Question

How to calculate motor speed?

Answer 1

Calculating the speed of an electric motor can depend on the type of motor (DC, AC, synchronous, or asynchronous) and its specifications. Here’s a detailed overview of how to determine motor speed for different types of motors:

### 1. **DC Motors**

For a DC motor, the speed can be calculated using the formula:

\[
N = \frac{V - I \cdot R}{k \cdot \Phi}
\]

Where:
- \(N\) = Motor speed in RPM (Revolutions Per Minute)
- \(V\) = Supply voltage (Volts)
- \(I\) = Armature current (Amperes)
- \(R\) = Armature resistance (Ohms)
- \(k\) = Motor constant (typically in units such as V/rad/s)
- \(\Phi\) = Magnetic flux (Weber)

In practical terms, if you know the voltage and current of the motor under load and its specifications, you can use this equation to find the speed.

### 2. **AC Motors**

For AC motors, especially synchronous motors, the speed can be calculated using the synchronous speed formula:

\[
N_s = \frac{120 \cdot f}{P}
\]

Where:
- \(N_s\) = Synchronous speed in RPM
- \(f\) = Frequency of the AC supply in Hz
- \(P\) = Number of poles in the motor

This formula gives you the speed at which the magnetic field rotates. For example, a 60 Hz supply and a motor with 4 poles would have:

\[
N_s = \frac{120 \cdot 60}{4} = 1800 \text{ RPM}
\]

#### 2.1 **Induction Motors**

Induction motors run slightly below synchronous speed due to slip. The actual speed can be determined using:

\[
N = N_s \cdot (1 - s)
\]

Where:
- \(s\) = Slip, calculated as \(s = \frac{N_s - N}{N_s}\)

For example, if the synchronous speed is 1800 RPM and the slip is 4% (0.04), the actual speed \(N\) would be:

\[
N = 1800 \cdot (1 - 0.04) = 1728 \text{ RPM}
\]

### 3. **Step Motors**

Step motors have a defined number of steps per revolution. The speed can be calculated as follows:

\[
N = \frac{S \cdot 60}{T}
\]

Where:
- \(N\) = Speed in RPM
- \(S\) = Steps per revolution (commonly 200 for a standard stepper motor)
- \(T\) = Time taken for one full revolution in seconds

If it takes 2 seconds for a full revolution:

\[
N = \frac{200 \cdot 60}{2} = 6000 \text{ RPM}
\]

### Summary

To calculate motor speed, you need to identify the type of motor and its specifications (voltage, current, resistance, number of poles, etc.). The formulas vary slightly depending on the motor type but generally revolve around the relationship between electrical input and mechanical output. For practical applications, it is also useful to monitor the actual motor speed using tachometers or other measurement tools to ensure optimal performance.

Always consult the motor's datasheet for specific parameters and constants needed for accurate calculations.

Answer 2

Calculating motor speed depends on the type of motor you're dealing with. Here’s a general guide for different types of motors:

### 1. **DC Motors**

For DC motors, the speed (in revolutions per minute, RPM) can be calculated using the following formula:

\[ \text{Speed (RPM)} = \frac{\text{Voltage} - \text{Voltage drop}}{\text{K} \times \text{Armature resistance}} \]

where:
- **Voltage** is the applied voltage.
- **Voltage drop** is the voltage drop across the armature.
- **K** is the motor constant.
- **Armature resistance** is the resistance of the motor's armature.

### 2. **Induction Motors**

For induction motors, speed is typically calculated using the synchronous speed and the slip:

\[ \text{Synchronous Speed (RPM)} = \frac{120 \times \text{Frequency}}{\text{Number of Poles}} \]

where:
- **Frequency** is the supply frequency (in Hz).
- **Number of Poles** is the number of poles in the motor.

The actual speed of the motor (Ns) is then given by:

\[ \text{Actual Speed (RPM)} = \text{Synchronous Speed} \times (1 - \text{Slip}) \]

where **Slip** is:

\[ \text{Slip} = \frac{\text{Synchronous Speed} - \text{Actual Speed}}{\text{Synchronous Speed}} \]

### 3. **Synchronous Motors**

Synchronous motors run at a constant speed regardless of the load, which is equal to the synchronous speed:

\[ \text{Speed (RPM)} = \frac{120 \times \text{Frequency}}{\text{Number of Poles}} \]

### 4. **Stepper Motors**

The speed of stepper motors is determined by the pulse rate and the stepping mode:

\[ \text{Speed (RPM)} = \frac{\text{Pulse Rate}}{\text{Number of Steps per Revolution}} \times 60 \]

where:
- **Pulse Rate** is the number of pulses sent to the motor per second.
- **Number of Steps per Revolution** is the number of steps the motor takes to complete one full revolution.

### 5. **Universal Motors**

Universal motors, which can run on either AC or DC, have their speed calculated similarly to DC motors. The speed varies with load and is influenced by the voltage applied and the internal resistance.

### **General Example**

Let’s say you have a 4-pole induction motor running on a 60 Hz supply:

1. **Calculate Synchronous Speed:**

   \[ \text{Synchronous Speed} = \frac{120 \times 60}{4} = 1800 \text{ RPM} \]

2. **If the slip is 0.02 (or 2%):**

   \[ \text{Actual Speed} = 1800 \times (1 - 0.02) = 1800 \times 0.98 = 1764 \text{ RPM} \]

These formulas will give you the necessary calculations to determine the speed of different types of motors.