SYNTHETIC / THEORETICAL VALIDATION

Conveyor load and changeover study

The calculations and generated trials below were executed using the supplied source and declared inputs. They are not measurements from manufactured hardware.

Decision

At the assumed 30 N central side load, the worst-case remaining carton clearance is 0.744 mm, above the allocated 0.25 mm. The reduced-order clearance boundary is 81.8 N. A 150 N jam and the added 0.8 mm wear state are rejected. The force result does not establish an impact-load or machine safety rating.

Inputs

parameter	value
basis	Declared static side-load and synthetic changeover envelope; no physical throughput or time-saving claim.
seed	80120180
operators	3
cycles_each_direction	10
directions	[-1, 1]
steel_E_MPa	193000
steel_yield_MPa	205
aluminum_E_MPa	69000
service_side_load_N	30
jam_side_load_N	150
vertical_carriage_load_N	25
required_residual_clearance_mm	0.25
minimum_friction	0.1
clamp_torque_Nm	3
nut_factor	0.25
bolt_diameter_mm	8
slip_design_factor	2
structural_design_factor	1.5
strap_length_mm	42
strap_width_mm	25
strap_thickness_mm	6
post_height_mm	165
post_x_width_mm	90
post_y_thickness_mm	20
worn_extra_radial_mm	0.8
indicator_policy	All four indicators must exactly match the selected carton width before restart.

Structural calculation

The 304 stainless rail is a simply supported beam with 360 mm support spacing. Lateral bending uses I = 30 x 6 cubed / 12 mm to the fourth, rather than the strong vertical axis. Central load deflection is F L cubed / (48 E I). The hanging straps and posts are conservative cantilevers, each carrying half the rail load. The shaft sees axial side load; a separate vertical sag case is evaluated. Joint compliance is omitted and retained as a model boundary.

side_load_N	rail_deflection_mm	strap_deflection_mm	post_deflection_mm	shaft_axial_mm	total_side_movement_mm	rail_bending_MPa	remaining_side_clearance_mm	clearance_accepted	stress_accepted
0	0.0	0.0	0.0	0.0	0.0	0.0	1.03	True	True
15	0.13989637305699482	0.0021326424870466323	0.0009698024611398964	2.4739110325165082e-05	0.14302355711550652	7.5	0.8869764428844935	True	True
30	0.27979274611398963	0.004265284974093265	0.0019396049222797928	4.9478220650330163e-05	0.28604711423101303	15.0	0.7439528857689869	True	True
60	0.5595854922279793	0.00853056994818653	0.0038792098445595857	9.895644130066033e-05	0.5720942284620261	30.0	0.457905771537974	True	True
100	0.9326424870466321	0.014217616580310882	0.006465349740932642	0.0001649274021677672	0.9534903807700433	50.0	0.07650961922995662	False	True
150	1.3989637305699483	0.02132642487046632	0.009698024611398964	0.0002473911032516508	1.4302355711550652	75.0	-0.4002355711550652	False	True

Side load versus remaining carton clearance

Clamping and repeatability

At 3 N m and K = 0.25, each M8 clamp preload is 1500 N. Two clamps on a rail provide 300 N nominal minimum-friction resistance, a margin of 5.00 against twice the 30 N reference load. The 180 synthetic changeovers include both approach directions, fixed support manufacturing errors and reseating variation. The minimum synthetic loaded clearance is 0.966 mm. No elapsed time or measured savings are invented.

Wrong-setting exercise

All 3 to the fourth four-indicator combinations are enumerated for each of three requested carton sizes. Only the three exact matches are released by the setup rule. The other 240 rows are rejected. This verifies the procedure logic; an operator can still bypass a written procedure.

Data files

All loads are in lateral-load-envelope.csv; the 180 setup observations are in synthetic-changeovers.csv; every indicator combination is in indicator-state-table.csv.

Executed acceptance matrix

id	description	expected	observed	passed
service-clearance	Nominal side load retains allocated carton clearance	>= 0.25 mm	0.7439528857689869	True
service-stress	Reference 304 rail stays below declared elastic screening allowable	<= 136.6667 MPa	15.0	True
jam-rejection	Large jam load is outside the clearance envelope	reject 150 N	-0.4002355711550652	True
clamp-slip	Two clamps per rail resist nominal side load with factor 2	margin >= 1	5.0	True
shaft-vertical	Conservative midspan vertical shaft sag fits the existing 8 mm overhead margin	< 8 mm	0.04398064057807125	True
repeatability-count	Three widths, three operators, two approach directions, ten cycles	180 changeovers	180	True
repeatability-clearance	Generated loaded setup trials retain positive clearance	>= 0.25 mm	0.9660860900100294	True
wrong-setting-table	Every mixed or wrong-size indication is rejected by setup rule	3 allowed states out of 243	{'allowed': 3, 'total': 243}	True
wear-rejection	Added 0.8 mm guide error consumes loaded clearance	reject worn state	-0.05604711423101316	True
beam-reference	100 mm square-section test beam hand value	0.0125 mm	0.0125	True

Model boundaries

Loads, friction and material data are declared assumptions. These results do not establish carton impact, conveyor speed, measured operator repeatability or changeover-time savings.
Linear beam models omit local carriage deformation, slot weakening, weld and bolt flexibility, nonlinear contact, fatigue and load dynamics. The calculated load envelope is a screening result, not a machine rating.
The indicator truth table tests a written restart rule. No installed sensor or electrical interlock prevents a wrong setting in this mechanical design.
The ground shaft and purchased clamps remain dimensioned reference envelopes. Procurement, retaining features and assembly details must match supplier hardware if fabricated.
The synthetic trials keep fixed errors correlated across repetitions; their bounded distributions are assumed and cannot establish production capability.

Reproduce

From this project folder, run python complete_validation.py. Run python test_completion.py for independent regression checks. Inputs are in completion-inputs.json; machine-readable outcomes and source hashes are in completion.json.