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 temperature is usually controlled via pulse width modulation (PWM) of the power. The frequency of the PWM signal influences the speed of the heater's on/off cycles. At low frequency (1 Hz) each cycle induces a large temperature variation of 10-30°C in the resistance wire and titanium sheath. At high frequency (100 Hz) the thermal mass of the heater smooths out the pulses so that the temperature variations are only 1–5 °C. Such temperature variations induce cyclic thermal strains in both the internal resistance wire, which is generally of a nickel-chromium alloy, and the titanium sheath. The reduction in stress amplitude each cycle at 100 Hz (vs 1 Hz) enhances the thermomechanical fatigue life by a factor of 5-10.

Thermomechanical Fatigue Mechanism Induced by Power Modulation

When it is turned on, the resistance wire heats up and stretches. This expansion causes strain on the surrounding magnesium oxide insulator and the titanium sheath. In each power off cycle cooling and contraction is obtained. The stress amplitude, ($\Delta\sigma$) is related to the temperature swing, ($\Delta$T) times the coefficient of thermal expansion. For NiCr wire a = 14 x 10-6 /°C. For titanium a = 8.6 x 10-6 /°C. At 1 Hz modulation with 30 °C temperature fluctuation, the cyclic strain of the NiCr wire is ~0.04%, enough to induce low cycle fatigue over millions of cycles. With a 5°C swing at 100 Hz modulation, the strain is only 0.007% which is below the fatigue limit for both materials and gives almost limitless life.

PWM frequency dependence of quantitative fatigue life

The fatigue lifetimes of Grade 2 titanium sheath heaters with NiCr resistance wires, at 15 W/cm 2 power density at different PWM frequencies, are given below on the basis of controlled tests. When operating continuously (no modulation, baseline), the life of the resistance wire surpasses 100,000 hours, without thermal wear of the titanium sheath. The resistance wire life is 2,000-5,000 hours with 0.1 Hz PWM (1 cycle every 10 seconds) and 40 °C swing; the titanium sheath develops cracks after 10,000-20,000 cycles. Resistance wire life at 1 Hz PWM with 30°C swing is 5,000–15,000 hours and titanium sheath fractures after 20,000–50,000 cycles. 20,000–50,000 hours resistance wire life at 10 Hz PWM with 15°C swing. No cracks in the titanium sheath within 100,000 cycles. The resistance wire life at 100 Hz PWM with 5°C swing is > 100,000 hours and no thermal stress in the titanium sheath. At 1,000 Hz PWM, the temperature variation is less than 2°C and performance is the same as continuous operation.

PWM sensitivity to power density and heater geometry effect

The influence of the PWM frequency is dependent on the thermal mass and power density of the heater. At a low power density of 5 W/cm², the temperature fluctuations are less for any given frequency, therefore a 1 Hz PWM signal will only fluctuate 10°C and the wire life will be 20,000–50,000 hours. At a high power density (25 W/cm2) a 1 Hz PWM signal results in a 50°C swing and wire life is reduced to 1,000-3,000 hours. The thermal mass of a thin wall tube (0.9mm) is lower and the temperature variations are larger. For a thick-wall tube (2.0 mm) the thermal mass is higher and temperature swings are decreased by 30-50 %. For a long heater (2 m) the thermal mass also dampens the temperature variation at the ends.

Titanium Sheath Heater PWM Frequency Selection Guide - -

The following table shows suggestions for PWM frequency based on power density, expected heater life and temperature control needs.

Power Density (W/cm²) Target Heater Lifetime (hours) Temperature Control Accuracy (±°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 Beyond PWM Frequency Selection Engineering

The titanium grade does not influence the thermal fatigue resistance of the resistance wire, while the Grade 7 titanium has similar thermal expansion as the Grade 2. The resistance wire material has a large effect on the fatigue life . The NiCr 80/20 wire has a greater thermal fatigue resistance than FeCrAl wire. The quality of the magnesia insulation is important, as well compacted MgO transport heat better, lowering the temperature difference between the wire and the sheath. Further reduction of thermal stress can be achieved via soft-start power regulation (gradual power increase instead of complete on-off pulses). Where accurate temperature control is required in the application, a higher PWM frequency (100 to 1000 Hz) is always desirable.

Formulating a well-informed specification

Power modulation of a titanium sheath heater with a PWM frequency of 100 Hz or higher is recommended to reduce thermomechanical fatigue. For high power density applications (> 20 W/cm2), utilise a 1,000 Hz PWM or a phase angle controller (smooth power control) instead of on-off modulation. For existing low frequency (1 Hz) heaters either install a smoothing inductor or change the controller to high frequency PWM. If a temperature control precision of ±2°C is suitable for most applications, then a frequency of 10 Hz will offer a sufficient thermal fatigue life. The engineer runs at 100 Hz PWM instead of 1 Hz, thus the temperature swing is reduced from 30°C to 5°C, which increases the fatigue life of the resistance wire and titanium sheath by 5–10 times.