Handbook of Small Electric Motors MAZ Part 14 doc

SYNCHRONOUS MACHINES 7.3FIGURE 7.3 Shaded-pole synchronous motor, permanent-magnet rotor end.. FIGURE 7.4 Shaded-pole synchronous motor, induction rotor end... FIGURE 7.6 Shaded-pole syn

CHAPTER 7 SYNCHRONOUS MACHINES

Chapter Contributors

Chris A Swenski William H Yeadon

7.1

This chapter covers some of the ac synchronous motors commonly encountered inthe industry While it could be said that the electronically commutated motors dis-cussed in Chap 5 are also synchronous motors, this chapter is confined to the typical

ac versions While larger polyphase machines are well covered by others, little mation is available on these smaller motors

These motors are built in a manner very similar to that for induction motors Theymay have polyphase windings or be designed as single-phase motors, such as capacitor-start, split-phase, or shaded-pole types

The rotors have a dual construction that allows for induction motor starting acteristics and salient-pole synchronous running conditions

char-These rotors may be made from induction motor stampings with some of theteeth removed, as shown in Fig 7.1 They are then die-cast in the same manner as aninduction motor rotor (Fig 7.2)

Some motors use a permanent magnet in conjunction with an induction motorrotor Figures 7.3 and 7.4 show such a motor This is a four-pole shaded-pole motor.Here the field coils are connected such that they directly produce two like poles andinduce two opposite poles at 90°in the unwound space between the coils In these

* Sections 7.1 to 7.3 contributed by William H Yeadon, Yeadon Engineering Services, PC.

figures, the rotor is shown to be enclosed by the stator Figure 7.3 shows the permanent-magnet part of the rotor, while Fig 7.4 shows the induction rotor end.The rotor is shown alone in Figs 7.5 and 7.6, with a piece of magnetic viewing filmover the permanent-magnet portion Figure 7.5 demonstrates the position of themagnetic poles, of which there are four on the rotor Figure 7.6 shows that the induc-tion rotor portion is a laminated structure with copper-wire bars swedged over copper-plate end rings.

SYNCHRONOUS MACHINES 7.3

FIGURE 7.3 Shaded-pole synchronous motor, permanent-magnet rotor end.

FIGURE 7.4 Shaded-pole synchronous motor, induction rotor end.

7.4 CHAPTER SEVEN

FIGURE 7.5 Shaded-pole synchronous motor showing magnetized poles.

FIGURE 7.6 Shaded-pole synchronous motor rotor showing induction motor bars and end rings.

7.2 HYSTERESIS SYNCHRONOUS MOTORS

These motors have a rotor made of a cobalt alloy or another material that can bemagnetized semipermanently by the stator field They have a rather weak second-quadrant demagnetization curve which can be easily demagnetized The demagneti-zation curves of some of these materials are shown in Figs 7.7, 7.8, and 7.9

Figure 7.10 shows a motor utilizing a wound-field distributed stator (Fig 7.11)and a cobalt hysteresis ring rotor (Fig 7.12) This motor is connected and run like apermanent-split-capacitor (PSC) motor It produces a speed-torque curve like theone shown in Fig 7.13

FIGURE 7.7 0.32-MGOe hysteresis material BR=10.4 kG, BD=7.0 kG, HC= 88 Oe, HD = 45 Oe,

BH =0.315 MGOe, BD/HD=155.6 (Courtesy of Arnold Engineering Company.)

7.6 CHAPTER SEVEN

FIGURE 7.8 0.054-MGOe hysteresis material: hardened A151050 BR=37.00 kG, BD= 2.0 kG,

HC=56 Oe, HD=27 Oe, BHmax =0.054 MGOe, BD/HD=24.1 (Courtesy of Arnold Engineering

Company.)

SYNCHRONOUS MACHINES 7.7

FIGURE 7.9 0.36-MGOe hysteresis material BR=9.5 kG, BD=6.0 kG, HC=116 Oe, HD= 60 Oe,

BHmax =0.360 MGOe, BD/HD=100.0 (Courtesy of Arnold Engineering Company.)

7.8 CHAPTER SEVEN

FIGURE 7.10 Wound-field motor.

FIGURE 7.11 Distributed wound stator.

Many timer motors and value actuators use a hysteresis ring but use the pole type of stator to provide starting torque Figures 7.14, 7.15, and 7.16 show atimer motor which utilizes this principle The shaded-pole stator provides the start-ing torque, but it also makes the motor unidirectional.

SYNCHRONOUS MOTORS

Many of these motors are used in clocks or timing devices Figure 7.17 shows a cal clock motor Note that the stator portion has an uneven distribution of magneticpoles (Fig 7.18) The purpose of this is to give the rotor a preferred starting pointwhile providing an apparent shift in field during starting due to the uneven reluc-tance of the stator Some of these motors have a spring return mechanism to reversethe rotation just in case it starts turning the wrong way

typi-Other PM synchronous motors are essentially PM stepper motors run as PSCmotors The motor shown in Fig 7.19 has a stator consisting of two sets of coils withthe teeth offset from each other by one-half tooth pitch (Fig 7.20) The rotor hasmagnetized poles along its length, as shown by magnetic viewing film (Fig 7.21).One stator half serves as the main field winding The other serves as the auxiliaryphase They are connected as in PSC motors, with a capacitor in series with the aux-iliary winding

FIGURE 7.12 Cobalt hysteresis ring rotor.

FIGURE 7.13 Synchronous motor speed-torque curves: Oz ⋅in versus (a) rpm, (b) Win, (c) PF, (d) amps,

(e) horsepower, and (f) efficiency.

FIGURE 7.13 (Continued) Synchronous motor speed-torque curves: Oz ⋅in versus (a) rpm, (b) Win, (c) PF,

(d) amps, (e) horsepower, and (f) efficiency.

SYNCHRONOUS MACHINES 7.13

FIGURE 7.16 Timer rotor.

FIGURE 7.17 Typical clock motor.

7.14 CHAPTER SEVEN

FIGURE 7.18 Uneven distribution of magnetic stator poles.

FIGURE 7.19 Permanent-magnet synchronous motor.

SYNCHRONOUS MACHINES 7.15

FIGURE 7.20 Half-tooth-pitch offset consisting of two sets of coils with offset teeth.

FIGURE 7.21 Rotor with magnetized poles.

parame-The hysteresis power is equal to the stator input power minus the stator losses,

friction and windage losses, and rotor parasite losses Stator losses include I2r1pluscore losses Parasitic losses include hysteresis and eddy current losses of minor loopsresulting from flux variation at tooth slot openings, losses resulting from harmonics

of a nonsinusoidal winding distribution, and double-frequency backward field teresis and eddy current losses

hys-Variables

B=slot span,°electrical

b=slot opening

C= series conductors per phase

C1= flux form coefficient

I= primary current (assumed)

I d= direct axis current

I q= quadrature axis current

k d= distribution factor

k g= gap factor

k p= pitch factor

k s= slot leakage constant

k w= total winding distribution tor

fac-kzz= zigzag leakage coefficient

k1= stator (primary) slot constant

k2= secondary slot constant

L g= physical length of air gap

Lmet= mean end-turn length of coil

L s= stator stack length

l g= effective length of air gap

L t1= length of teeth

L y1= length of yokeMTL = mean turn length

m= number of phases

m e= length of remaining portion

of coil extension

N s= synchronous speed

n= coils per group

P b= belt leakage permeance factor

PF = power factor

p= number of poles

Note: See figures for those variables not listed here, but used in the followingequations.

Calculation of Constants

Pitch factor k p:

k p=sin (pitch ⋅90°)where pitch is expressed as a fraction of the full pitch, such as 5⁄6, etc

r1= resistance per phase,Ω

S p= span (average coil throw)

SF = saturation factor

SFd= direct axis saturation factor

SFq= quadrature axis saturation

factor

Str= number of strands of wire in

parallel

s1= stator (primary) slots

s2= rotor (secondary) slots

T= torque, oz⋅in

T p1= primary tooth pitch

T p2= secondary tooth pitch

T f1= width of primary tooth face

T f2= width of secondary tooth face

Vph= volts per phase

Win= total input, W

W L= Loss, W

Wout= output, W

Wph= watts per phase

w= total series conductors

w2= axial rotor stack length

X d= total direct axis reactance

Xfctr= reactance factor

Xpc= primary end reactance

Xps= primary slot reactance

X q= total quadrature axis tance

reac-X1= total leakage reactance

X 1d= primary direct axis reactance

X 1q= primary quadrature axis tance

reac-Y= end-winding length cient

coeffi-θp= total pole pitch

θpd= direct axis pole pitch

θpq= quadrature axis pole pitch

ξ = efficiency

φ2= flux factor

Gap factor k g(see Fig 7.22):

Semiclosed slot

k g=Open slot

k g=Tunnel slot

Primary and Secondary Slot Constant Calculations k 1 and k 2

Note: See figures for variable descriptions k1represents the primary (stator) slot

constant, while k2represents the secondary (rotor) slot constant They are foundusing the same set of equations, being careful to use the equation which most closelyresembles that of the slot in question

Round-bottom slot constant k1or k2(note that F is different for the two constants):

Slot shape A (see Fig 7.23)

Slot shape B (see Fig 7.24)

k1or k2=F + +

Square-bottom slot constant k1or k2:Open slot (see Fig 7.25)

k1or k2= +Bridged slot (see Fig 7.26)

k1or k2= +

Flat-bottom slot constant k1or k2:Slot shape A (see Fig 7.27)

k1and k2= +Slot shape B (see Fig 7.28)

k1and k2= +1.5 +Slot shape C (see Fig 7.29)

FIGURE 7.23 Round-bottom slot, shape A.

FIGURE 7.24 Round-bottom slot, shape B.

FIGURE 7.25 Square-bottom open slot.

Closed slot

kzz=Direct axis pole pitch θpd(see Fig 7.30):

FIGURE 7.26 Square-bottom bridged slot. FIGURE 7.27 Flat-bottom slot, shape A.

FIGURE 7.28 Flat-bottom slot, shape B. FIGURE 7.29 Flat-bottom slot, shape C.

Quadrature axis pole pitch θpq(see Fig 7.30):

FIGURE 7.30 Rotor cross section showing θpd and θpq Dimensions in inches,

not degrees, measured along the circumference of the rotor.

Flux factor Φ2:

Φ2=

Area of the Air Gap:

Direct axis area A gd

A gd=  (L s+2G1F2)

Quadrature axis area A gq

A gq=  (L s+2G1F2)Direct axis saturation factor SFd:

SFd=Quadrature axis saturation factor SFq:

FIGURE 7.31 Dimensions for end-turn leakage reactance.

Primary Leakage Reactance. The primary leakage reactance X1is the sum of thepreceding reactances:

X1=Xps+Xpc+Xzz

Friction and Windage Losses. Friction and windage losses are obtained by testingsimilar machines (same frame size, bearing size, rpm, enclosure and cooling fan)

ξ =Power factor PF:

PF =Variables for direct and quadrature axis current calculations θ,δ,ψ:

θ =cos−1PF

δ =tan−1

ψ = θ + δwhere δ =torque angle

Direct axis current I d:

I d=I(sin ψ) Quadrature axis current I q: