Bolted Pressure Vessel Design and Machining

SOLIDWORKS rendering of a cylindrical aluminum pressure vessel with a central bolted flange and a threaded port in one end — The vessel assembly in SOLIDWORKS. One half has a threaded opening for the supplied brass fitting, and the other has a closed end.

Design record

Type	Record
Requirement	50 to 60 cm³ at 750 psig (5.17 MPa gauge), at least one O-ring seal, a threaded joint, a ¼ in NPT port and a $100 budget
Design dimensions	Ø25 mm bore, Ø35 mm tube, Ø63 × 5 mm flange, six Ø4 mm holes
Calculation	18.3 MPa von Mises at the bore, 2,450 N preload target, about 2 N·m of torque
Pressure test	Run by lab staff against the 750 psig requirement. Passed with no failures.

SOLIDWORKS drawing of one vessel half: an end view with a 35 millimeter tube, a 63 millimeter flange and a threaded port; a flange-face view with a 25 millimeter bore, the gland rings and six 4 millimeter holes; a side view with a 97.8 millimeter tube and 5 millimeter flange; and an isometric view — One vessel half from the preliminary proposal, in millimeters. The design review below revisits its length and gland width.

Wall sizing

We chose 6061 aluminum for its cost, machinability and strength, with a 25 mm inner diameter. A first estimate called for about 2.65 mm of wall, and we increased that to 5 mm, which makes the part easier to machine and gives a 35 mm outer diameter. A thick-cylinder check of the 5 mm wall at 750 psig gives 18.3 MPa von Mises at the bore, against a 55 MPa design yield strength.

Where the 2.65 mm estimate came from

The proposal set a thin-wall hoop stress expression equal to S_y/n, with S_y = 55 MPa and n = 2:

t = P_i n d_i / (2 S_y − n P_i)

With the proposal's absolute pressure of 5.27 MPa, this gives 2.65 mm, and with 5.17 MPa gauge it gives 2.59 mm. That is t/r_i ≈ 0.21, outside the usual thin-wall range of about 0.1, so it is only a first estimate. It also checks hoop stress alone. At the same target, a Lamé calculation of hoop stress needs about 2.62 mm and a maximum-shear calculation needs about 3.33 mm, and the selected 5 mm wall clears both.

Thick-cylinder check of the 5 mm wall

At t/r_i = 0.4, the selected wall needs a thick-cylinder treatment. These are Lamé stresses at the bore, where they are highest, for r_i = 12.5 mm, r_o = 17.5 mm and 5.17 MPa of internal gauge pressure:

σ_θ = p (r_o² + r_i²) / (r_o² − r_i²), σ_r = −p, σ_l = p r_i² / (r_o² − r_i²)

Analytical prediction	Stress at bore	Margin against 55 MPa
Hoop, σ_θ	15.9 MPa
Radial, σ_r	−5.2 MPa
Longitudinal, closed ends, σ_l	5.4 MPa
Von Mises equivalent	18.3 MPa	3.01
Maximum shear (σ_θ − σ_r)	21.1 MPa	2.60

Both margins clear the design target of 2. They cover the straight cylinder wall, away from the flange, end cap and threaded port. The 55 MPa yield strength is typical of annealed 6061-O and well below the roughly 276 MPa of 6061-T6, so it is a conservative value.

Face seal

The 38 mm O-ring outer diameter is larger than the 35 mm tube, so the O-ring sits in a gland cut into the flange face. When the bolts close the two faces, the 4 mm cross-section is squeezed into a 3 mm deep gland, which is 25% compression. The gland is sized so the uncompressed O-ring fills about 70% of its cross-section, leaving room for the rubber to deform.

Gland cross-section, to scale, from the calculated dimensions: 4 mm O-ring, 3 mm depth, 5.99 mm width, 30.9 mm gland inner diameter. This is a schematic of the calculation, not a section of the CAD model.

Choosing the seal material and gland

We compared silicone, fluoroelastomer, thermoplastic polyurethane and nitrile, and chose nitrile (Buna-N) for its abrasion resistance, strength, temperature range and resistance to gas permeation. The proposal selects a 30 mm inner diameter O-ring with a 4 mm cross section.

The gland follows from three targets: a gland about 3% larger than the O-ring's inner diameter, 25% compression, and about 70% fill. That gives a 30.9 mm gland inner diameter, 3 mm depth and 5.99 mm width.

Bolted joint

Pressure inside the vessel pushes the two halves apart. The bolts are tightened first, so the flange faces are already clamped together before that load arrives. Each bolt and the flange it clamps then share the separating load in proportion to their stiffness: the bolt takes the fraction C, and the rest goes to relieving the clamp.

F_bolt = F_i + C P, F_clamp = F_i − (1 − C) P, C = k_b / (k_b + k_m)

So a stiffer flange means less added bolt load, and more preload means more clamp to lose before the joint opens. The design uses six M4 × 0.7 bolts, 16 mm long, in property class 4.8. Preloading to 90% of proof load gives about 2,450 N per bolt and about 2 N·m of torque, using A_t = 8.78 mm², S_p = 310 MPa and k = 0.2.

Design review

I rechecked the preliminary proposal against the assignment and its own inputs. Its arithmetic holds, and these inputs changed:

Input	Preliminary proposal	Reviewed value
Pressure	5.27 MPa absolute for sizing, 5.17 MPa gauge for the joint	5.17 MPa gauge (750 psig) throughout
Length for 60 cm³	195.6 mm	122 mm, from L/D = 4.89 × the 25 mm bore
Bolt circle	Ø42 mm in the text	Ø49 mm, as drawn, which leaves 5 mm of edge distance on the 14 mm flange
Gland width	5.99 mm calculated, 2.99 mm on the drawing	5.99 mm, since 2.99 mm is narrower than the 4 mm O-ring
Member modulus	207 GPa, a steel value	69 GPa for aluminum flanges, which raises C from 0.144 to 0.335
Pressure area	The Ø25 mm bore	Out to the O-ring, since pressure reaches the seal

This table shows how much those inputs matter to each bolt, at 5.17 MPa with the 2,450 N preload target and a 2,722 N proof load:

Assumption	Load per bolt, P	C	Bolt load	Clamp left
Proposal: bore area, 207 GPa	423 N	0.144	2,510 N	2,087 N
Bore area, aluminum flanges	423 N	0.335	2,591 N	2,168 N
O-ring centerline (Ø34 mm), aluminum	782 N	0.335	2,712 N	1,929 N
Calculated gland OD (Ø42.9 mm), aluminum	1,244 N	0.335	2,866 N	1,622 N

The clamp stays positive in every case, so the faces stay together. The most conservative case passes the bolt's proof load, because a 90% preload leaves little room above it. On a next iteration, I would lower the preload or use a stronger bolt class.

Machining and test

After the design work, we machined the vessel in the student machine shop. Lab staff then pressure-tested it against the 750 psig requirement, and it passed with no failures.

Team

This was a team of three.