Option 3 : 1.5°

__Concept:__

Step angle of the hybrid stepper motor is given by

\(β = {{(N_s -N_r)× 360°} \over (N_s× N_r)}\)

Where N_{s} = Number of stator teeth

N_{r} = Number of rotor teeth

__Calculation:__

Given that, N_{r} = 60

N_{s }= 8 × 6 = 48

∴ stepping angle can be calculated as

\(β = {{(60 -48)× 360°} \over (60× 48)}\)

**β = 1.5°**

Option 2 : 3600

**Concept:**

**Step angle (β)**: It is the angle subtended by rotor position when one pulse is applied to the input of the stator. It is a measure of rotor position in degrees.

∴ β × (no. of revolutions) = Total revolution in degrees.

Also in general,

\(β=\frac{N_s-N_r}{N_s× N_r}× 360^\circ \)

Where,

Ns = No. of stator teeth

Nr = No. of rotor teeth

__ Calculation__:

Given, β = 2.5°

1 revolution = 360°

25 revolution = 25 × 360°

\(N=\frac{TR}{β}\)

Where,

N = Total no. of steps

TR = Total revolution in degrees

∴ \(\large{N=\frac{25\times 360}{2.5}=3600}\)

__Additional Information__

Stepper motors can be used to give controlled rotational steps but also can give continuous rotation with their rotational speed controlled by controlling the rate at which digital pulses are applied to it to cause stepping.

This gives a very useful controlled variable speed motor which finds many applications like in robotics, textile, etc.

Option 3 : 1.8°

**Concept:**

A **hybrid stepper motor** is a combination of variable reluctance and permanent magnet-type motors. The rotor of a hybrid stepper motor is axially magnetized like a permanent magnet stepper motor, and the stator is electromagnetically energized like a variable reluctance stepper motor

**The step angle** of the stepper motor is defined as the angle traversed by the motor in one step.

Step angle of the hybrid stepper motor is given by

\(\beta =\frac{{N_r -N_s}}{{N_s\times N_r}}\times 360^\circ \)

Where N_{s} = Number of stator teeth

N_{r} = Number of rotor teeth

__ Calculation__:

Given that, N_{r} = 50

N_{s} = 8 x 5 = 40

∴ stepping angle can be calculated as

\(\beta =\frac{{50 -40}}{{50\times 40}}\times 360^\circ \)

β = 1.8°

Which of the following is a disadvantage of a hybrid stepper motor as compared to a variable reluctance stepper motor?

Option 2 : High inertia

Stepper motor: it is a special type of synchronous motor which is designed to rotate through a specific angle (step) for each electrical pulses received by its control unit. The input command is in the form of a train pulse to turn a shaft through a specified angle.

Advantages:

- Compatible with the digital system
- No sensors are needed for position and speed sensing

__Types of stepper motor:__

Variable – reluctance stepper motor:

- It consists of single or several stacks of stator and rotor.
- Stator have a common frame and rotor have a common shaft.
- Stator and rotor teeth are of same number and size.
- Rotors are unexcited while stators are pulse excited. The static torque acting on the rotor is a function of angular misalignment θ.
- The rotor locks into stator in position θ = 0° or \(\theta = \frac{{360}}{T}\) where T= no of rotor teeth
- Stator teeth of various stacks differ by angular displacement of \(\alpha = \frac{{360}}{{nT}}\) where n= no of stacks.
- Directional control is possible with three or more phases.

Permanent magnet stepper motor:

- The rotor is made of ferrite or rare earth material which is permanently magnetised. Rotor move in steps of 22.5°
- This motor operates at larger steps up to 90° and a maximum response rate of 300 pulses per second.

Hybrid stepper motor:

- This is a permanent magnet stepper motor with the toothed and stacked rotor of the variable reluctance motor.
- Compared to permanent magnet motor finer steps for better resolution are obtained in hybrid motor by increasing the number of stack teeth and also by adding additional stack pans on the rotor.
- As compared to variable reluctance motor a hybrid motor requires less stator excitation current because of the PM excited rotor.
**Compared to a variable reluctance stepper motor it has high inertia.**

Option 1 : \(sps = \frac{rpm\times spr}{60}\)

**Step Angle (β):**

- The angle through which the motor shaft rotates for each command pulse is called the step angle β.
- The smaller the step angle, the greater the number of steps per revolution and the higher the resolution or accuracy of positioning obtained.
- The step angles can be as small as 0.72º or as large as 90º. But the most common step sizes are 1.8º, 2.5º, 7.5º, and 15º.

It is given by,

\(\beta=\frac{360^o}{mN_r}\)

Where,

m is the number of stator phase

N_{r} is the number of rotor teeth

A stepping motor has the extraordinary ability to operate at very high stepping rates (up to 20,000 steps per second in some motors) and yet to remain fully in synchronism with the command pulses.

If **N is the speed in revolution per minute (rpm)**, **S is the steps per second (sps)**, then **step per revolution (spr) **is given as,

\(sps=\frac{N\times S}{60}\)

Option 3 : 1.5°

__Concept:__

Step angle of the hybrid stepper motor is given by

\(β = {{(N_s -N_r)× 360°} \over (N_s× N_r)}\)

Where N_{s} = Number of stator teeth

N_{r} = Number of rotor teeth

__Calculation:__

Given that, N_{r} = 60

N_{s }= 8 × 6 = 48

∴ stepping angle can be calculated as

\(β = {{(60 -48)× 360°} \over (60× 48)}\)

**β = 1.5°**

Option 2 : 3600

**Concept:**

**Step angle (β)**: It is the angle subtended by rotor position when one pulse is applied to the input of the stator. It is a measure of rotor position in degrees.

∴ β × (no. of revolutions) = Total revolution in degrees.

Also in general,

\(β=\frac{N_s-N_r}{N_s× N_r}× 360^\circ \)

Where,

Ns = No. of stator teeth

Nr = No. of rotor teeth

__ Calculation__:

Given, β = 2.5°

1 revolution = 360°

25 revolution = 25 × 360°

\(N=\frac{TR}{β}\)

Where,

N = Total no. of steps

TR = Total revolution in degrees

∴ \(\large{N=\frac{25\times 360}{2.5}=3600}\)

__Additional Information__

Stepper motors can be used to give controlled rotational steps but also can give continuous rotation with their rotational speed controlled by controlling the rate at which digital pulses are applied to it to cause stepping.

This gives a very useful controlled variable speed motor which finds many applications like in robotics, textile, etc.

Option 3 : 1.8°

**Concept:**

A **hybrid stepper motor** is a combination of variable reluctance and permanent magnet-type motors. The rotor of a hybrid stepper motor is axially magnetized like a permanent magnet stepper motor, and the stator is electromagnetically energized like a variable reluctance stepper motor

**The step angle** of the stepper motor is defined as the angle traversed by the motor in one step.

Step angle of the hybrid stepper motor is given by

\(\beta =\frac{{N_r -N_s}}{{N_s\times N_r}}\times 360^\circ \)

Where N_{s} = Number of stator teeth

N_{r} = Number of rotor teeth

__ Calculation__:

Given that, N_{r} = 50

N_{s} = 8 x 5 = 40

∴ stepping angle can be calculated as

\(\beta =\frac{{50 -40}}{{50\times 40}}\times 360^\circ \)

β = 1.8°

Which of the following is a disadvantage of a hybrid stepper motor as compared to a variable reluctance stepper motor?

Option 2 : High inertia

Stepper motor: it is a special type of synchronous motor which is designed to rotate through a specific angle (step) for each electrical pulses received by its control unit. The input command is in the form of a train pulse to turn a shaft through a specified angle.

Advantages:

- Compatible with the digital system
- No sensors are needed for position and speed sensing

__Types of stepper motor:__

Variable – reluctance stepper motor:

- It consists of single or several stacks of stator and rotor.
- Stator have a common frame and rotor have a common shaft.
- Stator and rotor teeth are of same number and size.
- Rotors are unexcited while stators are pulse excited. The static torque acting on the rotor is a function of angular misalignment θ.
- The rotor locks into stator in position θ = 0° or \(\theta = \frac{{360}}{T}\) where T= no of rotor teeth
- Stator teeth of various stacks differ by angular displacement of \(\alpha = \frac{{360}}{{nT}}\) where n= no of stacks.
- Directional control is possible with three or more phases.

Permanent magnet stepper motor:

- The rotor is made of ferrite or rare earth material which is permanently magnetised. Rotor move in steps of 22.5°
- This motor operates at larger steps up to 90° and a maximum response rate of 300 pulses per second.

Hybrid stepper motor:

- This is a permanent magnet stepper motor with the toothed and stacked rotor of the variable reluctance motor.
- Compared to permanent magnet motor finer steps for better resolution are obtained in hybrid motor by increasing the number of stack teeth and also by adding additional stack pans on the rotor.
- As compared to variable reluctance motor a hybrid motor requires less stator excitation current because of the PM excited rotor.
**Compared to a variable reluctance stepper motor it has high inertia.**

Option 1 : \(sps = \frac{rpm\times spr}{60}\)

**Step Angle (β):**

- The angle through which the motor shaft rotates for each command pulse is called the step angle β.
- The smaller the step angle, the greater the number of steps per revolution and the higher the resolution or accuracy of positioning obtained.
- The step angles can be as small as 0.72º or as large as 90º. But the most common step sizes are 1.8º, 2.5º, 7.5º, and 15º.

It is given by,

\(\beta=\frac{360^o}{mN_r}\)

Where,

m is the number of stator phase

N_{r} is the number of rotor teeth

A stepping motor has the extraordinary ability to operate at very high stepping rates (up to 20,000 steps per second in some motors) and yet to remain fully in synchronism with the command pulses.

If **N is the speed in revolution per minute (rpm)**, **S is the steps per second (sps)**, then **step per revolution (spr) **is given as,

\(sps=\frac{N\times S}{60}\)