Ferromagnetism — Question 10

Question 10

Frequency scaling separates hysteresis loss from eddy-current loss

At fixed peak induction, a core loss model is $P(f)=af+bf^2$, where a and b are positive. Measurements give P=3.0 W at 50 Hz and P=8.0 W at 100 Hz. Suppose b is proportional to lamination thickness squared while a remains unchanged.

1. Infer a and b, with units, and separate the two loss contributions at 100 Hz.

2. Find the predicted power at 100 Hz after lamination thickness is halved, and determine the frequency where the two contributions are equal before this change.

Question 10 - Solution

Frequency scaling separates hysteresis loss from eddy-current loss

(a) Method and calculation

$$50a+2500b=3,\quad100a+10000b=8\Rightarrow\boxed{b=4.0\times10^{-4}\,\mathrm{W/Hz^2}}.$$$$\boxed{a=0.040\,\mathrm{W/Hz}};\quad P_h(100)=4.0\,\mathrm W,\quad P_e(100)=4.0\,\mathrm W.$$

(b) Interpretation and further calculation

$$b_{\mathrm{new}}=b/4\Rightarrow\boxed{P_{\mathrm{new}}(100)=4.0+1.0=5.0\,\mathrm W}.$$$$af=bf^2,\ f>0\Rightarrow\boxed{f_*=a/b=100\,\mathrm{Hz}}.$$

Physical check

These predictions hold at the same peak induction and within the supplied loss model; changing thickness does not remove hysteresis loss.