From fd1d485bf114f7b2309411289f2f47a2129690ac Mon Sep 17 00:00:00 2001 From: Luiz Enger Date: Mon, 5 Aug 2024 10:00:05 +0200 Subject: [PATCH 1/6] branch for updates on magnet modeling tuto --- .../examples_tutorial_modelling_magnets.md | 40 ++++++++++++++++++ ...examples_tutorial_magnet_CylinderLD025.png | Bin 0 -> 149883 bytes .../examples_tutorial_magnet_CylinderLD4.png | Bin 0 -> 138320 bytes .../examples_tutorial_magnet_datasheet3.png | Bin 0 -> 207088 bytes ...examples_tutorial_magnet_magnetpicture.png | Bin 0 -> 201877 bytes .../examples_tutorial_magnet_testbench.png | Bin 0 -> 471202 bytes 6 files changed, 40 insertions(+) create mode 100644 docs/_static/images/examples_tutorial_magnet_CylinderLD025.png create mode 100644 docs/_static/images/examples_tutorial_magnet_CylinderLD4.png create mode 100644 docs/_static/images/examples_tutorial_magnet_datasheet3.png create mode 100644 docs/_static/images/examples_tutorial_magnet_magnetpicture.png create mode 100644 docs/_static/images/examples_tutorial_magnet_testbench.png diff --git a/docs/_pages/user_guide/examples/examples_tutorial_modelling_magnets.md b/docs/_pages/user_guide/examples/examples_tutorial_modelling_magnets.md index c805f517b..40c1e6d63 100644 --- a/docs/_pages/user_guide/examples/examples_tutorial_modelling_magnets.md +++ b/docs/_pages/user_guide/examples/examples_tutorial_modelling_magnets.md @@ -77,7 +77,44 @@ Keep in mind that there are still many reasons why your simulation might not fit - Worst-case: the polarization can be inhomogeneous which is often a problem in injection-mold magnets. ## Example +For a concrete example, let's consider the case of a simple linear movement of the sensor under a magnet. Two cylinder magnets with axial magnetic polarization but different L/D ratios were chosen: one magnet has 20 mm height and 5 mm diameter (L/D = 4) while the other presents 2 mm height and 8 mm diameter (L/D = 0.25). The magnets are placed such that the magnetization points towards the Z-axis, and the Bz component is measured. The magnets are sintered NdFeB of BMN-35 grade, kindly provided by Bomatec (https://www.bomatec.com/en). According to the datasheet, the nominal remanence of such magnets is 1.22 T at 20 °C. But if this value is used in the magnetic polarization attribute when creating your cylinder magnet in Magpylib, you will see that the simulated field is higher than the measurement. Fortunately, Bomatec also provides well written datasheets from which one can estimate the actual value to be used due to magnet geometry: +![data sheet example](../../../_static/images/examples_tutorial_magnet_datasheet3.png) + +![comparison LD025](../../../_static/images/examples_tutorial_magnet_magnetpicture.png) + +### Magpylib simulation code +The code for a linear scan of the sensor under the magnet, keeping an air gap of 12 mm, is the following: +```python +import numpy as np +import magpylib as magpy + +magnet = magpy.magnet.Cylinder(dimensions=(5e-3, 20e-3), polarization=(0, 0, 1.22)) +sensor = magpy.Sensor(position=(0, 0, -22e-3)) # 22 mm from center of magnet, 12 mm airgap + +x = np.linspace(-15, 15, 61)*1e-3 # moving from X = -15 mm to X = +15 mm +move = [(xi, 0, 0) for xi in x] +sensor.move(displacement=move, start=0) + +field = sensor.getB(magnet) +``` +In which the cylinder magnet with L/D = 4 is considered. Keep in mind that we are using Magpylib version>5, with SI units. For the magnet with L/D = 0.25, cylinder dimensions have to be modified. + +### Experimental data and comparison +To obtain the experimental data, a 6-degrees of freedom testbench was used, in which we can place any magnet and magnetic sensor of choice. With independent rotation and linear movement stages, it is possible to control the air gap and sensor movement. The initial positioning of the sensor in the XY plane was calibrated using an optimization algorithm, to account for small displacements from the center of the magnet. + +![comparison LD025](../../../_static/images/examples_tutorial_magnet_testbench.png) + +Plotting the simulated field against the experimental data for the magnet with L/D = 4, we obtain the following: +![comparison LD4](../../../_static/images/examples_tutorial_magnet_CylinderLD4.png) + +To achieve a proper fit, the value used for magnetic polarization of the cylinder magnet was 1.17 T, a bit more than 4% below the nominal remanence and lower than what can be estimated from the hysteresis curve in the datasheet. It is expected that the difference is bigger for the magnet with L/D = 0.25, and this is confirmed with the following comparison: +![comparison LD025](../../../_static/images/examples_tutorial_magnet_CylinderLD025.png) +In this case, a value for 1.12 T for the magnetic polarization is what provides a good fit to the experimental data, more than 8% off from the nominal value. Such is the effect of having magnets with different geometrical aspect ratios. + +Surely, there are other aspects that will influence your magnetic readings that were not mentioned here, such as sensor offset, sensitivity, and higher order components of the magnetic field that are not taken into account in the analytical expressions solved by Magpylib. But understanding from the start that the geometry of the magnet itself affects its magnetic polarization value, and how to infer the corrected value from a well written datasheet, is an important step towards a better alignment between your simulations and the experimental data. + +If possible, the best practice is to characterize the magnet being used. As briefly mentioned, it is also possible to run optimization algorithms to better understand your experiment, but make sure to set realistic boundaries for the fitting parameters and double-check if the results make sense physically. ::::{grid} 2 :::{grid-item} :columns: 3 @@ -93,5 +130,8 @@ coming soon: 2. Experimental data 3. Comparison and discussion + +### + **Exterior reference** G. Martinek, S. Ruoho and U. Wyss. (2021). *Magnetic Properties of Permanents Magnets & Measuring Techniques* [White paper]. 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ztl+kChKw2KMa$AQxGeZ8K%@^DNdkmiP(7Jl?n8#q^e|2!q7#q-Hg<>R@Bq%(X&k1raFIDc8!@oRw$GUB`eGbdM%)LQ(YW zwS6b;Iki5iLJr+Ww6YMqwM(2bTCs-(s$Lb`a7`OwVa{q@R_J0U2@2Qj&6F>GM@q_P z(@8-l+(PTC;BSl(Ru4*8@t-negWxr~%Q+5xT-~tjxPA`|x*IS@60YAdgMEg+`ICbs zfh)-H)D0LXpZn<<#+hAxg2~}vcfkr@Y0RsHUgh`WOoCoFVRXKf*o%`m8`5h-7XbI4 z3FxzDbNpW#m@hB&Y`COZzvNRa1HQWa%$NFuE>E7PWnZAfiwWg~;#(GmG47Z-_f|b8 zF3+?Lxvu18@s0CPT`gVWOtnnzn~k?YCQjZ_oA;)L`B#$6lWd+UqkE7n1db7W-jul` z#mqIE>yQvGT z>7&aI??T`ViL=kS#1$e)*H^j5l}p26L8G3ur;WfM6A>oCDD-wk;WzT3}1 zNTcij=C>{%N~yICzp2me>!=dmVHS( zPS>2}X!-5l=#}JKr^3ryZmzw!P8Pf6?5Mt$r10xu^&1JeXa=bz+gb(68~P;_!``K-qbOfry6so5I*QZMG`^!#(W$w`iQV6vpKfBwALXH4IB_HBO2E;V=g zi_@% literal 0 HcmV?d00001 From 440cbfdaa348141f93443b2aa75d05c2a701aa1f Mon Sep 17 00:00:00 2001 From: Luiz Enger Date: Wed, 4 Sep 2024 08:49:44 +0200 Subject: [PATCH 2/6] updated tutorial magnet figures --- .../examples_tutorial_modelling_magnets.md | 15 ++++++++------- .../examples_tutorial_magnet_CylinderLD025.png | Bin 149883 -> 0 bytes .../examples_tutorial_magnet_CylinderLD4.png | Bin 138320 -> 0 bytes .../examples_tutorial_magnet_LD025_comp.png | Bin 0 -> 218487 bytes .../examples_tutorial_magnet_LD4_comp.png | Bin 0 -> 188347 bytes 5 files changed, 8 insertions(+), 7 deletions(-) delete mode 100644 docs/_static/images/examples_tutorial_magnet_CylinderLD025.png delete mode 100644 docs/_static/images/examples_tutorial_magnet_CylinderLD4.png create mode 100644 docs/_static/images/examples_tutorial_magnet_LD025_comp.png create mode 100644 docs/_static/images/examples_tutorial_magnet_LD4_comp.png diff --git a/docs/_pages/user_guide/examples/examples_tutorial_modelling_magnets.md b/docs/_pages/user_guide/examples/examples_tutorial_modelling_magnets.md index 40c1e6d63..57b1c0940 100644 --- a/docs/_pages/user_guide/examples/examples_tutorial_modelling_magnets.md +++ b/docs/_pages/user_guide/examples/examples_tutorial_modelling_magnets.md @@ -90,7 +90,7 @@ import numpy as np import magpylib as magpy magnet = magpy.magnet.Cylinder(dimensions=(5e-3, 20e-3), polarization=(0, 0, 1.22)) -sensor = magpy.Sensor(position=(0, 0, -22e-3)) # 22 mm from center of magnet, 12 mm airgap +sensor = magpy.Sensor(position=(0, 0, -15e-3)) # 22 mm from center of magnet, 5 mm airgap x = np.linspace(-15, 15, 61)*1e-3 # moving from X = -15 mm to X = +15 mm move = [(xi, 0, 0) for xi in x] @@ -101,16 +101,17 @@ field = sensor.getB(magnet) In which the cylinder magnet with L/D = 4 is considered. Keep in mind that we are using Magpylib version>5, with SI units. For the magnet with L/D = 0.25, cylinder dimensions have to be modified. ### Experimental data and comparison -To obtain the experimental data, a 6-degrees of freedom testbench was used, in which we can place any magnet and magnetic sensor of choice. With independent rotation and linear movement stages, it is possible to control the air gap and sensor movement. The initial positioning of the sensor in the XY plane was calibrated using an optimization algorithm, to account for small displacements from the center of the magnet. +To obtain the experimental data, a 6-degrees of freedom testbench was used, in which we can place any magnet and magnetic sensor of choice. With independent rotation and linear movement stages, it is possible to control the air gap and sensor movement. ![comparison LD025](../../../_static/images/examples_tutorial_magnet_testbench.png) -Plotting the simulated field against the experimental data for the magnet with L/D = 4, we obtain the following: -![comparison LD4](../../../_static/images/examples_tutorial_magnet_CylinderLD4.png) +The following figure presents the comparison for the Z-component of the magnetic field for a magnet with L/D = 4. The curves show simulation when using the nominal remanence, the remanence corrected from the B-H curve and the fitted remanence value obtained using the experimental data. Due to tolerances in airgap control and die position inside the sensor packaging, dashed lines are added representing sensor displacement of +/- 100 µm. +![comparison LD4](../../../_static/images/examples_tutorial_magnet_LD4_comp.png) +Whereas the nominal remanence is of 1.22 T and the corrected value estimated from the datasheet is 1.21 T, an optimization procedure using the experimental data resulted in 1.1847 T. This value is the closest one to what is obtained when performing the characterization of the magnet with a set of coils, which resulted in 1.17 T. Another point to notice is that, for this case, if the sensor was 100 µm closer to the magnet, the resulting curve is even above of that obtained with the nominal remanence. -To achieve a proper fit, the value used for magnetic polarization of the cylinder magnet was 1.17 T, a bit more than 4% below the nominal remanence and lower than what can be estimated from the hysteresis curve in the datasheet. It is expected that the difference is bigger for the magnet with L/D = 0.25, and this is confirmed with the following comparison: -![comparison LD025](../../../_static/images/examples_tutorial_magnet_CylinderLD025.png) -In this case, a value for 1.12 T for the magnetic polarization is what provides a good fit to the experimental data, more than 8% off from the nominal value. Such is the effect of having magnets with different geometrical aspect ratios. +The same comparison is made for a magnet with L/D = 0.25, for which greater differences are expected. +![comparison LD025](../../../_static/images/examples_tutorial_magnet_LD025_comp.png) +In this case, from the B-H one can estimate a remanence of 1.18 T, and the fitting with the experimental data yields 1.1254 T remanence. Again, this value is the closest one to what is obtained with magnetic characterization, which resulted in 1.11 T remanence. The same air gap tolerance analysis is performed, and if the sensor was 100 µm closer to the magnet even the B-H curve correction would indicate a remanence above the obtained data. Surely, there are other aspects that will influence your magnetic readings that were not mentioned here, such as sensor offset, sensitivity, and higher order components of the magnetic field that are not taken into account in the analytical expressions solved by Magpylib. 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deletions(-) diff --git a/docs/_pages/user_guide/examples/examples_tutorial_modelling_magnets.md b/docs/_pages/user_guide/examples/examples_tutorial_modelling_magnets.md index 57b1c0940..1694ef7cf 100644 --- a/docs/_pages/user_guide/examples/examples_tutorial_modelling_magnets.md +++ b/docs/_pages/user_guide/examples/examples_tutorial_modelling_magnets.md @@ -105,13 +105,13 @@ To obtain the experimental data, a 6-degrees of freedom testbench was used, in w ![comparison LD025](../../../_static/images/examples_tutorial_magnet_testbench.png) -The following figure presents the comparison for the Z-component of the magnetic field for a magnet with L/D = 4. The curves show simulation when using the nominal remanence, the remanence corrected from the B-H curve and the fitted remanence value obtained using the experimental data. Due to tolerances in airgap control and die position inside the sensor packaging, dashed lines are added representing sensor displacement of +/- 100 µm. +The following figure presents the comparison for the Z-component of the magnetic field for a magnet with L/D = 4. The curves show simulation when using the nominal remanence, the remanence corrected from the B-H curve and the fitted remanence value obtained using the experimental data. Due to tolerances in airgap control and die position inside the sensor packaging, the filled area represents sensor displacement of +/- 50 µm. ![comparison LD4](../../../_static/images/examples_tutorial_magnet_LD4_comp.png) -Whereas the nominal remanence is of 1.22 T and the corrected value estimated from the datasheet is 1.21 T, an optimization procedure using the experimental data resulted in 1.1847 T. This value is the closest one to what is obtained when performing the characterization of the magnet with a set of coils, which resulted in 1.17 T. Another point to notice is that, for this case, if the sensor was 100 µm closer to the magnet, the resulting curve is even above of that obtained with the nominal remanence. +Whereas the nominal remanence is of 1.22 T and the corrected value estimated from the datasheet is 1.21 T, an optimization procedure using the experimental data resulted in 1.1847 T. This value is the closest one to what is obtained when performing the characterization of the magnet with a set of coils, which resulted in 1.17 T. This is also an indication that a tolerance of +/- 50 µm is a realistic value in our testbench. The same comparison is made for a magnet with L/D = 0.25, for which greater differences are expected. ![comparison LD025](../../../_static/images/examples_tutorial_magnet_LD025_comp.png) -In this case, from the B-H one can estimate a remanence of 1.18 T, and the fitting with the experimental data yields 1.1254 T remanence. Again, this value is the closest one to what is obtained with magnetic characterization, which resulted in 1.11 T remanence. The same air gap tolerance analysis is performed, and if the sensor was 100 µm closer to the magnet even the B-H curve correction would indicate a remanence above the obtained data. +In this case, from the B-H one can estimate a remanence of 1.18 T, and the fitting with the experimental data yields 1.1254 T remanence. Again, this value is the closest one to what is obtained with magnetic characterization, which resulted in 1.11 T remanence. Surely, there are other aspects that will influence your magnetic readings that were not mentioned here, such as sensor offset, sensitivity, and higher order components of the magnetic field that are not taken into account in the analytical expressions solved by Magpylib. 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zNT=;Fznyou?zjKeNet|CJby(2`o2<_pPRC>Y$ZhCJkli&o)L3sLIE;CGiL_!25LUO zFvyzTsOD+u1c_~)hdS^C?8F?TPKu1|2cISCu`t|hWD!*4fcN|z;J{fZ5kMjQ?*8^_ zwr)){0xpn}q?wq3fq^Ud_Y&uhE2~hyL25YtcBIFj7z3df`uVh?hX(C|XaXrhNxFCi(fwK19A94n= Date: Mon, 5 Aug 2024 10:00:05 +0200 Subject: [PATCH 4/6] branch for updates on magnet modeling tuto --- .../examples_tutorial_modeling_magnets.md | 40 ++++++++++++++++++ ...examples_tutorial_magnet_CylinderLD025.png | Bin 0 -> 149883 bytes .../examples_tutorial_magnet_CylinderLD4.png | Bin 0 -> 138320 bytes .../examples_tutorial_magnet_datasheet3.png | Bin 0 -> 207088 bytes ...examples_tutorial_magnet_magnetpicture.png | Bin 0 -> 201877 bytes .../examples_tutorial_magnet_testbench.png | Bin 0 -> 471202 bytes 6 files changed, 40 insertions(+) create mode 100644 docs/_static/images/examples_tutorial_magnet_CylinderLD025.png create mode 100644 docs/_static/images/examples_tutorial_magnet_CylinderLD4.png create mode 100644 docs/_static/images/examples_tutorial_magnet_datasheet3.png create mode 100644 docs/_static/images/examples_tutorial_magnet_magnetpicture.png create mode 100644 docs/_static/images/examples_tutorial_magnet_testbench.png diff --git a/docs/_pages/user_guide/examples/examples_tutorial_modeling_magnets.md b/docs/_pages/user_guide/examples/examples_tutorial_modeling_magnets.md index fc00f1099..87f97b029 100644 --- a/docs/_pages/user_guide/examples/examples_tutorial_modeling_magnets.md +++ b/docs/_pages/user_guide/examples/examples_tutorial_modeling_magnets.md @@ -77,7 +77,44 @@ Keep in mind that there are still many reasons why your simulation might not fit - Worst-case: the polarization can be inhomogeneous which is often a problem in injection-mold magnets. ## Example +For a concrete example, let's consider the case of a simple linear movement of the sensor under a magnet. Two cylinder magnets with axial magnetic polarization but different L/D ratios were chosen: one magnet has 20 mm height and 5 mm diameter (L/D = 4) while the other presents 2 mm height and 8 mm diameter (L/D = 0.25). The magnets are placed such that the magnetization points towards the Z-axis, and the Bz component is measured. The magnets are sintered NdFeB of BMN-35 grade, kindly provided by Bomatec (https://www.bomatec.com/en). According to the datasheet, the nominal remanence of such magnets is 1.22 T at 20 °C. But if this value is used in the magnetic polarization attribute when creating your cylinder magnet in Magpylib, you will see that the simulated field is higher than the measurement. Fortunately, Bomatec also provides well written datasheets from which one can estimate the actual value to be used due to magnet geometry: +![data sheet example](../../../_static/images/examples_tutorial_magnet_datasheet3.png) + +![comparison LD025](../../../_static/images/examples_tutorial_magnet_magnetpicture.png) + +### Magpylib simulation code +The code for a linear scan of the sensor under the magnet, keeping an air gap of 12 mm, is the following: +```python +import numpy as np +import magpylib as magpy + +magnet = magpy.magnet.Cylinder(dimensions=(5e-3, 20e-3), polarization=(0, 0, 1.22)) +sensor = magpy.Sensor(position=(0, 0, -22e-3)) # 22 mm from center of magnet, 12 mm airgap + +x = np.linspace(-15, 15, 61)*1e-3 # moving from X = -15 mm to X = +15 mm +move = [(xi, 0, 0) for xi in x] +sensor.move(displacement=move, start=0) + +field = sensor.getB(magnet) +``` +In which the cylinder magnet with L/D = 4 is considered. Keep in mind that we are using Magpylib version>5, with SI units. For the magnet with L/D = 0.25, cylinder dimensions have to be modified. + +### Experimental data and comparison +To obtain the experimental data, a 6-degrees of freedom testbench was used, in which we can place any magnet and magnetic sensor of choice. With independent rotation and linear movement stages, it is possible to control the air gap and sensor movement. The initial positioning of the sensor in the XY plane was calibrated using an optimization algorithm, to account for small displacements from the center of the magnet. + +![comparison LD025](../../../_static/images/examples_tutorial_magnet_testbench.png) + +Plotting the simulated field against the experimental data for the magnet with L/D = 4, we obtain the following: +![comparison LD4](../../../_static/images/examples_tutorial_magnet_CylinderLD4.png) + +To achieve a proper fit, the value used for magnetic polarization of the cylinder magnet was 1.17 T, a bit more than 4% below the nominal remanence and lower than what can be estimated from the hysteresis curve in the datasheet. It is expected that the difference is bigger for the magnet with L/D = 0.25, and this is confirmed with the following comparison: +![comparison LD025](../../../_static/images/examples_tutorial_magnet_CylinderLD025.png) +In this case, a value for 1.12 T for the magnetic polarization is what provides a good fit to the experimental data, more than 8% off from the nominal value. Such is the effect of having magnets with different geometrical aspect ratios. + +Surely, there are other aspects that will influence your magnetic readings that were not mentioned here, such as sensor offset, sensitivity, and higher order components of the magnetic field that are not taken into account in the analytical expressions solved by Magpylib. But understanding from the start that the geometry of the magnet itself affects its magnetic polarization value, and how to infer the corrected value from a well written datasheet, is an important step towards a better alignment between your simulations and the experimental data. + +If possible, the best practice is to characterize the magnet being used. As briefly mentioned, it is also possible to run optimization algorithms to better understand your experiment, but make sure to set realistic boundaries for the fitting parameters and double-check if the results make sense physically. ::::{grid} 2 :::{grid-item} :columns: 3 @@ -93,5 +130,8 @@ coming soon: 2. Experimental data 3. Comparison and discussion + +### + **Exterior reference** G. Martinek, S. Ruoho and U. Wyss. (2021). *Magnetic Properties of Permanents Magnets & Measuring Techniques* [White paper]. 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.../examples_tutorial_magnet_CylinderLD4.png | Bin 138320 -> 0 bytes .../examples_tutorial_magnet_LD025_comp.png | Bin 0 -> 218487 bytes .../examples_tutorial_magnet_LD4_comp.png | Bin 0 -> 188347 bytes 5 files changed, 8 insertions(+), 7 deletions(-) delete mode 100644 docs/_static/images/examples_tutorial_magnet_CylinderLD025.png delete mode 100644 docs/_static/images/examples_tutorial_magnet_CylinderLD4.png create mode 100644 docs/_static/images/examples_tutorial_magnet_LD025_comp.png create mode 100644 docs/_static/images/examples_tutorial_magnet_LD4_comp.png diff --git a/docs/_pages/user_guide/examples/examples_tutorial_modeling_magnets.md b/docs/_pages/user_guide/examples/examples_tutorial_modeling_magnets.md index 87f97b029..d5961951c 100644 --- a/docs/_pages/user_guide/examples/examples_tutorial_modeling_magnets.md +++ b/docs/_pages/user_guide/examples/examples_tutorial_modeling_magnets.md @@ -90,7 +90,7 @@ import numpy as np import magpylib as magpy magnet = magpy.magnet.Cylinder(dimensions=(5e-3, 20e-3), polarization=(0, 0, 1.22)) -sensor = magpy.Sensor(position=(0, 0, -22e-3)) # 22 mm from center of magnet, 12 mm airgap +sensor = magpy.Sensor(position=(0, 0, -15e-3)) # 22 mm from center of magnet, 5 mm airgap x = np.linspace(-15, 15, 61)*1e-3 # moving from X = -15 mm to X = +15 mm move = [(xi, 0, 0) for xi in x] @@ -101,16 +101,17 @@ field = sensor.getB(magnet) In which the cylinder magnet with L/D = 4 is considered. Keep in mind that we are using Magpylib version>5, with SI units. For the magnet with L/D = 0.25, cylinder dimensions have to be modified. ### Experimental data and comparison -To obtain the experimental data, a 6-degrees of freedom testbench was used, in which we can place any magnet and magnetic sensor of choice. With independent rotation and linear movement stages, it is possible to control the air gap and sensor movement. The initial positioning of the sensor in the XY plane was calibrated using an optimization algorithm, to account for small displacements from the center of the magnet. +To obtain the experimental data, a 6-degrees of freedom testbench was used, in which we can place any magnet and magnetic sensor of choice. With independent rotation and linear movement stages, it is possible to control the air gap and sensor movement. ![comparison LD025](../../../_static/images/examples_tutorial_magnet_testbench.png) -Plotting the simulated field against the experimental data for the magnet with L/D = 4, we obtain the following: -![comparison LD4](../../../_static/images/examples_tutorial_magnet_CylinderLD4.png) +The following figure presents the comparison for the Z-component of the magnetic field for a magnet with L/D = 4. The curves show simulation when using the nominal remanence, the remanence corrected from the B-H curve and the fitted remanence value obtained using the experimental data. Due to tolerances in airgap control and die position inside the sensor packaging, dashed lines are added representing sensor displacement of +/- 100 µm. +![comparison LD4](../../../_static/images/examples_tutorial_magnet_LD4_comp.png) +Whereas the nominal remanence is of 1.22 T and the corrected value estimated from the datasheet is 1.21 T, an optimization procedure using the experimental data resulted in 1.1847 T. This value is the closest one to what is obtained when performing the characterization of the magnet with a set of coils, which resulted in 1.17 T. Another point to notice is that, for this case, if the sensor was 100 µm closer to the magnet, the resulting curve is even above of that obtained with the nominal remanence. -To achieve a proper fit, the value used for magnetic polarization of the cylinder magnet was 1.17 T, a bit more than 4% below the nominal remanence and lower than what can be estimated from the hysteresis curve in the datasheet. It is expected that the difference is bigger for the magnet with L/D = 0.25, and this is confirmed with the following comparison: -![comparison LD025](../../../_static/images/examples_tutorial_magnet_CylinderLD025.png) -In this case, a value for 1.12 T for the magnetic polarization is what provides a good fit to the experimental data, more than 8% off from the nominal value. Such is the effect of having magnets with different geometrical aspect ratios. +The same comparison is made for a magnet with L/D = 0.25, for which greater differences are expected. +![comparison LD025](../../../_static/images/examples_tutorial_magnet_LD025_comp.png) +In this case, from the B-H one can estimate a remanence of 1.18 T, and the fitting with the experimental data yields 1.1254 T remanence. Again, this value is the closest one to what is obtained with magnetic characterization, which resulted in 1.11 T remanence. The same air gap tolerance analysis is performed, and if the sensor was 100 µm closer to the magnet even the B-H curve correction would indicate a remanence above the obtained data. Surely, there are other aspects that will influence your magnetic readings that were not mentioned here, such as sensor offset, sensitivity, and higher order components of the magnetic field that are not taken into account in the analytical expressions solved by Magpylib. 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deletions(-) diff --git a/docs/_pages/user_guide/examples/examples_tutorial_modeling_magnets.md b/docs/_pages/user_guide/examples/examples_tutorial_modeling_magnets.md index d5961951c..cd7d18fcf 100644 --- a/docs/_pages/user_guide/examples/examples_tutorial_modeling_magnets.md +++ b/docs/_pages/user_guide/examples/examples_tutorial_modeling_magnets.md @@ -105,13 +105,13 @@ To obtain the experimental data, a 6-degrees of freedom testbench was used, in w ![comparison LD025](../../../_static/images/examples_tutorial_magnet_testbench.png) -The following figure presents the comparison for the Z-component of the magnetic field for a magnet with L/D = 4. The curves show simulation when using the nominal remanence, the remanence corrected from the B-H curve and the fitted remanence value obtained using the experimental data. Due to tolerances in airgap control and die position inside the sensor packaging, dashed lines are added representing sensor displacement of +/- 100 µm. +The following figure presents the comparison for the Z-component of the magnetic field for a magnet with L/D = 4. The curves show simulation when using the nominal remanence, the remanence corrected from the B-H curve and the fitted remanence value obtained using the experimental data. Due to tolerances in airgap control and die position inside the sensor packaging, the filled area represents sensor displacement of +/- 50 µm. ![comparison LD4](../../../_static/images/examples_tutorial_magnet_LD4_comp.png) -Whereas the nominal remanence is of 1.22 T and the corrected value estimated from the datasheet is 1.21 T, an optimization procedure using the experimental data resulted in 1.1847 T. This value is the closest one to what is obtained when performing the characterization of the magnet with a set of coils, which resulted in 1.17 T. Another point to notice is that, for this case, if the sensor was 100 µm closer to the magnet, the resulting curve is even above of that obtained with the nominal remanence. +Whereas the nominal remanence is of 1.22 T and the corrected value estimated from the datasheet is 1.21 T, an optimization procedure using the experimental data resulted in 1.1847 T. This value is the closest one to what is obtained when performing the characterization of the magnet with a set of coils, which resulted in 1.17 T. This is also an indication that a tolerance of +/- 50 µm is a realistic value in our testbench. The same comparison is made for a magnet with L/D = 0.25, for which greater differences are expected. ![comparison LD025](../../../_static/images/examples_tutorial_magnet_LD025_comp.png) -In this case, from the B-H one can estimate a remanence of 1.18 T, and the fitting with the experimental data yields 1.1254 T remanence. Again, this value is the closest one to what is obtained with magnetic characterization, which resulted in 1.11 T remanence. The same air gap tolerance analysis is performed, and if the sensor was 100 µm closer to the magnet even the B-H curve correction would indicate a remanence above the obtained data. +In this case, from the B-H one can estimate a remanence of 1.18 T, and the fitting with the experimental data yields 1.1254 T remanence. Again, this value is the closest one to what is obtained with magnetic characterization, which resulted in 1.11 T remanence. Surely, there are other aspects that will influence your magnetic readings that were not mentioned here, such as sensor offset, sensitivity, and higher order components of the magnetic field that are not taken into account in the analytical expressions solved by Magpylib. 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