21electri_motors

21electri_motors - Electric Motors from electrcal overview...

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Electric Motors Ref: Chapter 9 from electrcal overview M = K m ⋅Φ⋅ I K m = constant_for_given_motor (ref: 2.93) (9.1) Lorentz force. .. M = torque Nm Φ = magnetic_flux Wb = 1 weber I = current A = 1 amp 1Wb 1 A1 N = when rotating, electromotive force induced in rotor given by . . from electrical overview Faraday's force . .. E = K E n K E = constant_for_given_motor (ref: 2.96) (9.2) E = induced_electromotive_force V = 1 volt Φ = magnetic_flux Wb = 1 weber 1 n = rotation_speed rpm = 6.283 Wb rpm = 0.105 V min model motor as resistance in series with EMF generator (opposing applied voltage) U = E + (9.3) P = E I + I 2 R (9.4) I R I with . .. M = K m I (9.1) and . .. E = K E n (9.2) M E U m excited field R A E separately I := E := (U I R) n := K m ⋅Φ K E ⋅Φ U MR n collect ,Φ → U M R n = 2 (9.5) K E ⋅Φ K m K E Φ 2 K E ⋅Φ K E K m XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX to see an example of DC motor behavior assume a set of reasonable parameters. Not all are independent. for fixed magnetic field Φ and rpm at maximum power M = K m I , maximum current I m and maximum torque M m set Φ , n, R and applied voltage U maximum current Φ := 1Wb n := 100rpm R := 2 Ω U m := 400V I m := 10A derived U = E + I R E E := U m I m R E = 380 V 2 assuming EMF*I converted n2 into mechanical power EI m = M m n ⋅π M M m := m M m = 57.753 N m M 2 2 m P = U I = + I R = Mn ⋅π + I 2 R M m = K m I m K m K m := K m = 5.775 Φ⋅ I m E E = K E n K E K E := n K E = 36.287 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 1 11/15/2006
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2 2 K m ⋅Φ K E K m ⋅Φ K m ⋅Φ K E K m M = U n U m n = 57.753 N m R R R R 2 K m ⋅Φ K m K E a := b := ( , ) := ( MUn U a bn) calculate M when U and n known . .. R R Ua M nn U M ( , ) := calculate n when U and M known - b useful at ends of torque range 0 - M m := 0N m = nn U m , = 100 rpm derived check nn U m , 0 = 105.26316 rpm 57.753 N m M 0 M m ( M m ) ( ) for example at U = 0.25 U m , calculate n at 0 and maximum torque n11 := nn U m 0.25 , n11 = 21.053 rpm maximum torque ( M m ) n12 := nn U m 0.25 , n12 = 26.316 rpm 0 torque ( M 0 ) n1 := n11 n11 , + 0.1rpm .. n12 M m plot M vs n for U = 0.25*U m 50 MU m 0.25 , n1 ( ) Nm and if develop similar data for 0.5 * U m , 0.75 * U m and U m obtain the following plot 0 0 1 0 n1 rpm 2 3 plot data 0 20 40 60 80 100 120 140 0 20 40 60 0.25 * Um 0.5 * Um 0.75 * Um 1.0 * Um Mm max torque torque N*m rpm 2 11/15/2006
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21electri_motors - Electric Motors from electrcal overview...

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