Hysteresis loss is a form of energy loss that occurs in magnetic materials when they are subjected to alternating magnetic fields. It is particularly significant in transformers, electric motors, and inductors, where magnetic materials are commonly used. This loss arises due to the lagging of magnetic flux density (B) behind the magnetizing force (H), resulting in a hysteresis loop on the B-H curve.
### Key Concepts
1. **Hysteresis Loop**: The relationship between magnetic flux density (B) and magnetic field strength (H) is graphically represented as a loop when a magnetic material is cycled through magnetization and demagnetization.
2. **Energy Loss**: The area enclosed within the hysteresis loop represents the energy lost per cycle due to hysteresis.
3. **Factors Influencing Hysteresis Loss**:
- **Material**: Different materials have different hysteresis loss characteristics. Soft magnetic materials have lower hysteresis losses compared to hard magnetic materials.
- **Frequency**: Hysteresis loss increases with the frequency of the alternating magnetic field.
- **Peak Magnetic Flux Density**: Higher peak flux densities result in larger hysteresis losses.
### Hysteresis Loss Calculation
The hysteresis loss can be calculated using the following formula:
\[
\text{Hysteresis Loss (W)} = \eta \cdot B_{max}^n \cdot f \cdot V
\]
Where:
- \( W \) = Hysteresis loss in watts (W)
- \( \eta \) = Hysteresis loss constant (depends on the material)
- \( B_{max} \) = Maximum flux density (in teslas, T)
- \( n \) = Steinmetz exponent (typically ranges from 1.5 to 2.5)
- \( f \) = Frequency of the alternating magnetic field (in hertz, Hz)
- \( V \) = Volume of the magnetic material (in cubic meters, m³)
#### Explanation of Terms:
1. **Hysteresis Loss Constant (\(\eta\))**: This is a material-specific constant derived from experimental data. It can vary based on the type of magnetic material used.
2. **Maximum Flux Density (\(B_{max}\))**: This value represents the peak magnetic flux density experienced by the material during the alternating magnetic cycle. It is crucial for determining the extent of the hysteresis loss.
3. **Steinmetz Exponent (\(n\))**: This exponent represents the non-linear nature of magnetic materials and reflects how hysteresis loss scales with changes in magnetic flux density. The specific value of \(n\) varies with the type of magnetic material.
4. **Frequency (\(f\))**: As the frequency increases, the magnetic material undergoes more cycles of magnetization and demagnetization per second, leading to higher hysteresis losses.
5. **Volume (\(V\))**: The larger the volume of the magnetic material, the greater the hysteresis loss, as there is more material undergoing the magnetic cycle.
### Example Calculation
Let’s assume we have the following parameters for a magnetic material:
- Hysteresis loss constant (\(\eta\)) = 0.002 W/T^n
- Maximum flux density (\(B_{max}\)) = 1.5 T
- Steinmetz exponent (\(n\)) = 2
- Frequency (\(f\)) = 60 Hz
- Volume (\(V\)) = 0.01 m³
Using the formula for hysteresis loss:
\[
W = 0.002 \cdot (1.5)^2 \cdot 60 \cdot 0.01
\]
Now, we will calculate \(W\):
1. Calculate \( (1.5)^2 = 2.25 \)
2. Substitute back into the equation:
\[
W = 0.002 \cdot 2.25 \cdot 60 \cdot 0.01
\]
\[
W = 0.002 \cdot 2.25 \cdot 0.6
\]
\[
W = 0.0027 \, \text{W}
\]
Thus, the hysteresis loss in this example is approximately **0.0027 watts**.
### Summary
Hysteresis loss is an important consideration in the design and efficiency of electrical devices that utilize magnetic materials. By understanding how to calculate it and the factors that affect it, engineers can select appropriate materials and designs to minimize energy losses in applications such as transformers, electric motors, and inductors.
If you need more specific details or examples on hysteresis loss for a certain application or material, feel free to ask!