based on grids is applied to design an appropriate layout of the system, therefore promotes the system's performance and reduce cost. An experiment carried out at the Guidance, Navigation and Control laboratory (GNC Lab, 40 × 30 × 12 m) validates the prominent characteristic of C-wMPS and the fitness of the new calibration system and layout optimization method.

In gas turbines, seals that reduce the leakage between high and low pressure regions are critical for improved performance. Damaging rubs between the rotating and non-rotating parts of turbomachinery shaft seals occur due to thermal and assembly misalignments, and rotordynamic vibration during engine start-up and shut-down transients. These rubs lead to increased seal leakage and hence to reduced overall turbine efficiency and life span. The Film Riding Pressure Actuated Leaf Seal (FRPALS) is a non-contacting compliant seal under development to adapt to varying clearances without rubbing, while maintaining low leakage. This paper presents the measurements of the FRPALS in a test rig specifically designed to test novel shaft seals for turbomachinery. The rig features a 254 mm diameter rotor with a maximum surface speed of 200 m/s. Pressure drops of up to 3.5 bar can be achieved. The results of initial testing at zero rotational speed are presented for the FRPALS in a reverse orientation. The opening and closing translations of the leaves have been measured using eddy current displacement probes targeting the movable parts of the seal. The seal clearance has been shown to remain constant for a range of applied pressure drops, which indicates the stable operation of the seal, though resulting in contact with the rotor at 1.5 bar. Mass flow leakage measurements have also demonstrated the sealing performance of the FRPALS. They show the potential of the seal to film ride subject to design modifications to maintain a more uniform film thickness. The steady-state Reynolds equation for lubrication has been used to predict the pressure along the seal clearance. The predictions have been compared with pressure measurements from a transducer located in the clearance fluid thin film.

The interaction of a polymer-steel spur gear pair is naturally prone to cause wear of the softer polymer material. Experimental equipment was therefore designed and constructed to run a polymer-steel spur gear pair with sufficiently accurate instrumentation such that the load and speed could be measured under a range of operating conditions. Plastic deformation features on the polymer teeth surface were observed through scanning electron microscopy and these are considered to be the primary sources of polymer gear wear during service. The wear mechanism is discussed and models are presented to describe the process by which it is created. This is due to the sliding/rolling under conforming contact conditions that are intrinsic to the involute spur gear pair. An iterative model based on the nonlinear properties of the polymer is presented, which shows how the material is deformed permanently and progressively under each load cycle. A second model also shows how the wear deformation features are created. Worn gear teeth were inspected and the quantity of material worn correlates well with the predicted wear volume.

Dielectric elastomers are of interest for actuator applications due to their large actuation strain, high bandwidth, high energy density, and their flexible nature. If future dielectric elastomers are to be used reliably in applications that include soft robotics, medical devices, artificial muscles, and electronic skins, there is a need to design devices that are tolerant to electrical and mechanical damage. In this paper, the first report of self‐healing of both electrical breakdown and mechanical damage in dielectric actuators using a thermoplastic methyl thioglycolate–modified styrene–butadiene–styrene (MGSBS) elastomer is provided. The self‐healing functions are examined from the material to device level by detailed examination of the healing process, and characterization of electrical properties and actuator response before and after healing. It is demonstrated that after dielectric breakdown, the initial dielectric strength can be recovered by up to 67%, and after mechanical damage, a 39% recovery can be achieved with no degradation of the strain–voltage response of the actuators. The elastomer can also heal a combination of mechanical and electrical failures. This work provides a route to create robust and damage tolerant dielectric elastomers for soft robotic and other applications related to actuator and energy‐harvesting systems.

Indoor localization is a key enabling technology for mobile robot navigation in industrial manufacturing. As a distributed metrology system based on multi-station intersection measurement, the workshop measurement positioning system (wMPS) is gaining increasing attention in mobile robot localization. In this paper, a new, to the best of our knowledge, wMPS-based resection localization method is proposed using a single onmidirectional transmitter mounted on a mobile robot with scanning photoelectric receivers distributed in the work space. Compared to the traditional method that requires multiple stationary transmitters, our new method provides higher flexibility and cost-effectiveness. The position and orientation of the mobile robot are then iteratively optimized with respect to the constraint equations. In order to obtain the optimal solution rapidly, two methods of initial value determination are presented for different numbers of effective receivers. The propagation of the localization uncertainty is also investigated using Monte-Carlo simulations. Moreover, two experiments of automated guided vehicle localization are conducted, and the results demonstrate the high accuracy of the proposed method.

In contrast to conventional rolling element and oil film bearings, magnetic bearings have had a relatively short history. The practical implementation of active magnetic bearings using electromagnets has been accelerated and driven recently by the development of digital control technology. Since 1988, the International Symposium on Magnetic Bearings (ISMB) series has been convened every two years and has been leading the studies in this field. In the industrial sector, the ISO TC108/SC2/WG7 “Working Group on Active Magnetic Bearings” started its activities in 1997 to develop standards to promote the adoption of rotating machinery with active magnetic bearings and to support the steady and smooth advancement of associated industries. The standards have been released as the ISO 14839 series. This chapter describes the basic specifications of magnetic bearings, along with the related vibration control technologies.

Oil-lubricated plain bearings are used widely to support the main rotors of rotating machinery, because the hydrodynamic oil films formed in the bearing clearances can guarantee smooth rotation of shafts and effectively prevent or suppress rotor vibrations. This chapter explains the principles of oil film formation in typical plain bearings, based on conventional hydrodynamic lubrication theory. The circumferential oil film shape at the steady-state equilibrium is determined, so that the hydrodynamic pressure generated in the oil film can balance the oil film reaction force vectorially with the applied bearing load. In other words, the oil film separates the journal from the bearing surface and the journal can float and rotate on the oil film. The oil film shape determines the journal center position represented by the journal eccentricity ratio and the attitude angle in polar coordinates. The steady-state journal center position and in turn the corresponding oil film shape vary with the operating condition of the journal bearing, that is, Sommerfeld number. When the journal center is slightly perturbed at the equilibrium, the oil film is slightly deformed, resulting in the slightly modified pressure distribution. Then, the corresponding oil film force is found to consist of the static reaction force at the equilibrium and also the two mutually perpendicular components of the small dynamic reaction force. Each of the two components is expressed by the linear sum of the two stiffness components and also the two damping components. In total, four stiffness components and four damping coefficients are determined at the equilibrium. These coefficients are the key factors that dominate the vibrational behavior of the rotor supported in the plain bearings. The coefficients obtained for various types of journal bearing are found to vary with the Sommerfeld number. Consequently, journal bearings need to be selected and designed so that the dynamic coefficients of the hydrodynamic oil films can enable satisfactory control of rotor vibration.

According to ISO 18436-2, entitled “Condition monitoring and diagnostics of machines—Requirements for training and certification of personnel—Part 2: Vibration condition monitoring and diagnostics,” the introduction of the certification examination for vibration experts is mentioned. The certification level is divided into four categories: 1—for beginners; 2—for elemental experts (apprentices); 3—for advanced experts; and 4—for super-experts. This chapter, including 100 questions, is prepared for ambitious experts challenging categories 3, 4, and higher. Every question requires knowledge strongly related to basic engineering mathematics, practical signal processing, vibrational dynamics theory, standard modal analysis, model order reduction, and so forth. It excludes knowledge gained purely from experience. If you are students, it is a good opportunity to know how to apply undergraduate knowledge to the field. If you are vibration consultants, apply these simple and understandable modeling techniques in troubleshooting for your customers. Based on the experience of one of the authors as a JSME (Japan) examiner, he found that questions of the examination are divided approximately into two groups. The first group includes questions related to knowledge of field experience in the maintenance service, for example, permissible vibration levels decided by API and/or ISO standards, how to measure and report vibration data, and so on. The second group involves questions concerning mathematics and dynamics, for example, rotor balancing, the FFT algorithm, modal analysis, applying complex numbers. Many examinees may have difficulty to recall and manage the theoretical background for questions if they graduated some time ago. A total of 100 questions have been selected, specifically to enrich an expert’s understanding of the mathematics and dynamics for them. The following advises the reader on how to use this chapter: (1) Questions 1–30: The first 30 are multiple choice questions with five options. It is in the same style as the certification exam; hence, examinees can check their level. The actual exam contains 100 questions in a 4–5 h period. Therefore, it is recommended that you complete these 30 questions within 60 min. Finally, check your answers with the correct answers in Table Q30, located in Sect. 12.1. (2) Questions 31–100: The aim of these questions is to sharpen examinees’ thinking, so the questions may be slightly beyond their knowledge. On average, the difficulty of these questions is almost equivalent to vibration category level 3 and 4; some may be near category 4 and higher. Do not be afraid to try these questions to test your knowledge. From Question 31 onwards, the content is divided into two ways: Questions stated in Sect. 12.2 with answers and hints associated with each question in Sect. 12.3. Please try these exercises, which challenge readers to become world-leading experts in the rotor dynamic vibration field.

Turbomachinery shaft seals suffer from rubs caused by thermal growth, assembly misalignment and rotor dynamic vibration at engine start-up and shut-down. Rubs are detrimental to performance, leading to a decrease in overall efficiency and costly corrective maintenance. In recent years, compliant seals have been developed, allowing for variable clearances and a reduced frequency of seal rubs. The design goal for compliant seals is therefore, to maintain a tight clearance between rotating and non-rotating parts, throughout the transient conditions experienced in engines. This paper presents the design of a new high-speed rotating test facility developed for the performance characterisation of turbine shaft seals. The rig features a 254 mm diameter rotor, capable of rotating at speeds of up to 15,000 rpm (equivalent to rotor surface speeds up to 200 m/s). The maximum pressure difference across a seal is 3.5 bar. In the first experimental campaign, the performance of a labyrinth seal was investigated. The rotordynamic coefficients of the seal were calculated by exciting the casing with an electromagnetic shaker. The leakage performance, direct and cross-coupled seal stiffnesses and effective damping coefficients are determined.

This book aims to explain various phenomena and mechanisms of vibrations in rotating machinery based on theory and field experiences. It also aims to help engineers in carrying out diagnosis and in implementing countermeasures for various vibration problems in the field. It is normally easy to know the condition of machinery by means of measurement of vibrations and/or noise. However, it is rather difficult to interpret the observed phenomena correctly, derive real causes of the problems, and ascertain effective countermeasures, because a sufficient knowledge of case studies is needed. This chapter provides an overview of vibration problems in rotating machinery and general approaches for the countermeasures, and is intended to be helpful in solving vibration problems at the front line. Condition monitoring of a machine and vibration diagnostics including relevant ISO standards are illustrated. Case studies of vibration problems and the countermeasures in excess of 1000 cases, which have been collected until now by the Vibration Database (v_BASE) Committee under the Japan Society of Mechanical Engineers (JSME), are also referred to in this chapter.

This chapter explains the self-excited nature of vibration of a rotor caused by the destabilizing oil film force (oil whip or oil whirl); another self-excited vibration of a rotor caused by the destabilizing fluid force in seals and impellers (flow-excited vibration); and how to prevent the vibrations effectively by selecting appropriate specifications of plain bearings. Both of the unstable vibrations show two-dimensional whirl orbits of the rotor around the steady-state equilibrium position in the shaft rotating plane. The dominant component of the shaft whirl orbit is found to be the forward one, that is, orbiting in the same direction as the shaft rotation. The orbit size is sometimes enlarged when bending deformation of the rotating flexible shaft is added. In contrast with the unbalance vibration explained in Chap. 3, the whirl frequencies of the unstable vibrations are generally lower than the shaft rotating frequency, that is, subsynchronous, close to the natural frequency of the rotor-bearing system. These self-excited vibrations break out when the rotor-bearing systems exceed stability limits. When a linear vibration analysis is applied to the rotor-bearing system, the characteristic equation is derived in the form of an algebraic polynomial equation of the sixth degree from the equations of motion. When the Routh–Hurwitz criterion is applied to the characteristic equation, the stability limit of shaft speed can be obtained in the form of mathematical expression consisting of the rotordynamic coefficients of bearing oil film and the bending stiffness variable of shaft. The stability limit can be also found by means of eigenvalue analysis applied to the characteristic equation. In other words, when all the real parts of the eigenvalues have negative values for the given operating condition, the rotor-bearing system can remain stable. When at least one real part has a positive value, the system becomes unstable, starting oil whirl or oil whip. The effects of operating conditions and journal bearing configurations are demonstrated, and various effective countermeasures are derived. The flow-excited vibrations of a rotor by non-contact seals are characterized by dependence on load, because, with increase in load, the working fluid increases in pressure and flow rate, strengthening the destabilizing force (cross-coupled stiffness force) of the fluid flow. The magnitude of the destabilizing force is strongly dependent on the swirl velocity of the fluid in the direction of shaft rotation at the seal inlet. Consequently, one of the effective countermeasures against seal flow-excited vibration is to support the rotor by anisotropic bearings having oil film forces that give rise to elliptical whirl orbits. This is because the backward whirl component of the elliptical whirl orbit reduces the effect of the destabilizing seal force.

Oil-lubricated plain bearings used widely for large-sized rotating machinery can effectively suppress unbalance vibration amplitude of a rotor. This chapter outlines the nature of unbalance vibration amplitude of a rotor supported in plain bearings. The mathematical expression of unbalance vibration of a rotor is given in the rotating plane of the shaft. The two equations of motion given in the x–y-plane are converted into a single equation of motion derived with the complex expression of the displacement of the rotor. Then, the rotor is found to make an elliptical whirl orbit with major and minor axes around its equilibrium. The eight rotordynamic coefficients of a bearing oil film can be converted into the four effective coefficients expressed with the two coordinates of the major and minor axes. The vibration response and the whirl orbit are calculated and shown with varying shaft speed. The effects of bearing type and design variables on the unbalance vibration response are also calculated and compared. Furthermore, the effect of bearing pedestal characteristics on the unbalance vibration response is shown. Finally, it is shown how rotor-bearing systems can be designed to reduce the maximum amplitude of unbalance vibration when passing critical speeds.

This chapter is divided into three parts, which include our latest areas of interest. (1) Guyan reduction or mode synthesis: With respect to vibration analysis for actual machines, many types of codes, 3D-FEM and 1D-FEM (e.g., MyROT introduced in R1_Chap. 12), are available for engineering design based upon multi-DOF (degree of freedom) modeling. However, case studies of vibration problems show the benefits for understanding the vibration mechanisms and their practical and potential solutions using simplified models. In this book, Guyan reduction and the mode synthesis technique are strongly recommended for this purpose. (2) System instability in oil film bearing rotors: This model order reduction (MOR) is applied to a flexible rotor supported by oil film bearings to analyze system instability, often referred to as oil whip, oil whirl, and casing whirl. Stability analysis is generally performed by using complex eigenvalue codes in the 1D-FEM modeling. However, this chapter yields an alternative way without complex eigenvalue calculation, i.e., how to predict the limiting speed for stability and the resultant unstable frequency. (3) Blade modeling coupled with shaft vibration: The MOR by the mode synthesis technique is applied to a flexible blading system to analyze the vibration coupled with the rotating shafting system. Uncoupled eigen frequencies and modes may be analyzed initially for the rotating blading system only by a 3D-FEM code, based upon the rotating coordinates. As the result, the corresponding 2-DOF models for each eigen mode of blading are proposed by two methods depending upon the number of the nodal diameter, κ = 0 and κ = 1. The former is coupled with torsional and axial shaft vibration models and the latter with bending (lateral) shaft vibration models, respectively. These blade reduced models are combined into shaft vibration data by a 1D-FEM code for the evaluation of the coupling effect. The effectiveness of these procedures is confirmed by numerical examples.

Frequencies associated with self-excited vibrations are, in most cases, the natural frequencies of the system. The natural frequencies are not proportional to the rotational speed. Therefore, self-excited vibration is a form of non-synchronous vibration. In rotor systems, the lowest natural frequency is often below the rated rotational speed and it may become unstable, hence self-excited vibration is also known as sub-synchronous vibration. This chapter describes various case studies of self-excited vibrations, which are inherent in rotating machinery, as for a journal bearing, seal, centrifugal impeller, and blade for an axial flow machine. Also, the phenomena of internal friction, fluid trapped in a rotor, and rotor contacting with a stator, may produce strong self-excited vibration. While illustrating these unstable phenomena, the cause or mechanism of the instabilities and appropriate solutions are discussed by citing the v_BASE data. In addition, squeeze film dampers, which are used to stabilize the system by adding a damping effect, are explained.

The major problem in forced vibration response is resonance, where the frequencies of exciting forces coincide with the natural frequencies. Rotating machinery has different characteristics in resonance problems from general non-rotating structures. Therefore, the problems need be solved with this knowledge in mind, not only at the design stage, but also on-site. In the case of forced vibration, centrifugal forcing due to unbalance is a very typical example; however, various other external forces produced by different mechanisms may also become problematic and be experienced routinely. Examples include mechanically induced forces in gears, cross joints, and pulley belt systems; an electromagnetic force in a motor/generator; and rotating stall and impeller/blade interaction forces, which are induced by the fluid flow. Furthermore, torsional vibration is inevitable for rotating machinery and may become a large problem. In this chapter, these phenomena and appropriate countermeasures to implement are elucidated while referring to previously mentioned examples.

In the vibration diagnosis of rotating machines, the first attention is the evaluation of the unbalance vibration, i.e., the rotational synchronous point of vibration, noted as “1X” or “1N” vibration. A vector monitor (R1_Fig. 5.8) is a measuring instrument including a tracking filter that extracts only the 1X vibration component from the actual vibration waveform. In this chapter, the principle and the application of this vector monitor are explained. In the following, attention is given to the transformation from the waveforms in the time domain to amplitude (spectrum) in the frequency domain by using a FFT analyzer. We learn about the theory of signal processing related to FFT analysis, which is capable of providing numerous displays for easy understanding and effective diagnosis for vibration troubleshooting.

Rolling element bearings are used widely in rotating machinery. A significant variety of rolling element bearing types is available, and they are categorized by the shape of the ball or roller elements; the radial or axial loading direction; the ball type such as deep groove or angular contact; the roller type such as plain or tapered; etc. As most of them are standardized in ISO/JIS, interchangeability is guaranteed. This chapter introduces the dynamic properties of some rolling bearings, but does not make any reference to the static properties given in bearing manufacturers’ catalogues, such as load capacity, sizing, life estimation, and so on.

This paper demonstrates vibration reduction in a hollow rotating shaft by means of internal-stator active magnetic actuators, which are resiliently mounted. This problem requires further consideration over and above classic rotor/magnetic bearing systems on account of the flexible behavior of the magnetic actuator support structure. This paper presents an experimental facility conforming to the proposed topology, with a particular focus on the control problem such a system presents. The unique challenges are discussed, and a solution is presented in the form of H $_\infty$ -based control. Ultimately, experimental results demonstrate the system to be capable of substantial rotor vibration suppression, including while passing the rotor's first critical speed, which was not obtainable with simpler classical control techniques. This means the top achievable rotor speed was increased from approximately 3000 r/min without magnetic actuator vibration suppression to over 9000 r/min with vibration suppression active. At the rotor critical speed, the magnetic actuators affect a reduction in rotor vibration amplitude of over 70% compared to the rotor supported purely on mechanical bearings, while simultaneously avoiding excessive excitation of the flexible active magnetic actuator support structure.

Conventional multibody systems used in robotics and automated machinery contain bearing components that exhibit complex and uncertain tribological characteristics. These limit fundamentally the precision of the automated motion and also cause wear. Replacing traditional bearing joints with flexure couplings eliminates these tribological effects, together with wear, reducing necessary system maintenance and offering a potential for increased motion precision. A flexure-coupled multibody system is considered and a novel general solution technique is presented. Derivation of a large deflection flexure coupling model is provided and subsequently validated using an experimental facility. A focused study of a unique double-flexure-coupling rigid body system is given; the formulated nonlinear mathematical model can be used for feedforward control. Equivalent control is also applied to a corresponding system with traditional bearing joints. The feasibility of replacing bearing joints by flexure couplings is demonstrated in terms of accurate large displacement control and reduction of high-frequency disturbances.

A rotor spinning within an active magnetic bearing (AMB) system will normally be levitated and hence operate without rotor-stator contact. External disturbances and inherent unbalance may be compensated with appropriate control to keep rotor deviations within the clearance gap. However, AMBs have limited dynamic load capacity due to magnetic material field saturation. Hence overload conditions may result in rotor-stator contact. A touchdown bearing (TDB) and rotor landing sleeve are usually included to protect the expensive rotor, magnetic bearing and sensor components from damage. Once rotor-TDB contact has been made, rotor dynamic conditions may ensue resulting in persistent rotor bouncing or rubbing limit cycle responses. Prolonged exposure to these severe dynamics will cause TDB degradation and require regular replacement. If possible, a clear aim should be to restore contact-free levitation through available control capability in an efficient manner. This paper is used to guide the control options that are available to restore contact-free levitation. The use of AMB control is appropriate if the required control forces are within saturation limits. It is also possible to actuate TDBs and destabilize persistent rotor dynamic contact conditions. For example, piezo-based actuation offers larger control forces than those from magnetic bearing systems. Hybrid control action involving both types of actuation system has the greatest potential for completely robust restoration of contact-free levitation.

Typical rotor/active magnetic bearing (AMB) system layouts involving large, external stator AMBs may be difficult or inconvenient to apply to some rotor systems. Where space in the machine working envelope is at a premium, the space required by traditional AMBs may preclude them from inclusion in the design.

This paper presents a review of techniques to mitigate jamming in Electromechanical Actuators (EMA) for safety critical applications in aerospace. Published progress to date is evaluated, with the remaining challenges highlighted. Through the use of Hierarchical Process Modelling (HPM), two key approaches to mitigate jamming were identified: (1) Fault Diagnostics (FD) and (2) Fault tolerant design. The development of a fault tolerant EMA system is currently at an early stage for implementation within safety critical systems due to the increased complexity of such systems (for example the anti-jamming system may require FD functionality itself). Challenges also exist for FD approaches particularly in achieving a robust means of fault detection. It is proposed that a hybrid FD approach, using a combination of model based and data-driven techniques to predict the onset of jamming, would be beneficial in capturing the discrepancies between the predicted and observed behaviour used to isolate and identify faults. Furthermore, several aspects of modelling and of data-driven methodologies for FD in the literature omit potentially important behaviours, and recommendations are made to improve upon this. For example, the simulation of faults in test stand analysis and the fidelity modelling of the motor and mechanical components are key areas to develop.

Hinged joints are ubiquitous in machine and mechanism design where components must rotate relative to one another. Their simplicity and reliability, coupled with limited alternatives, make them an obvious choice. However, the propensity of such joints to exhibit unpredictable discontinuities in their operation can limit the precision with which a mechanism incorporating such a joint can be controlled. In particular, almost all hinged joints experience some degree of both backlash and stiction. An alternative to hinged joints in many applications may be the use of large-displacement flexure-link joints. The use of flexure joints in micro-mechanisms is already an established practice, but their use in joints with large angular displacements (e.g. 30 degrees) is far less common. Such joints are inherently non-linear, and introduce more complex motion than simple hinges, but they offer the considerable advantage of highly predictable behaviour, without the exhibition of discontinuities. These characteristics open the way to increased mechanism precision and repeatability, and consequent new possibilities in machine design. This work makes a comparison of the precision which can be achieved when controlling similar mechanisms employing each of i) a realistic hinged joint, and ii) a large-displacement flexure-link joint. The modeling techniques used to represent each mechanism are discussed, and a series of results are presented illustrating the performance and prospects for precision motion of each system.

Conventional multi-body mechanisms used in robotics and automated machinery can have limited motion due to the bearing and transmission parts. Replacing a traditional bearing joint with a compact deformable structure (flexure coupling) can improve the performance envelope for a mechanism. A dynamic nonlinear mathematical model is derived for a mechanism comprising a flexure coupling, which can undergo large deformations, connected to a rigid link. Direct actuation of the mechanism is assumed in three directions and an open-loop control methodology is designed to regulate the actuation forces to achieve a prescribed path with precise and repeatable small scale motion. A mechanism containing a flexure coupling is examined and compared to that of an ideal hinge joint. The results show that a flexure coupling allows an increased range of motion for the mechanism compared to a hinge coupling and can have multiple paths in the x and y direction for a prescribed angle trajectory at the end of the mechanism.

Due to their flexibility, low cost and large working volume, 6-axis articulated industrial robots are being used increasingly for drilling, trimming and machining operations. However, producing high quality components has proven to be difficult, as a result of the inherent problems of robots, including low structural stiffness, hence excitation of structural modes, low positional accuracy, and bandwidth limitations associated with dynamics and control. These limit robotic machining to non-critical components and parts with low accuracy and surface finish requirements. As a part of the “Light Controlled Factory” project at the University of Bath, studies have been carried out to improve robotic machine capability, specifically positioning accuracy and vibration reduction. This paper describes experimental studies in reducing robot machining vibrations induced by cutting forces with active vibration control, using accelerometers to measure vibration and inertial actuators to mitigate vibration forces. With a relatively simple controller, a 25% reduction of RMS vibration amplitude is demonstrated.

Under normal operation a rotor spinning within an active magnetic bearing system will be levitated and hence rotor-stator contact conditions do not exist. In such a case, external disturbances and inherent unbalance will cause rotor responses that are maintained by the magnetic bearing control system to be within the clearance gap. However, magnetic bearings have limited dynamic load capacity due to magnetic material field saturation. Hence large external disturbances may be sufficient to cause the clearance gap to become closed and result in rotorstator contact. A touchdown bearing is usually incorporated as a sacrificial stator component to protect the expensive rotor, magnetic bearing and sensor components. Once contact has been made, rotor dynamic conditions may ensue resulting in persistent rotor bouncing or rubbing limit cycle responses. Prolonged exposure to these severe dynamics will cause touchdown bearing degradation and require regular replacement. A clear aim is therefore to restore contact-free levitation through available control capability in an efficient manner. This paper provides an analysis to gain an understanding of the uncontrolled rotor/touchdown contact dynamics. These will then be used to guide the control options that are available to restore contact-free levitation. The use of magnetic bearing control is appropriate if the required control forces are within saturation limits. It is also possible to actuate touchdown bearings and destabilize persistent rotor dynamic contact conditions. For example, piezo-based actuation offers larger control forces than those from magnetic bearing systems.