What’s new in Axomek 0.2.0

Results that change when a saved project is solved again:

• Shafts with two steps (or a step and an end) closer together than a twentieth of an element (L/3000 by default: 0.133 mm on a 400 mm shaft, 1 mm on a 3 m one) keep the short section between them in the mesh. Before, such steps shared one node half way and the section (a neck, a groove) vanished with its stress and its give; a load inside it could join longer ones. Supports, loads and springs still move onto a step, an end or a support that close, by that distance at most (moves no longer add up), and an element that short takes its shear flexibility even with shearDeformation off (Euler–Bernoulli's 12·E·I/l³ would swamp the solve). For example a 0.1 mm Ø10 neck 100 mm into a 400 mm Ø50 shaft under 5 kN at midspan: largest von Mises stress 40.7 → 2549 MPa (the neck's 32·M/(π·d³)); a 1 mm Ø46 groove at 1400 mm on a 3 m Ø50 shaft under 5 kN at midspan: 305.6 → 366.5 MPa. Other shafts, and the templates, are unchanged.
• Critical speeds, mode shapes, whirl (Campbell diagram) and unbalance response of shafts whose bearings sit in housings that differ between the bending planes (a housing's seat stiffness or mass, down and sideways) solve both planes. Before, round bearings alone made them take the xy plane for both, and the xz plane's modes were lost: for example a 50 kg disc amid a stiff, light 400 mm shaft on bearings of 2e5 N/mm in housings of 5e5 N/mm, 1 kg down and 500 kg sideways, gave 22 679 rpm (xy) as the lowest critical speed where the xz plane's 9 289 rpm comes first. Bearings that differ between the planes, and housings alike in both, are unchanged.
• Planetary sets with a carrier: the pin bends under the planet's centrifugal force as well as the tooth forces (their vector sum, the planet pin load), and each mesh takes the planet's tilt along its own line of action (at its working pressure angle), so the centrifugal force, along the centre line, raises the sun–planet misalignment and lowers the planet–ring one. The results gain sunPlanetMisalignment and planetRingMisalignment, each the misalignment its pair's KHβ comes from; misalignment is the larger. Before, the pin carried the tooth forces alone at any speed and both meshes took the tilt times cos αt. For example the template's set with an overhung Ø30 × 40 mm pin: pin force 6984 → 6987 / 19 554 / 1 826 455 N at 1500 / 15 000 / 150 000 rpm, deflection 17.84 → 17.85 / 49.96 / 4667 µm, misalignment 25.15 → 25.39 / 49.09 / 2419 µm sun–planet and 24.91 / 1.21 / 2369 µm planet–ring. Shifted sets also move slightly at standstill (the working pressure angles in place of αt). Sets without a carrier are unchanged.
• Press fits with a speed: the shaft's yield check takes its own centrifugal stresses (a free turning disc, plane stress) on top of the joint pressure's, at its bore (or centre) and at the joint, at the pressures left turning at the smallest and the largest interference; shaftStress is the worst of these and the standing stress, and atSpeed gains shaftHoopStress and shaftStress. Before, the shaft kept its standing stress at any speed. For example a Ø100 solid shaft in a Ø200 hub, H7/n6, at 20 000 rpm (loose by then): 30.4 → 35.5 MPa, (3+ν)/8·ρω²R² at the centre. Fits at standstill, and turning ones whose standing stress stays the larger, are unchanged.
• A project with anything not computed (a bolted joint, fit, key, gear pair or other element withheld for invalid inputs, or any other validation error) no longer counts as solved: the report gains incomplete with the paths of what is missing, axm solve exits with code 3 (it gave 0, or 0 under --strict, when only such an element was in error), sweep rows have an error and allChecksPass false, the optimiser counts the design as unsolved, and the calculation report's verdict says not everything could be computed instead of "All checks pass". Before, only the shaft's and bearings' errors (and the gear pairs' in sweeps) were taken into account.
• Bolted joints with a transverseTorque MY but no frictionRadius ra (0, the default) are refused with an error at bolts.<id>.frictionRadius instead of solving without the torque: MY/(qM·ra·μT) was left out of the required clamp load FKQ. For example the bolted bracket with MY 1e9 N·mm needed 13 333 N and passed every check; with ra 10 mm it needs 666.68 MN.
• Shaft strength: a notch (or the most stressed plain section) right at a load, where the axial force, torque or moment steps, is assessed with the stresses of both adjacent elements and the worse kept (the lower of its fatigue and static safety), instead of the side with the larger moment and torque, or the left one on a tie, which ignored the axial force. For example a Ø40 shaft with 400 kN axial at a groove t 5 mm at the load, its locating bearing on the right: σzd 0 → 565.88 MPa and the static safety from unlimited to below 1. A compressive force there no longer helps the fatigue safety, as the side without it is the worse. The templates and snapshots are unchanged.
• Gear pairs whose transverse contact ratio εα leaves ISO 6336-2's contact ratio factor Zε without a value ((4 − εα)/3·(1 − εβ) + εβ/εα ≤ 0, as εα above 4 with εβ < 1) are refused with what to change, instead of a NaN contact stress shown as an unlimited contact safety that passed (z 1000/1000, mn 1, αn 10° or 12°, dedendum 1.6 and addendum 1.4 mn: εα 5.0 or 4.25). A stress that cannot be computed now gives a NaN (failing) safety in cylindrical, bevel and worm gear ratings rather than an unlimited one; results with finite stresses are unchanged.