Verification of the calculations
Every change to Axomek’s code runs its verification suite: the engine’s results against results worked out elsewhere. These are the results of axm verify (axm 0.2.5), generated on 2026-10-15: 1,471 of 1,471 cases pass, in 42 groups.
- 1,471 cases checked
- 1,471 pass
- 42 groups
Largest deviation is the largest relative difference between a group’s results and its references (a case whose reference is zero is compared absolutely and left out of it). Each case has its own tolerance, given with it in the suite’s JSON output: the reference’s printed rounding, or wider where the reference is itself approximate (an equation that rounds its constants, an approximation of the load integrals, a test-rig relation).
Closed-form theory 76/76
The solvers against exact solutions: shaft deflection and critical speeds against beam theory, contact pressure and the stresses below the surface against Hertz’s theory, ball screws ball by ball, the thermal growth of a located shaft.
| Group | Cases | Pass | Largest deviation |
|---|---|---|---|
| Shaft: beam theory | 9 | 9 | < 0.001 % |
| Shaft–bearing coupling: beam theory | 9 | 9 | < 0.001 % |
| Shaft: axial thermal growth and one-sided bearing contact | 7 | 7 | < 0.001 % |
| Hertz contact: subsurface stress | 11 | 11 | 0.28 % |
| Hertz contact module | 26 | 26 | 0.094 % |
| Bearing thermal speeds over a duty cycle: DIN 732 per load case | 6 | 6 | 0 % |
| Ball screws: ball by ball | 8 | 8 | 1.4 % |
Worked examples of the standards 682/682
The examples printed in the standards and guidelines, value by value: ISO/TR 6336-30 for gears, DIN 743 Beiblatt 1 and the FKM guideline for shafts, VDI 2230-1 Annex B for bolted joints, DIN 3996 Anhang I for worm gears and ISO 3408-4 for ball screws.
| Group | Cases | Pass | Largest deviation |
|---|---|---|---|
| Shaft strength: DIN 743 Beiblatt 1 examples | 78 | 78 | 0.18 % |
| Shaft strength: FKM guideline | 45 | 45 | 0.53 % |
| Shaft strength: FKM damage accumulation | 8 | 8 | 0.35 % |
| Bolted joints: VDI 2230 Annex B examples | 107 | 107 | 1.6 % |
| Worm gears: DIN 3996 Anhang I | 34 | 34 | 0.32 % |
| Ball screws: ISO 3408-4 rigidity and ISO 3408-5 life | 18 | 18 | 0.044 % |
| Gears: ISO/TR 6336-30 example 1 (Annex A) | 49 | 49 | 0.12 % |
| Gears: ISO/TR 6336-30 example 2 | 49 | 49 | 3.1 % |
| Gears: ISO/TR 6336-30 example 3 | 49 | 49 | 11 % |
| Gears: ISO/TR 6336-30 example 4 | 48 | 48 | 9.1 % |
| Gears: ISO/TR 6336-30 example 5 | 53 | 53 | 1.4 % |
| Gears: ISO/TR 6336-30 example 6 | 48 | 48 | 9.8 % |
| Gears: ISO/TR 6336-30 example 7 | 48 | 48 | 1.1 % |
| Gears: ISO/TR 6336-30 example 8 | 48 | 48 | 4.7 % |
Published tables and formulae 280/280
The standards’ tables from the engine’s own equations: ISO 286 and ISO 492 limits, the ISO 281 and ISO 76 load rating factors and reliability factors, ISO 898-1 property classes, VDI 2230 preloads and torques, DIN 5480 spline and DIN 6885-1 key dimensions, ISO 1328 tolerances, scuffing tables and the heat balance and thermal speeds of DIN ISO 15312 and DIN 732.
| Group | Cases | Pass | Largest deviation |
|---|---|---|---|
| Bearings: ISO 281 load ratings | 45 | 45 | 0.39 % |
| Bearings: ISO 76 static load ratings | 18 | 18 | 2.1 % |
| Bearings: ISO 281 modified rating life | 23 | 23 | 2 % |
| Bearing heat balance: ISO 15312 and DIN 732 | 9 | 9 | 0.047 % |
| Bearing thermal speeds: DIN ISO 15312 and DIN 732 | 16 | 16 | 0.86 % |
| Limits and fits: ISO 286 and ISO 492 | 26 | 26 | 0 % |
| Bolted joints: VDI 2230 preload and torque | 14 | 14 | 0.91 % |
| Gears: ISO 6336-2/-3:2019 work hardening and life factors | 15 | 15 | 0.0016 % |
| Gears: ISO 1328-1:1995 tolerances for the accuracy grade | 12 | 12 | 0 % |
| Gears: internal gear tooth root | 8 | 8 | 0.31 % |
| Gears: scuffing, flash temperature | 21 | 21 | 20 % |
| Gears: scuffing, integral temperature | 10 | 10 | 14 % |
| Splines and keys: DIN 5480 and DIN 6885-1 dimensions | 43 | 43 | 0.0097 % |
| Bolts: ISO 898-1 property classes | 20 | 20 | 0.3 % |
Reference calculations 433/433
The same cases calculated independently: the bearing solver against the reference solver it was ported from, case by case, and against an independent ISO/TS 16281 calculation; critical speeds against an open-source rotordynamics code; a DIN 743 shaft and spur gear factors against published calculations, ISO/TR 6336-30 example 1 against the JGMA reproduction of it, and bevel gear factors against an independent evaluation of the standard’s formulae.
| Group | Cases | Pass | Largest deviation |
|---|---|---|---|
| Shaft: critical speeds against an open-source rotordynamics code | 15 | 15 | 0.0084 % |
| Bearings: an independent ISO/TS 16281 calculation | 17 | 17 | 1.3 % |
| Shaft strength: DIN 743 against a published example | 23 | 23 | 0.88 % |
| Gears: ISO 6336 method B factors against a published calculation | 12 | 12 | 0.026 % |
| Gears: ISO/TR 6336-30 example 1 (JGMA reproduction) | 47 | 47 | 0.038 % |
| Bevel gears: ISO 10300-1 virtual gears and load factors, ISO 10300-2 pitting | 28 | 28 | < 0.001 % |
| Bearings: the reference bearing solver | 291 | 291 | < 0.001 % |
Run it yourself
The suite ships with the command line. axm verify prints every group with its count and any case that differs; --json gives every case for scripts; -o verification.html writes every case as a page. The comparison with the reference bearing solver needs its reference cases, a file kept with the source code and not installed with axm (--reference <file>); without it every other group runs. The command exits with code 4 when any case differs.
axm verify
axm verify --json
axm verify -o verification.htmlWhat it shows, and what it does not
- A passing case means the engine gives the reference’s result for that case within the stated tolerance, usually the reference’s printed rounding.
- It shows that a method is implemented as published. It does not show that the method, or your model, fits your design: the results are for checking designs, and you remain responsible for them.
- The guides say what each method assumes and where it stops, and every calculation report lists its methods and assumptions.