DESBALANCE ROTACIONAL

MARÍA NICOSIA - JINNA JIMÉNEZ - KAIS SAFI DINÁMICA APLICADA ING. ELECTROMECÁNICA

DESBALANCE ROTACIONAL

MARÍA NICOSIA - JINNA JIMÉNEZ - KAIS SAFI DINÁMICA APLICADA ING. ELECTROMECÁNICA

Sistema de unidades: Sistema Internacional

Masa : 50 kg POSICIÓN : Cte. De Resorte : 1.50E+07 N/m Ángulo :

Cte. De Amortiguamiento : 1500 N-s/mMasa de la excentricidad : 5 kg

Distancia de la excentricidad : 2 mVelocidad : 800 rpm

0 5 10 15 20 25 30 35

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

V Vs. T

0.004790854 m0.4914864173 °

0 5 10 15 20 25 30 35

-0.003

-0.002

-0.001

0

0.001

0.002

0.003

0.004

0.005

0.006

X Vs. T

0 5 10 15 20 25 30 35

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

V Vs. T

0 5 10 15 20 25 30 35

-40

-30

-20

-10

0

10

20

30

A Vs. T

0 5 10 15 20 25 30 35

-0.003

-0.002

-0.001

0

0.001

0.002

0.003

0.004

0.005

0.006

X Vs. T

0 5 10 15 20 25 30 35

-40

-30

-20

-10

0

10

20

30

A Vs. T

SistemaSistema InternacionalSistema Inglés

wn= 547.72255751

w= 83.776 wt wt-fiw^2= 7018.418176 83.776 83.2845136

mew^2= 70184.18176 167.552 167.060514k-Mw^2= 14649079.091 251.328 250.836514

cw= 125664 335.104 334.612514raiz= 14649618.072 418.88 418.388514

502.656 502.164514X= 0.004790854 586.432 585.940514

670.208 669.716514cw= 125664 753.984 753.492514

producto= 0.0085782867 837.76 837.268514radianes= 0.0085780763 921.536 921.044514

grados= 0.4914864173 1005.312 1004.820511089.088 1088.596511172.864 1172.37251

1256.64 1256.148511340.416 1339.924511424.192 1423.700511507.968 1507.476511591.744 1591.25251

1675.52 1675.028511759.296 1758.804511843.072 1842.580511926.848 1926.356512010.624 2010.13251

2094.4 2093.908512178.176 2177.684512261.952 2261.460512345.728 2345.236512429.504 2429.01251

2513.28 2512.78851

sen(wt-fi) cos (wt-fi) tiempo x sen (wt-fi) tiempo xw cos(wt-fi) tiempo0.9994781335 -0.0323026422 1 0.00478835 1 -0.01296494 1

-0.5278803708 -0.8493187353 2 -0.002529 2 -0.34088137 2-0.4714186545 0.8819095488 3 -0.0022585 3 0.35396197 30.9994589762 -0.0328900427 4 0.00478826 4 -0.0132007 4

-0.5283794351 -0.8490083466 5 -0.00253139 5 -0.34075679 5-0.4709002636 0.8821864552 6 -0.00225601 6 0.35407311 60.9994394737 -0.0334774318 7 0.00478817 7 -0.01343645 7

-0.5288783169 -0.8486976646 8 -0.00253378 8 -0.3406321 8-0.47038171 0.882463057 9 -0.00225353 9 0.35418413 90.999419626 -0.0340648094 10 0.00478807 10 -0.0136722 10

-0.529377016 -0.8483866895 11 -0.00253617 11 -0.34050728 11-0.4698629939 0.8827393539 12 -0.00225105 12 0.35429502 12

0.999399433 -0.0346521752 13 0.00478798 13 -0.01390795 13-0.5298755323 -0.8480754213 14 -0.00253856 14 -0.34038235 14-0.4693441156 0.8830153459 15 -0.00224856 15 0.35440579 150.9993788949 -0.035239529 16 0.00478788 16 -0.01414369 16

-0.5303738656 -0.8477638602 17 -0.00254094 17 -0.34025731 17-0.4688250751 0.883291033 18 -0.00224607 18 0.35451644 180.9993580116 -0.0358268707 19 0.00478778 19 -0.01437942 19

-0.5308720156 -0.8474520063 20 -0.00254333 20 -0.34013214 20-0.4683058727 0.8835664149 21 -0.00224359 21 0.35462697 210.9993367831 -0.0364142 22 0.00478768 22 -0.01461515 22

-0.5313699823 -0.8471398597 23 -0.00254572 23 -0.34000686 23-0.4677865086 0.8838414917 24 -0.0022411 24 0.35473737 240.9993152094 -0.0370015167 25 0.00478757 25 -0.01485088 25

-0.5318677655 -0.8468274205 26 -0.0025481 26 -0.33988146 26-0.4672669828 0.8841162631 27 -0.00223861 27 0.35484765 270.9992932906 -0.0375888206 28 0.00478747 28 -0.0150866 28

-0.5323653649 -0.8465146887 29 -0.00255048 29 -0.33975594 29-0.4667472957 0.8843907292 30 -0.00223612 30 0.35495781 30

xw^2 sen (wt-fi)-33.606669617.749564115.8510831

-33.606025517.766344815.8336526

-33.605369717.783119315.8162167

-33.604702417.799887715.7987753

-33.604023417.816649915.7813284

-33.603332817.833405915.7638761

-33.602630617.850155815.7464183

-33.601916817.866899615.7289551

-33.601191417.883637215.7114864

-33.600454417.900368515.6940124

DatosM 5m 0.4X 0.15ω 1ωn 1γ 0.025Deflexión 0.1C 6k 1

0.09375 m

0.1500469 m

2.5 kg

Excentricidad, deflexión pico del motor y Masa adicional que se debe agregar al motor si se

reduce la deflexión.

Deflexión de un motor eléctrico debido a desvalance rotatorio

Excentricidad

Deflexión pico

Masa adicional

0 5 10 15 20 25 30 35

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

X vs t

tiempo (s)

Xsen

(wt-

)𝜙

r 1 num 2 0.75r2 1 den 2 8 num 0.75(1-r2) 0 num 3 1 den 0.1(1-r2)2 0 den 3 0.04998437 divición 7.52yr 0.05 2y 0.05(2yr)2 0.0025 y2 0.000625den1 0.05 (1-y2) 0.999375MX/me 20 Raiz(1-y2) 0.99968745MX/me max 20.0062529 num 4 0.75023448

Excentricidad, deflexión pico del motor y Masa adicional que se debe agregar al motor si se

reduce la deflexión.

0 5 10 15 20 25 30 35

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

X vs t

tiempo (s)

Xsen

(wt-

)𝜙

0 5 10 15 20 25 30 35

-0.006

-0.004

-0.002

0

0.002

0.004

0.006V vs t

tiempo (s)

wXc

os(w

t-)𝜙

0 5 10 15 20 25 30 35

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

a vs t

tiempo (s)

-w2X

sen(

wt-

)𝜙

num de x 0.037516 -4 16

s1 -0.2 6 36s2 -1 den de x 7.21110255c1 #REF! X 0.00520031c2 #REF!

0 0 0 1 11 -0.2 -1 0.81873075 0.367879442 -0.4 -2 0.67032005 0.135335283 -0.6 -3 0.54881164 0.049787074 -0.8 -4 0.44932896 0.018315645 -1 -5 0.36787944 0.006737956 -1.2 -6 0.30119421 0.002478757 -1.4 -7 0.24659696 0.000911888 -1.6 -8 0.20189652 0.000335469 -1.8 -9 0.16529889 0.00012341

10 -2 -10 0.13533528 4.53999E-0511 -2.2 -11 0.11080316 1.67017E-0512 -2.4 -12 0.09071795 6.14421E-0613 -2.6 -13 0.07427358 2.26033E-0614 -2.8 -14 0.06081006 8.31529E-0715 -3 -15 0.04978707 3.05902E-0716 -3.2 -16 0.0407622 1.12535E-0717 -3.4 -17 0.03337327 4.13994E-0818 -3.6 -18 0.02732372 1.523E-0819 -3.8 -19 0.02237077 5.6028E-0920212223242526272829

0 5 10 15 20 25 30 35

-0.006

-0.004

-0.002

0

0.002

0.004

0.006V vs t

tiempo (s)

wXc

os(w

t-)𝜙

0 5 10 15 20 25 30 35

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

a vs t

tiempo (s)

-w2X

sen(

wt-

)𝜙

phi -0.9827937232

wX w2X Posicion Velocidad Aceleración0.00520031 -0.0052003143 0.98279372 0.004326923 0.00288462 -0.004326920.00520031 -0.0052003143 1.98279372 0.004765167 -0.00208242 -0.004765170.00520031 -0.0052003143 2.98279372 0.000822338 -0.00513488 -0.000822340.00520031 -0.0052003143 3.98279372 -0.003876544 -0.00346636 0.003876540.00520031 -0.0052003143 4.98279372 -0.00501135 0.00138912 0.005011350.00520031 -0.0052003143 5.98279372 -0.001538743 0.00496745 0.001538740.00520031 -0.0052003143 6.98279372 0.003348577 0.00397873 -0.003348580.00520031 -0.0052003143 7.98279372 0.005157231 -0.00066801 -0.005157230.00520031 -0.0052003143 8.98279372 0.002224351 -0.00470059 -0.002224350.00520031 -0.0052003143 9.98279372 -0.002753587 -0.00441147 0.002753590.00520031 -0.0052003143 10.9827937 -0.00519989 -6.6461E-05 0.005199890.00520031 -0.0052003143 11.9827937 -0.002865437 0.00433965 0.002865440.00520031 -0.0052003143 12.9827937 0.002103485 0.0047559 -0.002103480.00520031 -0.0052003143 13.9827937 0.005138473 0.0007996 -0.005138470.00520031 -0.0052003143 14.9827937 0.003449173 -0.00389185 -0.003449170.00520031 -0.0052003143 15.9827937 -0.001411281 -0.00500515 0.001411280.00520031 -0.0052003143 16.9827937 -0.004974209 -0.00151674 0.004974210.00520031 -0.0052003143 17.9827937 -0.003963873 0.00336615 0.003963870.00520031 -0.0052003143 18.9827937 0.00069083 0.00515422 -0.000690830.00520031 -0.0052003143 19.9827937 0.004710387 0.00220353 -0.004710390.00520031 -0.0052003143 20.9827937 0.004399236 -0.00277308 -0.004399240.00520031 -0.0052003143 21.9827937 4.344735E-05 -0.00520013 -4.3447E-050.00520031 -0.0052003143 22.9827937 -0.004352286 -0.0028462 0.004352290.00520031 -0.0052003143 23.9827937 -0.004746548 0.00212451 0.004746550.00520031 -0.0052003143 24.9827937 -0.000776855 0.00514196 0.000776860.00520031 -0.0052003143 25.9827937 0.003907074 0.00343191 -0.003907070.00520031 -0.0052003143 26.9827937 0.004998858 -0.00143342 -0.004998860.00520031 -0.0052003143 27.9827937 0.001494715 -0.00498087 -0.001494710.00520031 -0.0052003143 28.9827937 -0.003383663 -0.00394894 0.003383660.00520031 -0.0052003143 29.9827937 -0.005151116 0.00071363 0.00515112

Datos wn 1.58K 5.00 X 1.749271

M 2.00 r 1.6w 2.00 angulo -0.80y 0.50 me 6e 3.00 c 4

m 2.00

2.00Ẍ + 4ẋ + 5.00x =

DESBALANCE ROTACIONAL

Ecuación diferencial de movimiento

0 2 4 6 8 10 12 14 16

-2-1.5

-1-0.5

00.5

11.5

2

X Vs T

TIEMPO

x PO

SICI

ON

24 Sen( 2.00 t)

DESBALANCE ROTACIONAL

Ecuación diferencial de movimiento

0 2 4 6 8 10 12 14 16

-2-1.5

-1-0.5

00.5

11.5

2

X Vs T

TIEMPO

x PO

SICI

ON

0 2 4 6 8 10 12 14 16

-4

-3

-2

-1

0

1

2

3V vs T

0 2 4 6 8 10 12 14 16

-20

-15

-10

-5

0

5

10

15

20

A vs T

r

x =

0 2 4 6 8 10 12 14 16

-4

-3

-2

-1

0

1

2

3V vs T

0 2 4 6 8 10 12 14 16

-20

-15

-10

-5

0

5

10

15

20

A vs T

mew2 24mew2/K 4.8(w/wn) 1.6(w/wn)^2 1.6(1-(w/wn)^2)^2 0.362y(w/wn) 1.6raiz( (1-(w/wn)^2)^2+ 2y(w/wn) ) 2.744mew2/K / raiz( (1-(w/wn)^2)^2+ 2y(w/wn) ) 1.7492711370262sen(wt-o)

xSen(wt-o) Tiempo Sen(wt-o)1.2524783783441 0 0.71600013961.2081475761743 1 0.6906576977

-1.2774684733788 2 -0.730286144-1.1817236034882 3 -0.675551993

1.301911998109 4 0.74425969231.1547940253463 5 0.6601572512

-1.3257984942689 6 -0.757914806-1.1273703636827 7 -0.6444800581.3491177419199 8 0.77124564251.0994643518275 9 0.6285271211

-1.3718597638229 10 -0.784246498-1.0710879294861 11 -0.6123052661.3940148297074 12 0.7969118111.0422532376313 13 0.5958214342

-1.4155734604346 14 -0.809236162-1.0129726133082 15 -0.579082677

t 123456789

10111213

owxCos(wt-o) w^2 x sen(wt-o)-1.9491176796807 -14.32000279240082.62889114693324 -13.8131539542591

-0.238891789165409 14.6057228789642-2.43006302225669 13.51103986654842.26141786781003 -14.8851938450459

0.547899238656037 -13.2031450231258-2.71743093763663 15.1582961178077

1.7138013378096 12.88960115810581.29104492723718 -15.4249128492839

-2.78832986242957 -12.57054242256121.02966437576281 15.6849299663751.93134671707161 12.2461053271249

-2.63711202893293 -15.93823621965480.263504939850097 -11.9164286835845

2.4177985346666 16.1847232309685-2.27582336306974 11.58165354549