If you want to ensure your motor lasts a long time, you need to prevent overheating by leveraging motor temperature data. Not only can this data optimize motor loading and cooling, it can improve energy efficiency, reduce operational costs and facilitate predictive maintenance strategies.

There are a handful of both digital and analog methods to take accurate motor temperatures. One digital technique is the “I Squared T” (I²T) method we explored in a previous blog post. An analog, resistance-based approach is to use Steinhart-Hart coefficients.

Resistance-Based Temperature Measurement

Because the Steinhart-Hart equation models the relationship between temperature and resistance, it provides an empirical method of measuring motor temperatures. The equation is:

$\frac{1}{T}=A+B \ln (R)+C(\ln (R))^3$

Where:
T is the temperature in kelvin (K).
R is the resistance at T in ohms (Ω).
A, B and C are the coefficients that vary according to thermistor model and temperature range of interest.

Given three resistances (R₁, R₂ and R₃) and temperatures (T₁, T₂ and T₃) we can solve a system of equations to calculate the Steinhart-Hart coefficients.

$\left[\begin{array}{lll}1 & \ln R_1 & \ln ^3 R_1 \\ 1 & \ln R_2 & \ln ^3 R_2 \\ 1 & \ln R_3 & \ln ^3 R_3\end{array}\right]\left[\begin{array}{l}A \\ B \\ C\end{array}\right]=\left[\begin{array}{l}\frac{1}{T_1} \\ \frac{1}{T_2} \\ \frac{1}{T_1}\end{array}\right]$

\[
\begin{align*}
L_1 &= \ln R_1, \quad L_2 = \ln R_2, \quad L_3 = \ln R_3 \\
Y_1 &= \frac{1}{T_1}, \quad Y_2 = \frac{1}{T_2}, \quad Y_3 = \frac{1}{T_3} \\
y_2 &= \frac{Y_2 - Y_1}{L_2 - L_1}, \quad y_3 = \frac{Y_3 - Y_1}{L_3 - L_1} \\
C &= \left(\frac{y_3 - y_2}{L_3 - L_2}\right)(L_1 + L_2 + L_3)^{-1} \\
B &= y_2 - C(L_1^2 + L_1L_2 + L_2^2) \\
A &= Y_1 - (B + L_1^2C)L_1
\end{align*}
\]

As an example, we will consider a PTC thermistor that has a 90°C trip point when used with a Copley digital input that has a 4.99-thousand Ω internal pullup. The critical temperatures are:

80°C, where the motor is too hot to touch and the thermistor resistance is 250 Ω.
95°C, where the motor is approaching burnout and the thermistor resistance is 4,000 Ω.
100°C, where the motor is being damaged and the thermistor resistance is 20,000 Ω.

These resistances are known based on the thermistor’s properties. By entering the given relationships in a spreadsheet as shown below, the Steinhart-Hart coefficients can be calculated:

Copley Spreadsheet 1.png

Copley Spreadsheet 2.png

With known coefficients, you can pick an arbitrary resistance to calculate the temperature. In this case, 1,650 Ω provides 90.9°C. To calibrate the system to a different thermistor, simply take resistance measurements at three different critical temperatures and use those resistance and temperature values in the above calculation.

Keep in mind that Copley circuits have their own pull-up and pull-down resistors, so calculating the three resistances requires voltage measurements and equivalent circuit analysis.

Reach out to Copley applications engineers for any assistance.

Contact Us

Technology Blog

Prevent Motor Overheating With Analog Temperature Reading

Similar Posts

Exploring the “I Squared T” Motor Overload Protection Method

What is i2t?