Printed load-bearing joints

A printed part that carries load usually fails at a joint: an eye round a pin, the root of a boss, a screw. Those failures are often found only after the part is printed: a hole worn oval, a boss snapped off along a layer line, a screw backed out, a pin that will not go in. cadagent.mechanical.printed_joints checks the joints before printing, and cadagent.manufacturing.fit_coupons makes the first print a calibration of the fits. Each check returns pass, warn or fail with its margin, the source of every number and its limits. A check screens a design. It does not rate one: print the part or a coupon and test it.

A pin through a printed eye

Drawn by tools/printed_joint_figures.py from pin_eye on a worked example: a 5 mm pin pulling 900 N through an eye 6 mm thick in Bambu PETG Basic, its centre 10 mm from the end, 16 mm wide, bare or with an 8 mm metal bushing, printed flat (pin upright) or on its side.

pin_eye takes the three classic sections of a lug: bearing on the hole, P / (D t), and net tension across the hole, P / ((w − D) t) (Shigley 10th ed., Section 8-12); shear-out along two planes from the hole's sides to the end, P / (2 t (e − D/2)), the usual lug convention for the mode Shigley names. Each nominal stress is resolved on the print's layers by the criterion of the FEA layer check (cadagent.simulation.fea.layer_modes): opening across the layers and shear along them against the across-layer strength, the rest against the in-plane strength. What the example shows:

• Bearing is the first worry in a bare eye. 900 N on a 5 mm pin in 6 mm of PETG is 30 MPa. The check holds it to the in-plane datasheet strength, 48 MPa: a factor of 1.60, a warn. That is a cautious stand-in. Printed PLA and ABS reached 107 to 189 MPa ultimate in bearing (Khosravani et al., 2023), but a held bearing load creeps the hole oval long before.
• A bushing spreads the bearing but costs edge distance. An 8 mm bushing brings bearing to 2.56. Its hole is 8 mm now, so less plastic is left beyond it: shear-out falls from 2.77 to 2.22.
• On its side, the shear-out planes are layers. With the pin lying in the bed plane, the two shear-out planes (and the line along which the end splits) are layer planes, so shear-out is judged against the across-layer strength: 2.02 bare, 1.62 bushed. The layers row warns whenever the pin is more than 10° off the build direction.
• The failure mode. A short or narrow eye is more likely to break suddenly in net tension, shear-out or cleavage than to yield in bearing. Printed PLA failed in bearing from e/D 3 and w/D 6 (ASTM D5961's advice), but printed ABS cleaved there and needed 4.5 and 9 (Khosravani et al., 2023). The failure mode row takes PLA's ratios for PLA, ABS's for ASA, and ABS's, the stricter, for a filament with no test (PETG, CoPA, PA6-CF), and warns below them, whatever the stresses.
• A pin that turns (pivots=True) in a bare printed bore wears it: the pivot row warns until a bushing carries the rotation.

The root of a boss or rib

Drawn by tools/printed_joint_figures.py from root_peel on a worked example: a Bambu PLA Basic boss 16 mm across on a 5.5 mm bore, loaded 20 mm above its root, with an M5 rod tightened to 3 N·m.

A boss or rib built upright and loaded from the side bends at its root, and its bending stress, M c / I, crosses the layers: the bond peels open on the tension side. root_peel checks the tension side, the compression side and the neutral axis (shear: 4V/3A for a solid round, up to 2V/A for a thin tube, 3V/2A for a rectangle) against the layers.

In a highly stressed joint, a common fix is a threaded rod and nuts through the boss: its preload squeezes the layers together, so a side load must first undo that squeeze before the seam opens. root_peel with bolt=through_bolt(...) puts a number on it:

• Closed. The seam stays shut while the kept preload is at least the root's bending stress times its area (1102 N for a 12 mm boss at 100 N; 894 N for the 16 mm one). The layers closed row warns below it: a seam that opens on every step fatigues.
• Kept, not tightened. Torque gives preload only through a nut factor (0.18 to 0.30, Shigley's Table 8-15), and plastic in the clamp relaxes. The check counts on the least preload times retained, 0.5 by default, an assumption: no long-term preload figure for printed plastic was found (#230 holds the relaxation data).
• Not crushed. The most preload, plus the bending, squeezes the compression side. In the example the rod at 3 N·m keeps the 16 mm boss closed, but squeezes it to a factor of 1.47, a warn. advice["torque_window_nm"] gives the torque that keeps it closed (2.68 N·m and up) against the torque the squeezed side takes (1.99 N·m at most): here no torque does both, so widen the root. For the 12 mm boss the two ends are far apart (3.31 N·m against 0.42), so the rod alone cannot save it.

A screw that backs out

flowchart TD
    J["a screw in a joint<br/>that vibrates"] --> S{"side load under<br/>friction × kept<br/>preload?"}
    S -->|"no"| SL["it slips and loosens:<br/>carry the side load<br/>on a pin or bushing"]
    S -->|"yes"| L{"what locks it,<br/>in what thread?"}
    L --> F["threadlocker<br/>on plastic:<br/>fail"]
    L --> W["spring washer,<br/>jam nut, none:<br/>warn"]
    L --> P["locknut<br/>or wire:<br/>pass"]
    classDef here fill:#fffdf5,stroke:#173d3c,color:#173d3c
    classDef near fill:#eef1e4,stroke:#6f8a80,color:#173d3c
    classDef out fill:#ffe1cc,stroke:#bd3a12,color:#173d3c
    class S,L here
    class J near
    class SL,F,W,P out

A screw loosens when the joint slips sideways under its head and in its thread (Junker, 1969): a joint that slips loses its preload, and friction or a prevailing-torque nut does not stop it turning off. thread_locking checks that friction holds the side load: the friction of steel on plastic is taken at its low end (0.20, Covestro's table), on the preload the plastic keeps. Then it checks the locking element against the thread it is in:

• An anaerobic threadlocker on a printed thread fails. Henkel's own data sheets do not recommend it on thermoplastics, where it can stress-crack the part. In an insert it warns: it wicks out onto the plastic.
• A helical spring lock washer warns. It is flat once the screw is tight and does not lock (NASA RP-1228).
• A jam nut warns. NASA's manual finds it too unpredictable to be reliable, and a locknut the more practical choice (RP-1228, p. 7).
• A prevailing-torque locknut on a through-bolt passes, and so does a screw held captive by wire or a pin. They keep the nut on, though a joint that slips still loses its preload, so the slip row still counts.
• Plastic in the clamp path warns under vibration: its preload relaxes. A metal sleeve or bushing through the plastic keeps the clamp in metal (#230's limiters).

Fit coupons: let the first print calibrate the fits

A printed hole comes out smaller than drawn, by an amount that depends on the printer, the filament and whether the hole stands up or lies down. fit_coupons makes a plate per fit with holes swept round the expected CAD size, nominal + allowance + undersize, from research/process-profiles.yaml:

• Undersize 0.25 mm (fdm-hole-undersize-cnckitchen, one printer in PLA).
• Allowance by fit: slide 0.25 (Xometry's 0.2 to 0.3), free 0.3 (Prusa's minimum for moving parts), insert 0 over the insert maker's hole, so the undersize gives CNC Kitchen's 0.2 to 0.3 mm, and press 0: no interference for a press fit in a printed hole is published, so the sweep finds it.
• Orientation. A fit with axis="horizontal" is exported standing on its edge, its holes in the bed plane, as the part's will be.
• Wall. A press fit's grip depends on the plastic round the hole. Give wall_mm the part's own wall there, or the hole that presses right in the coupon may be too tight or too loose in the part.

Drawn by tools/printed_joint_figures.py from fit_coupons.layout for a 5 mm pin in a sliding fit.

write exports a STEP and a print-oriented STL per coupon, a measurement sheet (fit-coupons.csv, a row per hole with blanks for the measured size and the fit) and the plan. Print the coupons in the part's filament, try the real pin, bushing, bearing or insert in each hole, and from_coupon(fit, cad_mm) gives the offset to draw the part's holes with. Print them again when the printer, the filament or the slicer settings change.

From Python

from cadagent.mechanical import printed_joints as pj
from cadagent.manufacturing import fit_coupons as fc

pj.pin_eye("petg-bambu-basic", 900, pin_mm=5, thickness_mm=6, edge_mm=10, width_mm=16, bushing_mm=8,
           pin_axis=(0, 1, 0))["verdict"]                         # 'warn': shear-out on the layers, 1.62
r = pj.root_peel("pla-bambu-basic", 100, 20, pj.tube(16, 5.5), bolt=pj.through_bolt(5, 0.8, torque_nm=3))
r["advice"]["torque_window_nm"]                                    # (2.68, 1.99): no torque does both
pj.thread_locking("printed", "anaerobic")["verdict"]               # 'fail'
fc.write([fc.Fit("pivot pin", 5.0, "slide"), fc.Fit("608 seat", 22.0, "press", depth_mm=7)], "exports/coupons")

Every result has verdict, margin (the lowest safety factor of its stress rows), rows (check, verdict, value, limit, detail, source), the inputs, the material's strengths with their data-sheet editions, and limits. A stress row passes at a factor of 2 (safety, a judgement for short-term datasheet strengths, not a published value), warns from 1 and fails below 1. Materials are the keys of cadagent.mechanical.compliant.allowables.PRINTED.

Limits

Sources and survey

Tests that keep it honest

tests/test_printed_joints.py checks each stress against golden vectors worked by hand, the layer resolution against the FEA layer check on the same tensor, a planted defect per check (an overloaded bearing, a slack rod, a threadlocker on a printed thread, a joint that slips) and the case each one lets through, and that the figures here are current. tests/test_fit_coupons.py keeps the coupon's numbers in step with the process profile, and checks the coupon solid's holes, volume and print files.