SYNTHETIC / THEORETICAL VALIDATION

Mounting fixture commissioning study

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

Selected operating envelope

The revised reference fixture uses flanged hardened-steel bushes with 30 x 14 x 3 mm steel caps, two M3 x 10 screws per cap, and the supplied toe clamps. The calculated envelope is 40 N lateral force plus 0.6 N m drill torque, 150 N pullup, 350 N downward thrust, 2.8-3.2 N m M6 toe-clamp torque, friction at least 0.12, and fixture temperature 10-35 C. The 0.20 mm radial allowance applies to the stated unworn locating inputs. Caps use 0.22-0.28 N m seating torque and 5 mm thread engagement. Every selected-load acceptance check passes; the original bare fit and worn/loose cases are retained as rejected alternatives.

design_pullup_N	cap_bending_MPa	cap_allowable_MPa	screw_load_N	preload_max_N	screw_proof_capacity_N	thread_shear_capacity_N	flange_bearing_MPa	flange_allowable_MPa
300	110.52631578947368	166.66666666666666	150.0	518.5185185185185	2917.4	981.7477042468104	3.9788735772973833	60

Decision

The locating stack fits the 0.20 mm radial allowance in its unworn condition. The assumed 2.8-3.2 N m clamp torque range meets the stated side-load, pullup and elastic toe screens. Worn guides and loose/oily clamps are rejected. The bare press-fit alternative failed the axial-retention screen. The supplied CAD now includes flanged bushes and two-screw caps, with a checked retention load path independent of the interference fit.

Declared load and material envelope

parameter	value
seed	42017
operators	3
cycles_per_operator	10
screw_diameter_mm	6
torque_Nm	[2.8, 3.0, 3.2]
nut_factor	[0.18, 0.25]
heel_y_mm	54
screw_y_mm	50
toe_y_mm	39
toe_width_mm	20
toe_thickness_mm	4
clamp_yield_MPa	250
minimum_clamp_friction	0.12
normal_drill_torque_Nm	0.6
normal_lateral_force_N	40
maximum_pullup_N	150
maximum_downthrust_N	350
friction_lever_arm_mm	50
design_factor	2
stress_factor	1.5
worn_bushing_additional_radial_mm	0.025
steel_E_MPa	200000
steel_poisson	0.3
aluminum_E_MPa	69000
aluminum_poisson	0.33
steel_expansion_per_K	1.2e-05
aluminum_expansion_per_K	2.3e-05
bushing_engagement_mm	8
equivalent_host_outer_radius_mm	10
bushing_interface_friction	0.1
bushing_interference_mm	[0.002, 0.018]
temperature_C	[10, 20, 35, 60]
retainer	{'span_mm': 21, 'width_mm': 14, 'thickness_mm': 3, 'flange_diameter_mm': 14, 'stem_diameter_mm': 10, 'screw_tensile_area_mm2': 5.03, 'screw_proof_MPa': 580, 'thread_pitch_diameter_mm': 2.5, 'thread_engagement_mm': 5, 'aluminum_thread_shear_allowable_MPa': 50, 'flange_bearing_allowable_MPa': 60, 'seating_torque_Nm': [0.22, 0.28], 'nut_factor': [0.18, 0.25], 'drill_clearance_diameter_mm': 4.5}

Clamp and support calculation

Screw preload F = T/(K d). Toe force follows lever equilibrium about the heel: Ftoe = F (54-50)/(54-39). Both toe forces resist upward pull; conservative lateral demand is side force plus drilling torque divided by a 50 mm friction arm. Toe stress is M/Z with Z = b h squared / 6. The three pad reactions solve force and two moment equations for every drilled point.

torque_Nm	nut_factor	preload_N	toe_force_each_N	clamp_bending_MPa	friction_capacity_N	normal_force_margin	pullup_margin
2.8	0.18	2592.5925925925926	691.3580246913581	142.59259259259258	165.92592592592592	1.5954415954415955	4.609053497942387
2.8	0.25	1866.6666666666667	497.77777777777777	102.66666666666666	119.46666666666665	1.1487179487179486	3.3185185185185184
3.0	0.18	2777.7777777777774	740.7407407407406	152.77777777777774	177.77777777777774	1.709401709401709	4.938271604938271
3.0	0.25	2000.0	533.3333333333334	110.0	128.0	1.2307692307692308	3.555555555555556
3.2	0.18	2962.9629629629626	790.1234567901233	162.96296296296293	189.6296296296296	1.823361823361823	5.2674897119341555
3.2	0.25	2133.3333333333335	568.8888888888889	117.33333333333334	136.53333333333333	1.3128205128205128	3.7925925925925927

variant	hole	x_mm	y_mm	pad_1_N	pad_2_N	pad_3_N	minimum_reaction_N	maximum_pad_pressure_MPa	force_residual_N
A	1	-25	-20	503.36363636363643	308.919191919192	533.2727272727274	308.919191919192	4.715166142308375	1.1368683772161603e-13
A	2	25	-20	308.9191919191919	503.3636363636364	533.2727272727273	308.9191919191919	4.715166142308374	1.1368683772161603e-13
A	3	0	20	278.8686868686869	278.8686868686869	787.8181818181819	278.8686868686869	6.965842105224066	1.1368683772161603e-13
B	1	-28	-18	508.6666666666666	290.8888888888888	545.9999999999999	290.8888888888888	4.827699940454158	3.410605131648481e-13
B	2	28	-18	290.8888888888889	508.6666666666667	546.0	290.8888888888889	4.827699940454159	1.1368683772161603e-13
B	3	0	24	266.14141414141415	266.14141414141415	813.2727272727273	266.14141414141415	7.1909097015156345	1.1368683772161603e-13
C	1	-30	-22	529.1717171717172	295.83838383838383	520.5454545454545	295.83838383838383	4.678905251794733	1.1368683772161603e-13
C	2	30	-22	295.8383838383839	529.1717171717172	520.5454545454545	295.8383838383839	4.678905251794733	1.1368683772161603e-13
C	3	0	22	272.50505050505046	272.50505050505046	800.5454545454545	272.50505050505046	7.07837590336985	1.1368683772161603e-13

Synthetic multi-operator trial

Seed 42017 generates fixed locator/bushing errors per variant and bounded reseating, angular, guide-clearance and drill-walk errors. Radial terms are uniformly sampled in disks; rotation is uniform within its bound. These are assumed input distributions. Fixed errors remain fixed over the trial. The deterministic worst-case stack governs acceptance.

Synthetic radial errors for three plate variants

variant	normal_worst_radial_mm	worn_worst_radial_mm	target_mm	remaining_wear_radial_mm	normal_accepted	worn_accepted
A	0.18275597394173826	0.20775597394173825	0.2	0.017244026058261752	True	False
B	0.1846528925339747	0.2096528925339747	0.2	0.0153471074660253	True	False
C	0.187117793065494	0.212117793065494	0.2	0.012882206934506008	True	False

Bushing retention and thermal fit

Effective diametral interference equals cold interference minus D (alpha aluminum minus alpha steel) (T-20). Elastic thick-cylinder radial compliances of the insert annulus and hollow steel bush are added. Pressure is nonnegative; axial friction resistance is mu p pi D L. No shoulder or adhesive is assumed. The worst minimum fit loses contact at 60 C; at 20 C it also fails the factor-two pullup requirement.

temperature_C	initial_interference_mm	effective_interference_mm	contact_pressure_MPa	axial_retention_N	retention_target_N	meets_retention_target
10	0.002	0.0031	8.964974989356612	225.31439652943178	300	False
20	0.002	0.002	5.783854831842976	145.36412679318178	300	False
35	0.002	0.00035000000000000027	1.0121745955725214	25.43872218880683	300	False
60	0.002	-0.0023999999999999994	0.0	0.0	300	False
10	0.018	0.0191	55.23581364410041	1388.227410874886	300	True
20	0.018	0.018	52.05469348658678	1308.2771411386357	300	True
35	0.018	0.01635	47.28301325031632	1188.351736534261	300	True
60	0.018	0.0136	39.330212856532235	988.4760621936362	300	True

Files

CSV files include every synthetic hole observation, clamp corner case, pad reaction, wear budget and press-fit condition. Expected rejected cases remain in the acceptance matrix so a passing script cannot hide an unsuitable design condition.

Executed acceptance matrix

id	description	expected	observed	passed
clamp-normal	Declared normal drilling side load with factor 2	minimum capacity/demand >= 1	1.14872	True
clamp-stress	4 mm steel toe bending with factor 1.5	<= 166.6667 MPa	162.96296	True
clamp-pullup	Both clamps resist declared pullup with factor 2	margin >= 1	3.3185	True
pad-contact	Three supports remain compressed at every drilling point	all pad reactions > 0 N	266.1414	True
pad-equilibrium	Reaction forces balance toe load and thrust	residual < 1e-9 N	3.410605131648481e-13	True
reseating-count	Three operators, ten reseats, three variants, three holes	270 recorded hole locations	270	True
reseating-envelope	Synthetic hole errors stay within the conservative envelope	max <= 0.20 mm	0.11210907822177502	True
wear-rejection	An extra 0.025 mm radial bushing clearance exceeds allowance	reject every variant	[False, False, False]	True
hot-fit-rejection	Minimum press fit is lost at 60 C	effective interference < 0; zero retention	-0.0023999999999999994	True
retention-screen	Bare minimum-interference press fit does not satisfy pullup factor 2	reject minimum-fit retention at 20 C	145.364	True
loose-clamp-rejection	Loose oily clamps cannot meet side-force criterion	margin < 1	0.11965811965811966	True
retainer-cap	Selected retention cap carries factor-two pullup	bending <= yield/1.5	110.52631578947368	True
retainer-fasteners	Two M3 screws and tapped insert carry pullup plus maximum seating preload	load+preload below screw proof and thread screen	{'combined_N': 668.5185185185185, 'proof_N': 2917.4, 'thread_N': 981.7477042468104}	True
retainer-flange	Flange bearing is adequate under factor-two pullup/downward screen	pressure <= 60 MPa	3.9788735772973833	True

Model boundaries

The loads, friction coefficients, nut factors, elastic properties and process errors are declared scenarios. No measured drill forces, torque calibration or process capability is implied.
Clamp screening treats the toe as a rectangular elastic beam. Local fillets, screw-hole stress, threads, plate bending and impact require a more detailed model before hardware release.
The press-fit host is approximated as a concentric annulus of 10 mm outer radius. Nearby insert edges and holes make the real stiffness non-axisymmetric. This is a retention screening calculation, not a certified press-fit load.
The original bare press-fit alternative fails the retention screen and is rejected. The supplied revised CAD uses flanged bushes and two-screw retention caps; numerical retention checks do not establish physical assembly durability.
Synthetic operators share a bounded error model. The sample does not establish Cpk, operator performance or a real repeatability distribution.

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.