Engineering Calculations

Service interval prediction (air filter)

Service interval (hours) = DHC (grams) ÷ [dust concentration (mg/m³) × airflow rate (m³/h) × 0.001 (mg→g)]. Example: 500g DHC, 1 mg/m³ dust, 1,000 m³/h airflow → 500 theoretical hours. Apply service factor of 0.8–0.85 (replace at 80–85% of theoretical capacity).

Contamination budget

Particle ingress rate (particles/hour) = dust concentration × airflow × particle count per gram × efficiency gap. Particle removal rate (particles/hour) = total flow × filter efficiency at critical size. Balance requires removal rate ≥ ingress rate to maintain target cleanliness code.

Beta ratio to efficiency conversion

Efficiency (%) = (1 − 1/β) × 100. β = 2 → 50%; β = 10 → 90%; β = 75 → 98.7%; β = 200 → 99.5%; β = 1000 → 99.9%. The relationship is logarithmic — going from β = 10 to β = 200 is a qualitative change, not a 20× proportional improvement in protection.

Pressure drop estimation

ΔP scales approximately linearly with flow rate and fluid viscosity. ΔP at new conditions = ΔP_rated × (Q_new/Q_rated) × (η_new/η_rated) where Q = flow rate and η = dynamic viscosity. Cold-start viscosity (40°C) may be 5–10× operating viscosity (100°C), producing 5–10× rated initial ΔP — the basis for bypass valve sizing.

TCO differential calculation

TCO difference = (component life extension value) − (incremental filter cost). If ISO 16/14/11 extends hydraulic motor life 3× and motor costs USD $12,000, life extension value = 2× $12,000 = $24,000 per motor per asset. Incremental filter cost to achieve ISO 16/14/11 vs ISO 19/17/14 = USD $500–2,000/year. Net benefit: USD $22,000–23,500/motor replaced.

Service factor for DHC scheduling

0.80–0.85 (replace at 80–85% DHC)

β efficiency formula

Efficiency = (1 − 1/β) × 100%

β = 200 efficiency

99.5%

Cold start viscosity multiplier

5–10× operating viscosity (typical)

TCO filter cost share

1–5% of total maintenance cost