How Does the Frequency of Power Modulation (Pulse-Width Modulation at 1 Hz vs. 100 Hz) for a Titanium Sheath Heater Change the Thermomechanical Fatigue Life of the Resistance Wire and the Tube?

In electric titanium sheath heaters, the power is commonly controlled by means of pulse-width modulation (PWM) to control the temperature. The speed at which the heater turns on and off is determined by the frequency of the PWM signal. At the low frequency of 1 Hz, each cycle causes a large temperature swing of 10-30°C in the resistance wire and titanium sheath. At high frequency (100 Hz) the thermal mass of the heater smooths the pulses so the temperature swings are only 1-5 °C. The temperature variations cause cyclic thermal strains in the internal resistance wire (usually nickel-chromium alloy) and titanium sheath. The life of thermomechanical fatigue is increased 5-10 times at 100 Hz in relation to 1 Hz due to the smaller stress amplitude per cycle.

Thermomechanical Fatigue Mechanism by Power Modulation

Each power-on cycle heats the resistance wire, causing it to expand. The expansion puts stress on the surrounding magnesium oxide insulation and the titanium sheath. Cool and contract on every power-off cycle. The stress amplitude (Δσ) is proportional to the temperature swing (ΔT) multiplied by the coefficient of thermal expansion. For NiCr wire α = 14 × 10⁻⁶ /°C, for titanium α = 8.6 × 10⁻⁶ /°C. The NiCr wire is subjected to a cyclic strain of ~0.04 % at 1 Hz modulation and a temperature swing of 30°C, sufficient to cause low-cycle fatigue over several million cycles. The strain is only 0.007% with a 5°C swing at 100 Hz modulation, which is below the fatigue limit for both materials and hence gives almost limitless life.

Quantitative fatigue life vs. PWM frequency

Controlled tests of the Grade 2 titanium sheath heater with NiCr resistance wires at a power density of 15 W/cm2 have produced the following fatigue lifetimes at various PWM frequencies. The resistance wire has a life of more than 100,000 hours of continuous operation (no modulation, baseline) and the titanium sheath is not affected by thermal fatigue. 2,000-5,000 hours resistance wire life at 0.1Hz PWM (one cycle in 10 sec) with 40°C temperature variation and the titanium sheath splits after 10,000-20,000 cycles. The resistance wire life is 5,000–15,000 hours at 1 Hz PWM with a 30°C swing, while the titanium sheath fractures after 20,000–50,000 cycles. For the resistance wire, longevity is 20,000–50,000 hours at 10 Hz PWM with a 15°C swing, while the titanium sheath exhibits no cracks within 100,000 cycles. At 100Hz PWM with a 5°C swing, the resistance wire life is >100,000 hours and no thermal stress of the titanium sheath is experienced. At 1 kHz PWM the temperature variation is < 2 °C and the performance is the same as continuous operation.

PWM sensitivity effects on heater geometry and power density

The influence of PWM frequency relies on the power density and thermal mass of the heater. At low power density (5 W/cm²), the temperature fluctuations are less for any given frequency, therefore a 1 Hz PWM signal gives only a 10°C swing, and the wire life is 20,000–50,000 hours. At a high power density of 25 W/cm² and a 1 Hz PWM signal, a 50°C swing reduces wire life to 1,000 to 3,000 hours. For a thin-wall tube (0.9 mm) the thermal mass is smaller and the temperature changes are bigger. The thicker wall tube (2.0 mm) has a greater thermal mass, and the temperature swings decrease by 30–50%. For a long heater (2 m) the thermal mass also damps the temperature swing at the ends.

Titanium Sheath Heaters PWM Frequency Selection Guide.pdf

The following table gives suggestions for PWM frequency according to the power density, intended heater life and temperature control needs.

Power Density (W/cm²) Desired Life of Heater (hours) Required Control Precision (±°C) Recommended PWM Frequency (Hz) Expected Temperature Swing (°C) <10 >50,000 2 1 10–15 <10 >50,000 0.5 100 2–5 10–20 >50,000 2 10 8–12 10–20 >50,000 0.5 1,000 1–3 20–30 >20,000 2 100 3–6 20–30 >50,000 1 1,000 1–2 >30 >10,000 Any 1,000+ <2 Engineering Beyond PWM Frequency Selection

The grade of titanium does not effect the thermal fatigue resistance of resistance wire, nevertheless, Grade 7 titanium has similar thermal expansion as Grade 2. The resistance wire material is strongly a function of the fatigue life. The NiCr 80/20 wire has better thermal fatigue resistance compared to the FeCrAl wire. The quality of MgO insulation is also important as compacted MgO transfers heat better and reduces the temperature difference between the wire and the sheath. Soft-start power control (gradual rise of power, instead of on-off pulses) helps further reduce thermal stress. If you want accurate temperature management then a higher PWM frequency (100-1,000 Hz) is always better.

Making a Reasoned Specification

For power modulated titanium sheath heaters, a PWM frequency of 100 Hz or higher is recommended to minimize thermomechanical strain. For applications requiring high power density (above 20 W/cm2) utilize 1,000 Hz pulse width modulation (PWM) or a phase angle controller (smooth power control) instead of on-off modulation. For existing low frequency (1Hz) heaters add a smoothing inductor or update the controller to high frequency PWM. If a ±2°C temperature control accuracy is acceptable, then 10 Hz frequency is good enough to give sufficient thermal fatigue life for most applications. The engineer operates at 100 Hz PWM instead of 1 Hz, reducing the temperature variation from 30°C to 5°C and increasing the fatigue life of the resistance wire and titanium sheath by a factor of 5–10.