Assembly Calculations

How to Calculate the Core Metrics for Pump and Compressor Assembly

The five formulas every rotating-equipment build line lives on, worked through with real inputs, units, and where each number comes from.

Rotating-equipment assembly runs on a handful of formulas you compute daily. Start with assembly takt time: takt = available time / demand. On a shift with 27,000 productive seconds (450 min minus 30 min of breaks) and demand of 45 pumps, takt = 27,000 / 45 = 600 s, or 10.0 min per unit. Every station must finish inside that window. If station 3 measures 11.4 min of hands-on work, you are 84 s over takt and will bleed 6.3 units per shift. Feed real demand and true available time into the Assembly Takt calculator rather than nameplate hours.

Seal leak rate is the acceptance gate on most pump and compressor builds. For a pressure-decay test, Q = (ΔP × V) / (P_atm × t), expressed at standard conditions. Pressurize a 2.0 L cavity to 6.0 bar gauge, hold 120 s, and read a 0.15 bar drop: Q = (0.15 × 2.0) / (1.013 × 120) = 0.00247 std-L/s, about 148 std-cm3/min. Against a 100 cm3/min limit that unit fails. The Seal Leak Rate calculator converts decay, bubble-count, or mass-flow readings to one comparable figure so you are not mixing units across benches.

Impeller trim changes duty point by the affinity laws. For a diameter cut, H2 = H1 × (D2/D1)^2 and Q2 = Q1 × (D2/D1). Trim a 250 mm impeller to 235 mm, ratio 0.94: flow scales to 0.94 and head to 0.884. A pump making 120 m3/h at 62 m now delivers about 113 m3/h at 54.8 m, and shaft power drops with the cube, roughly 0.831, so a 30 kW draw falls near 24.9 kW. The Impeller Trim Effect calculator runs these three ratios at once so you size the cut to hit a duty point without over-trimming.

Compressor flow output ties displacement to delivered volume. For a positive-displacement stage, actual flow = V_swept × N × η_vol. A screw with 0.42 L per revolution at 2,950 rpm and 0.88 volumetric efficiency gives 0.42 × 2,950 × 0.88 = 1,090 L/min, about 1.09 m3/min or 38.5 cfm at inlet. Correct to standard conditions with the ideal-gas ratio (P_actual/P_std)(T_std/T_actual) before comparing to a spec sheet. The Compressor Flow Output calculator handles the standard-condition correction and lets you back-solve required rpm for a target delivery.

Bearing life is the L10 rating life: L10 = (C/P)^p × 10^6 revolutions, where p = 3 for ball and 10/3 for roller bearings. With dynamic capacity C = 32 kN and equivalent load P = 4.5 kN, (32/4.5)^3 = 359, so L10 = 359 million revolutions. At 2,950 rpm that is 359e6 / (2,950 × 60) = 2,028 hours, well short of a 20,000 hour target, so the load or bearing selection needs revisiting. The Bearing Life Estimate calculator applies the correct exponent and converts revolutions to hours at your operating speed.

Equivalent load P is itself a small calculation: P = X × F_radial + Y × F_axial, with X and Y from the bearing's e-factor table. A 3.0 kN radial and 2.2 kN axial load with X = 0.56 and Y = 1.6 gives P = 0.56 × 3.0 + 1.6 × 2.2 = 5.2 kN. Feed that P, not the raw radial force, into the L10 formula. Getting P wrong is the most common source of a life estimate that is off by 2x or more, because the exponent magnifies every input error.

Test-stand throughput sets whether the build line ever ships. Stand capacity = available time / cycle per unit, where cycle includes fixture, ramp, dwell, and teardown. A stand with 5 min fixturing, an 8 min performance run, and 4 min teardown clears 17 min per unit, so a 450 min shift yields 26 units against a 45 unit demand. That 19 unit gap means test, not assembly, is your constraint. The Test Stand Capacity calculator lets you model parallel stands and dwell overlap before you commit capital.

Chain these together to plan a build. Set takt from demand, confirm each station and the test stand beat takt, verify the seal decay math against your acceptance limit, and confirm bearing L10 clears the warranty horizon at operating load. Keep units explicit at every step: seconds not minutes, std-L/s not raw L/s, kN not N. A single unit slip, treating a 6.0 bar gauge reading as absolute, or dropping the volumetric-efficiency term, is what turns a clean calculation into a warranty return six months later.

Published 2026-07-01.