The thermal effects of rotor-to-stator rubbing resulting in rotor bowing, and subsequent changes in rotor vibrational responses are discussed in this paper. The rotor thermal bow is modeled following relationships quoted in rotordynamic literature. The rotor model takes into account its first lateral mode in which the rubbing spot differs from the modal mass location. It is shown that the rotor responds to the rub thermal effect in a “spiraling/oscillating” mode which represents a form of rotor self-exciting vibrations. A simplified model explains physical phenomena occurring in the rubbing rotor system. An example of the field data illustrates the rotor dynamic behavior.

Experimental measurements have been made to evaluate the rotordynamic performance of straight-through labyrinth seals under conditions that are realistic for many turbomachines. Both teeth-on-rotor and teeth-on-stator gas seals were tested, each with twelve blades, 173 mm (6.8″) blade diameter, and 102 mm (4″) total length. The nominal blade tip clearance was 0.5 mm (20 mils). The teeth-on-stator seal was tested with the blade tip clearances diverging (in the direction of the flow), uniform, and converging. The teeth-on-rotor seal was tested with uniform clearances. The inlet air pressure to the seals was varied from 1.7 bar to 14.6 bar (25 psi to 200 psig) with the last blade exhausting to the atmosphere. Coastdown tests of all the seals were performed on a rotordynamic test rig to show their effect on synchronous response to imbalance when passing through a 3700 rpm critical speed. For the teeth-on-rotor seal, rap tests at 4500 rpm were also conducted to measure the effective damping coefficient for subsynchronous vibration. The synchronous response to imbalance was generally increased by all the seals at inlet pressures up to about 11.2 bar (150 psig). The worst case was for the teeth-on-rotor seal at about 2.7 bar (35–45 psi) inlet pressure where the rotor whirl amplitude was increased from .1 mm (3.75 mils, peak to peak) to over .13 mm (5 mils). In most cases the rotor whirl amplitude was slightly decreased at inlet pressures above 13 bar (176 psig). The teeth-on-rotor seal provided a small amount of damping to attenuate the 61 Hz subsynchronous vibration with the rotor running at 4500 rpm. A computer model which includes both the rotor and housing dynamics was developed to evaluate the possible range of values of the rotordynamic seal coefficients. Simulations show that the effective subsynchronous damping coefficient of the teeth-on-rotor seal ranges from 175 N-s/m at 5.1 bar inlet pressure (1 lb-s/in at 75 psi) to 876 N-s/m at 10.2 bar (5 lb-s/in at 150 psi). This corresponds to a range of 0.3% to 1.4% of critical damping added by the seal for subsynchronous vibration, even though the seal increased the synchronous response at the critical speed. It is shown that the orbit conditions for the synchronous and subsynchronous tests were radically different, as they likely will be in most turbomachines.

This paper presents results of numerical simulation of the dynamic behavior of a one-lateral-mode unbalanced and radially side-loaded rotor with either loose pedestal (looseness in a stationary joint), or with one oversize bearing (looseness between a rotating and stationary joint), or with occasional rotor/stator rubbing. The nonlinearities of these systems (variable stiffness, impacting, and friction) are associated with intermittent contacts with the stationary element. The results, based on a local impact model, developed in the author’s previous publications, exhibit regular periodic, as well as chaotic vibration patterns of the rotor.

For motors with low speeds and loads, torque pulsation by the reluctance torque is an important source of vibration and control difficulty. In this paper, the magnetic field of a motor is calculated by finite element method and the periodic reluctance torque is determined using Maxwell stress method and time stepping method, and then decomposed using Fourier series expansion. The purpose of this paper is to characterize design parameters on the reluctance torque and to design a permanent magnet motor with a reluctance torque less vulnerable to vibration, without sacrificing the motor performance. The design parameters include stator slot width, permanent magnet slot width, airgap length and magnetization direction. A new design with a less populated frequency spectrum of the reluctance torque is proposed after characterizing individual effect of design parameters. Gradual magnetization, by gradually increasing the thickness of the permanent magnets at edges, yields a smooth shape for the reluctance torque with reduced harmonics.

A study which compares theoretical predictions of experimental rotordynamic and leakage results is presented for short (L/D = 1/6) honeycomb and smooth annular pressure seals. A computer code used in this comparison has been developed from a theory that employs a perturbation analysis of the governing equations flow and uses Moody’s pipe friction relationship for the surface friction of the rotor and stator. This study was undertaken to investigate how well an existing code could predict these characteristics with input provided from recorded test data and independent flat-plate tests. The results examine the effect that the following independent test parameters have on the experimental measurements and theoretical predictions: inlet preswirl, rotor speed, inlet pressure, pressure ratio across seal, seal clearance, and honeycomb cell width. Experimental results show that leakage is reduced by decreasing the honeycomb cell width. Rotordynamically, the short seals are stabilizing over all test parameter ranges. However, the short seals did not perform as favorably as longer (L/D = 1/3) seals. In general, the theory overpredicts rotordynamic coefficients and leakage.

This paper describes additional results from a continuing research program which aims to identify the dynamics of long annular seals in centrifugal pumps. A seal test rig designed to experimentally identify dynamic coefficients using a least-squares technique based on the singular value decomposition method. The analysis is carried out in the time domain using a multifrequency forcing function. The experimental method relies on the forced excitation of a flexibly supported stator by two hydraulic shakers. A rigid rotor supported in rolling element bearings runs through the stator. The only physical connection between shaft and stator is a pair of annular gaps filled with pressurised water discharged axially. The experimental coefficients obtained from the tests are compared with theoretical values.

Methods for calculating the effects of periodic contact between the stators and rotors of large turbine generator systems are discussed. The case of periodic contact between a stator and part of the LP turbine rotor of a modern turbine generator is selected for study. The rotor is part of a train which includes, in order, HP, IP, and (one) LP turbines, each supported by two journal bearings solidly coupled to each other and to an alternator which is supported by three bearings, one of which carries little load and is popularly known as a steady bearing. The periodic contact is supposed to be caused by poor alignment of the rotor relative to the stator and by vibration of the rotor due to unbalance. Comparisons are made between the effects predicted using modal analysis, using models of the LP turbine rotor of Jeffcott type (Wilkinson, 1987), and those obtained using more accurate methods. It is assumed that the normal forces generated during contact are proportional to the interference between rotor and stator and that the tangential force can be calculated with sufficient accuracy by using a coefficient of friction. It is shown that light rubs usually causes periodic synchronous responses but subharmonics may also appear. There is little doubt that chaotic vibration will ensue if rubs become heavier than those considered. It is suggested mat modal analysis methods are probably best for long rotor systems, however, the simplest models reveal the correct qualitative behaviour. The work forms part of a wider investigation of the effects of rotor/stator interaction and at the time of writing a test rig is being manufactured to facilitate the measurement of response to unbalance, the effects of misalignment and the response to light rubs. Aspects of the design of the six bearing rig, which is claimed to be a true scale model of a substantial fragment of the nine bearing turbine generator rotor system discussed earlier, are also described.

One of the main reasons for the acoustical noise and vibrations in electrical machines is the excitation of the stator due to the presence of magnetic harmonics in motors and generators. During the design of these machines one must care that the frequencies of the excitation forces do not coincide with the natural frequencies of the stator, which would increase considerably the acoustic noise levels and the vibrations. This work concerns the study of dynamic behavior of segmented (laminated) structures that will define the natural frequency of stators. Our main interest consists in the longitudinal modes of cylindrical segmented shells where the effect of discontinuous layers is more concentrated. A comparison of proposals for modelling of stators is done with the results of experimental modal analysis of a stack of metal sheets, clamped with tie rods and with the clamping pressure controled through strain gages. A study of these structures considered orthotropic (and not isotropic as one normally assumes) is done.

A parametric study was conducted to determine the effect of motor geometry on the force imbalance in an 8-pole/9-slot motor. The study is based on a quasi-static finite element analysis in which the force calculations were made by integrating the Maxwell stresses along the center of the airgap. For small variations from the base motor geometry, the study revealed the following trends. The magnitude of the force imbalance decreases as the slot width decreases. The imbalance also decreases as the airgap length increases. A rotor/stator eccentricity introduces a constant force imbalance which increases proportionally to, and in the direction of, the eccentricity. As the size of the motor is scaled up uniformly, the mass increases faster than the imbalance. The results suggest that the force imbalance is caused predominantly by the stress concentrations at the corners of the stator teeth.

Acoustic noise of generated in DC motors is difficult to predict, and its exact mechanism is unclear. It is a common observation that brushless DC motors with rare earth magnets are often acoustically inferior to motors of equivalent output built with conventional magnets. In this paper, the acoustic noise of electromagnetic origin is investigated using a magnetic frame which emulates a DC motor. The driving electromagnetic force is calculated using finite element analysis and the resulting vibration and acoustic noise is measured. Acoustic noise of purely electromagnetic origin was also measured from a DC brushless motor to confirm the results of the magnetic frame. The results of the study show that the mechanism of noise generation can be a quasi-static response of a stator not only at the fundamental frequency but also at higher harmonic frequencies of alternating switched DC excitation of motor phases. Noise generation is significantly aggravated when some of those harmonics match the resonant frequencies of the stator. Eddy current flow within the magnets due to the time varying electromagnetic field act as a shorted transformer secondary winding, and results in a reduction of the electrical phase impedance. This reduced impedance results in a faster rise time with a sharper current shape during transients, and increased current magnitude during steady state, thus making the motor noisier.

Stator laminations can have mutual excitation sources depending to the inertial forces that can excite the mechanical resonances and radial components of the electromagnetic forces that vary with the magnetic flux changes and the magnetostrictive forces. Magnetostrictive forces can appear depending to the material properties of the plates and have mechanical and magnetic causes Mechanical properties of the lamination plates can be determined both in numerical and experimental methods. Magnetostrictive effects of the laminations have significant contribution to the audible noise of electric motors. The combined effects of radial components of electromagnetic forces and magnetostrictive deformation can cause further amplification problems of noise. This study investigates the effects of magnetostrictive forces on the laminated mechanical structure of stator core by referring to the changes of the plate materials depending to applicable heat treatments, magnetic properties and silicon alloying that were all considered as factors to modify the effects of magnetostriction.

This paper presents the dynamic modeling and synthesis of a four-bar mechanism that is driven by a four-phase, variable-reluctance stepper motor. Dynamic models of both the mechanism and the motor are derived and subsequently combined in order to numerically determine the system dynamic response. In the stepper motor model, full circuit equations are derived for each of 8 stator poles, with full expressions for armature self- and mutual-inductances, as well as developed motor torque. The stepper motor model admits arbitrary input pulse trains, and includes both coil resistance and inductance. A set of five, simultaneous, nonlinear, second-order ordinary differential equations is analytically derived and numerically solved to determine stepper response. In the four-bar mechanism model, three dynamical properties (primary effective inertia, secondary effective inertia, and gravitational disturbance torque) are derived using a Lagrangian approach, and utilized to determine the dynamic suitability of candidate four-bars for three-position, rigid body guidance. Three candidate four-bar mechanisms are synthesized, and their dynamic response (when coupled to the variable-reluctance stepper motor) is compared. It is shown that an engineering trade-off exists between parallelogram and crank-rocker four-bars, in which the former may possess lower primary effective inertia, but the latter may possess lower gravitational disturbance torque.

A new type of on-line automatic balancing system — the electromagnetic balancing system is concerned in this composition. The balancing head in this system consists of two stators and two slide plates. Each slide plate, on which there is a correction mass, can be driven to move relative to the shaft in single direction by the electromagnetic force. The positions of both masses are able to be detected conveniently by corresponding sensors. The balancing method is a conventional one. The moving procedure of the correction mass to meet the slide’s single -direction rotating character is described. Experiment results of its application to flexible rotor are also included.

This paper deals with a special subsynchronous vibration problem, namely rotor instability caused by partly coupled effect of torsional and bending modes and partly improper bearing design. A theoretical model is presented to investigate such complicated vibration problem. The analysis shows that a single bending or torsional vibration analysis is not enough to predict the stability of a geared rotor system, which includes a turbine, a gear, a generator, several bearings, a squeeze film damper and stators. Either a bearing design, which gives stability in single lateral vibration analysis, cannot guarantee the stability if a torsional vibration mode is involved. This indicates that the bearing design plays much more significant role in a geared rotor system. The theoretical model has been successfully applied to a steam turbine set, which experienced such kind of subsynchronous vibration, by modifying the original bearing design.

One of the authors has shown in previous papers (Enrich, 1995; Ehrich, 1996) that, when high speed rotors are operated in the transcritical range with the rotor located eccentrically in its rotor/stator clearance with the rotor in intermittent contact with the stator, a nonlinear response, at speeds both slightly above and slightly below the critical speed, is induced. The response at a particular speed will include significant components at an asynchronous frequency which is approximately equal to the natural frequency of the system. In particular, when the speed (normalized by the natural frequency) S is approximately (J+1)/J, the dominant frequency (normalized by the natural frequency) F is precisely J/(J+1) times S or approximately 1 (where values of the whole number J < 1 give the subcritical set of speeds and values J > 1 give the supercritical set of speeds). The phenomenon has been termed spontaneous sidebanding . Observations of similar asynchronous responses noted in a Campbell diagram of the rotordynamic response of an actual high speed rotor clustered around a subharmonic response peak at a rotational speed twice the natural frequency suggest that the phenomenon is also possible at any subharmonic pseudo-critical response peak. In this more general case, we would expect that at rotational speeds in the vicinity of the M th subharmonic pseudo-critical normalized speed where S is approximately (MJ+1)/J and the dominant normalized frequency F is precisely J/(MJ+1) times S or approximately 1 [where values of the whole number J < 1 give the sub(pseudo)critical set of speeds and values J > 1 give the super(pseudo)critical set of speeds]. A simple numerical model of the nonlinear system verifies that these asynchronous responses are indeed possible. Operation of the model at a rotational speed approximately double the natural frequency yields data which closely reproduce the asynchronous response seen in the actual machine.

General solution of levitation control applicable to PM synchronous and induction type rotating motor is presented. It is intended for a single rotor to have both functions of magnetic bearing and rotating motor. The rotational control is achieved with the traditional P pole magnetic flux, while the radial force is controlled with either P+2 or P−2 pole magnetic flux in the stator. In the previous work, the proposed general theory of levitated motor is successfully confirmed with no load experiments. In this paper, the load capability of the levitated motor is tested using a horizontal type experimental setup. The stator has 8 concentrated wound electromagnets, each of which is controlled individually by a DSP and power amplifier. The radial load is the gravity of the rotor, while the produced rotating torque is measured with a noncontact variable torque load system. The results obtained are discussed in detail.

The paper describes near-resonance, non-stationary motion of a system consisting of symmetric rotor with constant unbalance and isotropic support. The source of torque (drive) is considered limited, allowing linearization near the resonance. The system is considered to be in planar motion. Interaction between the rotor and stator of the system is nonlinear. It provides diverse effects on the rotor motion due to the limited power of the drive. An example of such interaction is the well known Sommerfeld effect, when the system cannot pass a critical speed because all of the power provided by the drive is dissipated by resonance vibration of the rotor supporting system. Initial differential equations are reduced to a system of equations, mathematically similar to a system describing motion of a pendulum. Further reduction is possible using a specially developed hierarchic technique. An in-depth dynamic analysis makes it possible to apply control to the system, providing higher or lower resonance amplitudes.

This paper presents a detailed analysis of the dynamic behavior of a single rotor/stator brake system. Two separate mathematical models of the brake are considered. First, a non-rotational model is constructed with the purpose of showing that friction induced vibration can occur in the stator without assuming stick-slip behavior and a velocity dependent friction coefficient. Self-induced vibrations are analyzed via the application of the method of multiple scales. The stability boundaries of the primary resonance, as well as the super-harmonics and sub-harmonics are determined. Secondly, rotational effects are investigated by considering a mathematical brake model consisting of a spinning rotor engaging against a flexible stator. Again, a constant friction coefficient is assumed. The stability of steady whirl is determined as a function of the system parameters. We demonstrate that only forward whirl is stable for no-slip motion of the rotor. The interactions between chatter, squeal, and rotor whirl are investigated through numeric simulation. It is shown that rotor whirl can be an important source of the torsional oscillations (squeal) of the stator and that the settling time to no-slip decreases as the ratio of the stator to rotor stiffness is increased.

This paper describes a novel technique which has been proposed to simplify field orientation control system. This technique depends on zero crossing detection of different waveform of stator fluxes using the comparator reference signal which control the inverter transistors. By using this technique it is available to update the position θ and current components in the rotational reference frame up to twelve times per cycle. As a result, the transformation from two phase stationary reference frame (SRF) to two phase rotating synchronously reference frame (RRF), has been canceled which leads to less consumption time in software. Thus control algorithm requires less time to be implemented via software for position detection and speed estimation.

This paper investigates the vibration of an annular disk that is subjected to rotation and in-plane frictional traction distributed over a sector of the disk’s two faces. Technical applications include noise, vibration, and harshness in automotive and aircraft disk brakes, and other rotating machine components. To the degree that the rotor-to-stator friction in such cases is directed along the disk’s deformable surface, it is treated here as a nonconservative follower-type load. The vibration model incorporates membrane stiffness which derives from rotation and the stresses established as a result of friction. The plane stress state is determined in closed form as a Fourier series, and that solution is compared with the companion, but computationally intensive, results from finite element analysis. For the cases of sector-shaped and full annular loading, the vibration model predicts the critical mode, which is defined as the one that becomes dynamically unstable at the lowest friction level. Vibration modes that fall into opposite symmetry classes, both with and without rotation, also have opposite stability-characteristics in the presence of frictional loading.