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Hysteresis loop or B-H curve and Hysteresis loss

What is hysteresis loop or bh curve and hysteresis loss, hysteresis loop.

Hysteresis loop or B-H curve
  • The loop is produced by measuring the magnetic flux (B) of a ferromagnetic material when the applied magnetizing force is changed (H).
  • A ferromagnetic material which has been never before magnetized or demagnetized ferromagnetic material will trail the dashed line (see the figure) as magnetizing force (H) is increased.
  • The dashed line shows that, the larger the quantity of current applied (H+), the stronger the magnetic field in the component (B+).
  • At "a" point nearly all of the magnetic domains are aligned and an extra increase in the magnetizing force will generate very little increase in magnetic flux.
  • The magnetic saturation point has been reached for the material.
  • When magnetizing force (H) is decreased to zero, the curve will move or change from "a" point to "b" point.
  • At this point, we can notice that some magnetic flux leftovers in the material even though the magnetizing force (H) is zero. This is called as the point of retentivity on the graph and shows the remanence or level of remaining magnetism in the material. Some of the magnetic domains stay aligned, but some magnetic domains lose their alignment.
  • With the application of magnetizing force in reverse direction, the curve moves to "c" point, where the flux has been decreased to zero. This point is called as coercivity point on the curve or loop. The reversed magnetizing force has reversed plenty of the domains, so that the remaining flux within the material is zero.
  • To remove the residual magnetism from the material a force has to be apply, this required force is called as the coercive force or coercivity of the material.
  • In the negative direction when magnetizing force is increased, the material will become again magnetically saturated or material under goes in saturation, but in the opposite or reverse direction i.e. towards "d" point.
  • Decreasing magnetizing force (H) to zero brings the curve to "e" point. The available level of remaining magnetism is equal to that achieved in the other direction.
  • Increasing magnetizing force (H) back in the positive direction will return or bring back the magnetic flux (B) to zero.
  • We can notice that, the curve did not return back to the beginning or origin of the graph because some magnetizing force is needed to remove the remaining or residual magnetism.
  • Now the curve in the graph will take a diverse or different path from “f” point back to the saturation point, here at this point it with complete the loop.
B-H curve measurement on Oscilloscope

Advantages of Hysteresis loop or bh curve

  • The magnetisation process of a ferromagnetic core.
  • The part of the curve the ferromagnetic core is magnetised decides flux density because this depends on the circuits previous history which gives the core a form of “memory”.
  • Ferromagnetic materials have memory because they stay magnetised after the external magnetic field has been taken out.
  • Relays, solenoids and transformers can be easily magnetised and demagnetised because, they are made up of Soft ferromagnetic materials such as silicon steel or iron, which have very narrow magnetic hysteresis loops resulting in very small amounts of residual magnetism.
  • Residual magnetism can be overcome by a coercive force; energy which is in use is dissipated as heat in the magnetic material. This heat is known as hysteresis loss, the material’s value of coercive force decides the amount of loss.
  • A very small coercive force can be made that have a very narrow hysteresis loop by adding additive’s to the iron metal such as silicon. Magnetisation and demagnetisation of soft magnetic materials with narrow hysteresis loops are easy.
Hysteresis loop for Soft and Hard Material

Applications of Hysteresis

What is hysteresis loss.

b h curve experiment calculations

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The B-H Curve

The B-H curve (or a magnetization curve, excitation curve, magnetic hysteresis or saturation function) is the way to describe relation between a strength of a magnetic field H and a corresponding magnetic flux density B for a certain material. To have the understanding and ability to interpret the B-H curve, understanding both B and H is required. Therefore, the short introduction of both is following.

The strength of a magnetic field H

The strength a magnetic field H (or known as magneto-motive force) is a vector field quantity which means that it possesses a value and a direction for each point of space in which it exists. For the sake of the example, we are going to analyse the the coil with N turns through which current I is flowing. According to the Ampere’s law, the value of strength of a magnetic field is following:

\oint_C \bf{H} \cdot d \bf{l} = NI

where C is the closed integrating curve and dl is the infinitesimal element of that curve. The factor NI is more commonly known by a descriptive name of an ampere-turn. The same value of ampere-turn can be achieved by different combinations of numbers of turns and current since it is a product. From the Ampere’s law we can conclude that strength of a magnetic field is related to the ampere-turns because ampere-turns are the cause of the magnetic field. Finally, the unit of H is ampere-turn per meter, or A/m . The reason is that there is no unit for number of turns so the unit of ampere is alone. Where does the meter come from? Remember the line integral? Its unit is in meters. To completely understand why the meter exists in the H unit, we can consider two cases which include a coil with 10 turns and 1 ampere which results in 10 ampere-turns. In the first case, the coil is wound up tightly as possible. In the second case, the coil is very loosely wound so it has a lot of empty space between turns. The first coil will generate more concentrated magnetic field than the second one. To assess the spatial distribution of a magnetic field final unit ends up with meter in the denominator.

The density of a magnetic flux B

1/r^2

where A is the sample surface for which we are calculating the density. The unit of B is in teslas T. The value of B is easily measured with magnetic field meters. Knowing the magnetic flux is impossible with direct measurement. But knowing the definition for B , the flux is calculate-able. From last equation, the magnetic flux for a area A is following:

\phi_m = \iint_A B dA

The relation between H and B

\phi_m

The experiments have shown that reluctivity is proportional to length of a path for magnetic flux l and reverse proportional to the affected area A . Therefore:

\mathcal{R}=\frac{1}{\mu}\frac{l}{A}

By replacing the values that we derived for the magnetic field strength and the magnetic flux density we end with next relation:

\frac{NI}{l}=\frac{1}{\mu}\frac{\phi_m}{A}

or more commonly:

B=\mu H

To conclude why the relation between B and H is non-linear in nature is simple real world constrictions. When a magnetic material lies in the magnetic field the internal domains will orient in parallel to the existing magnetic field providing denser magnetic flux, according to the magnetic domain theory. After the (almost) linear part of hysteresis, the permeability of material decreases and the material gets saturated. That means that much more magneto-motive force is needed to increase flux in the material. Which, as a result, creates many headaches for power system operators when handling transformers and motors particularly which will be analysed in future posts.

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Magnetic Hysteresis Including B-H Curve – Importance of Hysteresis Loop

B-h curve or magnetisation curve.

The B-H curve or magnetisation curve is the graph plotted between magnetic flux density (B) and magnetising force (H). The B-H curve indicates the manner in which the magnetic flux density varies with the change in magnetising force.

The following figure shows the general shape of B-H curve of a magnetic material. The nonlinearity of the curve shows that the relative permeability μ r of a magnetic material is not constant but varies depending upon the magnetic flux density.

b h curve experiment calculations

Magnetic Hysteresis

The phenomenon of lagging of magnetic flux density (B) behind the magnetising force (H) in a magnetic material subjected to the cycle of magnetisation (i.e., it is magnetised first in one direction and then in the other) is called as magnetic hysteresis .

Hysteresis Loop

Consider a coil of N turns wound on an un-magnetised iron bar AB (see the figure). The magnetising force (H = NI/l) produced by the coil can be changed by varying the current through the coil. It can be seen that when the iron bar is subjected to one complete cycle of magnetisation, the resultant B-H curve traces a loop abcdefa called as hysteresis loop .

b h curve experiment calculations

Explanation

When the current in the coil is zero, the H is zero and hence B in the iron bar is zero. When H is increased by increasing the coil current, the magnetic flux density also increases until the point of maximum magnetic flux density $\mathit{(+B_{max})}$ is reached. At this point, the material is saturated and beyond this point, the magnetic flux density will not increase regardless of any increase of magnetising force (H). For this, the B-H curve follows the path oa (see the hysteresis loop).

Now, if the H is gradually decreased by decreasing the coil current, it is found that the magnetic flux density does not decrease along the path oa but follows the path ab . At point b , the magnetising force is zero but magnetic flux density in the material has a finite value (equal to ob ) called residual flux density $\mathit{(+B_{r})}$. The ability of retaining residual magnetism by a magnetic material is called as retentivity of the material.

In order to demagnetise the iron bar i.e. to remove the residual magnetism (ob) , the magnetising force is reversed by reversing the coil current. When H is gradually increased in the reversed direction, the B-H curve follows the path bc so that when H = oc, the residual magnetism is zero. The values of H = oc required to completely remove the residual magnetism is known as coercive force (H c ) .

Now, if H is further increased in reverse direction, the material again saturates in the reverse direction (point d ). Reducing H to zero and then increasing it in the positive direction traces the curve defa. Therefore, when an iron bar is subjected to one complete cycle of magnetisation, the B-H curve traces a closed loop abcdefa called hysteresis loop .

Importance of Hysteresis Loop

The shape and size of the hysteresis loop depends upon the nature of the material. The choice of a magnetic material for a particular application depends upon the shape and size of the hysteresis loop.

Consider the following cases of hysteresis loop to understand it importance −

The smaller the area of the hysteresis loop of a magnetic material, the less is the hysteresis loss (e.g. silicon steel). Therefore, the silicon steel is widely used for making cores of transformer and rotating electric machines which are subjected to rapid reversals of magnetisation.

b h curve experiment calculations

The larger the area of hysteresis loop of a magnetic material, the greater is the hysteresis loss (e.g. hard steel). Therefore, the hard steel is used for making permanent magnets because this material has high retentivity and coercivity.

b h curve experiment calculations

The hysteresis loop for wrought iron has fairly good residual magnetism and coercivity. Therefore, it is used for making cores of electromagnets.

b h curve experiment calculations

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Holmarc’s B-H curve experiment model no: HO-ED-EM-09 is used for the analysis of the magnetic hysteresis loop / B-H curve for soft iron & laminated iron cores used in two coils bound electromagnet with DC current supply. Magnetic field intensity H & flux density B is measured & hysteresis loop recorded using the dedicate software. Remenance & coercive field strength of soft & laminated iron cores evaluated with the help of software.

    Magnetic hysteresis loop recorded for soft iron core and laminated core electromagnet

    Find the coercive force, remenance, Residual magnetism, BH curve saturation from graph

b h curve experiment calculations

When we decrease the magnetic field flux density retain in the core shows residual magnetism Br. This time Magnetic field H is zero. Holmarc B-H software as per theory increase the magnetic field H in the reverse direction by increasing the current (i) for reducing flux density to zero & find Coercive force / field Hc. Further increment of H saturates the B in reverse direction. Decrease the H in to zero again, while the residual flux present in the reverse direction. Software increases the H value to make flux density zero & continues increment of H makes the flux density B saturates again. So this track / loop is known as magnetic hysteresis or B-H curve plot.

Either using soft/hard iron core materials in the electromagnet the size of hysteresis loop becomes different. In application by notice the hysteresis loop one can identify the heat loss/energy loss in transformers. Larger the hysteresis size greater the loss. Low hysteresis core materials are used in making electromagnets, solenoids, relays etc. Hysteresis in hard core material is useful for making hard disk drives, magnetic floppy disc etc.

b h curve experiment calculations

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JSmol Viewer

Non-destructive detection method of apple watercore: optimization using optical property parameter inversion and mobilenetv3.

b h curve experiment calculations

1. Introduction

2. materials and methods, 2.1. data acquisition, 2.2. simulation data collection, 2.2.1. three-layer model of apples.

  • Determine whether a photon crossed the boundary. If the boundary was not crossed, the photon was absorbed and scattered, and the weight was updated. If the boundary was crossed, it was determined whether the photon escaped from the apple tissue surface;
  • Determine whether a photon overflows. If it does not overflow, it is necessary to determine whether it is refracted or reflected and update the weights accordingly. If it overflows;
  • Whether this is the last photon is determined. If this is the last photon, the operation is terminated.

2.2.2. Intersection Point Calculation

: Junction calculation
Input: photon
Output: Photon out of bounds position
1: current_pos = photon.current.position
2: previous_pos = photon.current-1.position
3: current_layer = current_pos.current.layer
4: previous_layer = previous_pos.current.layer
5: abs (current_layer − previous_layer) == 1:
6:   True:
7:  midpoint = (current_pos + previous_pos)/2
8:  midpoint_layer = midpoint.current.layer
9:   current_layer == midpoint_layer:
10:   current_pos = midpoint
11:   
12:   previous_pos = midpoint
13:    midpoint_layer == current_layer or midpoint_layer == previous_layer:
14:   
15:  
16:   midpoint
17:

2.2.3. Photon Cross-Layer Constraint Algorithm

: Photon transboundary confinement
Input: photon
Output: Ensure the photon crosses the layer boundary correctly
1: current_pos = photon.current.position
2: previous_pos = photon.current-1.position
3: current_layer = current_pos.current.layer
4: previous_layer = previous_pos.current.layer
5: abs(current_layer − previous_layer) == 1
6:  midpoint = (current_pos + previous_pos)/2
7:  midpoint = Junction calculation(photon)
8:  current_layer = midpoint.current.layer
9: current_pos = midpoint
10:

2.2.4. Absorption and Scattering of Photons

2.3. data augmentation.

  • For the training set, the images are randomly cropped and the cropped images are resized to 224 × 224 pixels. The diversity of the images is enhanced by flipping the images randomly horizontally with 50% probability and mirroring the flipped images with 50% probability.
  • For the test set, the longer side of the image was resized to 256 pixels, keeping the aspect ratio constant. The center region was cropped from the adjusted image with a cropping size of 224 × 224 pixels. It ensures that the data processing of the validation set is consistent with the training set and keeps the image features of the validation set unchanged, so as to accurately evaluate the performance of the model.
  • The mean and standard deviation values obtained from the ImageNet dataset are used to normalise the pixel values of an image on both the test and training sets. This allows the data to have a distribution that is more suitable for training before feeding into the neural network.

2.4. Experimental Method

2.4.1. mobilenetv3 model and dilated convolution, 2.4.2. transfer learning, 2.4.3. comparison algorithm.

  • SVM [ 50 ] is a classical machine learning method that excels at handling small samples and high-dimensional data. It is used to compare the improvement of deep learning models in feature extraction and classification tasks.
  • ResNet50 [ 51 ] is a deep residual network that addresses the vanishing gradient problem in deep neural networks by introducing residual connections. It serves as a good reference for evaluating the performance of new models in complex tasks.
  • VGG16 [ 52 ] increases the depth of the network by stacking small convolutional kernels to enhance feature extraction capabilities. It performs well in large-scale image classification tasks and is a classic benchmark in comparative experiments.
  • ShuffleNetV2 is a lightweight neural network whose efficiency and low computational requirements make it ideal for comparison with MobileNetV3-small, especially in resource-constrained environments.
  • InceptionNetV3 [ 53 ] utilises the Inception module, whose complex architecture and multi-scale feature extraction capabilities provide a contrast with our model in terms of feature diversity and complexity.
  • MobileNetV3_large is another version of MobileNetV3, and comparing its performance with our model helps us understand the trade-off between model complexity and performance.

2.4.4. Evaluation Index

2.5. experimental environment and parameter setting, 3. results and discussion, 3.1. data augmentation effect and comparative analysis, 3.2. comparison of the model pre-training algorithms, 3.3. comparison experiments of transfer learning methods, 3.4. ablation experiment, 3.5. confusion matrix, 4. conclusions, author contributions, institutional review board statement, data availability statement, acknowledgments, conflicts of interest, abbreviations.

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Click here to enlarge figure

ClassificationClassification Criteria
Two-classArea = 0; Area! = 0
Three-classArea = 0; Area ≤ 0.15; Area > 0.15
Four-classArea = 0; Area ≤ 0.1; 0.1 < Area ≤ 0.2; Area > 0.2
Optical ParameterInterval RangeValue (mm )
[0.40, 1.60)1.00
[1.60, 2.80)2.20
[2.80, 4.00)3.40
[4.00, 5.20)4.60
[5.20, 6.40)5.80
[0.03, 2.20)1.10
[2.20, 4.40)3.30
[4.40, 6.60)5.50
[6.60, 8.70)7.70
[0.01, 0.65)0.30
[0.65, 1.30)0.90
[1.30, 1.95)1.50
[1.95, 2.70)2.10
[1.69, 60.00)30.00
[60.00, 75.00)67.50
[75.00, 90.00)82.50
[90.00, 110.00)100.00
[110.00, 260.00)190.00
[0.01, 15.00)7.50
[15.00, 30.00)22.50
[30.00, 45.00)37.50
[45.00, 60.00)52.50
[60.00, 75.00)67.50
[0.01, 7.50)5.00
[7.50, 15.00)12.50
[15.00, 22.50)20.00
[22.50, 30.00)27.50
InputOperatorExp SizeOutputSENLStep Size
224 × 224 × 3conv2d,3 × 3-16-HS2
112 × 112 × 16bneck,3 × 31616RE2
56 × 56 × 16bneck,3 × 37224-RE2
28 × 28 × 24bneck,3 × 38824-RE1
28 × 28 × 24bneck,5 × 59640HS2
14 × 14 × 40bneck,5 × 524040HS1
14 × 14 × 40bneck,5 × 524040HS1
14 × 14 × 40bneck,5 × 512048HS1
14 × 14 × 48bneck,5 × 514448HS1
14 × 14 × 48bneck,5 × 528896HS2
7 × 7 × 96bneck,5 × 557696HS1
7 × 7 × 96bneck,5 × 557696HS1
7 × 7 × 96conv2d,1 × 1-576HS1
7 × 7 × 576pool,7 × 7----1
1 × 1 × 576conv2d,1 × 1, NBU-1024-HS1
1 × 1 × 1024conv2d,1 × 1, NBU-k--1
ModelClassificationLossAccuracy
(%)
Precision
(%)
Recall
(%)
F1-Score
(%)
Model Size
(M)
Our MethodTwo-class0.029199.0598.4398.5898.2918.89
Three-class0.032796.7796.3096.4596.12
Four-class0.104894.4594.1294.0693.87
SVMTwo-class0.394180.1679.7679.2179.45114.6
Three-class0.431573.1872.6972.1772.43
Four-class0.481971.9971.7471.5371.68
ResNet50Two-class0.103296.1495.5395.7496.0397.7
Three-class0.139694.4393.8294.0694.11
Four-class0.231192.4392.1692.6391.95
VGG16Two-class0.150496.6996.4796.3196.48526.3
Three-class0.168594.8194.5994.4394.61
Four-class0.238192.1291.8891.4291.92
InceptionNetV3Two-class0.128394.2894.1093.8593.7191.16
Three-class0.161193.1993.0192.9492.88
Four-class0.252491.9891.7091.5991.29
ShuffleNetV2Two-class0.147193.8383.3193.2293.4828.8
Three-class0.193691.6491.1292.0491.99
Four-class0.273687.7688.1487.3187.14
MobileNetV3-largeTwo-class0.074897.8697.1997.9297.3820.6
Three-class0.091295.4595.1795.9695.16
Four-class0.175893.6293.1393.3493.10
Number of Unfrozen Network LayersLoss ValueAccuracy
(%)
Precision
(%)
Recall
(%)
F1-Score
(%)
Params
(M)
10.030897.2096.6597.1296.897.54
20.030497.6097.2497.3396.927.54
30.030497.6097.2497.3396.927.54
40.030497.6097.2497.3396.927.54
50.030497.6097.2497.3396.927.52
60.032296.7096.1896.2796.237.50
70.032296.7096.1896.2796.237.47
80.034995.9095.4795.2595.287.49
90.032296.7096.1896.2796.237.46
100.034995.9095.4795.2595.287.43
Transfer Learning MethodsClassificationLoss ValueAccuracy
(%)
Precision
(%)
Recall
(%)
F1-Score
(%)
Params
(M)
Freezing of all network layersTwo-class0.176892.2591.5391.7491.484.24
Three-class0.213689.7089.8289.2588.464.24
Four-class0.241587.5387.1287.0986.944.24
Partial freezing of the network layersTwo-class0.028899.1398.6798.5198.707.52
Three-class0.030497.6097.1997.2397.417.52
Four-class0.098295.3294.9194.9595.137.52
No freezing of network layersTwo-class0.034198.5598.2398.3697.927.54
Three-class0.037696.2095.9796.6896.457.54
Four-class0.041993.9793.6093.3493.657.54
MethodsClassificationLoss ValueAccuracy
(%)
Precision
(%)
Recall
(%)
F1-Score
(%)
Params
(M)
MobileNetV3Two-class0.325181.2381.6881.8081.422.54
Three-class0.406978.7678.3578.4478.942.54
Four-class0.478272.4372.0271.7872.112.54
MobileNetV3 +
Dilated convolution
Two-class0.247190.5890.2689.9790.1224.10
Three-class0.294986.9786.6486.5586.3424.10
Four-class0.318281.3581.0381.5280.9324.10
MobileNetV3 + Dilatedconvolution + transfer learningTwo-class0.028899.1398.6798.5198.707.52
Three-class0.030497.6097.1997.2397.417.52
Four-class0.098295.3294.9194.9595.137.52
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Share and Cite

Chen, Z.; Wang, H.; Wang, J.; Xu, H.; Mei, N.; Zhang, S. Non-Destructive Detection Method of Apple Watercore: Optimization Using Optical Property Parameter Inversion and MobileNetV3. Agriculture 2024 , 14 , 1450. https://doi.org/10.3390/agriculture14091450

Chen Z, Wang H, Wang J, Xu H, Mei N, Zhang S. Non-Destructive Detection Method of Apple Watercore: Optimization Using Optical Property Parameter Inversion and MobileNetV3. Agriculture . 2024; 14(9):1450. https://doi.org/10.3390/agriculture14091450

Chen, Zihan, Haoyun Wang, Jufei Wang, Huanliang Xu, Ni Mei, and Sixu Zhang. 2024. "Non-Destructive Detection Method of Apple Watercore: Optimization Using Optical Property Parameter Inversion and MobileNetV3" Agriculture 14, no. 9: 1450. https://doi.org/10.3390/agriculture14091450

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  22. procedure for calculations of B.H curve

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