Question

Help is much appreciated. Please use any necessary Part Charts or Part Schedules to choose an appropriate bolt size for the problem. Please, be as detailed as you can be, in both the description of your analysis and calculations. Thank you in advance.

A satellite component is in the shape of a cube with 10cm edges, has an evenly distributed mass of 2 kg and one bolt hole at each of four corners. If the maximum predicted random vibration environment is 10 Grms, what bolt size would be a good choice for restraint? What other factors might drive bolt size besides force/stress?

Answer 1

SOLUTION restraint forc is Assume that the equally divided between 4 oltk restraunt force Caleulat he F = mg F = 2 x1ox9.8) (as will beebm io times 10 Grms F 196.2 N toree On each bolt is Hence 196.2 F 4 F 49.05 N as metric clas 4.6 with bolt matexial Assume streng Hp = 225 MPa Proof Tensi strengit. Sut 400 MPa Yield sirength, S 240 Mfa either the oad Since horizontal Can be Or is also vertical amd chamging directions, to check for need tatigue bo th we Ahear ension amd

Check for fatique in tnsion are not provded. Since connecting member detaik whole of load is cauied that the arsume we the bolts by movement ef ttu Also to prevent ponent peload of 49.05 N ansume We bolt is bo1t Loac Hence maxi mum max 2 x 44.05 Fomax = 98-JN load is balt Minimum bolt Let He dia f hman Max stress , Oma - A 186 Td4 2.2 X 272 Pa d2 Omax conientration factor -2.2 Fatigue tress (eejen shiglay Omin O

Omax Omin Mean stress, 36 Om d2 2 Omax-Omin 36 Pa d2 Oa Stress amplitude - 2 Calauation of fatique strengit fatigue Atrengl is The rotating beam 200 MPa o.5 Sut O.5 X 400 The swtace condition factor ka a Sut amuming machined thread -O.265 451 X 400 Ka 0.9218 0.107 24 (to0od) Size factor (aniat) O.8S Kc Loading factor Temperatur foetor, | F PA E eliability factor 0.814/49. reliabilit;\ ke amumid

fatigue strength fr infiniti cydles Hence, actual kakb.k.kd.ke. Se Se fo.5921d) O.9218 X X o.85x IX O.814X200 .107 MRa Se =7S.53 moditi ed Goodman Vsing wiHh ansumed relation Aator of satety 4 - Se Sut n 136d 36d2 A -0.107 400 x J06 75.53d d o.o0223 m d 2.5 mm Say Checking tor shear failure Assuming Ainglee plane ctes Ahron 49 05 = 2.2 x A the Ahua ren, t = (o.002 T = 22 MPa

Coincident arial Load is preload af th bolt 49.05N 2,2 x 49.05 22 M Pa A There fore principa! sfresses are 2 35.6 HPa 2 =- 13.6 MPa 2 Von -mises slress js 2 σ = 4 4 MPa }Hen ce Ormax = 44 MPa tu bolt preload load is The mean wi Hhout hear 0ad . without Ahia Hh emile atress and is principal stresses will os von -misoA aA Siress Om 22 MPa Omare Gm = 22MP

tt values Calculabd abve Using endutance Ahrengt 22 400 22 o. lo7 (о 0оs ao) TS S3 n= 4.8 bolt is sate in shear also Hence, the designing Hhe restraint to chuck need For We excitation frequncies als o as the ramge Hhe natual frequenay Hh Aup povhng it Systum is withan the range of excitation. deutructive resonant vibratton freencies then occT. Tth happens .e, th natural Can treguenc the Yange af wiltin Support ic need to adjust exeitation freqencies) we diameter amd/or other bolt member dimens ions tomedify the support stiff nes Auch that natual frequncy Supporting stem is away from excitabon fvequencies