Radome Cooling System Installation Structural Substantiation

INTRODUCTION

Static-strength substantiation of the Radome Cooling System installation on a DHC-8-100, covering the two forward exhaust assemblies, aft intake shield, drain component, composite joints and the local radome cut-outs.

External aerodynamic demand is bounded at sea-level maximum operating speed and carried through component-level aerodynamic idealizations, 3D rigid-body fastener reactions, Classical Laminate Plate Theory (CLPT), PTFE plate/shear checks and radome stress-concentration assessment.

DESIGN ASSESSMENT

Radome Cooling System Installation Components

The following schedule captures the structural parts, material systems, thicknesses and laminate orientations that participate in the load path.

Material Properties

Material allowables used for the PTFE drain and the glass-fiber/epoxy laminate are summarized below.

Joints Allowables

The Methodology Used in Calculating the Joints Allowables

The Strength of Bolted Joints in Multidirectional CFRP Laminates

Composite mechanical-joint strength is fundamentally test-dependent because material system, layup, thickness and local constraint all affect failure. The source therefore uses published multidirectional-laminate trends as conservative knockdown guidance rather than treating a single generic laminate value as universally applicable [Analysis & Design of Composite & Metallic Flight Vehicle Structures by Richard Abbott].

Joint’s Bearing Strength:

General ultimate bearing stress values of 50 ksi and 40 ksi can be selected for carbon fiber laminates and glass fiber laminates, respectively, considering the worst environmental condition [Analysis & Design of Composite & Metallic Flight Vehicle Structures by Richard Abbott- Section 12.2.4.2]. This approach is applied as long as:

1. The thickness/Diameter ratio (t/D) is between 0.5 and 2, and

2. The edge distance/Diameter ratio (e/D) is greater than 3.0.

If one of these conditions, at least, is not met, the associated figure and/or the associated figure should be used to calculate the knockdown factors to scale down the aforementioned bearing stresses as a conservative approach. the associated figures outline the steps for determining when and how to calculate the knockdown factors.

It is noteworthy that the associated figure though the associated figure are for 0±45° tested laminates. Using these figures to calculate the knockdown factors represents a conservative approach since our laminate utilizes an addition ply orientation (90°) that will increase the overall laminate strength.

Moreover, the fastener sizes utilized to generate the associated figure though the associated figure are ¼, ⅜, and ½. Therefore, a knockdown factor will be calculated for the cases where the joint’s fastener size is smaller than the utilized fasteners in the charts.

Finally, the overall thickness of the tested laminate in the associated figure though the associated figure is 0.118 in. Therefore, a knockdown factor will be calculated for the cases where the incorporated laminate has an overall thickness less than the tested laminate thickness.

Joint’s Pull-Through Strength:

There is no reliable analytical method to determine the pull-through strength of fasteners in laminated composites. However, there is a semi empirical hand method (its results are considered conservative as stated in [Analysis & Design of Composite & Metallic Flight Vehicle Structures by Richard Abbott]) that correlates the joint failure to the interlaminar shear strength of a carbon fiber laminate. It is noteworthy that the interlaminar shear strength of a glass fiber laminate is similar to the interlaminar shear strength of a carbon fiber laminate with the same resin. Hence, the same formula can be used but with a 0.75 correction factor to account for the increased flexibility of glass. This formula can be expressed as below [Analysis & Design of Composite & Metallic Flight Vehicle Structures by Richard Abbott]:

$$F_{pull} = \frac{2\alpha t\pi D_{f}\tau_{\max}}{2.9 - 0.018\frac{t}{D_{s}} - 0.51\left( \frac{t}{D_{s}} \right)^{2}}$$

Where:

• $t$Laminate thickness, in
• $D_s$Bolt shank diameter, in
• $D_f$Bolt-head / washer diameter, in
• ${\tau }_{\text{max}}$Laminate interlaminar shear stress, psi
• $\alpha$Reinforcement factor: 1.0 carbon, 0.75 glass.

Using curve 1 in the associated figure the minimum shear strength at failure, is 151.62 MN/m² (22 ksi). Moreover, Based on the associated figure, the ILLS value equals 84.70 MN/m² (12.29 ksi). Conservatively, the knocked down value calculated in the relevant discussion will be used in our analysis, namely, $\tau_{\max} = 4.875\ ksi$.

S17114 and 94701A833 Screws

Considering the bolts cross-sectional areas the Ultimate Shear and Tensile Loads of both screws can be calculated as below:

Where A_s is the bolt cross-sectional area based on the nominal shank diameter and A_m is bolt cross-sectional area based on the minimum minor diameter of the external thread.

• Joint Pull-Through Strength:

The utilized 93785A500 washer has an outer diameter value of 0.51 in [Technical Data Sheet-93785A500]. Therefore, the joint’s Pull-Through Strength can be calculated as below:

In the FWD/LH&RH Exhaust Assemblies:

$$f_{pull} = \frac{2\alpha t\pi D_{f}\tau_{\max}}{2.9 - 0.018\frac{t}{D_{s}} - 0.51\left( \frac{t}{D_{s}} \right)^{2}} = \frac{2\pi \times 0.75 \times 0.31 \times 0.51 \times 4.875\ \times 10^{3}}{2.9 - 0.018\frac{0.31}{0.19} - 0.51\left( \frac{0.31}{0.19} \right)^{2}} = 2,400.56\ {lb}_{f}$$

In the AFT Intake Assembly – Joint 1

$$f_{pull} = \frac{2\alpha t\pi D_{f}\tau_{\max}}{2.9 - 0.018\frac{t}{D_{s}} - 0.51\left( \frac{t}{D_{s}} \right)^{2}} = \frac{2\pi \times 0.75 \times 0.25 \times 0.51 \times 4.875\ \ \times 10^{3}}{2.9 - 0.018\frac{0.25}{0.19} - 0.51\left( \frac{0.25}{0.19} \right)^{2}} = 1,469.41\ {lb}_{f}$$

In the AFT Intake Assembly – Joint 2

$$f_{pull} = \frac{2\alpha t\pi D_{f}\tau_{\max}}{2.9 - 0.018\frac{t}{D_{s}} - 0.51\left( \frac{t}{D_{s}} \right)^{2}} = \frac{2\pi \times 0.75 \times 0.313 \times 0.51 \times 4.875\ \times 10^{3}}{2.9 - 0.018\frac{0.313}{0.19} - 0.51\left( \frac{0.313}{0.19} \right)^{2}} = 2,467.3\ {lb}_{f}$$

Since the Ultimate Tensile Load, $f_{tu}$, is smaller than the Pull-Through Load, $f_{pull}$, the former will be considered as the out-of-plane joint allowable in the previous three joints.

• Joint Bearing strength:

the corresponding table summarizes the Joints Specifications utilized in the Radome Cooling System Installation. These parameters are essential to calculate the knockdown factors as follows:

In the FWD/LH&RH Exhaust Assemblies:

1. t_joint/D_s=0.31/0.19=1.63 → No knockdown factor is required.

2. e/D_s=2.63 → a knockdown factor is required.

   • F_bru@e/D=2.63=823.47 MN/m² and F_bru@e/D=3=900 MN/m²

   • The knockdown factor is 823.47/900=0.915.

3. The shank diameter is 0.19 in → a knockdown factor is required.

   • The knockdown factor is 0.19/0.25=0.76.

4. The overall thickness of the tested laminate is 0.118 in. Our incorporated laminate is 0.31 in thick; that is more than two times thicker than the tested laminate. This will increase the failure bearing stress. For conservatism, this minimum value is used.

Consequently, the adjusted Ultimate Bearing Strength for our glass fiber reinforced laminate is F_bru=0.915x0.76x40=27.816 ksi, and the Joint’s Ultimate Bearing Load is f_bru=27.816x0.31x0.19 =1,638 lb_f.

In the AFT Intake Assembly – Joint 1

1. t_joint/D_s=1.32 → No knockdown factor is required.

2. e/D_s=2.63 → a knockdown factor is required.

   • F_bru@e/D=2.63=823.47 MN/m² and F_bru@e/D=3=900 MN/m²

   • The knockdown factor is 823.47/900=0.915.

3. The shank diameter is 0.19 in → a knockdown factor is required.

   • The knockdown factor is 0.19/0.25=0.76.

4. The overall thickness of the tested laminate is 0.118 in. Our incorporated laminate is 0.25 in thick. For conservatism, this minimum value is used.

Consequently, the adjusted Ultimate Bearing Strength for our glass fiber reinforced laminate is F_bru=0.915x0.76x40=27.816 ksi, and the Joint’s Ultimate Bearing Load is f_bru=27.816x0.25x0.19=1,321 lb_f.

In the AFT Intake Assembly – Joint 2

1. t_joint/D_s=1.65 → No knockdown factor is required.

2. e/D_s=2.315 → a knockdown factor is required.

   • F_{bru@e/D=2.315}=739.80 MN/m² and F_bru@e/D=3=900 MN/m²

   • The knockdown factor is 739.80/900=0.822.

3. The shank diameter is 0.19 in → a knockdown factor is required.

   1. The knockdown factor is 0.19/0.25=0.76.

4. The overall thickness of the tested laminate is 0.118 in. Our incorporated laminate is 0.313 in thick. For conservatism, this minimum value is used.

Consequently, the adjusted Ultimate Bearing Strength for our glass fiber reinforced laminate is F_bru=0.822x0.76x40=25 ksi, and the Joint’s Ultimate Bearing Load is f_bru=25x0.313x0.19=1,486 lb_f.

In the Drain Component:

Conservatively, it is assumed that the screws pass through only the Drain Component.

The Ultimate Bearing Strength for the PTFE is F_bru=1.85 ksi. Hence, the Ultimate Bearing Load for the joint can be calculated as f_bru= 1.85x0.63x0.19=221.45 lb_f

Since the Ultimate Shear Load is smaller than the Joint Bearing Load, the former will be considered as the in-plane’ joint allowable in the previous four joints.

Summary

The resulting in-plane and out-of-plane joint allowables used in the component checks are summarized below.

Source note: the original summary repeats “AFT Intake – Joint 1” for the third row; it is labeled “Joint 2” here to match the preceding joint definitions and calculations.

LOAD CASES FORMULATION

Exhaust Assembly

LIFT IDEALIZATION

2D wing at maximum C_L

Each FWD exhaust is conservatively idealized as a 2D lifting body. The source relation is C_L,max = 1.94·AR, capped at 4π [Fluid-Dynamic Lift - Hoerner].

Drag Coefficient

The LH & RH FWD Exhausts can be conceptualized as an outlet opening, namely, a hood with half circular outlet.

The external drag coefficient is subdivided into two parts, (i) parasite drag originating on the exterior of the outlet and (ii) “base” drag due to the negative pressure (if any) behind the opening. For outlet ducted system (directed downstream) shown in the associated figure, the total drag coefficient including the suction is 0.1.

Lift and Drag Forces

• Level steady flight

• Maximum pitch-up attitude

• Maximum side slip

• Combination of pitch and yaw (sideslip)

Consequently, the exhaust aerodynamic forces are:

Applying the 1.5 ultimate factor gives:

AFT Intake Assembly

Drag Coefficient

The Shield Angle of the AFT Intake Assembly will be conceptualized as a semi-circle 2D body that is hollow at the rear side. The total drag coefficient including the suction is 1.20 [Fluid-Dynamic Drag-theoretical experimental and statistical information by Hoerner- Section 7 – Chapter III].

Drag Force

Hence, the total drag force applied on the Shield Angle can be calculated as below:

$${D_{\max} = \frac{1}{2}\ \ \rho\ V_{{MO}_{\max}}^{2}S\ C_{D} }{D_{\max} = \frac{1}{2}\ \times 0.00238\ \frac{slug}{{ft}^{3}} \times {408.45}^{2}\frac{{ft}^{2}}{s^{2}} \times \left( \frac{2.067}{144} \right){ft}^{2} \times \ 1.2 = 3.42\ {lb}_{f}}$$

Considering operational safety margins and potential peak operational conditions, this force is scaled up by a factor of 1.5, the ultimate drag force acting on the Shield Angle is:

$$D_{u} = 1.5 \times 3.42\ = \boxed{5.13}\ \ {lb}_{f}$$

Drain Component

SAME AERODYNAMIC FRAMEWORK

Drain treated as a small external lifting/drag body

The drain uses the same dynamic-pressure basis as the exhaust. Its projected areas define the aspect ratio and drag area, while the source hood coefficient is retained for drag.

Lift Coefficient

Based on the associated figure, the Aspect Ratio can be calculated as below:

Drag Coefficient

As shown in the associated figure, the total drag coefficient including the suction is 0.1.

Lift and Drag Forces

Applying the same 1.5 ultimate factor gives:

CLASSICAL ANALYSIS

Ultimate aerodynamic loads are applied at each component CoG and transferred to the local fastener pattern. The offset between the force line of action and attachment plane generates the moments used in the component and laminate checks below.

These moments will be considered in the laminate stress analysis as applied loads along with the aerodynamic loads later in this section.

Fasteners' Reaction Forces

3D rigid-body analysis resolves the aerodynamic force/moment system into local shear and axial demand at each Exhaust, AFT Intake and Drain fastener.

Stress Analysis for the Components’ Material

Exhaust Component

The Aerodynamic Loads and Bending Moments applied on the Exhaust.

Lift [lbf]	Drag [lbf]	Mx [in-lbf]		My [in-lbf]		Mz [in-lbf]
		Base	Top	Base	Top
26.96	1.83	±26.45	±53.49	1.80	-3.63	±2.32

The following CLPT outputs document the laminate definition and ABD stiffness, followed by the ply-level direct/bending stress recovery and minimum margins.

Drain Component

The drain geometry is separated into two mechanics problems so that each region is checked with an appropriate hand method: annular-plate bending at the base and direct shear through the outlet section.

Drain Component’s Base

BASE IDEALIZATION

Annular plate · outer edge simply supported · inner edge free

A uniform line moment is applied at the inner radius. The Roark annular-plate coefficient is used at the inner edge where the tangential unit moment governs [Roark’s Formulas for Stress and Strain, 9th Ed., annular-plate case].

The source uses the more conservative coefficient for b/a = 0.3 and ν = 0.3 even though the PTFE Poisson ratio is 0.46.

$$M_{t,\text{max}}=K_{M,tb}{M}_o$$

Therefore, the maximum unit tangential bending moment ($M_{t,max}$) due to M_x=±0.051 lb_f-in and M_y=6.12 lb_f-in are:

For further conservatism, it will be assumed that both moments act at the same time, so the maximum unit tangential bending moment ($M_{t,max}$) will be $M_{t,max} = - 0.0207 - 0.248 = - 0.269\ {lb}_{f} - in\ /\ in$, and the resulted maximum bending stresses will be:

$$F_{bt} = \frac{6M_{t}}{t^{2}} = \frac{6 \times - 0.269}{{0.125}^{2}} = 0.1033\ ksi$$

The yield compressive strength for the PTFE Plastic is F_cy=1.45 ksi. Therefore, the margin of safety can be computed as below:

Drain Component’s Outlet

The outlet portion of the drain component will be checked against shear loads. The load along the x- and y-axes equal 0.1003 lb_f and 0.083 lb_f, respectively. Hence, the shear stress at the XY surface is:

$$F_{s - xy} = \frac{\sqrt{{1.003}^{2} + {0.083}^{2}}}{0.554} = 1.82\ psi$$

The ultimate shear strength for the PTFE Plastic is 725 psi. Therefore, it passes by observation.

Radome’s Cut-Outs

Four local openings are introduced into the radome for the cooling-system hardware. The assessment treats the openings as geometric stress raisers and applies gross/net stress-concentration factors appropriate to each cut-out shape.

Where K_tg and K_tn are the stress concentration factors with the nominal stress based on gross and net areas, respectively. $\sigma$ and $\sigma_{n}$ are the gross and net stresses far from the hole, respectively. $\sigma_{\max}$ is the maximum stress at the edge of the hole.

The Radome is 0.1875 in thick and it is subjected to ultimate loads of 2,916.99 lb_f and 129.25 lb_f along the negative z-axis and positive x-axis, respectively. Hence, the in-plane gross and net stresses of the radome’s cooling system panels are as below:

the corresponding table lists the Gross and Net Stress Concentration Factors for the aforementioned holes considering the panels’ dimensions shown in the associated figure.

REFERENCES