WOBBLcast_motor_mount.step

How far can simulation stand in for testing this cast motor mount under a 2 kN belt pull?

Strength report
2026-10-14 01:24

MARGINAL

Peak 124 MPa on the 3.99 mm inside fillet (face 65) at (43.9, 8.96, 79.6). It survives the load, but the safety factor 1.33 is below the 2 target. Confidence is medium.

peak stress

124 MPa

safety factor

1.33

max deflection

0.265 mm

target

Confidence medium

load introduction: the off part loads enter through a distributing coupling (the attached part adds no stiffness). With a rigid attachment (the attached part does not flex) instead, the governing stress converges to 55 MPa on face 2 at (-34, 0, 29.5) (0.44x, safety factor 3.00) over 3 meshes refined around that peak: 54.2 -> 54.3 -> 55 MPa, last change 1.1%. The verdict depends on this assumption: check how the attached part really carries the load
the verdict depends on how the load enters the part (rigid attachment versus distributed); the answer assumes distributed

Simulation

Checks

status	check	result
pass	mesh convergence	von Mises stress settled: 122 -> 124 -> 124 MPa over 3 meshes, last change 0.1%
pass	force balance	reactions balance the loads to 1e-05% (forces) and 1.2e-06% (moments)
skip	hand calculation	no simple beam model applies (the governing point is not between the fixtures and the load, so no single section carries it)
pass	singularities	no sharp corner or support artifact is above the reported stress
pass	units and sanity	part 203 mm across, peak strain 0.0017, max deflection 0.265 mm (0.13% of size): all plausible
warn	load introduction	the off part loads enter through a distributing coupling (the attached part adds no stiffness). With a rigid attachment (the attached part does not flex) instead, the governing stress converges to 55 MPa on face 2 at (-34, 0, 29.5) (0.44x, safety factor 3.00) over 3 meshes refined around that peak: 54.2 -> 54.3 -> 55 MPa, last change 1.1%. The verdict depends on this assumption: check how the attached part really carries the load

How to fix it

Thicken the wall at the peak from 6 to 7.35 mm

The wall through the peak is 6 mm. To reach safety factor 2 it needs 7.35 mm (+22%), because bending stress falls with thickness squared.

Add a triangular gusset across the inside corner

The peak sits where two walls meet and bend. A gusset as thick as the wall, with legs about half as long as the shorter wall, ties them together and usually cuts the corner stress by half or more.

Switch to Aluminum 6061-T6

Stress stays about the same for the same shape and load, so Aluminum 6061-T6 (276 MPa) gives safety factor 2.23. It is 0.95x as stiff, so deflection scales by 1.05. Other options: Mild steel (ASTM A36) (2.02), Aluminum 7075-T6 (4.07).

Mesh convergence

level	nodes	global size mm	finest mm	governing MPa	change	max deflection mm	solve
0	88,155	5.97	1.16	122		0.263	97.1 s
1	99,657	5.07	0.628	124	+1.1%	0.264	153.3 s
2	111,956	4.31	0.302	124	+0.1%	0.265	136.2 s

Stress peaks

Every peak Wobbl found, with its value at each mesh. Peaks at sharp corners and idealized supports are excluded from the answer because their value depends on the idealization, not the part.

#	where	x, y, z (mm)	MPa by level	status
1	on the 3.99 mm inside fillet (face 65)	43.8, 8.76, 79.9	122 → 124 → 124	counted
2	on the 3.64 mm inside fillet (face 63)	45.8, 6.54, 82.9	114 → 121 → 123	counted
3	where load1 is pushed into the holes (face 2)	30.6, 0, 94.7	95.3 → 95.4 → 97.1	excluded
4	where load1 is pushed into the holes (the 6.6 mm hole (face 37))	31.4, 0, 101	92 → 93.3 → 91.9	excluded
5	where load1 is pushed into the holes (the 6.6 mm hole (face 37))	33, 6, 101	89.7 → 88.9 → 89.8	excluded

Uncertainty

The chance of failing against the yield strength is about 1 in 77 (1.3%, 95% interval 1.25% to 1.35%). The safety factor averages 1.35 with a standard deviation of 0.173, and 90% of samples fall between 1.08 and 1.65. By total Sobol index the spread comes from load (0.61) and yield (0.39). With loads entering through a rigid attachment instead of a distributed attachment, the chance of failing is below 1 in 54,000 (no failures in 200,000 samples, 95% upper bound 1.8e-05), so that choice bounds the answer too.

Inputs

input	what it is	kind	distribution
load	the 2000 N load	load	lognormal, mean 2000 N, sd 200 N, 10%
yield	yield strength	strength	normal, mean 165 MPa, sd 13.2 MPa, 8%
E	Young's modulus	stiffness	normal, mean 72400 MPa, sd 2172 MPa, 3%
mesh	discretization error, the last change over the mesh levels	numerical	normal, mean 1, sd 9.94e-04, 0.0994%

Answer

output	mean	standard deviation	90% of samples	98% of samples
safety factor	1.35	0.173	1.08 to 1.65	0.987 to 1.79
governing MPa	124 MPa	12.4 MPa	104 to 145 MPa	97.6 to 155 MPa
max deflection mm	0.265 mm	0.0277 mm	0.222 to 0.313 mm	0.207 to 0.336 mm

Probability

event	against	probability	reliability index
failure	the yield strength	about 1 in 77 (1.3%, 95% interval 1.25% to 1.35%)	2.23
below target	the target safety factor 2	99.9% (95% interval 99.9% to 99.9%)	-3.20
failure with loads entering through a rigid attachment		below 1 in 54,000 (no failures in 200,000 samples, 95% upper bound 1.8e-05)

What matters most

input	first order	95% interval	total	95% interval
load	0.608	0.437 to 0.781	0.611	0.593 to 0.627
yield	0.388	0.221 to 0.539	0.393	0.379 to 0.405
mesh	0.000	-0.002 to 0.001	0.000	0.000 to 0.000
E	0.000	0.000 to 0.000	0.000	0.000 to 0.000

200,000 Latin hypercube samples. The model is exact scaling of the converged solution, where stress follows the load and not the modulus and deflection follows the load over the modulus. Sobol indices use 8,192 base points of a scrambled Sobol sequence, with bootstrap intervals.

Comparison with tests

These readings are synthetic, made for a demonstration, and are not from a real test.

16 readings from readings.csv, which are synthetic and do not come from a real test. 16 of 16 agree with the simulation within twice their validation uncertainty, and the comparison error averages -2.3% of the reading. The pooled area metric is 0.121, within the 0.145 a model with the right spread would stay under 95% of the time. The readings favour a distributed attachment over a rigid attachment by a likelihood ratio of more than 1,000, with the modulus fitted to each. Calibration puts E at 70938 MPa (95% interval 70055 to 71834 MPa, 4.8x narrower than before the test).

Each reading against the simulation, with bars at twice the validation uncertainty. Points on the line agree.

ASME V&V 20 comparison

gauge	quantity	load	reading	simulation	E = S - D	u_val	\|E\| / u_val
SG1	strain	500	375 µε ± 7.6 µε	371 µε	-3.4 µε	14 µε	0.24	pass
SG1	strain	1000	765 µε ± 15.2 µε	743 µε	-22.6 µε	28.1 µε	0.81	pass
SG1	strain	1500	1099 µε ± 22.9 µε	1114 µε	14.9 µε	42.1 µε	0.35	pass
SG1	strain	2000	1566 µε ± 30.5 µε	1486 µε	-80.4 µε	56.2 µε	1.43	pass
SG2	strain	500	213 µε ± 5 µε	205 µε	-8.4 µε	8.19 µε	1.02	pass
SG2	strain	1000	417 µε ± 8.4 µε	409 µε	-7.99 µε	15.5 µε	0.52	pass
SG2	strain	1500	625 µε ± 12.6 µε	614 µε	-11.7 µε	23.2 µε	0.50	pass
SG2	strain	2000	844 µε ± 16.8 µε	818 µε	-26 µε	30.9 µε	0.84	pass
SG3	strain	500	-71 µε ± 5 µε	-67.9 µε	3.1 µε	5.44 µε	0.57	pass
SG3	strain	1000	-140 µε ± 5 µε	-136 µε	4.6 µε	6.6 µε	0.70	pass
SG3	strain	1500	-205 µε ± 5 µε	-204 µε	1.6 µε	8.17 µε	0.20	pass
SG3	strain	2000	-276 µε ± 5.6 µε	-272 µε	4.09 µε	10.3 µε	0.40	pass
D1	displacement	500	0.0676 mm ± 0.005 mm	0.0662 mm	-0.00138 mm	0.00542 mm	0.25	pass
D1	displacement	1000	0.135 mm ± 0.005 mm	0.132 mm	-0.00297 mm	0.00653 mm	0.45	pass
D1	displacement	1500	0.204 mm ± 0.005 mm	0.199 mm	-0.00585 mm	0.00805 mm	0.73	pass
D1	displacement	2000	0.269 mm ± 0.005 mm	0.265 mm	-0.00373 mm	0.00978 mm	0.38	pass

Area metric

gauge	load	readings	area	of the reading
SG1	500	1	9.79 µε	2.6%
SG1	1000	1	26.8 µε	3.5%
SG1	1500	1	30.7 µε	2.8%
SG1	2000	1	81.3 µε	5.2%
SG2	500	1	8.94 µε	4.2%
SG2	1000	1	12.2 µε	2.9%
SG2	1500	1	18.2 µε	2.9%
SG2	2000	1	30.2 µε	3.6%
SG3	500	1	3.22 µε	4.5%
SG3	1000	1	5.21 µε	3.7%
SG3	1500	1	5.31 µε	2.6%
SG3	2000	1	7.63 µε	2.8%
D1	500	1	0.00202 mm	3%
D1	1000	1	0.00415 mm	3.1%
D1	1500	1	0.00703 mm	3.4%
D1	2000	1	0.00735 mm	2.7%

Pooled over all readings the area is 0.121 against 0.145 for a model whose spread is right, at 95%.

Which idealization the readings favour

load attachment	modulus fitted to the readings	rms residual in reading uncertainties	rms error
a distributed attachment (assumed)	70862 MPa	0.63	1.6%
a rigid attachment	16900 MPa	21.84	51%

The readings favour a distributed attachment, log10 likelihood ratio 1656.0.

Calibration

input	before the test	after	95% interval	narrower by
E	72400 ± 2172 MPa	70938 ± 451 MPa	70055 to 71834 MPa	4.8x

Residuals fall from 1.04 to 0.63 reading uncertainties (root mean square). Adaptive Metropolis, 20,000 steps, acceptance 44%, about 3,980 independent draws.

Credibility

Model risk 4 of 5 (high influence, medium consequence), so Wobbl proposes a high goal for each factor. The evidence meets it on 4 of 9 factors. Short on model form, comparator, output comparison, applicability, uncertainty in the answer.

Context of use. A linear elastic static model of cast_motor_mount.step in Custom material (cast), under 2000 N -0.8660254,0,-0.5 at 0,-30,66 @ holes d=6.6, held by fixed z=min, used to judge the von Mises stress against 165 MPa with a target safety factor of 2.

question	model influence	decision consequence	model risk	proposed goal
How far can simulation stand in for testing this cast motor mount under a 2 kN belt pull?	high	medium	4 of 5	high

Factors

group	factor	level	goal		evidence
verification	code verification	high	high	pass	14 of 14 strength cases with known answers pass their tolerance, run through the same pipeline, the largest error 4.3% (PLA shelf bracket, 6 mm fillet)
verification	solution verification	high	high	pass	The mesh convergence check passes, von Mises stress settled: 122 -> 124 -> 124 MPa over 3 meshes, last change 0.1%. The force balance check passes, reactions balance the loads to 1e-05% (forces) and 1.2e-06% (moments)
verification	inputs as intended	high	high	pass	every load, support and material was stated explicitly
validation	model form	low	high	warn	The load introduction check reports the off part loads enter through a distributing coupling (the attached part adds no stiffness). The readings favour a distributed attachment over the other idealization by a likelihood ratio of more than 1,000, but the readings are synthetic, so this shows how a real test would settle it. To close it, measure where the idealizations differ most, so a test decides between them.
validation	model inputs	high	high	pass	4 inputs propagated with 200,000 samples by exact scaling of the converged solution, where stress follows the load and not the modulus and deflection follows the load over the modulus. Of these, load drives most of the spread, total Sobol index 0.61
validation	comparator	low	high	warn	16 readings from readings.csv, synthetic and not from a real test, 16 with a stated uncertainty. To close it, test real parts with calibrated gauges (see the test plan).
validation	output comparison	low	high	warn	16 of 16 readings within twice the validation uncertainty (ASME V&V 20), pooled area metric 0.121 against 0.145, but the readings are synthetic. To close it, compare with real readings, and agreement within the validation uncertainty sets this high.
applicability	applicability	low	high	warn	4 readings within 5 mm of the governing point, test loads reach 100% of the design load, the readings are synthetic. To close it, put a gauge at the governing point and test up to the design load.
applicability	uncertainty in the answer	low	high	warn	probability of failure about 1 in 77 (1.3%, 95% interval 1.25% to 1.35%), and up to 0.013 across the idealizations Wobbl solved. To close it, the failure probability or the margin leaves too little room, so narrow the dominant input.

Wobbl supplies credibility evidence and proposes levels. It does not certify the model, and the reviewer decides whether the evidence is enough for the decision.

Test plan

4 tests would most reduce the risk, in this order, a validation test, a gauge where the idealizations differ, a service load measurement and material coupons.

1. validation

A static load test with strain gauges and a dial gauge, loaded in steps of 500 N, 1000 N, 1500 N and 2000 N.

It supplies the comparison with tests that V&V 20 needs, at the point the decision rests on and up to the design load.

gauge	x, y, z mm	axis	load	predicted, 95% band
peak	43.8, 8.91, 79.4	-0.18, -0.63, +0.76	500	371 ± 22.3 µε
peak	43.8, 8.91, 79.4	-0.18, -0.63, +0.76	1000	743 ± 44.6 µε
peak	43.8, 8.91, 79.4	-0.18, -0.63, +0.76	1500	1114 ± 66.9 µε
peak	43.8, 8.91, 79.4	-0.18, -0.63, +0.76	2000	1486 ± 89.1 µε
far field	12.2, 0, 101	-0.95, +0.00, +0.31	500	205 ± 12.3 µε
far field	12.2, 0, 101	-0.95, +0.00, +0.31	1000	409 ± 24.5 µε
far field	12.2, 0, 101	-0.95, +0.00, +0.31	1500	614 ± 36.8 µε
far field	12.2, 0, 101	-0.95, +0.00, +0.31	2000	818 ± 49.1 µε
deflection	24.2, 0, 112	-0.19, -0.97, -0.14	500	0.0662 ± 0.00397 mm
deflection	24.2, 0, 112	-0.19, -0.97, -0.14	1000	0.132 ± 0.00795 mm
deflection	24.2, 0, 112	-0.19, -0.97, -0.14	1500	0.199 ± 0.0119 mm
deflection	24.2, 0, 112	-0.19, -0.97, -0.14	2000	0.265 ± 0.0159 mm

the stress changes 26% under a 3 mm grid here, so use a 1 mm grid or read the gauge as an average over its length

2. model form

A strain gauge at (-34, 0, 29.5), where the rigid attachment puts its peak.

With a rigid attachment the peak sits here at 55 MPa, and with the distributed one Wobbl predicts 18.1 MPa at the same spot. A reading here tells which idealization the real assembly is closer to, a choice that moves the answer more than any input scatter.

3. service load

Measure the 2000 N load in service, with a load cell or a strain gauged link.

Knowing the load exactly removes about 61% of the variance of the safety factor, taking its standard deviation from 0.173 to about 0.108.

4. material coupons

Tensile test coupons from the same lot, casting or print settings, measuring the yield strength (yield).

Knowing the yield exactly removes about 39% of the variance of the safety factor, taking its standard deviation from 0.173 to about 0.135.

At least 10 coupons, since the uncertainty in the lot mean falls with the square root of their number, to a third of the scatter at 9.

Which tests the simulation can stand in for

test		verdict	why
a static proof test at the design load	warn	not yet	the readings are synthetic, the failure probability is not small enough to stand on the model alone, credibility factors are short of their goals
strain surveys of later design variants	warn	not yet	no validated survey exists to carry over
a test to failure	fail	cannot	Wobbl's strength model is linear elastic and stops at the first yield, so it says nothing about how the part fails after that
material coupons	fail	cannot	they measure the inputs the model rests on
fatigue, impact and vibration tests	fail	cannot	this run is a static strength study and does not model them

The plan keeps the validation test whenever a validation factor is short of its goal, the discriminating gauge whenever the model form is, and input measurements by first order Sobol index until they cover 80% of the variance measuring could remove.

Setup


material	Custom material (cast)
limit	165 MPa
target safety factor	2
mass	359 g
load	2000 N -0.8660254,0,-0.5 at 0,-30,66 @ holes d=6.6
fixture	fixed z=min
part	5 holes, 35 inside fillets, 0 sharp inside corners, walls about 6 mm

Assumptions

Linear elastic material and small deflections (no yielding redistribution, no buckling).
Custom material (cast): E 72400 MPa, Poisson 0.33, von Mises vs yield 165 MPa (user supplied; the rest from Aluminum A356-T6 (sand cast)).
Loads are static and applied all at once; no impact, vibration or fatigue.
Cast part treated as sound and uniform; porosity or shrinkage in thick sections can lower the real strength, which is why castings carry larger safety factors.
Fixed faces are perfectly rigid; real mounts flex a little, which lowers peak stress next to them.
Remote loads and moments are spread over their faces without stiffening them.
Contact between separate parts, friction and preload are not modeled.

Notes

Thin walls need a large first mesh (88,155 nodes), so this study takes longer than usual.
3 curved elements folded on thin walls, so this mesh uses straight sided second order elements.
1 curved elements folded on thin walls, so this mesh uses straight sided second order elements.