Impact of Magnetic Relative Permeability of Ferromagnetic Target on Back-Biased Sensor Output
Impact of Magnetic Relative Permeability of Ferromagnetic Target on Back-Biased Sensor Output
By Yannick Vuillermet,
Allegro MicroSystems Europe Ltd
Introduction
This application note aims to describe the target relative magnetic permeability impact on Allegro back-biased magnetic sensor output.
Sensor performance depends highly on the target mechanical geometry. In the case of speed applications, tooth and valley geometries are critical—but these mechanical properties are not the topic of this application note. Here, it is assumed that the target is well-designed for the customer application. Instead, this application note focuses on the target ferromagnetic material properties and especially the magnetic permeability.
这个应用程序的实际目标笔记define the minimum target material relative permeability to guarantee optimum sensor performance in the application. This application note applies to any applications using a back-biased sensor associated with a ferromagnetic target: speed sensors (cam, crank, transmission, etc.), position sensors (linear, angle, etc.), etc.
Ferromagnetic Material Properties
A material is said to be ferromagnetic when it tends to acquire a magnetization when placed in an external field (from a permanent magnet, from a current in a coil, from earth field, etc.). In a ferromagnetic material, the material magnetization is aligned with the resulting internal field. On the contrary to permanent magnets, the remanent magnetization of a ferromagnetic material is very small when no
external field is applied.
图1是表示上述属性的简化方式。在该图中，假设材料行为在低场中纯度是线性的，并且没有滞后（这相当于这里没有再伸缩磁化）。His the magnetic field,Jis the magnetic polarization,JS.is the polarization at saturation, andμis the magnetic permeability. The magnetic polarizationJis linked to the magnetizationM通过这种关系：
J = μ0 × M(1)
相对渗透率定义为材料的渗透率与自由空间的渗透性相比μ0:
在下文中，假设材料仅用于线性范围。此假设在Allegro传感器目标的大多数应用程序中都是完全有效的。亚博尊贵会员在这种线性条件下，μ – μ0is the slope of theJ(H)curve, and:
B = μ0×μr×h(3)
因此，对目标材料很重要的唯一磁性参数是相对渗透性，μr. Basically, the permeability represents the material capability to be magnetized by an external field.
图2示出了钢铁1010的测量数据，其是与Allegro传感器组合使用的经典材料。看来，这种材料的相对渗透性总是在材料的线性范围内大于600，即表示H < 1000 A/m.
该材料中的1000A / m磁场值，相当于〜12.5 OE（oSED） - 该看起来非常小 - 不得与空气中的磁场相比，例如由后偏置磁体产生。磁铁可以在空气中容易地生产几百高斯的B字段。然而，放置在该大B场中的铁磁材料将具有更小的内部H字段。作为示例，对于在空气中产生600g磁场的磁体，根据等式3和4，通常仅看到300的相对渗透性的铁磁性材料通常仅看到5 OE（或〜400A / m）H字段，并且典型的形式尺寸为0.4（见下一个部分）。这种行为是由于退磁领域，否则表示，从该领域开始，该领域本身就会产生。总之，重要的是要记住，从后偏磁铁（几百个高斯）的空气中的大场并不一定意味着铁磁材料在其非线性模式下工作。
该表提供了一些常用材料的磁性相对渗透性。
| 材料 | Magnetic Relative Permeability |
| 空气 | 1 |
| Copper | 1 |
| 钕磁铁 | 1.05 |
| Steel* | 1 to 4,000 |
| Permololoy. | 8,000 |
| μ-金属 | >20,000 |
Source:https://en.wikipedia.org/wiki/permeability_（Electromagnetism）
* Note that some steel variants are not magnetic, some stainless steel, for example.
渗透率与形状因素
The magnetization of a ferromagnetic material is driven by two main parameters: the magnetic permeability and the shape (form factor) of the object.
The following shows how these two parameters impact the magnetization on a very simple example.
In the case of an ellipsoid object, the magnetization is uniform inside the material, whatever the uniform external field applied to the object. Note that this ellipsoid could be seen as a very rough approximation of a speed target tooth.
Figure 3 shows an ellipsoid placed in a uniform field何alongxand the uniform magnetizationJ.
In this case, assuming there is no material magnetic saturation, the magnetization is given by:
在这个等式中，Nxis the form factor of the ellipsoid alongx. This parameter depends on the ellipsoid shape and is always below 1. An object elongated in thex方向将有一个小的Nx(for exampleNx= 0.1). A specific case is the sphere which hasNx= 1/3。
Figure 4 displays the object polarization versus the relative permeability for a few form factors. It clearly appears that objects elongated in the external field direction are easier to magnetize. More interestingly, one can notice that, above a given level of permeability, the object polarization only depends on the object shape. This clearly happens when 1 / (μr– 1) becomes negligible versus the form factor Nx.
图5显示了相同的曲线，但具有归一化极化，以更好地看到渗透率。看来，无论对象形状如何，一旦相对渗透率大于300，就达到了至少95％的最大磁化。
This number will be confirmed in next paragraph in a realistic application.
Example of a Typical Application: Allegro 60X Reference Target with ATS699LSN Speed Sensor
现在，考虑使用典型的速度应用程序ATS699LSN放置在Allegro 60x参考目标前面的传输部分（图6）。ATS699LSN是一个差分部分，具有三个霍尔板（左，中心，右）和两个差分通道（左心和中心右）。以下仅考虑一个通道的输出。
Typical working air gaps for this part are 1 mm and 2 mm, air gap being defined by the distance between the branded face of the sensor and the top of the target teeth.
图7给出了当目标在一个半时段前方传感器前方的一个通道的归一化输出。该图表明差分场波形几乎不依赖于相对磁导率。可以观察到，在波形之间只有（小）差异μr= 10 for positions around 3°. Positions around 0° have similar behavior whatever the relative permeability because these positions correspond to a valley of the target.
图8和图9分别给出了通道与1mm和2mm气隙的相对渗透率的峰峰差。这些数字证实了先前所见的内容：为了保证最佳性能，目标材料相对渗透性应至少为300.相对渗透性的任何进一步增加对由传感器测量的磁信号具有边缘撞击。
如果铁磁靶材料具有小于300的相对渗透性，则并不意味着背偏偏置装置不起作用。它只适用于堕落的性能
compared to a target with large permeability. For example, the maximum working air gap of the application could be reduced.
Conclusions
Finally, this application note gives a simple answer to the question, “Is my target material suitable for a back-biased application?”: in order to have optimum performances, the magnetic relative permeability of the target material must be at least 300 for H-field < 2000 A/m.
何wever, this is a necessary but not a sufficient condition; having a proper target mechanical design is also mandatory to achieve application desired performances.
Allegro engineers can help evaluate whether the target’s material is adapted to a back-biased arrangement or not. If the material has a low relative permeability, Allegro can also provide support to estimate the impact on the application’s performance.