1 Step motor: load angle BsBs N S S N I1I1 BrBr 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 – I1I1 I2I2 N S S N S N S N SNSN S N S N S N 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 – I1I1 I2I2 N S S N S N S N SN 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. T av =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 – I1I1 I2I2 N S S N S N S N SNSN S N S N S N Load angle is always positive Torque is always positive Two-phase PM step motor: one phase on drive (4)

6 Ph1 + Ph1 – Ph2 + Ph2 – I1I1 I2I2 N S S N S N S N SN Θ=0° Θ=90° Θ=0° Θ=90° Θ=0° Θ=90° + 90 > Θ > 0 Phase turn-on: Θ=90° Phase turn-off: Θ=0° Θ = 45° ; T av = 2 T PK  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 – I1I1 I2I2 N S S N S N S N SNSN S N S N S N Load angle is always positive Torque is always positive Two-phase PM step motor: one phase on drive (7)

9 Ph1 + Ph1 – Ph2 + Ph2 – I1I1 I2I2 N S S N S N S N SN Θ=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° ; T av = 0.9 T PK 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) BsBs N S S N I1I1 BrBr At steady-state, the average load angle self-regulates to ensure T av = T LOAD

12 Two-phase PM step motor: two phase on drive (1) Total torque Ph 1 + Ph 2 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. T av =0

13 Two-phase PM step motor: two phase on drive (3) Total torque Ph 1 + Ph > Θ > 0 Θ = 45° ; T av = 2 T PK  T PK (TPO) = 1.4 T PK (OPO)

14 Two-phase PM step motor: two phase on drive (3) Total torque Ph 1 + Ph 2 135° > Θ > 45° Θ = 90° ; T av = 0.9 T PK T PK (TPO) = 1.4 T PK (OPO)