ACOUSTIC NOISE AND VIBRATIONS OF ELECTRICAL TRACTION CHAINS

Transcription

1 ACOUSTIC NOISE AND VIBRATIONS OF ELECTRICAL TRACTION CHAINS Focus on electromagnetically-excited NVH for automotive applications and EV/HEV Part 1 Intro & physics of electromagnetically-excited NVH LE BESNERAIS Jean contact@eomys.com Note: this presentation is based on extracts of EOMYS technical training EOMYS ENGINEERING

2 I. PRESENTATION Young Innovative Company* created in may 2013 Located in Lille, North of France (1 hour from Paris) Activities : engineering consultancy / applied research 6 R&D Engineers (electrical engineering, vibro-acoustics, heat transfer, scientific computing) 80% of export turnover Sectors : transportation (railway, automotive, marine, aeronautics), energy (wind, hydro), home appliances, industry *"Jeune Entreprise Innovante": the French government recognises that EOMYS runs significant R&D activities EOMYS ENGINEERING

3 II. REFERENCES EOMYS ENGINEERING

4 III. SERVICES Diagnosis and solving of NVH issues on electrical systems Multiphysic design optimization of electrical systems Technical trainings on vibroacoustics of electrical systems EOMYS can be involved both at design stage & after manufacturing of electric machines & passive components EOMYS ENGINEERING

5 IV. MANATEE software Electromagnetic and vibro-acoustic simulation software of electrical machines (Matlab-based) Only software suitable for NVH assessment both in basic design (semi analytical models) or detailed design phase (coupling with electromagnetic FEA and structural FEA e.g. Optistruct/Ansys) Fault simulation (e.g. eccentricity, broken bar, demagnetization, pole displacement) More than 100 post processing graphs to quickly find NVH root cause Up to 40 db reduction obtained on industrial cases See more at EOMYS ENGINEERING

6 V. EXPERIENCE Vibroacoustic analysis of more than more than 50 electric machines Wide range of electrotechnical solutions (e.g. skewing, current injection, notches, pole shaping) Wide range of topologies: induction & PM machines, inner and outer rotor, from 5 rpm to 150 krpm, from 100 W to 3 MW Extended NVH measurements (OMA, EMA, ODS) focusing on magnetic noise & vibrations, including telemetry EOMYS ENGINEERING

7 VI. NVH test facilities Combined semi-anechoic chamber & electrical lab NVH hardware 5 microphones (Piezotronics) 12 miniature accelerometers (B&K) 4 tri-axial accelerometers (B&K) 6 mono axis accelerometers (B&K) Impact hammer (DJB) and electrodynamic shakers (LDS) Laser vibrometer (Ometron) Tachometer (B&K) NVH software Dewesoft with 16 channel dynamic acquisition system for combined measurement of voltage, current, vibration and noise LEA Sound Lab from Genesis NVH post-processings Sound Power Level Order tracking and spatiograms Operational Modal Analysis, Experimental Modal Analysis Operational Deflection Shape EOMYS ENGINEERING

8 VII. PARTENAIRES Partenariats avec des laboratoires : - - Laboratoire Systèmes Electrotechniques et Environnement (LSEE, Béthune) - Réseaux industriels & universitaires : - cluster industriel Maîtrise Energétique des Entraînements Electriques (MEDEE) - pôle de compétitivité en R&D Automobile et Transports publics (MOVEO) - pôle de compétitivité des Transports Innovants (ITRANS) Partenaires financiers : EOMYS ENGINEERING

9 VIII. R&D INTERNAL RESEARCH PROGRAMME Analysis of electromagnetically-excited NVH current injection & influence of control development of fast hybrid simulation methods (FEM / semi-analytic) 3D electro-vibro-acoustic simulation of rotating machines (asymmetries, skewing) magnetostriction and Maxwell force simulation (GetDP) psychoacoustics of electromagnetically-excited noise advanced post processings of electrical machines NVH (e.g. spatiograms) new characterization methods of electrical machines structural behaviour EOMYS ENGINEERING

10 Recent publications (see EOMYS ENGINEERING

11 ACOUSTIC NOISE AND VIBRATIONS OF ELECTRICAL TRACTION CHAINS Focus on electromagnetically-excited NVH for automotive applications I. Physics of electromagnetic noise & vibrations II. NVH ranking of electric motors for EV / HEV III. Review of electrical actuators and passive components in EV / HEV IV. NVH experimental characterization of electric motors V. Modelling & simulation tools of electromagnetically-excited NVH VI. Noise reduction techniques of passive components and electric motors VII. Conclusions EOMYS ENGINEERING

12 PHYSICS OF ELECTRO-MAGNETIC NOISE & VIBRATIONS EOMYS ENGINEERING

13 ELECTRICAL SYSTEMS UNDER STUDY Active electrical systems: rotating electrical machines, electromechanical actuators Passive electrical systems: transformers, inductors, capacitors, resistors, cables Topologies of electrical machines: - inner rotor / outer rotor - induction machine / synchronous machines - PMSM / WRSM - AC / DC electrical machines Topologies of transformers/inductors: - planar / wound - tape wound / step-lap / laminated cores - toroidal / EI shape Topologies of capacitors - ceramic - plastic film (polymer) - electrolytic - metallised film [B48] [BMW window motor] [AVX website] [FEEM, railway-technology.com] EOMYS ENGINEERING

14 What do we call electro-magnetic acoustic noise and vibrations? noise and vibrations arising from variable electro-magnetic forces in audible range [20 Hz, 20 khz] Dynamic deflections due to variable magnetic field B (Maxwell, Laplace, magnetostriction) Dynamic deflections due to variable electrical field E (Maxwell=electrostatic, piezoelectric, electrostriction) variable current source rotating permanent magnet or DC current source variable voltage source Electrical machines Transformers, inductors Electrical machines Capacitors Note: in electric machines, magnetic noise is sometimes called electromagnetic noise (because magnetic field is created by electrical currents) but it has nothing to do with electrical field EOMYS ENGINEERING

15 Noise of an electric traction machine during starting: mechanical sources (e.g. bearings, gearbox) aerodynamic sources (e.g. fans) electromagnetic sources (e.g. pole/slot) Electromagnetic acoustic noise is characterized by strong tonalities compared to other noise sources Tonality is penalized by standards (usually 3dB per tonality) EOMYS ENGINEERING

16 Definitions Magnetic forces = «forces arising from the presence of a magnetic field» Magnetic noise and vibration = «noise and vibrations arising from magnetic forces» Magnetic field can be created by current sources or permanent magnets As noise and vibrations are dynamic quantities field source must vary with time: magnetic noise and vibrations are due to AC current or rotating permanent magnets Force types Local magnetic forces acting on the active parts can be - magnetostrictive forces (acting inside the material) B 2 - Maxwell forces (acting mainly at the interface of the material with air) B 2 Laplace forces acting on conductors IB EOMYS ENGINEERING

17 Definitions Electrical forces = «equivalent forces arising from the presence of an electrical field» Electrical noise and vibration = «noise and vibrations arising from electrical forces» Electrical field can be created by electrical charges As noise and vibrations are dynamic quantities field source must vary with time: electrical noise is due to varying electrical fields, so to AC voltage Force types Local electrical forces acting on the active can be - electrostrictive forces (acting inside the material) E 2 - electrostatic (acting mainly at the interface of the material with air) E 2 - reverse piezoelectric E EOMYS ENGINEERING

18 MAGNETIC FORCES IN ELECTRICAL SYSTEMS Laplace/Lorentz forces in electric motors Laplace forces apply to conductors In electrical machines B is small is slots so Laplace forces can be neglected Laplace forces are mainly considered when studying winding overhang vibrations of large machines [B38] EOMYS ENGINEERING

19 Laplace/Lorentz forces in passive components Laplace forces can be involved in cable noise issues in high current traction application Laplace forces generate transformer winding vibrations at load due to interaction with stray magnetic field [B39] Laplace forces acting on windings are generally negligible in inductors [B52] EOMYS ENGINEERING

20 Magnetostriction Magnetostriction includes [B6] - volume magnetostriction (isotropic): occurs for H>8kA/m, can be neglected in laminations - Joule and transverse magnetostriction (anisotropic): what is called here by «magnetostriction» Magnetostriction acts Magnetostrictive forces evolve with the square of the magnetic flux density ~1 to 10 µm/m EOMYS ENGINEERING

21 Magnetostrictive equivalent forces in electric machines (case of an induction machine): [B7] [B10] [B46] Magnetostriction forces can create radial vibrations of the outer yoke of electrical machines, thus they can potentially create acoustic noise From EOMYS experience, magnetostriction has never been the root cause of electric machine NVH issues EOMYS ENGINEERING

22 Magnetostrictive equivalent forces in transformers / inductors [B40] [B41] [B42] [B49] Magnetostriction tends to enflate the magnetic core Depending on bounday conditions dynamic deflections of the magnetic core may be able to produce acoustic noise In inductors vibrations due to magnetostriction is generally negligible [B41] compared to Maxwell forces EOMYS ENGINEERING

23 Maxwell forces: 1D illustration of noise and vibration Simple set-up to show the effect of Maxwell forces: tuning fork excited by a variable frequency current Variable frequency current creates a variable frequency magnetic field Magnetic field is guided by the iron of the tuning fork and creates a magnetic dipole at the fork tips Maxwell force is the magnetic attraction between the equivalent North and South poles of the fork tips The airgap tends to be reduced by Maxwell forces airgap N S EOMYS ENGINEERING Magnetic field line distribution 23

24 Maxwell forces: 1D illustration of noise and vibration Forced excitation (AC current with fixed frequency) Strong tonal noise is created without any mechanical contact between coil and tuning fork EOMYS ENGINEERING

25 Maxwell forces: 1D illustration of noise and vibration Resonant excitation (AC current with variable frequency f s ) f s =200 Hz A resonance (high noise level) is observed when feeding the coil at 200 Hz EOMYS ENGINEERING

26 Maxwell forces: 1D illustration of noise and vibration What happens at resonance for f s =200 Hz? I[A] B[T] I P[ N ] B 2 V[ m ] P L m 2 s p[db] 20log 10 (V) 200 Hz 200 Hz Maxwell 400 Hz 400 Hz acoustic 400 Hz The tuning fork natural frequency is close to 400 Hz (first bending mode) The match between exciting magnetic forces and tuning fork natural frequency create a resonance (high vibration level) Tuning fork behaves like a linear quadrupole and radiates acoustic noise at vibration frequency of 400 Hz EOMYS ENGINEERING

27 Maxwell forces: 2D extension to electrical machines Airgap reluctant (Maxwell) forces Modal basis of the magnetic circuit rotor stator (400 Hz) (648 Hz, m=2) (2585 Hz) (1356 Hz, m=3) Fork/fork-modes.html (2892 Hz, m=4) M. Boesing, «Acoustic Modeling of Electrical Drives, Noise and Vibration Synthesis EOMYS ENGINEERING

28 Maxwell forces: 2D extension to electrical machines [B7] [B10] [B46] Maxwell and magnetostriction forces / vibration / acoustic lines occur at same frequencies (quadratic function of the flux density) EOMYS ENGINEERING

29 Maxwell forces in transformers [B44] [B43] Maxwell forces concentrate in the region of reluctivity changes (air/iron interface) so in joint regions of step-lap transformer cores EOMYS ENGINEERING

30 Maxwell forces in inductors [B41] [B49] Maxwell forces concentrate in the airgap of inductors EOMYS ENGINEERING

31 Overview of electrical systems and main electromagnetic forces affecting their NVH behaviour Rotating machines Inductors Transformers Capacitors Cables Function Electrical to mechanical power conversion Maxwell + (stator / rotor attraction) Laplace - (overhang / leakage flux) Magnetostriction - (magnetic core) Magnetic energy storage (AC current filter) + (airgap reluctant forces) - (overhang / leakage flux) + (magnetic core) Electrical power conversion (AC voltage converter) + (airgaps in corners) + (winding / leakage flux at load) + (magnetic core) Electrical energy storage (AC voltage filter) Electrostatic + (armature attraction) Piezoelectric + (ceramic capacitors) Electrostriction - (electrostrictive polymers) Electrical power transmission + (external magnetic flux) EOMYS ENGINEERING

32 NVH characteristics (frequency content, potential resonances) highly depend on the electrical system topology Ex: Maxwell harmonic frequencies are different for PMSM and SCIM Ex: main vibration in passive component can be at f rip (current ripple frequency) or 2f rip depending on the presence or absence of a DC component in the current EOMYS ENGINEERING

33 Maxwell stress in electric machines - mathematical considerations The general formulation of the magnetic forces per unit volume in Cartesian direction i=1,2,3 is given by Lorentz force per unit volume magnetic permeability inhomogeneities torque if H and B are not colinear The combination of these forces can be expressed as a tensor, called «Maxwell tensor» The Maxwell stress experienced by the surface ds in normal and tangential directions is therefore given by EOMYS ENGINEERING

34 Due to Ostrogradski (or Gauss) theorem, the global body force acting on the stator (resp. rotor) can be obtained by integrating the Maxwell stress tensor over a surface enclosing the stator (resp. rotor) f S = ම fdτ = ම div(t)dτ = ඵ TdS = ර σds S S V si s V s The surfaces outside the active parts do not see any flux and do not contribute to the global force Therefore both rotor and stator magnetic forces are given by the Maxwell stress integration over the airgap cylinder (oriented) surface Sso Ssi V s Ss=Sso U Ssi B=0 Sri Sr=Sro U Sri Sro B=0 Inner rotor topologies are only considered in this presentation except when specified f S = ර σds S si f R = ර σds S ro EOMYS ENGINEERING

35 Taking cylindrical coordinates (global frame R linked to the stator), Maxwell stress can be written as stator volume dv σ = 1 μ (B r 2 B 2 θ B 2 z ) B r B θ B r B z 1 B r B θ 2 (B θ 2 B 2 r B 2 z ) B z B θ 1 B r B z B z B θ 2 (B z 2 B 2 r B 2 θ ) R airgap Ssi df S ds=-dsu r In 2D assuming B z =0, the equivalent local magnetic force df s acting on the part of the stator dv df S = σds = { 1 2μ 0 (B r 2 -B θ 2 )(ds.u r ) + 1 μ 0 (B r B θ )(ds.u θ )} u r σ r ds +{ 1 (B 2 2μ r -B 2 θ )(ds.u θ ) + 1 (B 0 μ r B θ )(ds.u r )} u θ 0 σ θ ds EOMYS ENGINEERING

36 For the airgap ds radial orientation (from outer stator or outer rotor viewpoint): σ r =- 1 2μ 0 (B r 2 -B θ 2 ) σ θ =- 1 μ 0 (B r B θ ) For the airgap ds radial orientation (from inner rotor or inner stator viewpoint): σ r =+ 1 2μ 0 (B r 2 -B θ 2 ) σ θ =+ 1 μ 0 (B r B θ ) The Maxwell stress can be expressed in complex form as σ = σ r + jσ θ = B2 2μ 0 B = B r + jb θ Other expression of Maxwell stress: EOMYS ENGINEERING

37 Taking the local field line frame, the Maxwell tensor becomes σ = μ H H μ H H 2 from [B3] from [B3] (law of maximal magnetic flux) (law of minimal reluctance) EOMYS ENGINEERING

38 Maxwell stress - physical considerations The module of df s is independent of the surface orientation ds, it corresponds to the local energy density Due to lower magnetic permeability, most of the magnetic energy is concentrated in the airgap energy cannot be stored without stress Energy density is homogenous to pressure, σ is in N/m 2 The integration of the Maxwell force over the whole rotor is the opposite of its integration over the whole stator A simple consequence of this is the counter torque experience on the stator side Similarly, all the radial force harmonics experienced by the stator are experienced by the rotor but with a frequency shift (detailed later) Radial and tangential stress have the same harmonic content (same pattern of null time & space harmonics in their FFT2) Maxwell stress can be extended to electrical field (expression of the electrostatic stress in capacitors) EOMYS ENGINEERING

39 For a ds in the airgap from [B7] «traction» attraction «shear» «compression» repulsion Noise & vibrations Noise & vibrations (also!) Torque Case 1: most common at interface iron / air in linear case EOMYS ENGINEERING

40 Example of the Maxwell stress in an ideal electric machine without time nor space harmonics B r = B r0 cos ω s t + pα s B θ = B θ0 cos(ω s t + pα s + φ) average radial force harmonic radial force σ r = 1 (B 2 2μ r B 2 θ ) = 1 (B 2 0 4μ r0 B 2 θ0 ) + 1 (B 2 0 4μ r0 B 2 θ0 cos(2φ))cos 2ω s t + 2pα s + 1 B 0 4μ r0 B θ0 sin 2φ sin 2ω s t + 2pα s 0 σ θ = 1 μ 0 B r B θ = 1 2μ 0 B θ0 B r μ 0 B θ0 B r0 cos 2ω s t + 2pα s 1 4μ 0 B θ0 B r0 sin 2φ sin 2ω s t + 2pα s σ r, σ θ electromagnetic static torque harmonic torque 0 2p wavenumber 2f s Hz EOMYS ENGINEERING

41 2p is called the wavenumber, it corresponds to the number of maxima of the wave (spatial frequency along the airgap) Space order is the normalization of the wavenumber with respect to p, wavenumber 2p means space order=2 A fundamental field of 0.5 T creates a radial pressure at 2f s of 10 5 N/m 2 i.e. ~10 tons per m 2 In an ideal machine the excitation at 2f s is always present, it is the strongest and it is directly linked to electromagnetic (not reluctant) torque production A magnetic noise or vibration issue at 2f s can therefore be very hard to tackle without degrading torque EOMYS ENGINEERING

42 2D illustration of noise and vibration due to Maxwell forces Forced excitation (rotating magnet) N stator angleα s ωr S steel tube (slotless stator) 1-pole magnet (p=1) rotating shaft at ω R Magnets create a fundamental flux B with 1 minium and 1 maximum (p=1 pole pair) along the airgap, but the stator deformation (so magnetic force) has 2 minima and 2 maxima Magnetic force F is proportional to the square of flux density and has therefore 2p=2 pole pairs (two maxima & two minima) r=2p is called wavenumber Quadratic relationship between B and F affects both time (cf. tuning fork) and space domains Ferromagnetic materials can be deformed under Maxwell stress, resulting in forced vibration and acoustic noise B = B 1 cos pω R t + pα s F = F 0 + F 2 cos 2pω R t + 2pα s frequency wavenumber EOMYS ENGINEERING

43 Magnitude [T] Magnitude [N/m2] Magnitude [T] Magnitude [N/m 2 ] No-load flux density of a PMSM, ideal case (no mmf space harmonic, no slotting harmonic) p=12 adial flux density at t = 0 s as a function of space x Airgap radial force at t = 0 s as a function of space Angle [ ] Airgap radial flux density FFT over space Angle [ ] x 10 4 Airgap radial forcee force FFT over space Space harmonic [] Space harmonic [] EOMYS ENGINEERING

44 r [N/mm2] 6 4 x Airgap radial force FFT2 zoom out down to 0 Hz {2f s,2p} {0,0} Frequency [Hz] spatial order [r] An ideal machine (sine mmf, no slots, no PWM) creates a single Maxwell stress wave at twice the electrical frequency and twice the number of pole pairs EOMYS ENGINEERING

45 Magnitude [T] Magnitude [N/m2] Magnitude [T] Magnitude [N/m 2 ] No-load flux density of a PMSM, real case (mmf space harmonic + slotting harmonic) rgap radial flux density at t = 0 s as a function of space x Airgap radial force at t = 0 s as a function of space Angle [ ] Airgap radial flux density FFT over space Angle [ ] x 10 4 Airgap radial forcee force FFT over space Space harmonic [] Space harmonic [] EOMYS ENGINEERING

46 Airgap radial force FFT2 r [N/mm2] f=2f s =191 Hz r=3 f=4f s =382 Hz r= Frequency [Hz] spatial order [r] Slotting and winding harmonics enrich Maxwell stress with force harmonics of lower wavenumber and higher electrical frequencies EOMYS ENGINEERING

47 Radial & tangential magnetic force waves Airgap magnetic stress can be decomposed using Fourier transform: σ t, α s = n,r σ nr cos 2πnf s t + rα s + φ nr r and frequency nf s travelling in the airgap r nodes α s is the airgap angle in the stator frame nf s is the electrical frequency, the mechanical rotation frequency of the force wave being nf s /r EOMYS ENGINEERING

48 Magnitude [N/m2] Magnitude [N/m 2 ] Magnitude [db] Magnitude [N/m2] Magnitude [N/m 2 ] Progressive (=rotating) force wave of order r=+2 at 6f s =360 Hz F=F 0 cos(6w s t+2α s ) noted {6f s, 2} Airgap radial force at t = 0 s as a function of space Maxwell tensor main lines and stator natural frequencies rotation in anti-trigonometric direction at 6f/r Angle [ ] Airgap radial forcee force FFT over space {6f s,+2} Space harmonic [] Frequency [Hz] Spatial order [r] Airgap radial force at t = s as a function of space Angle [ ] Airgap radial forcee force FFT over space Space harmonic [] EOMYS ENGINEERING

49 Magnitude [N/m2] Magnitude [N/m 2 ] Magnitude [db] Magnitude [N/m2] Magnitude [N/m 2 ] Progressive (=rotating) force wave of order r=-2 at 6f s =360 Hz F=F 0 cos(6w s t-2α s ) noted {6f s, -2} Frequency [Hz] 500 X= 360 Y= -2 Z= rotation in trigonometric direction at 6f s /r {6f s, -2} Spatial order [r] Airgap radial force at t = 0 s as a function of space Angle [ ] Airgap radial forcee force FFT over space Space harmonic [] Airgap radial force at t = s as a function of space Angle [ ] Airgap radial forcee force FFT over space Space harmonic [] EOMYS ENGINEERING

50 Magnitude [N/m2] Magnitude [N/m 2 ] Magnitude [db] Magnitude [N/m2] Magnitude [N/m 2 ] Standing (=pulsating) force wave of order r=-2 at 6f s =360 Hz F=F 0 cos(6w s t)cos(2α s ) noted {6f s, +/-2} Maxwell tensor main lines and stator natural frequencies Airgap radial force at t = 0 s as a function of space Angle [ ] Airgap radial forcee force FFT over space Frequency [Hz] {6f s,+2} & (6f s,-2} Spatial order [r] Space harmonic [] Airgap radial force at t = s as a function of space Angle [ ] Airgap radial forcee force FFT over space Space harmonic [] EOMYS ENGINEERING

51 Illustration of the decomposition of a standing wave in two travelling wave of opposite direction Acos 2πf s t + rα s + Acos 2πf s t rα s = 2Acos 2πf s t)cos(rα s steady vibration nodes At same magnitude a rotating vibration makes 3 db more than a pulsating vibration in SWL The pulsating force wave has steady nodes in the stator frame only, the rotor sees two rotating waves with different velocities EOMYS ENGINEERING

52 The airgap stress waves projection on the stator and rotor give the resulting magnetic force Example on the 14 stator teeth of a fractional slot winding PMSM (r=0, 2, 8): from [B27] EOMYS ENGINEERING

53 STATIC EFFECT OF MAGNETIC FORCES Effect of radial force harmonics on an outer stator, r=0 A radial force wave of wavenumber r=0 gives a stator radial deflections of wavenumer 0 r=0 r=1 r=0 r=2 The radial displacements of the yoke are qualitatively given by [B8] U w0 F w0 1 E R h E equivalent Young modulus of the yoke L stator length R yoke average radius h yoke average width F rw magnitude of r-th order radial force wave at frequency w/(2π) not pressure The thicker (high h) and the smaller (small R) is the yoke, the lower is static radial displacement EOMYS ENGINEERING

54 Effect of radial force harmonics on an outer stator, r=1 A radial force wave of order 1 corresponds to an unbalanced magnetic pull which can tilt the stator, especially if the lamination is only clamped at one end It is also called a rigid body motion EOMYS ENGINEERING

55 Effect of radial force harmonics on an outer stator, r>1 A radial force wave of wavenumber r gives a stator radial deflections of order r with same phase (if Z s /2 r=6 r=2 The radial displacements of the yoke are qualitatively given by [B8] U wr F wr 1 Er 4 R h 3 3 E equivalent Young modulus of the yoke R yoke average radius h yoke average width F rw magnitude of r-th order radial force wave at frequency w/(2π) not pressure Radial displacement of due to r>1 decrease much quickly with h/r than displacement due to r=0 Radial yoke deflection decrease in r 4 : only low spatial order force harmonics are of interest Due to quadratic relationships, high wavenumber flux density harmonics can generate high vibrations EOMYS ENGINEERING

56 Effect of tangential force harmonics on an outer stator A tangential force wave of order r=0 gives a torsional deflection of the yoke with same phase A tangential force wave of order r>1 gives a radial deflection of the yoke of order r with different phase due to the teeth bending moment from [B1] from [B2] Torsional deflection Radial deflection EOMYS ENGINEERING

57 Effect of radial force harmonics on an inner rotor Radial force wave of order r>1 and r=0 do not create deflections due to high shaft stiffness Radial force wave of order r=1 (Unbalanced Magnetic Pull) generate bending of the rotor shaft Effect of tangential force harmonics on an inner rotor Tangential force waves of order r=0 induce torsion of the rotor shaft Fy<0 net force Tangential force waves of order r>0 do not create torsion EOMYS ENGINEERING

58 Case of an outer rotor with PM Radial force waves creates similar deflections as on the stator Tangential force harmonics with r>0 also create radial deflection of order r Standing airgap force wave {f,r}+{f,-r} is seen as two progressive force waves of different frequencies {f+/-rf R,r} Frequency shift is proportional to r times the rotating frequency (rf R ) Inner rotor Outer rotor see [B15] EOMYS ENGINEERING

59 STRUCTURAL MODES OF ELECTRICAL MACHINES Structural modes of the stator lamination Structural modes of the external structure (stator or rotor) are generally characterized using an analogy with a cylinder Cylinder deflections can be characterized by circumferential (m) and longitudinal (n) spatial frequencies Each structural mode is then associated to a pair of integers (m,n) Note the distinction with the excitation wave number r and the structural mode order m Example of 3D modes (2,0) (2,1) (3,0) (3,1) EOMYS ENGINEERING

60 The spatial order m and n can be linked to the number of nodes (null vibration) of the deflection m is half the number of circumferential nodes, n is the number of axial nodes Example of 2D circumferential modes with free-free BC BC modulation function Example of a 3D circumferential modes with clamped end U(α, z) = γ(z)u mn cos(mα + nz L + φ mn) (4,0) - 1 axial node (4,1) - 2 axial nodes EOMYS ENGINEERING

61 Cylinder modes (m,n>1) are generally higher in frequency than (m,0) modes frequency= 516Hzfrequency= 1384Hzfrequency= 1693Hzfrequency= 2498Hz frequency= 2539Hz frequency= 2822Hzfrequency= 3166Hz mode=(2,0) THD= mode=(3,0) THD=0.019 mode=(3,1) THD=0.17 mode=(4,0) THD=0.029 mode=(1,1) THD=0.18 mode=(4,1) THD=0.16 mode=(2,2) THD=0.26 frequency= 3281Hzfrequency= 3315Hzfrequency= 3362Hz frequency= 3654Hzfrequency= 3681Hzfrequency= 3761Hzfrequency= 4067Hz mode=(0,1) THD=0.19 mode=(0,0) THD=0.084 mode=(3,2) THD=0.25 mode=(1,2) THD=0.34 mode=(2,1) THD=0.14 mode=(5,0) THD=0.036 mode=(5,1) THD=0.16 frequency= 4075Hzfrequency= 4168Hzfrequency= 4856Hz mode=(0,2) THD=0.31 mode=(4,2) THD=0.24 mode=(1,0) THD=0.2 Results from MANATEE software Longitudinal modes importance is linked to the axial length to diameter ratio of the machine EOMYS ENGINEERING

62 Remarkable modes: - -> generally it has the highest frequency - (1,0) is the bending mode excited by unbalanced pull - (2,0) is the ovalization mode - (0,1) is a torsional (tangential) or tilting (radial) mode (Clamped-free stator) EOMYS ENGINEERING

63 The local modes of the teeth are called tooth rocking modes [B4] There exist some teeth modes alone, or some coupled modes between teeth and back core The importance of teeth modes is linked to the tooth to yoke height ratio (0,0) tooth mode (1,0) tooth mode (2,0) tooth mode (4,0) tooth mode When there are few teeth several modes appear at close frequencies EOMYS ENGINEERING

64 (2,0) (2,1) (2,1) (2,0) EOMYS ENGINEERING

65 Structural modes of an inner rotor Only bending modes and torsional modes are of interest Strong electromechanical coupling can occur when rotating at the first rotor flexural frequency in large IM n=1 n=2 From [B11] From [B11] EOMYS ENGINEERING

66 DYNAMIC EFFECT OF MAGNETIC FORCES Generalities Resonances (high vibration and noise amplification) can occur at two conditions [B8] time frequency match between the exciting force and the structural mode natural frequency spatial frequency («order») match between the exciting force and the structural mode shape EOMYS ENGINEERING

67 Stator resonance in 2D EXCITATION FORCE One pole pair (r=2 pole pairs) excitation rotating at nf s /r F = F 2 cos 2πnf s t + rα s EXCITED STRUCTURE Elliptical mode of the stator stack (m=2) of natural frequency f 2 nf s <f 2 U = U 2 cos 2πf 2 t)cos(mα s nf s =f 2 RESONANCE nf s >f 2 EOMYS ENGINEERING

68 In 2D resonances (high vibration and noise amplification) occur at two conditions: match between the exciting force frequency f and the structural mode natural frequency f m : match between the exciting force pattern r and the structural mode shape m: f=f m r=m The frequency match does not hold on the mechanical frequency, but on the electrical frequency This is valid for the excitation of purely radial modes but also torsional modes (a torsional modal deflection has all its points moving in phase so r=0 is necessary) Far from resonance, the vibration pattern is given by the exciting force pattern (rotating vibration if rotating force, same wavenumber) At resonance, the vibration pattern fits with the pulsating modal shape (fixed node positions) EOMYS ENGINEERING

69 Far from resonance, the vibration pattern is given by the exciting force pattern (rotating vibration if rotating force, same wavenumber) At resonance, the vibration pattern fits with the pulsating modal shape (fixed node positions) Note that significant acoustic noise can be created without resonance EOMYS ENGINEERING

70 The resonance speed has been proved analytically by Soedel [B8] Both a progressive rotating force wave and a standing pulsating force wave can resonate under resonance conditions, whatever the rotation direction This is the case of the ideal resonance, but a r=4 exciting force can slightly make the ovalization mode m=2 respond (lower magnification) in the presence of geometrical or mass assymetries main resonance From [B9] secondary resonance In this example the secondary resonance has 10 times less magnitude (-20 db for noise & vibration levels) EOMYS ENGINEERING

71 The modal participation factor of magnetic forces can be quantified using Modal Force Matrix MFM: [B51] EOMYS ENGINEERING

72 FROM MAGNETIC VIBRATION TO ACOUSTIC NOISE Vibroacoustic transfer paths Circumf erential wavenu mber Force direction r>0 Radial, tangential Transfer path Air borne Description Radial circumferential deflection of the outer stator yoke and frame or outer rotor (rotating in forced regime, pulsating at resonance) r=0 Radial Air borne Radial pulsating circumferential deflection of the stator yoke and frame or outer rotor r=0 Tangential (cogging torque / torque ripple) r=0 Tangential (cogging torque / torque ripple) r=1 Radial (unbalance magnetic pull) r=1 Radial (unbalance magnetic pull) Structural borne Air borne Air borne Structural borne Propagation of rotor torsional vibration to rotor shaft line and gearbox mount, or bearing sleeves and outer stator frame Deflection of the outer stator yoke and frame or outer rotor following a unbalanced torsional mode due to particular boundary conditions Bending / tilting deflection of the outer stator frame or outer rotor, in particular in clamped-free conditions Propagation of rotor bending vibration to rotor shaft line and gearbox mount, or bearing sleeves and outer stator frame NA Axial Air borne Axial deflection of the end-shields EOMYS ENGINEERING

73 EXAMPLES Pure slotting noise in SCIM during sinusoidal run-up Asynchronous PWM noise at starting of a SCIM EOMYS ENGINEERING

74 Boundary conditions Different frame boundary conditions : - Clamped / clamped for most horizontal motors - Clamped / free for some horizontal motors or vertical motors - Free / free never met under operation - More complex boundary conditions exist on real machines (asymmetrical mounting ears) [B50] EOMYS ENGINEERING

75 Real boundary conditions modify the natural frequencies, more or less depending of the type of structural mode Real boundary conditions generally breaks the symmetries and multiply the number of cylindrical modes (for instance two (2,0) appear at different frequencies) in particular fixations can introduce some order 1 in the yoke deflections which can then be excited by UMP forces, or some order 0 which will be excited by torque ripple (2,0) (2,0) (2,0) (2,0) (3,0) [B37] EOMYS ENGINEERING

76 Structural damping Each modal deflection can be associated to a structural damping quantifying the energy dissipation due to friction Damping mainly comes from the winding & lamination insulation, and resin Depending on the VPI process the contribution of resin differs In practice reduced damping varies from 1 to 2% (xi/xic) Damping is higher for longitudinal modes such as (2,1) B11] and PMSM EOMYS ENGINEERING