DESIGN ENGINEERING Calculation REF

8/9/2019 DESIGN ENGINEERING Calculation REF

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MACHINE DESIGN

SRI MALLIKARJUN V



Machine design—what is it?

Suset !" Mechanica# design$which isSuset !" Enginee%ing design$which is

Suset !" Design$&which is

Suset !" the t!'ic !" (%!#e) S!#*ing

+hat is a )achine? $a c!)inati!n !"%esistant !dies a%%anged s! that , thei%

)eans the )echanica# "!%ces !" natu%e can e

c!)'e##ed t! d! w!%- acc!)'anied , ce%tain

dete%)inate )!ti!ns&



.ig 'ictu%e

Mechanics

Statics D,na)ics

-ine)atics Kinetics

)!ti!nM!ti!n and "!%ces

Change

with ti)e/i)e n!t a

"act!%



/he Design (%!cess

•Rec!gni0e need1de"ine '%!#e)

•C%eate a s!#uti!n1design

•(%e'a%e )!de#1'%!t!t,'e1s!#uti!n

•

/est and e*a#uate•C!))unicate design



I)'!%tant t! %e*iew the

"unda)enta#s !"$&•Statics

•D,na)ics

•Mate%ia#s1)ate%ia# '%!'e%ties

•e#asticit,

•h!)!geneit,

•is!t%!',

•)ass and a%ea 'a%a)ete%s



Lets egin !u% %ie" %e*iew



/2I %!ta%, )!ti!n e3ui*a#ent !" 42MA

I2 )ass )!)ent !" ine%tia M5%67 dM

n!t t! e c!n"used with the a%ea )!)ent !" ine%tia which

we wi## discuss #ate%&

Remember the parallel axis theorem

I" Icg is a )ass )!)ent !" ine%tia a!ut s!)e a8is 9aa: th%u the

cent%!id ;cg< !" a !d, then the )!)ent !" ine%tia a!utan a8is 9: which is 'a%a##e# t! 9aa: and s!)e distance 9d:

awa, is gi*en ,=

I 2 Icg > ;d67<5 M whe%e M is the )ass

N!te= This same theorem also works for area moments of inertia in thesame way



M!%e gene%a##, I2M -67 whe%e - is ca##ed the %adius !" g,%ati!n

which can e th!ught !" as the %adius whe%e a## the )ass c!u#d

c!ncent%ated ;%e#ati*e t! the a8is !" inte%est< t! gi*e the sa)e

)!)ent !" ine%tia I that the !d, with dist%iuted )ass has&

4!% a s!#id c,#inde%

I2 M;-67< 2 M ;R67< whe%e

R2 %adius

M2 )assK2 %adius !" g,%ati!n

4!% a h!##!w c,#inde%

I 2 M;-67< 2 M;R@67 > R767<

N!te= this intuiti*e#, see)s #i-e it sh!u#d e ;R@67 R767<

ut that is n!t the case& De%i*ing this is a g!!d %e*iew !" asic

ca#cu#us&



Area Moment of inertia for some shapes



Re*iew '%!#e) B@



Solution synthesis= +e -n!w I2 h1@7

"!% a %ectangu#a% secti!n&

Solution execution= +e )ust decide !n

the )a8 I& +i## I88 !% I,, e #a%ge%& 4!% I88 2F and h2@7& .ut "!% I,, 2@7 and

h2F s! it is !*i!us that I88 wi## e

#a%ge%& Since the tue is h!##!w we )ust

sut%act !ut the c!nt%iuti!n !" the)ate%ia# that d!es n!t e8ist$&the

%ectangu#a% ai% s'ace !n the inside&

Hence the s!#uti!n is=

I2!h!

1@7 ihi

1@7+he%e !2F h!2@7 i2 hi2@@

/his gi*es I2;F<;@76<1@7 ;<;@@6<1@7

I2@@7&2&$&the answe% ;d<



Factors of safety

N 2 a##!wa#e st%ess ;!% #!ad< !" )ate%ia#

+!%-ing !% design !% actua# st%ess

M!%e gene%a##, N 2 #!ad which wi## cause "ai#u%e

L!ad which e8its



"ten sa"et, "act!% is a '!#ic, 3uesti!n& He%e a%e s!)e %u#es

" thu)&

Rec!))ended N )ate%ia#s #!ads en*i%!n& C!nd&

@&7 @& *e%, %e#ia#e ce%tain c!nt%!##ed

@&7 we## -n!wn det& Easi#, "ai%#, c!nst&

77& a*g& Can e det& %dina%,7& #ess t%ied 9: 9:

unt%ied )at#s 9: 9:

we## -n!wn unce%tain unce%tain



Design relationships for elastic design

A8ia# #!ading

2 S,1N 2 41A

+he%e 42 a8ia# "!%ce

A 2 c%!ss secti!na# a%ea

/%ans*e%se shea%

2 Ss,1N 2 V1;I5<

+he%e V 2 *e%tica# shea% 2 , dA

2 )a8 at the neut%a# a8is




.ending

+he%e

2 )a8 a##!wa#e design st%ess

S, 2 ,ie#d st%ess !" )ate%ia# tensi#e

N 2 sa"et, "act!%

) 2 design )!)ent

C 2 distance "%!) neut%a# su%"ace t! !ute% "ie% I 2 a%ea )!)ent !" ine%tia a!ut neut%a# a8is



H!!-es #aw1st%esses1st%ains

(%!#e)= a %!und )eta# %!d @: dia is @ "t #!ng& A tensi#e

#!ad !" @ #" is a''#ied and it is dete%)ined that the %!de#!ngated a!ut &@ inches& +hat t,'e !" )ate%ia# is the

a% #i-e#, )ade !" ? H!w )uch did the dia)ete% !" the

%!d change when the #!ad was a''#ied ?



Plan+e wi## a''#, H!!-es #aw t! dete%)ine what the )!du#us

!" e#asticit, E is& /hen we sh!u#d a#s! e a#e t! a''#,the sa)e #aw t! dete%)ine the change in dia)ete% !" the %!d&

+e %eca## H!!-es #aw as "!##!ws



L!ads and st%esses e8a)'#e

Unde% ce%tain c!nditi!ns a whee# and a8#e is suOected t! the

#!ading sh!wn in the s-etch e#!w&

a< +hat a%e the #!ads acting !n the a8#e at secti!n AA?

< +hat )a8i)u) di%ect st%esses a%e de*e#!'ed at thatsecti!n?



PlanPSu) "!%ces and )!)ents

PC!)'ute ending )!)ent

PC!)'ute ending st%essPC!)'ute tensi#e !% c!)'%essi*e st%ess

!xecution

Su))ing 48 we dete%)ine the a8ia# tensi#e #!ad at AA2#" Su))ing 4, di%ect shea% #!ad 2 @ #"

Su))ing )!)ents a!ut the AA secti!n at the neut%a# a8is

+e "ind the ending )!)ent2 @5 > 5@2 #in




/!%si!n

2 Ss,1N 2 /5%1J

+he%e /2 t!%3ue a''#ied% 2 %adius

J2 '!#a% )!)ent !" ine%tia ;a%ea<

J2 ;'i<;%6<17 2 ;'i<;d6<17 J2 ;'i<;D6 d6<1 7



"ombined stress

In a tw! di)ensi!na# st%ess "ie#d ;whe%e <the '%inci'a# st%esses !n the '%inci'a# '#anes a%e gi*en

,=



"ombined stress continued

In c!)ined st%esses '%!#e)s in*!#*ing shaft designwe a%e gene%a##, dea#ing with !n#, ending and t!%si!n

i&e& whe%e 2

In this case



Theories of failure

@< Ma8i)u) n!%)a# st%ess

.ased !n "ai#u%e in tensi!n !% c!)'%essi!n a''#ied t! )ate%ia#sst%!ng in shea% wea- in tensi!n !% c!)'%essi!n&

Static loading

a< Design ased !n ,ie#ding -ee'=

;"!% )ate%ia#s with di""e%ent c!)'%essi*e and tensi#e st%engths<

< 4!% brittle materials ;n! ,ie#d '!int< $design "!%=



Theories of failure cont#d

4atigue #!ading ;"#uctuating #!ads<

Se2C"5C%5Cs5Cw5Sn

+he%e Sn 2 endu%ance #i)it

Se 2 a##!wa#e w!%-ing st%ess

!% )!di"ied endu%ance #i)it

N!te= st%ess c!ncent%ati!n "act!%

K" is n!t in this "!%)u#a "!% Se& K"

is inc#uded #ate% t! e part specific

Sn

Sn

B c,c#es

ti)e

st%ess



Soderberg failure line for fatigue

sa"e st%ess #ine

SeSe1N

a8is

S,'1N S,'

State !" st%essK"5

K"



Maximum shear theory of failure

4!% design with ductile materials and it is c!nse%*ati*e and

!n the '%e)ise= "ai#u%e !ccu%s when the )a8i)u) ;s'atia#<

shea% st%ess e8ceeds the shea% st%ength& 4ai#u%e is , ,ie#ding&

sa"e st%ess #ine

Ses17Se17N

a8is

S,'17N S,'17

State !" st%essK"5

K"



Formulae for si$ing a shaft carrying

bending and torsion

4!% a h!##!w sha"t$&:D!:2!utside dia 9Di: 2 inside dia

4!% a s!#id sha"t Di2 and the e3uati!n ec!)es=

+he%e 9D!: wi## e the s)a##est a##!wa#e dia)ete% ased !n

)a8 shea% the!%,& M is the ending )!)ent and / is the t!%si!n

/ is the )ean t!%3ue assu)ed t! e stead, he%e$and M is the

.ending )!)ent which ec!)es the "#uctuating #!ad as the sha"t

R!tates&



%ther shaft si$ing considerations

the% c%ite%i!n !" sha"t design )a, e %e3ui%e)ents !n t!%si!na#

Rigidit, ;twist< and #ate%a# %igidit, ;de"#ecti!n<

/!%si!na# %igidit,

+he%e=

theta2 ang#e !" twist deg%ees

L 2 #ength ;ca%%,ing t!%3ue< in inches/ 2 t!%si!na# )!)ent #in

G 2 t!%si!na# ;shea%< )!du#us !" e#asticit,

;@@&8@6 'si stee#s< ; &F8@6 'si A# a##!,s

D 2 sha"t dia)ete% inches

/heta 2 F5 /5L1;G5;D!6Di6<< "!% h!##!w ci%c& sha"t

/heta 2 F5 /5L1;G5;D!6<< "!% s!#id ci%c& sha"t



Re*iew '%!#e) B@@



Shea% and M!)ent sign c!n*&

P (!siti*e shea%

P Negati*e shea%

P (!siti*e )!)ent

P Negati*e )!)ent



(%!#e)= I" the a!*e i)'#e)ent '%!#e) had een gi*en

this sa)e V! "!% a ha#"%idge ci%cuit what w!u#d ha*e een

the "!%ce acting !n the i)'#e)ent?



(%!#e)= I" the a!*e i)'#e)ent '%!#e) had een gi*en

this sa)e V! "!% a ha#"%idge ci%cuit what w!u#d ha*e een

the "!%ce acting !n the i)'#e)ent?

S!#uti!n= 4!% a ha#" %idge V!1Ve8 2 G45ε17

htt'=110!ne&ni&c!)1de*0!ne1cda1tut1'1id1

7/hus "!% the sa)e V! ⇒ ε )ust e twice a #a%ge

S! i" ε is twice as #a%ge the #!ad is )ust e twice as #a%ge&



C!#u)n uc-#ing

A h,d%au#ic actuat!% is needed t! '%!*ide these"!%ces= )ini)u) "!%ce in c!nt%acti!n$ #&Ma8i)u) "!%ce in e8tensi!n ;'ush< $F#&

/he %!d is )ade !" stee# with a tensi!n !%c!)'%essi!n ,ie#d st%ength !" 'si& Assu)ea h,d%au#ic s,ste) '%essu%e !" 7'si&

a& +hat n!)ina# ;nea%est @1@:< dia)ete% %!d is

%e3ui%ed "!% a sa"et, "act!% !" and what n!)ina# !%e?

& +hat si0e 'ist!n is needed?



+e s-etch the c,#inde% as sh!wn he%e=

+ith F #s !" 'ush ca'ai#it, we )ust e c!nce%ned a!ut

'!ssi#e uc-#ing !" the %!d in its )!st *u#ne%a#e '!siti!n

which w!u#d e at "u## e8tensi!n t! 7: #ength& +e wi## n!tw!%%, a!ut the c,#inde% itse#" uc-#ing and c!nce%n !u%se#*es

with the %!d&P+hat d! ,!u %eca## a!ut s!#*ing a uc-#ing '%!#e)?PLets %e*iew a "ew asics



PIs the %!d c!nside%ed t! e #!ng !% sh!%t c!#u)n?P+hat a%e the end c!nditi!ns?P+e )ust design "!% (a##!wa#e2F#s2(c%1N

P.ut N the sa"et, "act!% 2 s! (c%2#s

Reca## "%!) uc-#ing the!%,=



(#an=PIn a t,'ica# '%!#e) we w!u#d dete%)ine i" the c!#u)n

is #!ng !% sh!%t then a''#, the Eu#e% !% J!hns!n e3u& acc!%ding#,

ut in !u% case he%e we a%e designing the si0e !" the c!#u)n

and the si0e in"!%)ati!n is n!t gi*en s! what d! we d!?P(ist!n dia)ete% )ust e dete%)ined ased !n "!%ces %e3ui%ed

and the s,ste) '%essu%e and the %!d si0e&

E8ecuti!n=

Since we a%e t%,ing t! c!)'ute %!d dia)ete% we c!u#d si0e

the %!d t! e a sh!%t !% a #!ng c!#u)n -ee'ing in )ind that

the Eu#e% "!%)u#a a''#ies t! #!ng c!#u)ns whe%e the st%ess

is #ess than S,17 and whe%e the s#ende%ness %ati! L1%n is

g%eate% than the c%itica# *a#ue gi*en , the ta#e a!*e&

Lets use Eu#e% and design it as a #!ng c!#u)n&



Assu)e C 2 Q 4!% 94i8ed 4%ee:

BUT

d=1.448

( ) ( ) ( ) ( )7 7 I

JNE NNN 7N J 1 CN @N N&7@I I π ∴ = ∗ × =



4!% a "!%ce in tensi!n 2#s

;(ist!n a%ea<;7'si<2(ist!n a%ea 27& in67 e""ecti*e a%ea

.ut e )ust %e)e)e% that in c!nt%acti!n the %!d is !ccu',ing

(a%t !" the c,#inde% a%ea&

A%ea !" the %!d 2 ;(i<;d67<12&@5;@&67<12@& in67

/hus the t!ta# !%e a%ea )ust e 7& > @&2& in67

Hence ;'i<5;D67<12&

D672&

D27&@in 7&7 in dia 'ist!n

Can a 'ist!n 7&7 in dia gene%ate F#s 'ush with a 7'si

H,d%au#ic '%essu%e?

4!%ce 'ush2(5A%ea2 75;'i<5;7&767<12 7#s s! K&



&ets work a follow'on example

Assu)e ,!u want t! chec- the c!nnect!% in a s#ide% c%an-

)echanis) which is t! gene%ate a "!%ce at the s#ide%

Lets assu)e ,!u ha*e ch!sen the "!##!wing=C!nnect!% #ength @7:

C%!sssecti!n Q 8 @ inch a%ea 2 Q inch s3&

Mat# A# E2 @&8 @6 'si

Ma8 #!ad in c!nnect!% wi## e #"

Lets assu)e we need a sa"et, "act!% N27

(%!#e) de"initi!n= we need (a##!wa#e2 #"

4!% sa"et, N27 wi## the ch!sen design ha*e ade3uate

uc-#ing st%ength?

Plan



Plan=

C!)'ute the s#ende%ness %ati! and decide i" the c!nnect!% c!#u)n

Is 9#!ng: !% 9sh!%t: then a''#, eithe% Eu#e% !% J. J!hns!n t!

c!)'ute (c%&I" (c%1N2(c%172(a##!wa#e2 #" then the '%!'!sed si0e is K

!xecution=

.uc-#ing wi## !ccu% a!ut ,, i" we assu)e a 'inned'inned O!inta!ut !th a8es at each end&

Slenderness Ratio = 166.2



N!w e*a#uate the c%itica# s#ende%ness %ati!=

whe%e C2@ "!% 'inned'inned and S,27'si

"!% sa, A# 7@@ / a##!,



I" - d i h # d i i " h



I" we g! ac- and w%ite the s#ende%ness %ati! in te%)s !" the

/hic-ness we sh!u#d e a#e t! c!)'ute the thic-ness %e3d

4!% the #" ;N27< a##!wa#e #!ad %e3ui%e)ent&

N!w the c!nnect!% wi## sti## e 9#!ng: s! '#uggingEu#e%=

+e need (c%2@ #" ;ie s! that (c%17 2 #"<



E8a)'#e Sha"t (%!#e)

(%!#e) state)ent= /he d%i*e sha"t in the s-etch e#!w is )ade

!" )i#d stee# tue ;&: D 8 &F wa##< we#ded t! uni*e%sa#

O!int ,!-es and a s'#ined sha"t as sh!wn& It is d%i*en , an

engine de*e#!'ing 7 h' at 7 %') what is the st%ess in the

sha"t tue? I" the sha"t is c!nside%ed t! ha*e uni"!%) '%!'e%ties

end t! end what is the c%itica# s'eed !" the sha"t?



(#an= this is a t!%si!n '%!#e) with a h!##!w sha"t& /he st%ess

in the sha"t wi## e due t! shea%ing st%ess& +e wi## need t! a''#,

the "!%)u#a "!% shea% st%ess "!% a h!##!w sha"t& 4!% the c%itica#

s'eed 3uesti!n we a%e then dea#ing with a *i%ati!n issue$atwhat "%e3uenc, ;%')< wi## the sha"t e inc#ined t! g! int! a

%es!nant c!nditi!n$what d! we -n!w a!ut this? S'%ing %ate?

static de"#ecti!n? /he Ra,#eighRit0 "!%)u#a? Etc$since the

sha"t has !n#, dist%iuted )ass we c!u#d %ea- it int! seg)entsand a''#, the Ra,#eighRit0 ut that w!u#d e a #!t !" w!%-

gi*en !u% ti)e c!nst%aint$s! that is n!t #i-e#, what is

e8'ected$the si)'#est thing we can s! d! is c!)'ute the )a8

static de"#ecti!n and use that t! c!)'ute the a''%!8i)ate

"%e3uenc,&

N!te= Ra,#eighRit0 sa,s=

/he "i%st c%itica# "%e3 ;%')< 2 @F&

S!#uti!n e8ecuti!n=



+he%e J is the (!#a% M!)ent "!% A H!##!w Sha"t

/ 2 /!%3ue

C 2 Radius t! ute%)!st 4ie%

4!% H!##!w Sha"t

S!#uti!n e8ecuti!n=

St%ess in the sha"t due t! t!%si!na# shea%ing st%ess



A((ENDIT



S!)e Enginee%ing .asics

DESIGN ENGINEERING Calculation REF

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