Verification methods — analysis, test, inspection, demonstration: Exercises

3.6.28 · D4 · Physics › Spacecraft Structures & Systems Engineering › Verification methods — analysis, test, inspection, demonstra

Yeh page ek self-test hai. Har problem ko pehle padho, pen aur paper se try karo, phir collapsible solution kholo. Problems L1 (sirf idea pehchano) se L5 (sab kuch ek saath lagao) tak jaati hain. Yahan use kiye gaye har symbol ko parent note mein banaya gaya tha — agar confused ho, pehle woh dobara padh lo.

Level 1 — Recognition

Exercise 1.1 (L1)

Har requirement ke liye ek best verification method batao (analysis, test, inspection, ya demonstration):

(a) "Total spacecraft dry mass 180 kg se zyada nahi honi chahiye."
(b) "Structure launch ke dauran 8 g RMS random vibration survive karni chahiye."
(c) "Reaction wheels spacecraft ko 10 °/s se <0.1 °/s tak 120 s ke andar on orbit despin karein."
(d) "Primary strut mein peak stress 8 g quasi-static launch load ke neeche yield se kam rehni chahiye."

Recall Solution

(a) Inspection — mass ek static property hai. Isko scale par rakhte hain aur read karte hain. Koi physics prediction nahi, koi environment nahi, koi operation nahi chahiye.
(b) Test — vibration survival actual dynamic behaviour hai ek aise environment mein jo model karna mushkil hai. Isko shaker par rakhte hain aur dekhte hain ki survive karta hai ya nahi. Dekho Vibration Testing.
(c) Demonstration — yeh ek operational capability hai: actual control loop chalao aur dekhte raho ki woh task perform karta hai. Hum koi physical quantity high precision se measure nahi kar rahe, hum dikha rahe hain ki "yeh kaam karta hai."
(d) Analysis — launch loads ke neeche stress ek predicted behaviour hai deterministic physics se ( $σ = M c / I$ ). Isko flight hardware banane se pehle compute karte hain. Dekho Finite Element Analysis.

Exercise 1.2 (L1)

Blank bharo: qualification testing ek level higher than flight apply karta hai, jabki acceptance testing ek level equal to flight limit apply karta hai. Standard factors batao.

Recall Solution

Qualification level $= Flight Limit \times == 1.25 ==$
Acceptance level $= Flight Limit \times == 1.0 ==$

Qualification unit ko zyada stress kiya jaata hai design prove karne ke liye; flight unit ko sirf flight level tak stress kiya jaata hai taaki uski fatigue life consume na ho. Dekho Acceptance Testing.

Level 2 — Application

Exercise 2.1 (L2)

Ek rectangular aluminium strut apne fixed root se $L = 0.30 m$ door ek tip mass $m = 4 kg$ carry karta hai. Cross-section: width $b = 0.020 m$ , height $h = 0.010 m$ . Launch load $n = 8$ g, $g = 9.81 m/s^{2}$ .

$σ = \frac{6 m n g L}{b h ^{2}}$ (parent note se) use karke peak bending stress nikalo.

Figure — Verification methods — analysis, test, inspection, demonstration

Recall Solution

Hum kya karenge: formula mein plug karenge. Kyun: saare quantities diye hain, isliye analysis ek direct calculation hai. $σ = \frac{6 \cdot 4 \cdot 8 \cdot 9.81 \cdot 0.30}{0.020 \cdot ( 0.010 ) ^{2}}$ Numerator: $6 \times 4 = 24$ ; $\times 8 = 192$ ; $\times 9.81 = 1883.52$ ; $\times 0.30 = 565.056$ . Denominator: $0.020 \times 0.0001 = 2 \times 1 0^{- 6}$ . $σ = \frac{565.056}{2 \times 1 0 ^{- 6}} = 2.83 \times 1 0^{8} Pa \approx== 282.5 MPa ==$

Exercise 2.2 (L2)

Aluminium 6061-T6 ki yield strength $σ_{y} = 276 MPa$ hai. 2.1 ke stress ko use karke Margin of Safety compute karo aur batao ki requirement "MoS > 0" meet hoti hai ya nahi.

Recall Solution

$MoS = \frac{σ _{y}}{σ _{applied}} - 1 = \frac{276}{282.5} - 1 === - 0.023 ==$ MoS negative hai → requirement analysis se NOT met. Strut load ke neeche yield ho jaata hai. Fix: $h$ badhao (stress $\propto 1/ h^{2}$ hai, isliye yeh jaldi fayda deta hai) ya zyada strong alloy choose karo. Ise Requirements Development ko wapas feed karo.

Exercise 2.3 (L2)

Flight limit random vibration $8 g RMS$ hai. Qualification level aur acceptance level compute karo.

Recall Solution

Qualification: $8 \times 1.25 === 10 g RMS ==$
Acceptance: $8 \times 1.0 === 8 g RMS ==$

Level 3 — Analysis

Exercise 3.1 (L3)

Manufacturing ek component ki natural frequency mein $\pm 12%$ variation introduce karta hai; flight environment $\pm 9%$ variation add karta hai. Independence assume karte hue, combined 1-sigma uncertainty $σ_{total}$ nikalo, aur 3-sigma test level (mean ka multiple) nikalo. Industry 1.25× factor se compare karo.

Recall Solution

Root-sum-square kyun: independent uncertainties quadrature mein add hoti hain, linearly nahi — variances add hoti hain, isliye standard deviations $σ_{1}^{2} + σ_{2}^{2}$ se combine hoti hain. $σ_{total} = 0.1 2^{2} + 0.0 9^{2} = 0.0144 + 0.0081 = 0.0225 === 0.15 ==$ 3-sigma test level: $Mean + 3 σ = 1.0 + 3 (0.15) === 1.45 ==$ Strict 3-sigma coverage 1.45× demand karta hai, jo industry 1.25× se zyada hai. 1.25× factor ek cost/risk compromise hai — har unit ko over-design karne se bachne ke liye 3-sigma coverage se thoda kam accept karna.

Exercise 3.2 (L3)

Ek thermal analysis battery cold-case minimum $5^{\circ} C$ aur hot-case maximum $38^{\circ} C$ predict karta hai. Requirement $0$ – $40^{\circ} C$ hai. Dono ends par temperature margins compute karo. Kya dono satisfy hain? Kaun sa end design driver hai?

Recall Solution

Cold margin: $5 - 0 === 5^{\circ} C ==$ lower limit se upar ✓
Hot margin: $40 - 38 === 2^{\circ} C ==$ upper limit se neeche ✓ Dono pass hain. Hot case design driver hai — sirf 2 °C ka slack hai, isliye yeh model error ke liye sabse zyada vulnerable hai. Dekho Margin Philosophy aur Thermal Math Modeling.

Level 4 — Synthesis

Exercise 4.1 (L4)

Ek requirement kehti hai: "Deployable antenna ko command ke baad 30 s ke andar, on orbit, $- 40^{\circ} C$ par fully deploy hona chahiye." Ek combined verification approach design karo jo ek se zyada method use kare, aur har choice justify karo.

Recall Solution

Koi single method ise cleanly cover nahi karta — synthesise karo:

Analysis — deployment kinematics aur spring torque vs. hinge friction at $- 40^{\circ} C$ model karo taaki deploy time predict ho sake. Sasta hai, jaldi ho jaata hai, design ko inform karta hai.
Test — hinge mechanism ka $- 40^{\circ} C$ par thermal-vacuum test karo taaki actual friction measure ho sake, jise analysis sirf estimate kar sakta hai. Yeh model validate karta hai — dekho Model Validation.
Demonstration — flight-like article ka full deploy (gravity-offloaded) karo taaki end-to-end operational capability dikhao: command → full deployment.
Inspection — as-built latch geometry aur cable routing verify karo ki woh us design se match karti hai jo analyse/test ki gayi; ensure karta hai ki tested config flight config ke barabar hai. Configuration Management se track karo.

Har method ek alag sub-question ka jawab deta hai: analysis predict karta hai, test uncertain input measure karta hai, demonstration operation prove karta hai, inspection confirm karta hai ki article sahi wala hai.

Exercise 4.2 (L4)

Exercise 2.1 ki strut ko redo karo taaki requirement 1.5× safety factor ke saath pass ho (yaani $σ \leq σ_{y} /1.5$ ). $b = 0.020 m$ rakho; minimum height $h$ solve karo. $σ_{y} = 276 MPa$ use karo.

Recall Solution

Target stress: $σ_{allow} = 276/1.5 = 184 MPa = 1.84 \times 1 0^{8} Pa$ . $σ = \frac{6 mn g L}{b h ^{2}}$ ko $h$ ke liye rearrange karo: $h = \frac{6 mn g L}{b σ _{allow}} = \frac{565.056}{0.020 \times 1.84 \times 1 0 ^{8}}$ Denominator: $0.020 \times 1.84 \times 1 0^{8} = 3.68 \times 1 0^{6}$ . $h = \frac{565.056}{3.68 \times 1 0 ^{6}} = 1.5355 \times 1 0^{- 4} === 0.01239 m ==\approx 12.4 mm$ Toh $h$ ko 10 mm se ≈12.4 mm tak badhana full 1.5× factor deta hai — kyunki stress $1/ h^{2}$ se girta hai, 24% height increase 54% stress drop deta hai.

Level 5 — Mastery

Exercise 5.1 (L5)

Tum ek Traceability Matrix close out kar rahe systems engineer ho. Ek requirement kehti hai: "Primary structure 8 g launch load MoS > 0 ke saath withstand karni chahiye AUR 8 g RMS random vibration survive karni chahiye."

Tumhari team report karti hai:

FEA analysis: peak stress 282.5 MPa vs. yield 276 MPa.
Qualification level par vibration test: koi failures nahi, natural frequency test ke baad 6% shift ho gayi.

Vibration test ke liye acceptance criterion tha "frequency shift < 5%". Full requirement ka verification status decide karo aur apna action batao. Numbers cite karo.

Recall Solution

Static (analysis) part: MoS $= 276/282.5 - 1 = - 0.023 < 0$ . FAIL. Structure 8 g quasi-static load ke neeche yield karta hai. Dynamic (test) part: frequency shift $= 6% > 5%$ acceptance limit. 5% se zyada shift stiffness degradation signal karta hai (crack, delamination, ya loosened joint structure ko soft karta hai aur resonance lower karta hai). FAIL.

Overall status: NOT VERIFIED. Dono halves independently fail karte hain. Action: dono failures ka ek shared root cause ho sakta hai — ek under-sized structure. Redesign karo (jaise Ex 4.2 ki taller strut), FEA re-run karo MoS > 0 restore karne ke liye, phir shaker par re-qualify karo. Traceability Matrix status "open" update karo aur change Configuration Management ke under log karo. "Test mein physically nahi toota" ki basis par ship mat karo — 6% shift hidden damage ka direct evidence hai.

Recall Quick self-check

Mass requirement kaun verify karta hai? ::: Inspection Flight ke upar qualification factor? ::: 1.25× Independent uncertainties kaise combine hoti hain? ::: Root-sum-square (quadrature) Rectangular beam mein stress scale kaise karta hai? ::: $1/ h^{2}$ Vibe ke baad 6% frequency shift ka matlab? ::: Stiffness degradation — ek failure