Test fixture crosshead

Executed 2D plane-stress finite element study of three crosshead profiles at 500 N, with mesh refinement, eccentric loading, and support-stiffness sensitivity.

Completed commissioning study

12 mm flange profile; vertical support stiffness>=30 MN/m and rotational stiffness>=500 N m/rad per support. Load<=550 N, E>=66 GPa, thickness>=19.9 mm, load at x 120 or 150 mm, off-plane offset<=2 mm. Combined worst-case movement plus response-fit allowance<0.05 mm.

Executed synthetic/theoretical results, rejected cases and acceptance matrix. Source: complete_validation.py.

Model

240 x 40 mm planar domain, constant 20 mm thickness; E = 69 GPa, Poisson ratio 0.33, density 2700 kg/m3.
Quadratic triangular displacement elements. Plane-stress Lamé lambda = E nu/(1-nu^2), mu = E/[2(1+nu)].
Top patch force is integrated as a traction. Two distributed spring supports provide vertical restraint; one horizontal DOF removes rigid translation.
The reported displacement is the force-weighted patch displacement, f^T u / F. All reaction sums include the full spring support.

Comparison

Profile	Load x (mm)	Support (MN/m)	Displacement (mm)	Target met
solid	120	5.0	0.06259	False
solid	120	20.0	0.02507	True
solid	120	100.0	0.015	True
solid	150	5.0	0.06507	False
solid	150	20.0	0.02418	True
solid	150	100.0	0.01322	True
window_8mm	120	5.0	0.12348	False
window_8mm	120	20.0	0.08596	False
window_8mm	120	100.0	0.07585	False
window_8mm	150	5.0	0.11734	False
window_8mm	150	20.0	0.07644	False
window_8mm	150	100.0	0.06544	False
window_12mm	120	5.0	0.0824	False
window_12mm	120	20.0	0.04488	True
window_12mm	120	100.0	0.0348	True
window_12mm	150	5.0	0.08201	False
window_12mm	150	20.0	0.04112	True
window_12mm	150	100.0	0.03015	True

Selected reference profile

The 8 mm flange alternative fails the 0.05 mm allowance even with the stiffest support. The 12 mm flange alternative is retained for the nominal 20 MN/m support case.
Windowed 12 mm flange profile reduces mass by 20.0% relative to the solid model.
At 20 MN/m supports and centered load its displacement is 0.04488 mm; mass is 0.41472 kg.
At the weak 5 MN/m support case, displacement reaches 0.08240 mm. The geometry alone does not satisfy the requirement for that mount.

Verification

mesh_size_m	FEA_tip_displacement_mm	Euler_Bernoulli_mm	Timoshenko_reference_mm	relative_difference
0.005	1.4568358233280443	1.4492753623188406	1.4608405797101451	0.002741405487856441
0.0025	1.4574766450284935	1.4492753623188406	1.4608405797101451	0.002302739072540629
0.00125	1.4576998731171806	1.4492753623188406	1.4608405797101451	0.002149931098975664

43 automated convergence, equilibrium, analytical-reference, and CAD/mesh checks passed.
Finest mesh spacing is 1.25 mm. Every profile changes less than 2% between the last two mesh levels.
The cantilever reference includes the Euler-Bernoulli bending term plus a Timoshenko shear correction; it is a model verification case, not a physical test.

Physical validation plan

Mount the crosshead on the intended supports; independently measure each support stiffness.
Load through the same 20 mm contact patch at 120 and 150 mm from the left edge.
Measure displacement at the loading patch and at both supports with calibrated displacement indicators.
Apply at least five loads up to the agreed working load, unload, and inspect for residual movement.
Compare compliance and uncertainty before assigning a fixture correction or load rating.

Limits

This is quadratic-triangle 2D plane-stress FEA, not a 3D contact or bolt-joint analysis. Thickness is constant at 20 mm.
The load is distributed across a 20 mm top-edge patch; supports are 10 mm bottom-edge patches with declared vertical stiffness.
Ideal window corners are sharp. Stress is sampled at least 4 mm from corners and loaded/support edges; those reported values do not certify notch strength.
The 5 MN/m supports fail the proposed displacement allowance. Physical support stiffness must be measured before accepting the fixture.
Wire EDM with a small internal radius is the proposed manufacturing route. Radius, surface finish, mounting details, and physical load testing remain unqualified.
The 500 N load and 0.05 mm allowance are reference requirements, not a load rating.

References

scikit-fem API and official elasticity example. The analytical reference equations are implemented explicitly in solver.py.

FEA vertical displacement for the three profiles

Support compliance governs the weak-support cases

Reference design by CJ Ackley. Numerical and geometry checks are not a physical qualification.