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Showing papers on "Rotor (electric) published in 1987"


Journal ArticleDOI
TL;DR: In this paper, an attempt is made to analyze two-dimensional flow past the rotor/stator con- figuration of an axial turbine using state-of-the-art tools and computing facilities.
Abstract: An accurate numerical analysis of the flows associated with rotor/stator configurations in turbomachinery can be very helpful in optimizing performance. In this study, the unsteady, thin-layer, Navier-Stokes equations are solved using a system of patched and overlaid grids for a rotor/stator configuration of an axial turbine. The equations necessary for an accurate transfer of information between the several grids are briefly described within the framework of an iterative, implicit algorithm. Results in the form of Mach number contours, time-averaged pressures, unsteady pressures, amplitudes, and phase are presented. The numerical results are also compared with experimental data and the agreement is found to be good. HE aerodynamic processes associated with the flow of fluid through turbomachines pose one of the toughest challenges to the computational fluid dynamicist. The un- steady nature of the flow, the complex geometries involved, the motion of some parts of the system relative to others, and the periodic transition of the flow from laminar to tur- bulent are some of the factors that contribute to the com- plexity of the problem. A clear understanding of these types of flows is essential for the optimization of the performance of turbomachiner y. In this study, an attempt is made to analyze two-dimensional flow past the rotor/stator con- figuration of an axial turbine using state-of-the-art computa- tional tools and computing facilities. The two-dimensional analysis of stator airfoils in isolation or rotor airfoils in isolation is a relatively straightforward task. Such an analysis is valid when the two rows of blades are set far enough apart so that the interaction effects are minimal. However, the desire to minimize engine length re- quires the stator and rotor airfoils to be closely spaced. Clearly, the interaction effects will become more important as the axial gap between the rows is reduced. In fact, the flow becomes periodically unsteady for small values of the axial gap. The experimental results of Ref. 1 show that the temporal pressure fluctuation (the difference between the minimum and maximum pressure values) near the leading edge of the rotor can be as much as 12% of the exit dynamic pressure when the axial gap is reduced to 15% of the chord length (for the operating conditions and geometry chosen). Hence, it is important that the rotor and stator airfoils be treated as a single system when the interaction effects become predominant. A computational tool that provides the design engineer with the necessary aerodynamic data can be used to great advantage in redesigning rotor and stator airfoils to enhance performance. Such a tool has to accurately simulate the unsteady flow associated with rotor/stator con- figurations exhibiting a strong interaction. A finite-differe nce solution to the Navier-Stokes equations requires the generation of a computational grid for the

271 citations


Patent
01 Sep 1987
TL;DR: In this article, a control system for a multi-phase brushless permanent magnet motor has circuitry for periodically generating signals representing the relative position of the rotor with respect to the stator.
Abstract: A control system for a multi-phase brushless permanent magnet motor has circuitry for periodically generating signals representing the relative position of the rotor with respect to the stator, circuitry for decoding the periodically generated signals to determine the presence of the rotor at one of a plurality of predetermined rotary positions with respect to the stator, and circuitry for generating an interrupt signal in response to the presence of the rotor at one of the plurality of predetermined rotary positions with respect to the stator. Electrically controllable switches are connected to the phase windings to control the flow of current therethrough. A microprocessor is responsive to the interrupt signal for controlling in a closed loop manner the switches to commutate the phase windings of the motor a predetermined time after receipt of the interrupt signal. The microprocessor is also responsive to the speed of the motor to start the motor in a open loop mode and to shift commutation to the closed loop mode once the motor reaches a predetermined speed.

197 citations


Journal ArticleDOI
TL;DR: In this paper, a tradeoff between the low speed-torque limit and the extent of the speed range above base speed is achieved by variations in magnet dimensions and the depth of inset of the magnets in the rotor iron.
Abstract: Recent developments of high-energy permanent magnet (PM) materials such as neodymium-iron-boron have focused attention on the use of PM synchronous motors supplied from inverters for a wide variety of speed control applications PM motor drives are readily applicable where full torque is required up to full or base speed They are, however, limited in their ability to operate in the power-limited regime where the available torque is reduced as the speed is increased above its base value In contrast with the field weakening approach used in dc drives, the magnet is permanent The torque-speed operating limits of PM motor drives, of conventional design are explored, and then design measures which can substantially extend operation into the power-limited regime are proposed A trade-off between the low speed-torque limit and the extent of the speed range above base speed is achieved by variations in magnet dimensions and the depth of inset of the magnets in the rotor iron Experimental results are presented for two motors of different design, each using neodymium magnets and each supplied from a current-controlled inverter with hysteresis control of current waveshape

178 citations


Journal ArticleDOI
TL;DR: In this article, a non-linear analytical rotor casing rub interaction simulation is solved, which yields insights as to the interrelationship between rub force histories, energy levels, rub duration, incidence separation angles, and backward whirl initiation, as well as the overall rotor orbit during successive rubs.

125 citations


Patent
13 Jul 1987
TL;DR: In this article, a system for filtration of matter from a liquid suspension through a membrane uses a rotor within a concentric shell rotating with a surface velocity which, together with the rotor-shell gap and suspension viscosity, establishes vigorous vortex cells about the rotor.
Abstract: A system for filtration of matter from a liquid suspension through a membrane uses a rotor within a concentric shell rotating with a surface velocity which, together with the rotor-shell gap and suspension viscosity, establishes vigorous vortex cells about the rotor. At least one of the rotor and shell surfaces include a filter membrane. Tangential velocity components at the membrane surface constantly sweep the membrane surface to limit cell deposition tendencies while constantly replenishing the medium to be filtered. The vortex cells are established along the length of the membrane despite the constant extraction of filtrate and the resultant change in physical characteristics of the suspension.

118 citations


Patent
14 Dec 1987
TL;DR: In this article, a field orientation control system for an interior permanent magnet synchronous motor includes function generating means responsive to a torque command signal for producing direct and quadrature axis direct current signals which are converted to synchronously-varying two-phase signals for coupling to power control means, for effecting sinusoidal energization of the permanent magnet motor.
Abstract: A field orientation control system for an interior permanent magnet synchronous motor includes function generating means responsive to a torque command signal for producing direct and quadrature axis direct current signals which are converted to synchronously-varying two-phase signals for coupling to power control means, for effecting sinusoidal energization of the permanent magnet motor. The function generators modify the torque command signal as a predetermined function of the motor parameters. Rotor position information is derived from measured stator voltages and currents without the use of a separate rotor position sensor. The control system includes means for establishing a preselected amplitude of a stator α-axis current in the motor at start-up prior to establishing orthogonal β-axis current such that the motor rotor is caused to become initially aligned with the selected α-axis.

118 citations


Proceedings ArticleDOI
01 Jun 1987
TL;DR: In this paper, a finite-difference, unsteady, thin-layer Navier-Stokes approach to calculate the flow within an axial turbine stage is presented, where the relative motion between the stator and rotor airfoils is made possible with the use of patched grids that move relative to each other.
Abstract: Fluid flows within turbomachinery tend to be extremely complex. Understanding such flows is crucial to efforts to improve current turbomachinery designs, and the computational approach can be used to great advantage in this regard. This study presents a finite-difference, unsteady, thin-layer Navier-Stokes approach to calculating the flow within an axial turbine stage. The relative motion between the stator and rotor airfoils is made possible with the use of patched grids that move relative to each other. The calculation includes end-wall and tip-leakage effects. Results in the form of time-averaged surface pressures, pressure amplitudes (corresponding to the pressure fluctuation in time), near-surface velocity vectors, and pressure contours in the passage areas are presented. The numerical results are compared with experimental data wherever possible, and the agreement between the two is found to be good.

105 citations


Patent
04 Nov 1987
TL;DR: In this article, a compass and method of operation are disclosed for finding the heading of a vehicle using a compass having a rotor with a compass magnet thereon and means on the rotor defining a reference line in known relation with the polar axis of the magnet.
Abstract: A compass and method of operation are disclosed for finding the heading of a vehicle. The heading is found using a compass having a rotor with a compass magnet thereon and means on the rotor defining a reference line in known relation with the polar axis of the magnet. The angular displacement of the rotor is measured between alignment with the direction reference axis and alignment with the local magnetic field. A search coil is used to torque the rotor so that it reaches a reference position in which the reference line thereon is aligned with the direction reference axis. A reference position encoder generates a pulse when alignment is achieved. An angular displacement encoder produces a digital signal which changes with each predetermined increment of rotation of the rotor and which is indicative of the direction of rotation. A microcomputer processes the signals to provide a cumulative count of the increments of rotation. The microcomputer adds a stored magnetic variation value to the cumulative count to provide an indication of true heading. A direction display is adapted to exhibit one direction symbol of a set of symbols for different vehicle headings with each symbol corresponding to a different range of counts in the cumulative count. The microcomputer converts the cumulative count to a different direction value for each different range and the display is changed when there is a change of direction value. The microcomputer provides a logical hysteresis to prevent the display from flashing between different symbols when the cumulative count is at a marginal value of a given range. The microcomputer also provides a time damping of the display by imposing a time delay before changing the display from one symbol to another.

102 citations


Patent
30 Jan 1987
TL;DR: In this article, the maximum value of an input DC current to a motor drive circuit is held and the phase of the rotor position detection signals is changed in accordance with the held value of the input dc current to prevent the phase detection signals from varying with the load on the brushless DC motor.
Abstract: A control system for brushless DC motors detects counter electromotive force voltages induced in motor windings and produces rotor position detection signals from the counter electromotive force voltages. The maximum value of an input DC current to a motor drive circuit is held and the phase of the rotor position detection signals is changed in accordance with the held value of the input DC current to prevent the phase of the position detection signals from varying with the load on the brushless DC motor.

102 citations


Journal ArticleDOI
TL;DR: In this article, a partially flux-split, implicit numerical algorithm was used to calculate the flow fields of a hovering rotor blade at subsonic and transonic conditions, and the results were in good agreement with experimental data for both nonlifting and lifting rectangular blades.
Abstract: Unsteady, thin-layer Navier-Stokes equations written in rotor coordinates are solved using a partially flux-split, implicit numerical algorithm to calculate the flowfields of a hovering rotor blade at subsonic and transonic conditions. Numerical results are in good agreement with experimental data for both nonlifting and lifting rectangular blades. For the lifting case, the rotor wake effects are modeled by applying a correction to the geometric angle of attack of the blades. Alternate methods of calculating the hovering rotor flowfields in blade-fixed mode that have the same circulation distribution as a hovering blade are explored. All of the results presented in this paper were computed on a Cray-2 supercomputer.

101 citations


Patent
27 Oct 1987
TL;DR: In this article, an indirect position estimator for a switched reluctance motor applies short duration, low level sensing pulses to two unenergized phases of the motor to produce an indication of a pair of estimated angles for each of the unslotted phases.
Abstract: An indirect position estimator for a switched reluctance motor applies short duration, low level sensing pulses to two unenergized phases of the motor. A change in phase current during a sampling period, resulting from the application of the sensing pulse, is sensed and processed to produce an indication of a pair of estimated angles for each of the unenergized phases. A pair of angles for one such unenergized phase is shifted by a value equal to the phase displacement between the two unenergized phases and the shifted angles are then compared to the angles of the second phase to determine which angles match. The matching angle is produced as a signal indicative of the estimated instantaneous rotor position. If any stator phase changes state during the sampling period, or if the two initially unenergized phases do not remain unenergized throughout the sampling period, a signal corresponding to an extrapolated rotor position is produced instead of the signal indicative of estimated instantaneous rotor position. Extrapolation preferably includes a least squares recursive estimation, with exponential forgetting, of speed.

Patent
18 Sep 1987
TL;DR: A gas turbine engine cooling system has cooling air cooling in order, the first stage disk (50) and blades (22), the second stage vanes (24), and the second-stage air seal (82) as discussed by the authors.
Abstract: A gas turbine engine cooling system has cooling air cooling in order, the first stage disk (50) and blades (22), the second stage vanes (24), and the second stage air seal (82). Air passes to the second stage vane from the rotor through a reaction nozzle (62) effecting a reaction stage adding energy to the rotor and cooling the air.

01 Feb 1987
TL;DR: In this article, the quadrupole term of the Williams-Hawkings equation is written in a new form which separates the contributions of regions of high gradients such as shock surfaces.
Abstract: This paper is theoretical in nature and addresses applications of the acoustic analogy in helicopter rotor noise prediction. It is argued that in many instances the acoustic analogy has not been used with care in rotor noise studies. By this it is meant that approximate or inappropriate formulations have been used. By considering various mechanisms of noise generation, such abuses are identified and the remedy is suggested. The mechanisms discussed are thickness, loading, quadrupole, and blade-vortex interaction noise. The quadrupole term of the Ffowcs Williams-Hawkings equation is written in a new form which separates the contributions of regions of high gradients such as shock surfaces. It is shown by order of magnitude studies that such regions are capable of producing noise with the same directivity as the thickness noise. The inclusion of this part of quadrupole sources in current acoustic codes is quite practical. Some of the difficulties with the use of loading noise formulations of the first author in predictions of blade-vortex interaction noise are discussed. It appears that there is a need for development of new theoretical results based on the acoustic analogy in this area. Because of the impulsive character of the blade surface pressure, a time scale of integration different from that used in loading and thickness computations must be used in a computer code for prediction of blade-vortex interaction noise.

Journal ArticleDOI
TL;DR: In this article, a numerical method is presented to determine the steady-state nonlinear response of a rotor-support system due to deadband and rubbing using discrete Fourier transformation and inverse DFT.
Abstract: A numerical method is presented to determine the steady-state nonlinear response of a rotor-support system due to deadband and rubbing using discrete Fourier transformation and inverse discrete Fourier transformation. Damaging subharmonic and superharmonic responses are found to occur in presence of a side force. The calculated results agree with the general trends which have been observed experimentally by other investigators. The effects of selected nondimensionalized parameters on rotor response are studied.


Patent
31 Aug 1987
TL;DR: In this article, a method and apparatus for detecting rotor faults in an induction motor is presented, where a flux sensor generates a flux signal corresponding to the magnetic flux at a predefined flux detection point external to the motor.
Abstract: A method and apparatus for detecting rotor faults in an induction motor. A flux sensor generates a flux signal corresponding to the magnetic flux at a predefined flux detection point external to the motor. A current sensor generates a current signal proportional to the current drawn by said motor. A time series of data points is stored, representing the values of the flux signal and the current signal over a period of time. The time series are transformed by FFT into a set of flux spectra and into a set of current spectra. Then the line frequency of the motor's power supply is determined by finding the maximum of the current spectra. Similarly, the slip frequency of the motor is determined by finding the maximum of the flux spectra in a predefined spectral range (e.g., below 2 Hz). The analysis of the rotor is then performed by comparing the amplitude of the current spectra, at a set of rotor fault harmonic frequencies, with specified fault threshold criteria. Each rotor fault harmonic frequency is a predefined function of the line frequency and the slip frequency. The presence of a rotor fault is denoted if the amplitude of any of said current spectra exceed a corresponding fault threshold criteria.

Journal ArticleDOI
01 May 1987
TL;DR: In this paper, the relationship between the homopolar flux generated by a statically eccentric rotor and the unbalanced magnetic pull in two-pole induction motors is considered, and it is shown that due to this kind of eccentricity, a homopholar flux is generated having the supply frequency, yielding a vibrational component of the unbalance magnetic pull with the double supply frequency.
Abstract: In this paper, the relationship between the homopolar flux generated by a statically eccentric rotor and the unbalanced magnetic pull in two-pole induction motors is considered. We will show that due to this kind of eccentricity, a homopolar flux is generated having the supply frequency, yielding a vibrational component of the unbalanced magnetic pull with the double supply frequency.

Journal ArticleDOI
TL;DR: In this article, a 1/7-scale model main rotor of the AH-1 series helicopter was compared with averaged full scale, inflight acoustic data under similar nondimensional test conditions.
Abstract: Acoustic data taken in the anechoic Deutsch-Niederlaendischer Windkanal (DNW) have documented the blade vortex interaction (BVI) impulsive noise radiated from a 1/7-scale model main rotor of the AH-1 series helicopter Averaged model scale data were compared with averaged full scale, inflight acoustic data under similar nondimensional test conditions At low advance ratios (mu = 0164 to 0194), the data scale remarkable well in level and waveform shape, and also duplicate the directivity pattern of BVI impulsive noise At moderate advance ratios (mu = 0224 to 0270), the scaling deteriorates, suggesting that the model scale rotor is not adequately simulating the full scale BVI noise; presently, no proved explanation of this discrepancy exists Carefully performed parametric variations over a complete matrix of testing conditions have shown that all of the four governing nondimensional parameters - tip Mach number at hover, advance ratio, local inflow ratio, and thrust coefficient - are highly sensitive to BVI noise radiation

Patent
22 Sep 1987
TL;DR: In this paper, a pressure pulse generator which generates relatively sinusoidal pressure pulses in a fluid flowing in a borehole is disclosed, where the rotor and stator are arranged such that the area of the adjacent gaps between the stator and rotor through which the fluid may flow in a direction parallel to the borehole varies approximately with the inverse of the square root of a linear function of a sine wave.
Abstract: A pressure pulse generator which generates relatively sinusoidal pressure pulses in a fluid flowing in a borehole is disclosed. The pressure pulse generator for a MWD tool broadly comprises: a housing adapted to be connected in a tubing string so that fluid flowing in the string will at least partially flow through the housing; a stator mounted within the housing and having a plurality of lobes with intervening gaps; a rotor coaxial to the stator which rotates relative to the stator and which is mounted within the housing and has a plurality of lobes with intervening gaps between adjacent lobes, wherein the lobes of the rotor and stator are arranged such that as the rotor rotates relative to the stator, the area of the adjacent gaps between the lobes of the stator and rotor through which the fluid may flow in a direction parallel to the borehole varies approximately with the inverse of the square root of a linear function of a sine wave. Preferably, the geometrical arrangement of the stator and rotor are substantially identical with a plurality of lobes with intervening gaps around a central circular hub. A first side of each lobe is defined by a radial extension from the circular hub, and the second side of each lobe is substantially parallel to the first side.

Patent
28 Dec 1987
TL;DR: In this article, a phase advance command signal and rotor position signals are used to drive an inverter switch circuit to energize a brushless DC motor with a preselected pattern stored in a memory.
Abstract: A control operates a permanent magnet brushless DC motor utilizing a phase advance signal to control motor torque. Input signals to the motor comprise a phase advance command signal and rotor position signals. The control provides switching signals to drive an inverter switch circuit to energize the motor. A start circuit is responsive to an analog rotor position signal and develops switching signals according to a preselected pattern stored in a memory. A run circuit compares a periodic sawtooth signal representing motor speed and a maximum desired phase advance, to a phase advance command signal to develop switching signals. The control switches from the start circuit to the run circuit at a preselected speed.

Patent
16 Jan 1987
TL;DR: In this paper, a belt driven vehicle alternator is enclosed by front and rear brackets/casing members, in combination with an aluminum housing surrounding the rotor and stator cores/coils, defining flow passages for a liquid coolant branched off from the engine cooling system.
Abstract: A belt driven vehicle alternator is enclosed by front and rear brackets/casing members 26, 30 which, in combination with an aluminum housing 24 surrounding the rotor and stator cores/coils, define flow passages for a liquid coolant branched off from the engine cooling system. The coolant inlet and outlet ports 28, 29 are both provided in the rear casing member 30 and are circumferentially proximate each other to minimize the space occupied by the alternator cooling system and tubes in the crowded engine compartment.

Patent
09 Mar 1987
TL;DR: In this article, a rotary material crusher with a rigid hammer assembly attached to a rotor is described, and a cap means is removably connected to the extension for crushing the material on rotation of the rotor, the cap defining an undercut portion which cooperates with the hammer member.
Abstract: A hammer assembly for attachment to a rotor of a rotary material crusher is disclosed. The hammer assembly includes a hammer member rigidly connected to the rotor and an extension of the hammer member having a longitudinal axis disposed parallel and spaced relative the axis of rotation of the rotor. The extension has a uniform transverse cross-sectional configuration along the length of the extension. A cap means is removably connected to the extension for crushing the material on rotation of the rotor, the cap defining an undercut portion which cooperates with the extension for locking the cap adjacent the hammer member.

Patent
19 Aug 1987
TL;DR: In this paper, a selfloading peristaltic pump with a rotor rotatably mounted about a rotor axis and a race having an internal surface for supporting a flexible tube in a pumping region between the rotor and the race is described.
Abstract: A self-loading peristaltic pump including a rotor rotatably mounted about a rotor axis, and a race having an internal surface for supporting a flexible tube in a pumping region between the rotor and the race, the surface including points that are at equal radii from the rotor axis in planes that are perpendicular to the rotor axis, the rotor including a roller for intermittently and progressively compressing the flexible tube against the race in the pumping region, the rotor including a radially extending rotor tab located outside of the pumping region for displacing the flexible tube toward the pumping region as the rotor rotates.


Journal ArticleDOI
TL;DR: Analyse numerique de l'ecoulement tridimensionnel d'un fluide visqueux dans un rotor de compresseur transsonique as discussed by the authors.
Abstract: Analyse numerique de l'ecoulement tridimensionnel d'un fluide visqueux dans un rotor de compresseur transsonique. Comparaison avec l'experience

Patent
28 May 1987
TL;DR: In this paper, a variable speed control-led induction motor with a rotor and a plurality of stators is described, where the stator windings are connected in series and the conductive members are short-circuited by connecting members at an air space or a non-magnetic core portion disposed between the rotor cores.
Abstract: This invention relates to a variable speed control­led induction motor. The motor has a rotor (8) formed in one-piece and a plurality of stators (24,25), the rotor having a plurality of rotor cores (2,3) and a plurality of conductive members (5) interconnected and the stators having respective stator windings (22,23). The stator windings (22,23) are connected in series, the conductive members (5) are short-circuited by connecting members (r) at an air space or a non-magnetic core portion disposed between the rotor cores (2,3) and at least one of the plurality of stators (24,25) is associated with a phase shifter (38;47;50;51) providing the voltage of a given phase to the stator windings, whereby the rotational speed can be controlled easily over a wide range with the excellent torque characteristics and efficiency being maintained.

PatentDOI
TL;DR: An apparatus for vibrating a pipe string in a borehole comprises at a downhole location a hydraulic motor having a stator part (2) and a rotor part (3).
Abstract: An apparatus for vibrating a pipe string in a borehole comprises at a downhole location a hydraulic motor having a stator part (2) and a rotor part (3), the stator part (2) forming part of the string (1) and the rotor part (3) being coupled to a percussion device (6) which longitudinally moves the rotor part (3) relative to the stator part (2) in an oscillating manner during the course of each rotation of the rotor part relative to the stator part.

Patent
28 Dec 1987
TL;DR: In this article, formed rotor laminations are employed to reduce eddy current losses in the pole faces and body of the rotor for homopolar, switched reluctance, or interior permanent magnet motor.
Abstract: In a homopolar, switched reluctance, or interior permanent magnet motor, formed rotor laminations are employed to reduce eddy current losses in the pole faces and body of the rotor. The homopolar and switched reluctance motor lamination is comprised of a magnetic portion having a plurality of pole pieces extending generally radially outward from the core portion and forming a plurality of interpole spaces. Non-magnetic, high resistance segments are bonded between the pole pieces to minimize windage losses and increase strength. The non-magnetic segments may be thinner in the axial direction than the magnetic portion to prevent contact between stack laminations. Additionally, a gap may be left between the interior core portion and the non-magnetic segment to facilitate use of automated welding techniques. In the interior permanent magnet motor lamination, the non-magnetic segments perform the function of circumferential bridges, with or without restraining ligaments, to increase the rotor strength and speed capability and increase specific torque.

Patent
02 Mar 1987
TL;DR: In this paper, the ratchet head is engaged with the drive rotor by means of a pawl in the ratchechet head and a ratchet gear on the rotatable drive rotor.
Abstract: A power driven wrench includes a rotatable drive rotor journalled between fixed arms of a yoke affixed to one end of a wrench handle containing a motor. Disposed between the yoke arms is a ratchet head which is driven in reciprocal angular motion by the motor. The ratchet head is engaged with the drive rotor by means of a pawl in the ratchet head and a ratchet gear on the drive rotor. A direction switching lever within the ratchet head permits the direction of rotation of the drive rotor to be manually selected. The switching lever extends from the sides of the ratchet head, such that the direction of rotation of the wrench can be easily changed even if the wrench is inadvertently backed up against an immovable object while removing a nut or bolt. The location of the switching lever enables it be actuated with the same hand holding the wrench, and also results in the wrench having a thin profile which is useful in confined spaces. In the preferred embodiment the drive rotor includes a hexagonal bore and a smaller diameter throughbore, which enable the wrench to function as a power driven box end wrench when used with suitable tool inserts.

Journal ArticleDOI
TL;DR: In this article, an out-of-flow directional microphone element array is used with a directivity pattern whose major directional lobe projects on the rotor disk to examine noise source distributions over a helicopter rotor model.