1000 L Agitated Tahini Mixing Tank

Take a 1000 L batch vessel for a highly viscous, shear-thinning food paste from a functional requirements table through concept selection, detail design and independent finite element verification, sized and checked against process, structural, hygienic and safety requirements rather than drawn to a target volume alone.

• 1Batch working volume 1000 L ± 5%; agitator concept selected and verified for full-vessel turnover on a ≈60 Pa·s shear-thinning paste, with no stagnant zones.
• 2Product-contact construction meets EN 1672-2 / EHEDG hygienic design: Ra ≤ 0.8 µm finish, ≥ 3 mm internal corner radii, and a checked CIP spray-coverage argument.
• 3Shell, lid and drive shaft sized for internal pressure, external-pressure (vacuum) upset, bending, deflection and critical speed, with every governing check independently FEA-verified.
• 4Support frame carries the full filled weight (1763.6 kg) to the floor with a checked tip-over margin and a sized floor-anchor detail.
• 5Full GD&T datum scheme and tolerance stack-up across all five parts, closing the loop from the shell bore to the agitator's 5 mm running clearance.

Five stainless-steel parts, each independently modelled, sized and toleranced, that come together as one vessel: the lid bolts to the shell through a gasketed 36-bolt joint, the shaft carries the agitator on two bearings and a double mechanical seal, and the whole assembly rests on a four-leg support frame.

The development of this assembly follows a structured engineering design process: Problem Definition and Requirements, Conceptual Design, Embodiment Design, Material Selection, Engineering Sizing and Design Basis, Detailed Design of the four individual components (including complete dimensioning and engineering calculations), FEA Verification, Manufacturability Assessment, GD&T and Tolerance Stack-Up Analysis, and Assembly and Close-Out. The sections that follow document each stage in turn.

Before any part was sized or modelled, the vessel's shape, arrangement and material were decided and justified in writing: a functional decomposition and requirements table, a weighted concept-selection matrix stress-tested by sensitivity analysis, an embodiment freeze with six traceable decisions, an independent structural cross-check, and a two-stage material selection. Detail Design and the finite element verification that follow sized, modelled and checked what this stage decided.

17 requirements decomposed in total across five weight tiers (2 to 5); the six weight-5 "must" requirements are shown.

Three agitator concepts were generated, screened for feasibility, and scored against the weighted requirements table above using a weighted decision matrix.

A single weighted matrix is not treated as sufficient justification on its own: the weights were perturbed twice, in two different directions, to test whether Concept A's lead would survive a reasonable engineer disagreeing with the baseline weighting. Concept A wins the baseline matrix and a mixing-performance-weighted variant decisively, and only loses in a variant that requires suppressing two need-linked criteria below a defensible floor. Concept A, the anchor-and-scraper agitator, is confirmed for Detail Design.

Embodiment Design freezes the physical arrangement, the topology of how the major components are positioned and connected, that Detail Design then sizes, models and simulates. Six decisions are frozen as the baseline; reopening any of them in Detail Design requires a documented reason, not a silent redraw.

• 1Drive & shaft support: top-entry gearmotor; two-bearing shaft (upper pillow block + lower guide bearing at the product line).
• 2Shaft seal: double mechanical seal, EHEDG hygienic class, at the cover penetration.
• 3CIP / spray layout: single top-mounted spray ball; wall-coverage argument accepted, arm/blade-surface coverage carried forward as an open item.
• 4Vent / breather: 0.2 µm hygienic filter, cover-mounted, isolated from the spray path.
• 5Jacket / gearbox / motor: simplified envelope volumes, no internal detail.
• 6Support frame: four-leg welded tube frame, ring-borne, levelling feet; bracing finalised as a mid-span ring during Detail Design.

The structural configuration was selected and frozen using a weighted matrix and a qualitative arrangement freeze. This step re-examines it at a finer grain, part by part, using a two-level method: a per-part morphological screen and, where two or more variants survive, an independent Analytic Hierarchy Process (AHP) grading.

Only the bottom shape and the support-frame type had genuine multi-way competition; every combination of their surviving variants was checked for part-to-part compatibility before scoring, not a chosen subset. The cone bottom plus four-leg frame combination ranks first, ahead of the runner-up (cone plus three-leg) by roughly 15%, confirming independently the same configuration already selected in 3.2 and frozen in 3.3.

Applied independently to the three components whose governing failure mode differs: the shell (external-pressure buckling), the shaft (torsion/bending strength), and the agitator blades (bending strength, wear-exposed). Stage 1 derives an Ashby-style index directly from each component's governing physics; Stage 2 weighs the Stage-1 survivors against the project's own weighted requirements using a QFD-style scoring method.

Corrosion resistance is enforced as a non-compensatory hard screen before Stage 2 scoring: a minimum PREN ≥ 23 is required regardless of how well a candidate scores elsewhere. 304 stainless (PREN 18) does not clear this threshold and is eliminated; 316L (PREN 24) and 2205 duplex (PREN 35) both proceed to Stage 2 scoring.

Duplex's real structural advantage is small at the shell (≈3.7%, since buckling is a stiffness-governed mode where the two alloys are close) and not needed at the shaft or blades, where 316L already carries comfortable margin. 316L is selected throughout the product-wetted train; a 2205 duplex or hardfaced scraper edge is flagged as the most defensible upgrade path if wear, not strength, becomes the limiting factor in service. Engineering sizing itself, turning these decisions into governing numbers, is covered in Design-Basis Sizing (05).

Tahini behaves as a shear-thinning (pseudoplastic) paste: its apparent viscosity depends on the shear rate the agitator itself generates, a circular problem that the Metzner–Otto correlation resolves by treating the impeller as generating one characteristic shear rate proportional to its speed.

Single source of truth for the governing sizing results: the numbers Detail Design built from and Finite Element Verification (07) checked.

Every governing hand calculation was independently re-verified by finite element analysis. Three results changed the released design; the rest confirmed it, several with a wider margin than the hand calculation itself predicted.

Four studies, each modelling the real geometry, fillets, keyways and all, rather than the idealised sections the hand calculations use, and each converged and mesh-checked before its result was accepted.

01

Drive Shaft: Torsion, Bending & Critical Speed

Requirement

Survive the full motor-rated design torque (2722 N·m, a 1.76× overload factor over the process duty) at a keyed cross-section, stay within the 5 mm running clearance under the agitator's bending load, and keep the critical (whirling) speed at a large margin over the 25 rpm operating speed.

FS = τ_allow / τ(T_design)  (keyway stress concentration K_t = 1.6)

FS 1.17

governing (FEA)

619×

critical-speed margin

The hand calculation (FS 1.29) missed a real 3D effect: the FE model found the true peak stress at the open end of the drive-end keyway (FS ≈ 0.83 at the original geometry, predicting local yielding). A variable-radius fillet, holding the DIN-constrained 0.4 mm along the keyway root and tapering to a larger radius at the open corner, resolved it to FS ≈ 1.17, and was carried into the released drawing.

Fig. 5. After the fillet redesign: 145.27 MPa peak (FS≈1.17), down from ≈205 MPa at the original geometry.

02

Agitator Arm: Root Bending at the Hub Weld

Requirement

The anchor arm's root, the hand-calculated margin found anywhere in the project (FS 2.28, idealised as an untapered flat bar), needed FEA confirmation before accepting the as-designed section without a thicker or tapered root.

FS = σ_y / σ(root fillet, FEA)

FS 1.99

root fillet (FEA)

2.70×

tip-clearance margin

A symmetry model of the hub-and-arm weld, loaded with a drag pressure calibrated to the same root moment as the hand calculation, confirms the untapered 100×25 mm arm section: no redesign required. The fillet's modest stress concentration (K_t ≈ 1.15) explains the 15% gap to the hand calculation's uniform-section estimate.

Fig. 6. Von Mises stress along the arm: 85.6 MPa peak at the root, decaying to the tip.

03

Tank Shell: External-Pressure (Vacuum) Buckling

Requirement

The 4 mm shell wall is sized against a vent-limited vacuum event, not an unmitigated full vacuum. The classical hand-calculation screen had flagged the cone, not the cylinder, as the weak point, with a margin below the vacuum breaker's own set point. This called for a full eigenvalue buckling analysis of the real geometry.

[K^E + λ·K^G(σ_ref)]{φ} = 0  (linear eigenvalue buckling)

379 kPa

critical pressure (FEA)

3.74×

FS vs. full vacuum

Contrary to the hand calculation's own expectation, the governing mode is a five-lobe circumferential wave confined to the cylinder, and the cone shows essentially zero participation. Its continuously decreasing radius makes it intrinsically more buckling-resistant than the flat effective-cylinder approximation used for screening suggested; the hand-calc bound is confirmed conservative, not a close call the FEA happened to clear.

Fig. 7. Governing buckling mode: a five-lobe wave in the cylinder; the cone does not participate.

04

Girth-Weld Junction: Discontinuity Stress

Requirement

The cone-to-cylinder junction has a 58.8° half-angle, well past the ≈30° threshold at which pressure-vessel codes require either a knuckle radius or a formal special analysis, and this design uses neither. An axisymmetric wedge-sector model quantifies the local bending stress the junction's sharp geometry produces under internal pressure.

H = N₁·tan(α)  →  σ_b = 6M_max/t²  (shell discontinuity theory)

10.2 MPa

peak discontinuity stress (FEA)

16.7×

FS vs. yield

Note: The reported stress value of 48 MPa should be treated with caution, as it occurs at a sharp geometric corner/edge. Stress concentrations at such locations can result in a localized, non-physical FEA singularity; therefore, the peak stress is not considered representative of the actual structural response.

Based on these findings, the FEA-derived peak is roughly five times lower than the conservative hand-calculation screen (56.7 MPa). The symmetric edge-shear-split approximation the hand method relies on is a poor fit for this vessel's unusually steep half-angle. No knuckle radius or thickness increase is required on structural grounds.

Fig. 8. Wedge-sector model: stress concentrated near the junction kink, decaying into each shell.

The drawings below carry each part's final dimensions together with the datum scheme, feature control frames and general tolerances developed in Manufacturability, GD&T & Tolerance Analysis, released as a six-sheet package.

Project close-out, checked three ways: sub-function by sub-function, risk by risk, and requirement by requirement.

The functional decomposition from Overview (01), closed out: each sub-function checked against what was actually designed, sized and verified.

The nine product risks scored at concept selection (03), closed out: what actually mitigated each one across Detail Design, FEA and Manufacturability.

The specification table from Overview (01), checked item by item against final status at project close-out.

Beyond the pass/fail results, the verification campaign surfaces where the design has room and where it genuinely does not.