Motor Acoustics Overview

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1 Motor Acoustics Overview Ceter for Acoustics & Vibratio May 5, 9 Dr. Marti L. Pollack

2 APS Backgroud Research, Developmet, & Egieerig Small Busiess Approximately 57 Egieers & Scietists ~ ½ hold PhDs i Egieerig, Physics, Math Offices i Groto, CT; Lexigto, MA; Arligto, VA Focus i Acoustics, Sigal Processig Hydrodyamics, Electromagetics Customer Base primarily Natioal Defese R&D Commuity Office of Naval Research, DARPA 579 slide

3 Backgroud Uio Graduate College Motor Acoustics Course Marty Pollack Chuck Slavik Mark Debortoli 579 slide 3 3

4 Motor Acoustics Themes Motor Geerated Vibratio Sources --- Curret & Flux Field --- Distributed Forces & Torques Iverter Fed Motors ---ifluece of iput curret wave forms Stator System Vibratio & Soud Radiatio --- shell dyamics --- radiatio efficiecy Focus of the CAV Overview 579 slide 4 4

5 Motor Acoustics Themes Rotor System Noise & Vibratio --- rotor dyamics --- bearig dyamics Aerodyamic Noise Coolig System --- fa oise --- flow oise Noise Cotrol Approaches --- isolatio --- dampig --- source reductio 579 slide 5 5

6 Some Motor Fudametals Electrical power Voltage, curret Mechaical power Torque, speed How is this doe i a AC motor? Rotor is magetized Stator currets form rotatig magetic field Iteractio produces torque o rotor (DC But Rotatig magetic field deforms stator dyamically Features & oidealities produce harmoic forces & torques 579 slide 6 6

7 Motor Acoustics Process Overview Aalysis Process Iput Electromagetic Force Model Structural Dyamics Model Acoustic Model Forces, Torques Vibratio Velocity Soud Radiatio Soud Power Determiistic Aalysis Models Electromagetic Forces: Fiite Elemet Models, Aalytical Models Structural Dyamics: Fiite elemet Models, Aalytical Models Soud Radiatio: Boudary Elemet Models, Fiite Elemet Models, Aalytical Models 579 slide 7 7

8 The Air Gap Magetic Field of a AC Motor Two magetic fields, rotor ad stator fields, are preset i the air gap of all AC motors. Each field has both a radial ad tagetial compoet, So, i geeral four field compoets must be cosidered: B B B Total Rotor Stator Radial Radial Radial B B B Total Rotor Stator Tagetial Tagetial Tagetial 579 slide 8 8

9 The Rotatig Magetic Field phased periodic currets rotatig curret, MMF, & flux field Phase A peakig Phase - C peakig Phase A Phase B Phase C This example is for a two-pole field, where the magetic field travels oe full revolutio i 1 electrical cycle. Phase B peakig 5 6 Phase -A peakig 579 Phase C peakig slide 9 9 Phase -B peakig

10 MagetoMotive Force (MMF 579 slide 1 1

11 The Fudametal Radial Field The air gap field of a motor is the summatio of the rotor field ad the stator field. I theory, each compoet is depedet o r, ad time. z-depedece is igored. BAirGap r,, t Brotor r,, t Bstator r,, t The air gap field ca be re-writte ito the followig form B AirGap r,, t B o r cos p t Cotais all of the radial depedece Cotais all of the theta ad time depedece This is the simplest compoet of the air gap field ad is the Fudametal Flux Desity Wave, with B o a costat. (measured i tesla (T 579 B cos p t o slide 11 11

12 Radial Force Field: Evolvig Complexity Rotatig Curret Field MagetoMotive Force Magetic Flux Distributed Forces &Torques Perfect Motor with Perfect Power Sparse Spectrum: Pole Passig Perfect Motor with Imperfect Power ( harmoic cotet i power Imperfect Motor with Imperfect Power Rich Spectrum: Pole Passig ( eccetric rotor Breathig Mode Beam Bedig 579 slide 1 1

13 Perfect Motor Perfect Power Air gap flux desity field of motor: B airgap r,, t B r cos p t o Radial stress fuctio: P Radial r,, t B r cos p t o o Key Relatio Bo r Bo r PRadial r,, t cos p t 4 4 o o This is the pole-passig oise compoet. It exists i all AC machiery, motors of ay type ad also i geerators. It sets a lower limit o the miimum oise a electric machie produces. It always occurs at twice the power lie frequecy (E ad this magetic pressure wave always cotais p pole-pairs (the order of the forcig fuctio Note: cos p t 1 cos p t slide 13 13

14 Air gap flux desity wave. Magetic Pressure Poles.4 Perfect Motor- Perfect Power Compariso of 6Hz flux desity wave with 1 Hz pressure wave for a 4-Pole motor. Note: There are 4 magetic flux desity poles i this graph ad 8 magetic pressure poles (relative to the Ave. magetic pressure value AC Motor (6Hz, 4-Pole 3 Ave. Magetic Pressure Magetic Air Gap Agle (rad. Flux Poles 4 Magetic Pressure Wave 579 slide

15 Amplitude of magetic pressure wave Perfect Motor- Perfect Power For 6 Hz. lie frequecy Amplitude of magetic pressure wave is about 6 psi for a 1 Tesla air gap field E Aalytical Frequecy Model spectrum Calculatio of square of air gap B-field Perfect Motor + Perfect (Siusoidal 6Hz. Power frequecy (Hz 579 Pole-passig oise at twice supply frequecy (E exists i all AC machies slide 15 15

16 Adjustable speed motor drive circuit Three-phase 5 or 6 Hz AC power source at left. AC-to-DC Rectifier (left box. DC power trasmitted via itermediate circuit (i middle. Iverter circuit which employs solid-state switches switched at high frequecy to geerate variable frequecyvariable voltage AC power (right AC motor at far right. Iverter Fed Motors AC Motor 579 DC Power High Speed Solid- State Switches Variable Voltage Variable Frequecy AC Power slide 16 16

17 Perfect Motor with Imperfect Power Time harmoic currets from power supply Cosider just a sigle time harmoic curret ad the fudametal curret. Both appear i the air gap field. Bairgap, t Bo cos p t B cos p t Usig Maxwell stress We arrive at P mag P mag B airgap B cos p t B cos p t o o o 3 k widig N stph I P B B cos p t o B 4 o B o 1 cos p t 1 cos p t 4 4 B B cos t o o o The two squared terms produce pole-passig oise; oe for the fudametal ad oe for the time harmoic. The cross-product term cotais two compoets; where B 4 o The first is a p-mode pressure wave with frequecy -+ ; The secod is a zero-mode pressure wave with the opposite frequecy 579 slide 17 17

18 Magetic pressure (relative uits Perfect Motor with Imperfect Power Time harmoic currets from power supply 3 E Magetic pressure vs frequecy for AC motor with 5 th, 7 th, 11 th & 13 th time harmoic currets. Frequecy spectrum of Square of air gap B-field 14 4E 6E Sum ad differece terms 6 8E 1E 1E 14E frequecy (Hz 579 slide 18 18

19 Imperfect Motor: Rotor Eccetricity 579 slide 19 19

20 Magetic pressure (relative uits Imperfect Motor with Imperfect Power Time harmoic currets from power supply & rotor eccetricity Magetic pressure vs frequecy for AC motor with 5 th, 7 th, 11 th & 13 th time harmoic currets, with rotor eccetricity. 3 E Frequecy spectrum of square of air gap B-field 14 6E 6 4E 8E 1E 1E 14E frequecy (Hz slide

21 Magetic Torque P ta 1 ( r,, t [ B ( r,, t B ( r,, t] : distributed load rad ta Torque( R, t [ P ta ( R, Motor Sources of Torque Ripple: 1. Coggig Effect : iteractio betwee rotor magetic flux & variable permeace of air gap due to stator teeth & slot opeigs. Distortio of siusoidal or trapezoidal distributio of magetic flux i air gap 3. Differeces betwee permeaces of air gap alog d (radial- ad q (tagetial-axes, t d Power Supply Sources of Torque Pulsatio: 1. Curret ripple resultig from PWM or rectifier harmoics. Phase curret commutatio ] R L 579 slide 1 1

22 Phase Curret (A 579 Ifluece of the switchig frequecy of a iverter The phase voltage waveforms for PWM ad Siusoidal are: zero V a t V Iverter Phase voltage for Phase-A Iverter Phase voltage for Phase-B t sec zero V T cos e t slide V Siusoidal Phase Voltage for Phase-A Siusoidal Phase Voltage for Phase-B zero zero Phase-A Phase-A Curret V T cos evs. t Waveform Time 3 8 V b t V V t sec t 1 sec Amp frequecy (5 Hz Lots of curret harmoics time (secods 4 t sec

23 Magetic Pressure MageticTorque MageticTorque Curret Ifluece of the switchig frequecy of a iverter The FFT s of phase curret, radial magetic pressure, motor torque. 1 1 Phase A Curret FFT of Phase-A Curret Waveform Lots of harmoics Frequecy (Hz Each harmoic i the curret waveform produces two magetic pressure waves ad a pulsatig torque harmoic. (ref. slides & 9.1 Figure 6: FFT of the phase curret waveform show i Figure 5. Switchig frequecy is 5, Hz. Supply frequecy preseted to the motor is 5 Hz. Graph produced by the APS trasiet motor-motor drive model. FFT of Magetic Pressure 1 1 FFT FFT of of Magetic Magetic Torque Torque Frequecy (Hz Frequecy (Hz Frequecy (Hz Figure 7: FFT of the magetic pressure produced by the motor model drive by the voltage waveform show i Figure 4. Switchig frequecy is 5, Hz. Supply frequecy Figure 8: FFT of the magetic torque produced by motor model whe drive by the slide 3 3 preseted to the motor is 5 Hz. Graph produced by the APS trasiet motor-motor drive voltage waveform show i Figure 4. Switchig frequecy is 5, Hz. Supply frequecy model. preseted to the motor is 5 Hz. Graph produced by the APS trasiet motor-motor drive

24 Structural Dyamics of Motor Distributed EM Forces & Torques excite Stator & Rotor Stator Modeled as Shell Structure --- classical aalytical methods --- umerical methods (FEA, Impedace --- complexity of built up structure scatterig mechaisms Rotor Modeled as Beam --- accout for shaft, bearigs, load --- may eed shell dyamics i viciity of motor force field Wide Badwidth of Iterest: Low High Frequecy 579 slide 4 4

25 slide Stator: Dyamics of Shell ] [(1 1 ( ( (1 ( ] [(1 (1 (1 ] [(1 ] [(1 ] [(1 ( ] [(1 ] [(1 4 t w E w h R w v R x u R t v E w R v R x v x u R t u E x w R x v R u R x u Goverig Equatios of Motio (e.g. Doell cos( si( cos( W e w e V e v e W e w L x i i t i L x i i t i L x i i i i i :Separable Solutios Low Frequecy focus Separated Modes

26 Simplified Stator Resoace Frequecies (Gieras Classical approaches: stator system (i.e. stator core, widigs, frame cosidered as sigle rig loaded with teeth & widig. Natural frequecy of stator system of circumferetial mode : f (1 K M K : equivalet stiffess of stator system (Nm M : equivalet mass of stator system (Kg Oly captures vibratios of stator core aloe, without ay frame ad ed bells, ad with partial ifluece of widigs & teeth. Actual stator is complex structure cosistig of lamiated stack with yoke & teeth, widig distributed i slots, pottig ecapsulatio, & frame. 579 slide 6 6

27 Simplified Stator: Breathig Mode K 4 ( Echc Li Dc; M M k c md D h c c L i c k k i md Breathig mode (=: h c : thickess M c : mass D c : mea diameter c : mass desity k i : stackig factor k md : mass additios factor k 1 ( M M M md t w i M c M t : mass of all stator teeth M w : mass of stator widigs M c : mass of stator core cylider f (1 D E ( c c c i md k k 579 slide 7 7

28 Modal Approach to Shell Dyamics Modal Equatio of Motio M [ q q q ] Q equatio of motio w( x,, t 3 1 m 1 q ( tcos( w ( x;[ e. g. w ( x ~ W si( m x L] x v( x,, t 3 1 m 1 q ( tsi( v ( x;[ e. g. v ( x ~ V si( m x L] u( x,, t 3 1 m 1 q ( tcos( u ( x;[ e. g. u ( x ~ U cos( m x L] simply supported shell Participatio Factors: U W ; V W Q : Geeralized Forces due to Radial & Tagetial Distributed Loads 579 slide 8 8

29 Modal Approach to Shell Dyamics Q... S S F w ( x, F ( x, u, t, t w u ( xcos( ( xcos( ds ds S F ( x, v, t v ( xsi( ds Geeralized Force: ecompasses motor forces & torques icludes attached structure iteractios M h S [ w ( xcos ( v ( xsi ( u ( xcos ( ] ds : Geeralized Mass q Q { M [(1 4 ( ]} : Geeralized Deflectio High Mobility of Low Order Modes Critical to Respose --- forces i =, 1, modes drive receptive shell major resposes --- forces i pole passig mode drive stiff shell low respose 579 slide 9 9

30 Mobility, db re. 1 mn-s odimesioal mobility Drive Poit Mobility: Radial Drive Typical Drive Poit Mobility -7-8 Modal Drive Mobility Y - Drive Node Yrr 1 Nodimesioal Mobility of Sigle Degree of Freedom System stiffess mass 1 stiffess cotrolled mass cotrolled Frequecy, Hz frequecy ratio shell oscillator 579 slide 3 3

31 Soud Radiatio Efficiecy Soud geerated i medium by vibratios of structure. Acoustic effects quatified by soud pressure & soud power. Trasfer fuctio from structural vibratio to acoustic respose describes eergy trasfer mechaisms. Soud radiatio efficiecy, : [ cs v ] : soud power radiated from structure S: area of radiatig surface : desity of medium c : speed of soud i medium <v > : spatial averaged mea square velocity over structure radiatig surface Relates radiated soud power to spatial averaged vibratio level 579 slide 31 31

32 Modal Radiatio Efficiecy of Cylidrical Shells Soud power radiated per uit legth for ka<<1 & k z <<k:.5 c a( ka v 1.5 c a( ka 3 v 1 (1 64 c a( ka 5 v (Fahy text ( a c v ; modal radiatio efficiecy v v 4; slide 3 3

33 High Frequecy Motor Acoustics Forcig fuctios motor drive switchig iteractig with motor Structural Dyamics: SEA &or semi-ifiite view of structure Hybrid modelig with impedace & SEA methods Radiatio efficiecy : comparable modal efficiecy at high waveumbers 579 Stator Shell Structural Dyamics & Soud Radiatio Chage -- Comparable Modal Structural Mobilities -- Comparable Soud Radiatio Efficiecies Greater Focus o Pole Passig Motor Forces slide 33 33

34 Mechaical Sources of Noise & Vibratio Rotor Dyamics --- classical rotatig machiery sources Bearigs --- classical discrete sigals due to bearig defects Coolig Fas blade passig toes turbulet flow broadbad excitatio Classical approaches to Aalysis & Quietig 579 slide 34 34

CALCULATION IN THE FIELD OF SEGMENTAL ROTOR MACHINES TAKING INTO ACCOUNT WINDING HARMONICS AND ROTOR AIRGAP IRREGULARITIES

CALCULATION IN THE FIELD OF SEGMENTAL ROTOR MACHINES TAKING INTO ACCOUNT WINDING HARMONICS AND ROTOR AIRGAP IRREGULARITIES CLCULTION IN THE FIELD OF SEGENTL OTO CHINES TKING INTO CCOUNT WINDING HONICS ND OTO IGP IEGULITIES Y STCT The stator mmf over a segmet of the segmetal rotor reluctace machie is treated as a ifiite array