Starting the FEA engine

Downloading Python runtime…

The solver is fea_engine.py, running in your browser via Pyodide. Nothing is sent to a server.

Geometry & Hardware ▾

Rod size (API 11B) Coupling class Coupling OD 1.625 in Centralizer / guide OD (in) Guide length (in) Free span, coupling face to guide face (in) Tubing ID (in)

Axial Loading ▾

Load source

SPM Stroke length (in) Pump depth (ft) Window depth (ft) Fluid SG Plunger diameter (in) Net lift (ft) Downstroke drag / plunger resistance (lbf)

Drag is the dominant real source of near-pump compression. With little rod hanging below the window, this is what drives the axial force negative on the downstroke.

Inclination from vertical (°) 30°

Lateral gravity is what pushes the coupling onto the low side. At 0° (truly vertical) only the initial crookedness breaks symmetry.

Material & Fatigue ▾

Rod grade

Modified Goodman uses the minimum tensile strength. API Grade D is a 115–140 ksi range, so 115 ksi is the design value; the high-strength grades are quoted as minimums already.

Service condition (API RP 11BR)

Grade strengths match the Valevant fatigue simulator catalog exactly, so the two tools never disagree on allowables.

Contact & End Conditions ▾

Rod / tubing friction coefficient End condition

Guided is the physical case: above the coupling the string runs ~25–30 ft to the next guide, so the coupling really can swing across its clearance and lie on the wall. Pinning both ends forces it concentric and hides exactly the behaviour this tool exists to show.

Distance to next support, each end (in)

This is the most influential input in the model. It sets the rotational restraint standing in for the rod beyond each cut, and the critical load falls roughly as 1/L. At 24 in the window sits well below critical (P_cr ≈ 2,300 lbf); at 120 in it is above it, and at 360 in nearly 4×. Use the real spacing to the next guide or coupling, and read the band on the critical-load tile rather than the single value.

Initial crookedness (span / n)

Solver ▾

Strokes simulated Steps per stroke Elements in the free span Include inertia (Newmark-β) — withdrawn

Deformed geometry inside 2-7/8" tubing

Radial magnification 1.0× Cutaway tubing

— Speed

Rod colour = instantaneous von Mises / yield <70% 70–100% >100% ring = node loaded against the wall Goodman fatigue utilisation is in the stats and stress chart. Above 1× magnification, displacement is exaggerated but the tubing is not, so hardware may appear to cross the wall.

Buckling & contact response

Deflected shape along the window Rod centreline against the clearance envelope, at the frame shown above. The envelope steps because coupling, rod and guide have very different clearance.

Stress envelope along the window Max and min fibre stress over the whole cycle.

Wall contact force vs time Where the wear happens, and when in the stroke.

Buckling signature — axial force vs lateral bow The tension/compression effect in one plot. Compression softens lateral stiffness until contact caps the bow.

Table view (accessible alternative)

Hand off to the fatigue simulator

This window model answers a local question: how does this one span bow and touch the wall. The Valevant fatigue simulator answers the screening question across a whole segment. Carry these values over:

Open the fatigue simulator

Model scope, assumptions and limits