Executive Summary
Servo motors generate heat as a byproduct of operation — from copper losses (I²R) in the windings and from iron losses in the lamination stack. Motor temperature depends on duty cycle, ambient temperature, cooling effectiveness, and current loading. Without accurate, continuous temperature monitoring, the only protection is a binary overcurrent cutoff that activates only after damage has already begun. Continuous analog temperature measurement enables proactive load management, extended motor life, and predictive maintenance scheduling.
Why Binary Temperature Protection Is Insufficient
Binary PTC Thermistor Operation
The simplest motor thermal protection uses a PTC (Positive Temperature Coefficient) thermistor embedded in the motor winding. At the thermistor's trip point (e.g., 90°C for a common motor protection thermistor), resistance rises sharply from a few hundred ohms to tens of kilohms. The drive's digital input, which has a pull-up resistor creating a voltage divider with the thermistor, reads the high-resistance state as a logic fault and disables the drive.
Limitation: The trip is binary — the drive operates normally up to the trip point, then shuts down. Between normal operation and trip, there is no visibility into actual motor temperature or how close the motor is to its thermal limit. Repeated operation near the trip threshold accelerates insulation aging without triggering the protection.
What Continuous Monitoring Enables
Continuous analog temperature monitoring provides:
- Preemptive load reduction: Reduce commanded torque or duty cycle before the trip threshold is reached
- Cycle time optimization: Increase cycle rate when the motor is cool; reduce it when approaching the thermal limit
- Cooling system feedback: Trigger cooling fan speed-up or coolant flow increase based on actual motor temperature
- Predictive maintenance: Track thermal cycling history and trigger maintenance intervals based on actual thermal stress accumulation
- Warranty and reliability data: Log temperature profiles for root cause analysis of failures
The Steinhart-Hart Model for Thermistor Resistance-to-Temperature Conversion
The relationship between temperature and thermistor resistance is nonlinear. The Steinhart-Hart equation provides an accurate empirical fit across a wide temperature range:
1/T = A + B·ln(R) + C·(ln(R))³
Where:
- T = temperature in Kelvin
- R = resistance in ohms at temperature T
- A, B, C = Steinhart-Hart coefficients (thermistor-specific)
Determining Coefficients
The three coefficients A, B, and C are determined from three known (R, T) pairs. Selecting three pairs at critical temperatures maximizes the accuracy across the range of interest.
Example calibration for a 90°C trip point thermistor:
| Temperature | Thermistor Resistance |
|---|---|
| 80°C (353 K) | 250 Ω — motor too hot to touch |
| 95°C (368 K) | 4,000 Ω — approaching burnout |
| 100°C (373 K) | 20,000 Ω — damage occurring |
Setting up the three simultaneous equations:
1/353 = A + B·ln(250) + C·(ln(250))³ 1/368 = A + B·ln(4000) + C·(ln(4000))³ 1/373 = A + B·ln(20000) + C·(ln(20000))³
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Solving this system (via matrix algebra or spreadsheet) yields A, B, and C.
Verification: Substituting R = 1,650 Ω into the Steinhart-Hart equation should yield T ≈ 363.9 K (90.9°C) — confirming the coefficients are consistent with the thermistor's trip behavior.
Implementation in Servo Drive Systems
Voltage Divider Circuit
The servo drive's analog input circuit provides the measurement. The drive has an internal pull-up resistor (example: 4.99 kΩ) connected between a reference voltage and the thermistor input. The thermistor is connected from this input to ground. The thermistor resistance and the pull-up resistance form a voltage divider:
V_measured = V_ref × R_thermistor / (R_pullup + R_thermistor)
The analog-to-digital converter in the drive measures V_measured. Converting to resistance:
R_thermistor = V_measured × R_pullup / (V_ref – V_measured)
The drive's firmware then applies the Steinhart-Hart equation to convert R_thermistor to temperature in Kelvin, which is converted to Celsius for the application.
Drive-Specific Pulldown Resistors
Some drive input circuits include both pull-up and pull-down resistors. In this case, the equivalent circuit is a three-element resistor network, and the resistance calculation requires equivalent circuit analysis using the actual drive circuit topology. Drive application engineers should provide the equivalent circuit for accurate calibration.
Two Common Calibration Scenarios
Scenario A: Known thermistor model The thermistor manufacturer's datasheet provides resistance vs. temperature data. Select three operating-relevant temperature points (e.g., 25°C, 80°C, 100°C), read the corresponding resistances from the datasheet, and compute A, B, C. The resulting model is immediately usable.
Scenario B: Unknown thermistor or embedded winding Take physical temperature and resistance measurements at three controlled temperature conditions (e.g., cold soak, normal operating temperature, elevated operating temperature). Use these measured pairs to compute A, B, C. This empirical approach works even when thermistor model data is unavailable.
Operational Deployment: Thresholds and Actions
With continuous temperature data, the servo drive or PLC can implement multi-level thermal management:
| Temperature Level | Action |
|---|---|
| < 70°C | Normal operation |
| 70–80°C | Reduce maximum commanded torque by 20% |
| 80–85°C | Trigger cooling fan to maximum speed |
| 85–90°C | Reduce duty cycle; issue operator warning |
| > 90°C | Disable drive (thermal fault) |
This graduated response prevents abrupt shutdowns during production while providing thermal protection. The specific thresholds are calibrated to the motor's insulation class rating — Class F (155°C continuous) or Class H (180°C continuous) insulation withstands higher temperatures than Class B (130°C).
I²T Motor Overload Protection
A complementary protection method is I²T (I-squared-T) monitoring, which integrates the square of the motor current over time to estimate winding temperature rise from copper losses:
Estimated temperature rise = k × ∫(I² dt)
I²T protection models the thermal accumulation continuously and can detect impending overtemperature before any physical sensor reaches the trip threshold — particularly useful for pulse-mode operation where large current bursts occur faster than the thermal sensor can respond.
Combined I²T plus thermistor-based temperature monitoring provides overlapping protection that covers both high-current transient events and sustained moderate-overload conditions.
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