1

Step motor: load angle

Bs

θN

S

S

N

I1

Br

The load angle θ

... is defined as the angle with which the rotor magnetic field lags behind the stator magnetic field while rotating synchronously with it. ...

2

Ph1+

Ph1–

Ph2+

Ph2–

I1

I2

N

S

S

N

SN

S

N

S NS N

S

NS

N

SN

Two-phase PM step motor: one phase on drive (1)

• Rotor and stator magnetic fields

are synchronous

• Phase turn-on time corresponds to 90° rotation of the rotor

• No-load condition: - Rotor magnetic field first lags

then leads the stator magnetic field

3

Ph1+

Ph1–

Ph2+

Ph2–

I1

I2

N

S

S

N

SN

S

N

S N

Θ=45°

Θ=45°

Θ=45°

Θ=-45°Θ=45°

Θ=-45°Θ=-45°

Θ=-45°

+ 45° (motor) > Θ > - 45° (brake)

• Phase turn-on: Θ=45°

• Phase turn-off:Θ=-45°

Θ=0, i.e. Tav=0

Two-phase PM step motor: one phase on drive (2)

4

• Zero average torque, but positive and negative istantaneous torques

• Motor runs jerkily, with high torque ripple

Two-phase PM step motor: one phase on drive (3)

5

Ph1+

Ph1–

Ph2+

Ph2–

I1

I2

N S

S

N

SN

S

N

S NS N

S

NS

N

SN

Load angle is always positive

Torque is always positive

Two-phase PM step motor: one phase on drive (4)

6

Ph1+

Ph1–

Ph2+

Ph2–

I1

I2N S

S

N

SN

S

N

S N

Θ=0°

Θ=0°

Θ=90°Θ=0°

Θ=90°Θ=0°

Θ=90°Θ=90°

+ 90 > Θ > 0

• Phase turn-on: Θ=90°

• Phase turn-off:Θ=0°

Θ = 45° ; Tav= 2 TPK

Two-phase PM step motor: one phase on drive (5)

7

• Positive (motor) average torque

• Still high torque ripple

Two-phase PM step motor: one phase on drive (6)

8

Ph1+

Ph1–

Ph2+

Ph2–

I1

I2

N

S

S

N

SN

S

N

S NS N

S

NS

N

SN

Load angle is always positive

Torque is always positive

Two-phase PM step motor: one phase on drive (7)

9

Ph1+

Ph1–

Ph2+

Ph2–

I1

I2

N

S

S

N

SN

S

N

S NΘ=135°

Θ=45°Θ=135°

Θ=45°

Θ=135°

Θ=45°

Θ=135°Θ=45°

+ 135° > Θ > 45°

• Phase turn-on: Θ=135°

• Phase turn-off:Θ=45°

Θ = 90° ; Tav= 0.9 TPK

Two-phase PM step motor: one phase on drive (8)

10

With Θ = 90° :

• average torque is maximum

• torque ripple is minimum

(30% of the peak torque)

Two-phase PM step motor: one phase on drive (9)

11

Step motor: load angle (conclusion)

Bs

θN

S

S

N

I1

Br

At steady-state, the average load angle self-regulates to ensure

Tav = TLOAD

12Two-phase PM step motor: two phase on drive (1)

Total torque

Ph1 + Ph2

• Zero average torque, but positive and negative istantaneous torques

• Motor runs jerkily, with high torque ripple

+ 45° (motor) > Θ > - 45° (brake)

Θ=0, i.e. Tav=0

T

ωt

i1

t

i2

t

T1 T2 T1' T2' T2T1

i1+, i2

+

i1-, i2

+i1

-, i2

-

i1+, i2

-

Hm

13Two-phase PM step motor: two phase on drive (3)

Total torque

Ph1 + Ph2

+ 90 > Θ > 0

Θ = 45° ; Tav= 2 TPK

TPK(TPO) = 1.4 TPK (OPO)

T

ωt

T1 T2 T1' T2' T2T1

i1

t

i2

t

i1+, i2

+

i1-, i2

+i1

-, i2

-

i1+, i2

-

Hm

14Two-phase PM step motor: two phase on drive (3)

Total torque

Ph1 + Ph2

135° > Θ > 45°

Θ = 90° ; Tav= 0.9 TPK

TPK(TPO) = 1.4 TPK (OPO)

T

ωt

T1 T2 T1' T2' T2

TTOT

i2

t

i1

t

T1

i1+, i2

+

i1-, i2

+i1

-, i2

-

i1+, i2

-

Hm