Journal of Advanced Mechanical Design, Systems, and Manufacturing

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1 Joural of Advaced Mechaical Deig, Sytem, ad Maufacturig Vol., No. 5, 007 Verificatio of the Deig Cocept o Nut i Bolt/Nut Aembly for the Reviio of ISO 898- ad ISO * Maaya HAGIWARA ** ad Hiroaki SAKAI *** **Nagoya Ititute of Techology (Tukuri College), Gokio-cho, Showa-ku, Nagoya , Japa hagiwara.maaya@itech.ac.jp ***Graduate Studet, Nagoya Ititute of Techology, Gokio-cho, Showa-ku, Nagoya , Japa Abtract The ISO ut of tyle ad pecified i ISO 898- ad ISO are deiged to prevet the thread trippig failure mode baed o the calculatio method called the Alexader theory. However, it have bee poited out that the thread trippig ometime occur i over-loaded bolt/ut aemblie of certai ize ad property clae due to the iadequate pecificatio i the relevat Iteratioal Stadard. Thi paper treat the deig cocept o ISO ut for the reviio of the above ISO Stadard, which i ow takig place. The imulatio program ha bee reproduced baed o the Alexader theory, ad the calculated value were compared with the pecified oe. The reult clearly how that there are both over-deiged pecificatio ad iufficietly deiged oe with higher rik of trippig. Therefore, the poible way to exclude uch problem have bee coidered baed o the ditributio of the bolt/ut thread tregth ratio calculated. Fially, it i how that that the mot practical way i to chage the harde rage of ut, ad the program to obtai the adequate pecificatio i propoed with verificatio. Key word: Fixig Elemet, Nut, Bolt/ut Aembly, Deig Cocept, Mechaical Property, ISO Stadard, Specified Value, Failure Mode, Alexader Theory. Itroductio *Received 6 July, 007 (No. 07-0) [DOI: 0.99/jamdm..755] The ISO ut of tyle ad pecified i ISO 898- () ad ISO () are deiged to cotrol the thread trippig failure mode baed o the Alexader theory (), i which the miimum ut height ad the proof load value are calculated from the geometrical coditio of bolt/ut aembly ad the mechaical propertie of their material. The applicability of the Alexader theory had bee verified by experimet uig the taircae method (4) ad the FEM aalyi takig ito accout the effect of the ut dilatio ad the thread bedig (5). However, i the relevat ISO Stadard, the ut height for idividual tyle ad ize are uified for all the property clae ad the type of thread (coare or fie pitch). Thi may reult i the iadequate combiatio of bolt/ut aemblie. The aim of thi tudy i to preet the ratioal bai for the reviio of the above ISO Stadard, which i ow takig place i ISO/TC /SC /WG 0. Firt of all, the imulatio baed o the Alexader theory ha bee performed to poit out the problem i the preet pecificatio, ad to coider the poible way to exclude the problem. The the method to amed the pecified value i dicued. 755

2 Joural of Advaced Mechaical Deig, Sytem, ad Maufacturig. Nomeclature Vol., No. 5, 007 A A S A C C C D D D D c d d d F B F S F F S m m * m c P r σ σ B : Shear area for bolt thread : Shear area for ut thread : Stre area of bolt : Modificatio factor for ut dilatio : Modificatio factor for thread bedig applied for bolt : Modificatio factor for thread bedig applied for ut : Nomial diameter (of ut) : Mior diameter of ut : Pitch diameter of ut : Couterik diameter of ut : Major diameter of bolt : Pitch diameter of bolt : Mior (root) diameter of bolt : Breakig load of bolt : Strippig load for bolt/ut aembly : Strippig load for bolt thread : Strippig load for ut thread : Nut height : Effective ut height for the calculatio of trippig load : Critical ut height havig ame probabilitie of trippig ad breakig : Pitch of the thread : Root radiu of bolt thread : Width acro the flat of ut : Teile tregth of bolt material : Teile tregth of ut material. The Alexader Theory. Priciple ad Baic Formulae Figure ummarize the cocept of the Alexader theory. For the bolt/ut aembly havig a pecific material property combiatio, the thread trippig load F S i proportioal to the hear area of the matig thread, i.e., the effective ut height m * or the umber of thread mated while the breakig load F B ha othig to do with it. Therefore, we ca cotrol the failure mode of a bolt/ut aembly by chooig the ut height a a parameter. The failure load ca be calculated by uig the followig formulae aumig that the hear tregth i 60% of the teile tregth both for bolt ad ut material: Failure load FS, FB Critical ut height mc* FS=FB Strippig load FS Breakig load FB 0 D Effective ut height m* Fig. The relatiohip amog failure load F ad F B ad the effective ut height m* 756

3 Joural of Advaced Mechaical Deig, Sytem, ad Maufacturig Vol., No. 5, 007 Table Aumed deviatio for variable cocered Variable For ut For bolt Teile tregth σ B 60 N/mm σ 60 N/mm Major diameter D d 0% of the tolerace Pitch diameter D 0% of the tolerace d 5% of the tolerace Mior diameter D 50% of the tolerace d Calculated from P ad r Root radiu r 0.0 P Nut height m 60% of the tolerace Couterik agle 5 Couterik diameter D c 0.0 D F F F F B S S = σ = mi( F B, F S S ) () I the imulatio for obtaiig the miimum ut height, the deviatio how i Table are aumed for the variable cocered, ad each ditributio i placed i the tolerace zoe o that the trippig i more likely to occur. Moreover, the breakig load i reduced to 0.95F B coiderig the cae of tighteig loadig.. Ifluecig Factor I Eq. (), the followig three modificatio factor are itroduced: C C C = ( D) +.8( D).6 (for.4 D <.9) = R = (for = R = (for R.896R R ) R ) 6.057R +.96R R 4 (for 0.4 < R (for < R < ) <.) () The factor C i for ut dilatio affectig o the reductio of the hear area, ad the factor C ad C are for thread bedig related to the tregth ratio R (= σ B A S /σ A ) of bolt ad ut thread, repectively. Figure how the relatiohip amog the factor C ad C, ad the tregth ratio R. It i importat to ote that R value i oly the deciive elemet for failure mode eve though the trippig load chage a little bit due to the factor C or C. 4. Verificatio o the Specified Value i ISO 898- ad ISO C, C...0 Nut thread trippig C Bolt thread trippig C Stregth ratio R = σ B A S /σ A Fig. Factor C ad C for thread bedig 757

4 Joural of Advaced Mechaical Deig, Sytem, ad Maufacturig Vol., No. 5, Miimum Nut Height m mi Figure how the relatiohip betwee the ditributio of the critical ut height m c ad the pecified miimum ut height m mi. Accordig to the Alexader' theory, the miimum ut height hall be et to 0 percetile of the critical ut height imulated. However, we ca alo ee two udeirable cae where m mi i placed below the ±σ rage of m c uch a for M0 ad larger tyle ut with property cla 9, ad m mi i placed above the ±σ rage of m c uch a for M6 ad maller tyle ut with property cla. The latter cae i over-deiged ituatio ad ha o harmful effect o their applicatio, but the former cae icreae the rik of trippig which hould be avoided. Table ad how the ditributio of the tregth ratio R i the imulatio, where the color idicate the followig categorie: : Iufficiet deig (miimum ut height hould be icreaed); : Over deig (miimum ut height had better be decreaed); : Acceptable deig. The iufficiet deig coditio for certai property clae ad ize may be caued by the iadequate electio of ut material i the tadardizatio procee. Critical ut height m c /d PC 8, tyle PC 8, tyle PC 9, tyle PC 9, tyle PC0, tyle PC0, tyle PC, tyle PC, tyle M 5 M 6 M 8 M0 M M6 M0 M4 M0 M6 Nomial deigatio Fig. Ditributio of the critical ut height m c for ut pecified i ISO 898- Thread d Specified ut height mmi (tyle ) Specified ut height mmi (tyle ) Table Ditributio of the tregth ratio R for ut pecified i ISO 898- Property clae tyle tyle tyle tyle tyle tyle mi max mi max mi max mi max mi max mi max M M M M M M M M M M

5 Joural of Advaced Mechaical Deig, Sytem, ad Maufacturig Table Ditributio of the tregth ratio R for ut pecified i ISO Thread d P Property clae Vol., No. 5, tyle tyle tyle tyle tyle mi max mi max mi max mi max mi max M M M M M M M M M Proof Load F p Figure 4 repreet the compario of the tre uder proof load S p betwee calculatio ad pecificatio. I the imulatio, the proof load i calculated for the combiatio of the hardeed madrel ad ut, ad the proof load i determied baed o the miimum trippig load F S for ut thread. Coiderig the fact that the tre uder proof load S p i defied a the proof load divided by the omial tre area A of bolt, it eem to be greater tha the pecified miimum teile tregth of the bolt mated. However, uch a coditio i ot alway realized a log a we maitai the deig cocept baed o the Alexader' theory ice the proof load i calculated for the weaket ut havig the combiatio of miimum ut height, miimum ut hear area, ad miimum ut harde, which would, i practice, ever exit. It hould alo be oted that the tre uder proof load S p ted to be maller for ut with maller ize due to the relatively large fudametal deviatio. 4. Policie to be Take for the Reviio Coiderig the fact metioed above, we have to make a deciio from the followig Stre uder proof load Sp N/mm PC 8, tyle PC 8, tyle PC 9, tyle PC 9, tyle PC0, tyle PC0, tyle PC, tyle PC, tyle 800 M 5 M 6 M 8 M0 M M6 M0 M4 M0 M6 Nomial deigatio Fig. 4 Stre uder proof load S p for ut pecified i ISO

6 Joural of Advaced Mechaical Deig, Vol., No. 5, 007 Sytem, ad Maufacturig optio for the amedmet of pecified value i ISO 898- ad ISO898-6 to prevet the trippig failure mode: (A) Optimize (amed) the ut height i accordace with the Alexader' theory. (B) Fix the ut height a they are, ad amed the harde rage for ome property clae ad tyle. From the practical poit of view, the optio (B) i more preferable ice the harde rage are pecified oly i ISO 898- ad ISO while the ut height or "tyle" are pecified i the idividual product tadard uch a ISO 40 (6), ISO 40 (7), ISO 867 (8), ad ISO 8674 (9). From Fig., we ca ee that the trippig load F would icreae by icreaig the tregth ratio R up to.6 eve whe R i more tha uity. The reult i Table ad how the poibility to cotrol the failure mode of bolt/ut aemblie by electig the adequate R value or miimum harde of ut. 5. Propoal o the Procedure for Obtaiig the Nut Harde Rage 5. Simplified Calculatio Method Baed o the Alexader' imulatio program, the adequate harde rage for ut could oly be obtaied by trial ad error. Therefore, the implified ad formulated method hould be developed to maitai both the efficiecy of the reviio work ad the clarity of the procedure to eure the coitecy for the future reviio. The propoed method i baed o the aumptio that the harde reverely calculated by uig the mea value of variable obtaied from Table uder the coditio of 0.95F B = F S give the mea harde value, ad that the 60 N/mm deviatio of σ B i Table ca be applied to obtai the miimum harde value. For the revere calculatio, Eq. () i traformed a, F F S B S * ( - a) or, F C S = mi( C, C * ) ( - b) By applyig the coditio of 0.95F B = F S, ad the ivere fuctio of C ad C *, the tregth ratio R ca be obtaied a, R R = C 5.6C C (for R < ) = C C.47C (for R > ) (4 - b) (4 - a) where, 0.95 C = 0.6 (5) The the teile tregth of ut obtaied from R value ca be coverted to the Vicker harde value (HV) by uig the coverio table uch a i SAE J 47 (0) via Briell harde (HB) a, σ B.45 HB (6) Table 4 ad 5 ummarize the propoal for the miimum harde of ut. The color are remaied alo i thee table a i Table ad, ad almot all the value correpod to the followig categorie: 760

7 Joural of Advaced Mechaical Deig, Sytem, ad Maufacturig : Higher harde value (for iufficiet deig ituatio); : Lower harde value (for over deig ituatio); : Almot the ame harde value (for acceptable deig ituatio). Vol., No. 5, 007 Thi fact highlight the uefule of the propoed method a a whole. Cocerig the pecificatio for the maximum harde of ut, it hould be determied by takig ito accout the proce cotrol abilitie i maufacturig ut. I the preet Stadard, the tolerace for harde are et to 60 to 0 Vicker uit, ad the maximum harde i limited to 5 HV. Therefore, the maximum harde limit may be recoidered for ut that eed the miimum harde greater tha 00 HV. Furthermore, it i advied that the reductio of the miimum harde which reult i the decreae of the proof load i, of coure, ot alway eceary for thi reviio. 5. Verificatio of the Reult Figure 5 how the reult of the Alexader' imulatio uig the ameded harde rage obtaied from the method decribed i 5.. I all the cae, the pecified ut height fall ito the lower part of the idividual critical ut height ditributio. Thi how that the pecified harde rage are adequate. Thread d Table 4 Compario of the miimum harde HV mi for ISO 898- Property clae tyle tyle tyle tyle tyle tyle Std * Cal * Std * Cal * Std * Cal * Std * Cal * Std * Cal * Std * Cal * M M M M M M M M M M * : Specified value i the preet Iteratioal Stadard. * : Calculated miimum value for the reviio. Thread d P Table 5 Compario of the miimum harde HV mi for ISO Property clae 8 0 tyle tyle tyle tyle tyle Std * Cal * Std * Cal * Std * Cal * Std * Cal * Std * Cal * M M M M M M M M M6 7 9 * : Specified value i the preet Iteratioal Stadard. * : Calculated miimum value for the reviio. 76

Joural of Advaced Mechaical Deig, Sytem, ad Maufacturig Critical ut height m c /d.0.05.00 0.95 0.90 0.85 PC 8, tyle PC 8, tyle PC 9, tyle PC 9, tyle PC0, tyle PC0, tyle PC, tyle PC, tyle Vol., No.

8 Joural of Advaced Mechaical Deig, Sytem, ad Maufacturig Critical ut height m c /d PC 8, tyle PC 8, tyle PC 9, tyle PC 9, tyle PC0, tyle PC0, tyle PC, tyle PC, tyle Vol., No. 5, Specified ut height mmi (tyle ) Specified ut height mmi (tyle ) 0.70 M 5 M 6 M 8 M0 M M6 M0 M4 M0 M6 Nomial deigatio Fig. 5 Ditributio of the critical ut height m c for ut pecified i ISO 898- after modifyig the harde rage 6. Cocluio The mai cocluio obtaied i thi tudy are ummarized a follow: () The Alexader' imulatio ha bee performed for ut pecified i ISO 898- ad ISO 898-6, ad the ut havig iadequate pecificatio were poited out. () The policie for the reviio have bee coidered from the practical poit of view, ad the mot adequate method to amed the harde rage of ut wa propoed. () It ha bee verified by the imulatio that the ameded pecificatio are uitable for the purpoe of the relevat Iteratioal Stadard. Referece () ISO 898-: 99, Mechaical propertie of fateer Part : Nut with pecified proof load value Coare thread. () ISO 898-6: 994, Mechaical propertie of fateer Part 6: Nut with pecified proof load value Fie pitch thread. () Alexader, E. M., Aalyi ad Deig of Threaded Aemblie, SAE Paper, No (977), pp. -5. (4) Hagiwara, M., Ito, S. ad Kodoh, S., Loadability of Bolt-Nut Aemblie Determiatio of Critical Nut Height by Staircae Method, Iteratioal Joural of the Japa Society for Preciio Egieerig, Vol. 9, No. 4 (995), pp (5) Hagiwara, M., Okubo, H. ad Nakamura, H., Loadability of Bolt-Nut Aemblie Effect of Nut Specificatio o the Failure Mode ad Failure Load, Joural of the Japa Society for Preciio Egieerig, Vol. 67, No. (00), pp (6) ISO 40:999, Hexago ut, tyle Product grade A ad B. (7) ISO 40:999, Hexago ut, tyle Product grade A ad B. (8) ISO 867:999, Hexago ut, tyle, with metric fie pitch thread Product grade A ad B. (9) ISO 8674:999, Hexago ut, tyle, with metric fie pitch thread Product grade A ad B. (0) SAE J 47:98, Harde Tet ad Harde Number Coverio. 76

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