Pumping unit strokes per minute and motor sheave
Strokes per minute from the motor speed, the V-belt sheave diameters and the gearbox ratio, and the motor sheave diameter for a required stroke rate.
N = n_m · (d_m / d_r) · (1 − ε) / id_m = N_req · i · d_r / (n_m · (1 − ε))v = π · d_m · n_m / 60The stroke rate equals the crank speed. Sheaves come from the standard series and must not be smaller than the minimum diameter for the belt section; V-belt speed is usually kept below 25–30 m/s. A variable speed drive changes the stroke rate smoothly: N is proportional to the supply frequency.
Source: Belt drive and gearbox kinematics: Shigley's Mechanical Engineering Design
Inputs
You can change a field's unit: the value is converted to the formula's units automatically.
Pitch diameter of the V-belt groove.
From the gearbox nameplate, usually about 30–40.
V-belts: 1–2 %.
To size the motor sheave.
Unit converter for this formulaRotational speed · Length · Velocity · Fraction and percent
- rpm1
- rev/s0.0166667
- rad/s0.10472
- d_m,req — Motor sheave diameter for N_req–
- v — Belt speed–
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Results are engineering estimates from standard formulas; for design decisions check them against the codes, project documents and specialists' calculations. The formulas carried over from the original set are unchanged, and their errors are described in the notes.