Painted vs Bare Gearbox: Emissivity Reverses the Ranking
Two identical 45 kW gearboxes drive parallel conveyors. Unit 1 has a matte black painted housing (ε ≈ 0.95) and reads 78 °C. Unit 2 has a bare cast-aluminium housing (ε ≈ 0.30) and reads 50 °C. The thermographer left the camera emissivity at 0.95 for both scans. Plant SCADA shows oil sump temperatures of 72 °C on unit 1 and 81 °C on unit 2. Ambient is 30 °C, reflected apparent temperature is 30 °C, and both units are at steady load. The maintenance planner asks which gearbox to inspect first, assuming the one with the higher IR reading is worse.
1. Which gearbox should be inspected first? Correct the bare-aluminium reading and show why the IR ranking is reversed.
Read the worked answer
Unit 2 should be inspected first. Unit 1, with ε ≈ 0.95, is read approximately correctly at 78 °C. Unit 2 is read with the camera set to ε = 0.95 although the actual ε is about 0.30, so the camera underestimates its temperature.
Using T_disp = 50 + 273 = 323 K and T_refl = 303 K: L/σ = 0.95(323⁴) + 0.05(303⁴) = 0.95(1.088 × 10¹⁰) + 0.05(8.43 × 10⁹) = 1.076 × 10¹⁰ K⁴
Actual surface: 0.30·T_true⁴ + 0.70(303⁴) = 1.076 × 10¹⁰ 0.30·T_true⁴ = 1.076 × 10¹⁰ − 5.90 × 10⁹ = 4.86 × 10⁹ T_true⁴ = 1.62 × 10¹⁰ T_true ≈ 357 K ≈ 84 °C
So unit 2 is about 84 °C, hotter than unit 1 at about 78 °C. The SCADA oil temperatures (81 °C vs 72 °C) corroborate this. The IR ranking was reversed by the emissivity error.
2. What procedural changes would prevent this error, and what else could explain the SCADA/IR discrepancy?
Read the worked answer
Preventive changes: set emissivity per surface and record it; apply a high-emissivity tape or paint patch to bare aluminium and re-scan; compare only surfaces with the same finish; use contact sensors for confirmation; and include emissivity, reflected temperature and surface finish in the report.
Other possible explanations for the discrepancy: different loads or duty cycles, different oil levels or cooler fouling, blocked airflow, different sensor locations, or paint thickness and insulation effects. Those should be checked, but the corrected IR result and the SCADA oil temperatures both point to unit 2 as the warmer machine. Inspect unit 2 first, then verify its cooler, oil level and load.