Geometry • Section 9.2
Lug Eccentricity & Side Taper Angles
Geometric modeling of tapered profiles, bore offsets, and boundary clearance limits
1. Engineering Context of Tapered and Eccentric Lugs
While textbook problems often assume straight, rectangular lugs with concentric bores, production aerospace fittings are frequently tapered and eccentric:
- Weight Optimization: Removing non-load-bearing material behind the pin hole reduces parasitic weight.
- Clearance Constraints: Tapering avoids geometric interference with adjacent structure, mating clevis forks, or actuator bodies during articulation.
- Non-Axial Load Paths: Offset bores align the pin with oblique line-of-action vectors to minimize bending moments in the supporting lug shank.
2. Taper and Eccentricity Parameters in LugCalc™
Under the Male Lug (and Female Lug) configuration cards, LugCalc provides dedicated fields for taper angles and hole offsets:
| Parameter | Symbol | Definition | USAF Validity Range |
|---|---|---|---|
| Upper Taper Angle | $\alpha$ | Angle of the upper side edge relative to the longitudinal centerline. | $0^\circ \le \alpha \le 45^\circ$ |
| Lower Taper Angle | $\beta$ | Angle of the lower side edge (toward the transverse load direction) relative to the centerline. | $0^\circ \le \beta \le 45^\circ$ |
| Axial Eccentricity | $e_{cca}$ | Axial distance of the hole center relative to the semicircular head radius center ($e_{cca} = e - w/2$). | Must satisfy $a = e - D/2 > 0$ |
| Transverse Eccentricity | $e_{cct}$ | Transverse offset of the bore center from the longitudinal symmetry axis (positive toward the lower side). | Limited by edge breakout check |
3. Automated Edge Breakout & Ligament Clearance
When a lug is both tapered and eccentric, the hole can break through the tapered side boundary before reaching the forward semicircular tip. The LugCalc calculation engine continuously executes an automated minimum ligament clearance check:
- Calculates the shortest perpendicular Euclidean distance from the bore center $(p_x, p_y)$ to the upper side tangent, lower side tangent, and forward semicircular arc.
- Subtracts the bore radius $D/2$ to find the true minimum ligament thickness.
- If the hole center is positioned such that material thickness reaches zero or negative values, the software displays an immediate boundary violation flag: "Bore breaks through lug outline".
4. Impact of Taper on Lug Strength
Transverse Strength Reduction: Tapering reduces the material section on the trailing and leading sides of the pin hole. This reduces the radial edge segments $h_1 \dots h_4$ and drastically lowers the effective dimension $h_{avg}$, resulting in lower transverse capacity $P_{tru,L}$ (per USAF Figure 9-8).