对于继电器线圈奇怪的H-B曲线的实验测量

时间：2023-03-02 15:00:00 继电器t1

■ 问题的提出

在昨天的 电磁铁的磁芯实验 继电器线圈施加的电压和测量磁芯磁感应强度的奇怪曲线，即不同于通常的磁滞曲线8绕行字的情况。见下面的线圈电压与Hall输出关系。

那为什么会这样呢？

■ 猜测可能的原因

这种情况极有可能是线圈在施加电压（实验中的电压为±24V，线圈温度的变化远大于线圈的额定工作电压)，从而改变了线圈的电阻。这样，在相同的外部施加电压下，实际的线圈电流不再与外部施加的电压呈线性关系。

然后通过以下两种方式进行验证：

验证方案1 ：将电流采样电阻直接串联到线圈上，测量流过线圈的电流值，重新绘制H-B曲线，看是否符合传统磁滞曲线；
验证方案2：测量线圈温度与施加电压的关系。

01实验研究

1.测量电流和磁芯的磁感应强度B

测量方法是将10欧姆的电阻串联到继电器线圈中作为电流取样电阻。通过测量电流取样电阻上的电压来反映流过的电流。最后，绘制电流与磁芯的磁感应强度之间的关系。

以下是重新测量的施加电压与磁芯磁感应强度之间的曲线。和昨天一样。

^{▲ 施加电压与Hall输出}

以下是测量施加电压与流过的电流之间的关系（从电流取样电阻的电压转换中获得）。你可以看到它们之间的表现奇怪8字曲线特征。

^{▲ 施加电压与电流的变化关系}

绘制电流和HALL线圈磁芯磁感应强度之间的关系可以看出，曲线呈现出相对标准的软磁性特征，没有8字曲线的奇怪特征。

^{▲ 线圈电流与磁芯磁场强度的关系曲线}

以下是拉长测量曲线，以清楚地显示它们之间的关系。

^{▲ 线圈电流与磁芯的HALL测量的信号关系曲线}

2.测量继电器线圈温度的变化

■ 实验方法

将热电偶粘贴在继电器的铁芯上，直接测量铁芯的温度。

该温度与继电器线圈内的温度有一定的延迟，但其变化趋势应相似。

■ 数据分析
正弦变化的缓变电压也应用于继电器线圈，收集100个数据点，每个采样点之间的时间间隔约为2秒。以下是测量线圈上的电压和铁芯温度随时间变化变化曲线。

^{▲ 随着时间的推移，线圈施加电压和磁芯温度变化曲线}

^{▲ 施加电压与温度曲线之间的关系}

t0=27.5e-6 tt0 = 28.5 t1 = 84.33e-6 tt1 = 48.7 def v2t(v):     return (v-t0)*(tt1-tt0)/(t1-t0)   tt0

v=[0.000000,1.522174,3.038219,4.542030,6.027552,7.488803,8.919899,10.315078,11.668722,12.975380,14.229790,15.426903,16.561896,17.630201,18.627515,19.549823,20.393410,21.154881,21.831168,22.419549,22.917654,23.323478,23.635386,23.852123,23.972816,23.996979,23.924515,23.755715,23.491259,23.132212,22.680020,22.136503,21.503851,20.784610,19.981677,19.098284,18.137990,17.104660,16.002456,14.835816,13.609437,12.328257,10.997437,9.622333,8.208483,6.761581,5.287453,3.792034,2.281345,0.761470,-0.761470,-2.281345,-3.792034,-5.287453,-6.761581,-8.208483,-9.622333,-10.997437,-12.328257,-13.609437,-14.835816,-16.002456,-17.104660,-18.137990,-19.098284,-19.981677,-20.784610,-21.503851,-22.136503,-22.680020,-23.132212,-23.491259,-23.755715,-23.924515,-23.996979,-23.972816,-23.852123,-23.635386,-23.323478,-22.917654,-22.419549,-21.831168,-21.154881,-20.393410,-19.549823,-18.627515,-17.630201,-16.561896,-15.426903,-14.229790,-12.975380,-11.668722,-10.315078,-8.919899,-7.488803,-6.027552,-4.542030,-3.038219,-1.522174,-0.000000] t=[0.000006,0.000005,0.000005,0.000005,0.000005,0.000005,0.000005,0.000005,0.000005,0.000005,0.000005,0.000006,0.000006,0.000006,0.000006,0.000006,0.000007,0.000007,0.000008,0.000008,0.000009,0.000010,0.000010,0.000011,0.000012,0.000013,0.000014,0.000015,0.000017,0.000018,0.000019,0.000020,0.000022,0.000023,0.000025,0.000026,0.000027,0.000029,0.000030,0.000031,0.000033,0.000034,0.000035,0.000036,0.000037,0.000038,0.000039,0.000040,0.000041,0.000042,0.000043,0.000043,0.000044,0.000045,0.000045,0.000045,0.000046,0.000046,0.000046,0.000047,0.000047,0.000047,0.000048,0.000048,0.000049,0.000049,0.000050,0.000050,0.000051,0.000052,0.000052,0.000053,0.000054,0.000055,0.000055,0.000056,0.000057,0.000058,0.000059,0.000060,0.000061,0.000063,0.000064,0.000066,0.000068,0.000069,0.000070,0.000072,0.000073,0.000075,0.000076,0.000077,0.000078,0.000079,0.000080,0.000081,0.000082,0.000082,0.000083,0.000084]

■ 铜丝温度与电阻关系

根据 铜的电阻率与温度的关系 ,铜丝的电阻为：

其中：

$R$ :在温度T下铜丝的电阻
$R_{ref}$ ：在参考温度（通常为20℃，或者0℃）下的铜线的温度
$\alpha$ ：铜线的电阻温度系数
$T,T_{ref}$ 是测量温度和参考温度的数值，同时使用摄氏度

铜的温度系数为：

根据 电磁铁的磁芯实验 中测量电磁线圈的电阻在室温下为： $R_{ref} = 90.4\Omega$ ，室温： $T_{ref} = 27$ ℃。
根据前面测量的数据，可以绘制出随着时间变化，线圈的电阻的变化曲线为：

^{▲ 根据}温度计算出线圈的电阻随着时间的变化

■ 绘制电流变化曲线

根据随着时间变化的电压值以及前面线圈的电阻值变化，可以绘制出电压与线圈电流之间的关系。

考虑到在测量时，线圈上串联了10Ω测电阻，所以在计算的时候需要考虑到这个关系。已知电压 $V\left[ n \right]$ ，以及线圈电阻 $R\left[ n \right]$ ，则对应的电流为：

下面是绘制出电压与电流的曲线。可以看到与前面实际测量的数值所呈现的**奇怪的“8”**形状是相似的。

^{▲ 电压与电流之间的变化曲线}

之所以不严格相同，是因为此处所测量的文档只是继电器线圈铁芯的温度，与线圈的温度之间还是有相当大的延迟和差别。但是从趋势上来看，的确是温度造成了前面所测量的奇怪的结果。

※ 结论

如果施加在线圈上的电压超过的它的额定电压值，就像本文中的实验那样，就会造成线圈温度的上升，从而引起线圈电阻的变化。

在测量过程中所呈现的施加的电压与磁芯内部磁感应强度之间的奇怪的“8”字型的变化关系，到头来都是温度惹的祸。

在线圈的实际使用中，需要遵循线圈的额定电压的限制。如果过压过久，高温就会造成线圈的永久性损坏，包括铁芯的退磁等。

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对于继电器线圈奇怪的H-B曲线的实验测量

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