report group b

8/18/2019 Report Group b

1/21

University of Puerto Rico

Mayagüez Campus

INME 4011 Machine Component esign 1! "00#$I

Prosthesis evice %&'e(e) *oe Part+

,orge Coru-o .an)/n %0"$0"$11#+

&rancisco *orres %0"$02$4#2+

Irvin )e 'a Paz %0"$02$1303+

,avier Cruz %0"$00$1#03+

epartment of Mechanica' Engineering

University of Puerto Rico at Mayagüez

May #! "00#


2/21

Objective

*he pro-ect out'ine is to )esign an) ana'yses 'oa)s an) stress

concentrations for the f'e(e) toe part of the prosthesis of *ony o'pentest5 6t the

same time thin7ing in properties of materia's! )esign an) safety5


3/21

Description

*he pro-ect consists of an e(isting )esign invo'ving a prosthetic )evice

a'rea)y in use 8y runners 'i7e *ony o'pentest5 *he goa' of our team is to rethin7

an) if possi8'e improve upon the current )esign5 If no su8stantia' ne9 )esign can

8e foun) 9e 9i'' concentrate our pro-ect on the e(isting )esign an) ho9 the

com8ine 'oa)s affect it as 9e'' as 9hat materia' it shou') 8e in or)er to fu'fi'' its

engineering an) economica' )eman)s an) specifications5 *he entire pro-ect %the

9ho'e prosthesis+ consist of various part 8ut on'y one 9i'' 8e consi)ere) for the

fu'' in )epth )esign5 6s e(presse) 8efore 9e 9i'' concentrate on the f'e(e) toe

part5 *he focus of our )esign 9ou') 8e 8ase) on the stan)ar)s a'rea)y esta8'ish

to create) a )evice that 9i'' 8e use un)er the )iverse 'oa)s5 :ecause 9e are

)esigning prosthesis for use in sport! it 9i'' 8e su8-ecte) to heavy a ;uic7

changing 'oa)s! thus 9e nee) to choose a materia' 9hich 9ou') 8e )ura8'e an)

can resist fatigue5 *he other important )etai' 9hen choosing a materia' for

)esigning sport prosthesis is the 9eigh! this nee)s to 8e strong an) f'e(i8'e 8ut

as 'ight as possi8'e5

6s mention! the f'e(e) toe 9i'' 8e su8-ecte) to com8ine 'oa)s5 .ome of these!

9hich 9e are e(pecting to fin) )uring our ana'ysis %8ut not 'imite) to on'y these+!

9i'' 8e< :en)ing! sheer an) norma' compressive in the region 9here the soc7et

meets the f'e(e) toe5 6'so there shou') 8e sheer an) norma' compressive forces

at the 8ottom of the toe %9here the feet=s toes shou') 8e+5 *his 9ou') 8e cause


4/21

8y the in)ivi)ua'=s 9eight an) friction 9ith the f'oor5 >e are current'y not

e(pecting any mayor torsion force! since our

Pre'iminary ana'ysis sho9s that for torsion to act it 9ou') re;uire for part of the

f'e(e) toe to someho9 -am %get stuc7+ an) for the in)ivi)ua' to fa'' to his?her si)e5


5/21

Design Details

*he )esign process first consiste) in generating enough information! so

9e cou') have a so'i) 8ase of )ata to se'ect the appropriate materia'5 .evera'

consi)eration 9ere ta7en into count! in our )esign the important aspects 9ere

9eight an) the a8i'ity of the materia' to 8e f'e(i8'e 8ut sti'' 8e strong enough to

resiste) the a'ternating 'oa)s5 *he re'ationship of )ensity 9ith respect to tensi'e

stress 9as the ma-or criteria5 Using this has a )eparture point 9e 9ere a8'e to

come up 9ith an) e;uation to minimize mass 8y re)ucing this re'ation5

ρ σ

ρ ρ ρ ρ L F

Lr r bbhL ALVol m y

=−==== )()( 12

y

y

F A

A

F

σ σ =→=

y FLm σ

ρ

=

>here & is the ma(imum forces app'y at the 8eam an) @ is the 'ength5

*his t9o are assume) constant for the purpose of this ana'ysis5 *he va'ue of the

force 9as A00 '85 an) @ 9as chosen to 8e 13 in5 In the case of the other t9o

varia8'es a )ifferent approach 9as ta7en! first it consists of presuming a

minimum va'ue of tensi'e stress 9hich 9as "3500 psi5 >ith the use of a graph of

strength$)ensity! a range of materia's 9ere se'ecte)5


6/21

6t the en) 9e finish 9ith four materia's for 9hich 9e after choose the

8est that 9i'' fit our necessities5 *he four materia's are a se'ecting of a

thermop'astic! titanium a''oy! nic7e' a''oy an) a .RCR A1005 6 thermop'astic is a

7in) of materia' that is a8'e to 8e )eforming p'astica''y! it 8ecomes more 8ritt'e at

'o9er temperatures! 8ut it has a great strength against fatigue5 6 titanium a''oy

Beutche *itan *i7rutan R* 1 P) @o9$6''oye) *itanium! titanium is a materia'

that has a high D. va'ue! 8ut it has a higher )ensity va'ue than other materia'

9ith simi'ar properties5 *itanium is use in many aircraft app'ications an) engines!

a'so for part that 9ou') 8e in constant use an) e(pose to corrosion5 6 nic7e' a''oy

N04400 it has a high va'ue of D.! 8ut it is a heavy materia'5 *he 'ast materia' isnt


7/21

that common an) not that much information 9as o8taine) a8out it5 6 ta8'e 9ith

the )ensity an) D. va'e are sho9n ne(t5

*a8'e 1F ensity! Die') an) Mass of materia's

Materia' ensity%'8?inG2+ HDie')H %psi+ Mass %'8+*hermop'astic 05043 2A!000500 0504#*itanium a''oy 051A20 4A!400500 15"3N04400 Nic7e' 052130 2!000500 2524#

.RCR A100 050#41 2"!000500 0500

>ith the respecte) va'ues of )ensity an) D. mass 9as ca'cu'ate) for the

)esign part! resu'ts that any of the three materia's 9ou') 9or7e)5 .ti'' *itanium

9as se'ecte) 8ecause it has a 'o9 mass an) the highest va'ue of D.5 *his gives

us the a)vantages to )esign the prosthetic 'eg to resist higher 'oa)s5 It has to 8e

mentione) that in our se'ecting of the materia' the cost of the materia' is not 8een

a))e) to the parameters of the )esign5

nce the materia' is se'ecte)! the ne(t step is to ana'yses the )ifferent

'oa)s that are app'ie)5 &or the purpose of this part on'y the 8en)ing moment 9as

ta7en to account 8ecause the part is more 'i7e'y to fai' 8y stress than shear5 *he

on'y effect the shear force 9i'' have is to create a force that 9ou') 8e counte) as

the force of friction5 *his force is neg'ecte) 8ecause in comparison the magnitu)e

is sma''er than the one of 8en)ing5 *he 'ocation of this force is app'ying para''e'

to the curve 8eam5 *he force 9as assume) to 8e "00 '8

In tension an) $A00 '8 in compression! the respect moments! stress an) on

Misses stress are sho9n 8e'o95

*a8'e "F &orces! moments an) on Misses stresses


8/21

Ma(imum &orce

%'8+

Minimum &orce

%'8+

6mp'itu)e &orce

%'8+

Mean &orce

%'8+"00 $A00 400 $"00

Moment 6mp5

%'8$in+

Moment Mean

%'8$in+

.tress of 6mp5

%psi+

.tress Mean

%psi+1000 $00 $11!1"05#3 !A0523

on Misses 6mp5

%psi+

on Misses Mean

%psi+

@ength

%in5+1"!"2"5# A!11A542 13

*he negative va'ue of the stress of amp'itu)e ref'ects that the force is in

compression5 >ith the va'ues of the on Misses stresses an) the va'ues of .e

an) .ut the safety factor can 8e o8taine) 9ith the Jo)man e;uation5 *he va'ue

of .e is ca'cu'ate) first 8y )etermine 9hat 7ing of materia' is after a conversion

factor is app'ie) to minimize it 8y ha'f5 6fter this process the ne9 va'ue of .e is

o8taine)! sti'' this one is not correct the va'ues of the )ifferent 7s 9ere

ca'cu'ate)5

*a8'e 2F Ks! .ecorrecte) an) .afety &actor

7 %'oa)+ 7 %temp+ 7 %size+ 7 %surf+1 1 051" 0531

7 %re'ia8i'ity+ .e %not correcte)+ .e %correcte)+ .afety factor 05#0" 4"!00500 "A!1A151" 15A


9/21

86.11

=

+

=

ut

m

e

a

S S

nσ σ

*he va'ue o8taine) is 15A 9hich is a perfect va'ue to )esign 9ith5 *his

8ecomes c'ear after rea'izing the part 9as ma)e to have an) infinite 'ive of more

than 1(10GA cyc'es5 :y o8taining a safety factor for the pro-ect! the materia'

se'ecte) 9as a titanium a''oy5

.tatic 6na'ysis


10/21

Fig 1.0 Reactions of our Specimen

&or our materia'

=>−==∑ θ cos0 F F F fr x LN&cos

)

M&)

F

N

&fr

LN


11/21

θ θ sinsin0 F mg F N F y −=−==∑

>e assume)F &ma( $A00'8! #51O an) g2"5"ft?s"

*his means thatF

N & sin #51 #3 '8

&fr &cos #51 $14'8

No9 8ecause 9e can assume this is one ;uarter circ'e thus 9e can assume the

greatest momentum an) 8en)ing 9i'' occur 9hen the p'ane of the circ'e is at 4O

)egrees %see figure 2)5

Fig 2.0 Internal forces

*o ca'cu'ate moment 9e have that M&) 8ut 8ecause it is easier to convert N

an) &r in magnitu)e! magnitu)e is lb Fr N F 600154579 2222 =+=+= at #51

)egrees5 *he )istance is "5 then moment is "5A001005

.hear force is given 8y static e;uationF

13515445cos013545cos NormalCosV NormalCos Fr V F x −−==−+=∑

135sin57945sin0135sin45sin Normal V Normal N V F y ++==++=∑

.o'ving the previous t9o e;uations for an) Norma' 9e have

$5"'8

Norma'$1254 '8


12/21

No9 app'ying e;uation for curve 9e have

psi

Rr Ar

r R M bending 3937

)71.77.7(95.7*12.1

)95.771.7(1500

)(

)(=

−

−=

−

−=σ

psi A

Normal axial 726

12.1

54.813===σ

psibending axial x 46633937726 =+=+= σ σ σ

:ecause 9e have a rectangu'ar cross section the shear simp'ify 9i'' 8e

psi A

V 07.7

12.1*2

28.5*3

2

3===τ

*his means shear has no noticea8'e effect on our static 'oa)ing5

No9 ca'cu'ating principa' stresses 9ith matri( 9e have

0

00

0007.7

007.74663

=

−

−

−+

σ

σ

σ

>e have that psi0107.01 =σ an) psi46632 −=σ

.hear ma( 9i'' 8e

R psi xy y x

51.233107.72

04663

2

2

2

2

2

=+

−=+

−τ

σ σ

Figure 3.0 Mohr )iagram

ca'cu'ate) for force of $A00'8


13/21

Figure 4.0 P'ane .tress )iagram for .tatic force of A00 poun)s in compression5

Deflection of urve! "eams

&or our particu'ar materia' the cha''enge is )eve'op a formu'a for a curve)

8eam5 *he app'ication of the f'e(ure formu'a for a straight 8eam resu'ts in error5

>hen a'' Bfi8ers of a mem8er have the same center of curvature the concentric

or common type curve) 8eam e(ists5 .uch a 8eam fortunate'y is )efine) 8y


14/21

>in7'er Q :ach theory5 6'so )ef'ections can 8e foun) 8y use of Castig'ianos

theorem5 In our case 9e use) the moment area theory given 8y e;uations 15"5

∫ =∆

g

EI

Myds x

0 ∫ =∆

g

EI

Mxds y

0

%15"+

It is important for our materia' that the )ef'ection not is to 'itt'e or too much

8ecause the materia's have to a8sor8 energy an) re'ease energy5 >e assume)

that our f'e( toe 9as a fourth of a circ'e for simp'icity purposes5 6 program in

e(ce' 9as ma)e for faster ca'cu'ations5 *he )erivation of the formu'a is sho9e)

8e'o9 in fig 50

Fig.#.0 &'e( *oe i)ea'ization

in EI

R R F inout B 3241.0

41

009.0*15200000*2

]49.795.7[600

41

2

][ 233233−=+−−=+−=

π π

Discussion

>ith the changes on the materia's that 9e assume! 9e hope to 8ui') more

'ong 'asting an) re'ia8'e prosthesis5 *his is 9ithout comparing 9ith other

companies an) 9ithout ta7ing in consi)erations the cost5 *he finish 'ine 9as to


15/21

8ui') the 8est part for the prosthesis that 9e cou') )esign! -ust ta7ing in

consi)eration the mechanica' properties of the )esign an) materia's avai'a8'e5

&irst 9e ta7e in consi)eration -ust one critica' point 8ecause the secon) critica'

point is )eprecia8'e in comparison5 *his 'et us change the materia' an) 'oo7 for

other properties for a 8etter )esign5 Changing the materia' to titanium a''oy 9e

can ma7e a stronger prosthesis an) more re'ia8'e significant'y increasing the

safety factor5 *he properties of the titanium ma7e the prosthesis a 'ong 'asting

one since it 9as )esign 9ith infinite 'ife in min)5 .o far the on'y tra)e off has

8een in cost5 >ith this 9e can assure the c'ient that his prosthesis isnt going to

8ra7e 9hi'e he is using it5 ne of the )isa)vantage against this )esign is that it

might 9eight a s'ight'y more than the commercia''y avai'a8'e! composite ma)e

prosthesis5 It a'so 9ou') cost significant'y more 8ecause titanium materia' isnt

cheap! this can 8e seen 9hen 9e compare the titanium cost 9ith the composite

cost5

.ome of the merits that have our )esign areF

• Resisti8'e to corrosion


16/21

• @ight 9eight

• .imp'e an) very user frien)'y for users

• Mu'tipurpose

• >i)e range of customer app'ications

.ome suggestions to ma7e 8etter our )esign are fin) cheaper materia's that

are 7no9n 8ut 9e )ont have the properties5 6'so 9ith these materia's 9e can

ma7e the prosthesis more 'ight 9eight for the runner5 Main pro8'ems of our

)esign are the cost an) the via8i'ity of the prosthesis 8ecause is har) to fa8ricate

an) to 8uy5


17/21

onclusions

*hru this 9ho'e process 9e 9here e(pose to a series of ne9 concepts 9e

9here not accustome) to use5 In particu'ar the mechanics of 9or7ing 9ith

curve) 8eams! this is )ue since the 9ho'e part in essence is simp'y a curve)

8eam5 nce the 9ho'e mechanics 9here un)erstoo) 9e 9here a8'e to )ive into

the 9ho'e process of materia' se'ection5 *his process prove) to 8e a cha''enging

one! since it re;uire) a materia' 9ith e(ceptiona' high strength yet a )ensity 'o9

enough so that the runner )i)nt fee' he 9as running 9ith cement 8'oc7 attache)

to his 'egs5 *his 'e) us to appreciate ho9 far materia' sciences have a)vance) in

the 'ast 20 years5

Materia' se'ection 9as 9ithout a )ou8t the toughest part as a 9ho'e!

fo''o9e) c'ose'y 8y the )ynamic ana'ysis< one is )irect'y affecte) 8y the other5

*his 9as emphasize) 8y the fact that the materia's 9e 9here 9or7ing 9ith such

a titanium! car8on fi8er! an) other strong u'tra 'ight materia's 9e arent use) to

)ea'ing 9ith5 *hru tria' an error 9e 9here a8'e to esta8'ish a 'ist of fina'ists out of

9hich 9e fina''y ma)e our )ecision! an a''oy of titanium )iscovere) thru our

search in the 9995mat9e85com )ata8ase5 6'though in rea'ity an) practica'ity this

a''oy is very 'i7e'y to e(pensive for the )esign! a 'ac7 of re'ia8'e an) comp'ete

information foun) a8out ne9er an) stronger po'ymers an) thermop'astics ma)e

us choose sai) a''oy5

&ina''y 9e o8tain a )esign capa8'e of 8eing uti'ize) 8y an up to "00 poun)

person! 9ith a safety factor of n 15A yet sti'' en-oying a remar7a8'y 'ight )esign5

http://www.matweb.com/http://www.matweb.com/


18/21

$ppen!i%

Joverning E;uations

θ sin][ inout R R y −= ]cos1][[ θ −−= inout R R x

θ d R Rds inout ][ −= θ sin][ inout R R F M −=

∫ −

=−

=∆2

0

33

2

33

4

][sin

][

π

π θ

EI

R R F

EI

R R F inout inout x B

EI

R R F

EI

d

EI

R R F inout inout B

2

][

4

)cos1[sinsin

][ 332

0

2

33 −−=

−=

−=∆ ∫

π

θ θ θ θ

in EI

R R F inout B 3241.0

41

009.0*15200000*2

]49.795.7[600

41

2

][ 233233

−=+−−

=+−

= π π


19/21


20/21

Radio Interno (in.) Radio Externo (in.) Ancho (in.) Altura (in.)

7.49 7.95 2.5 0.46

Area Seccional (in.^2) Ditancia (in.) An!ulo (!rado) "ar!o (in.)

#.#5 2.5 75 #9

r ($arra) (in.) R r (in.) S (ut) (%i)

7.720 7.7#& 7.950 &5600

'uera axi*a (l$) 'uera ini*a (l$) 'uera A*%litud (l$) 'uera ean (l$

200 +600 400 +200

o*ento A*%. (l$+in) o*ento ean (l$+in) E,uero de A*%. (%i) E,uero ean (%

#000 +500 +##-#20.79 5-560.9

/on ie A*%. (%i) /on ie ean (%i) "ar!o (in.) ,#2-22.&7 6-##6.4 #9 #.#

1 (load) 1 (te*%) 1 (ie) 1 (ur,)

# # 0.& 0.9&

1 (relia$ilit) Se (no corre!ido) Se (corre!ido) 'actor de Se!urid

0.702 42-&00.00 26-#6#.#2 #.&6

aterial Denidad (l$3in^) ield (%i) aa (l$)

er*o%latico 0.0495 6-000.00 0.5047itaniu* allo 0.#60 46-400.00 #.2&95

04400 ic1el 0.#90 5-000.00 .457

SR8R 6#00 0.074# 2-000.00 0.&500


21/21

@in7s use) in the pro-ectF

13 *he .eatt'e &oothttpF??99959ashington5e)u?research?path8rea7ers?13a5htm'

:en)ing of Canti'ever :eamhttpF??)ocuments59o'fram5com?app'ications?structura'?:en)ingofCanti'ever:eams5htm'

Comparison of the .eatt'e @ite &oot an) Jenesis II Prosthetic &oot )uring9a'7ing an) runninghttpF??9995oan)p5org?-po?'i8rary?"000010035asp

e'rin Materia'httpF??en59i7ipe)ia5org?9i7i?e'rin

Is the Use of 6)vance) Materia's in .ports E;uipment Unethica'ShttpF??9995tms5org?pu8s?-ourna's?,M?3#0"?&roes$3#0"5htm'

*ony o'pentesthttpF??encarta5msn5com?me)ia4A1030##A1A"1"2$11?*onyo'pentest5htm'

*ransti8ia' prosthesishttpF??en59i7ipe)ia5org?9i7i?*ransti8ia'prosthesis
http://www.washington.edu/research/pathbreakers/1985a.htmlhttp://documents.wolfram.com/applications/structural/BendingofCantileverBeams.htmlhttp://documents.wolfram.com/applications/structural/BendingofCantileverBeams.htmlhttp://www.oandp.org/jpo/library/2000_01_009.asphttp://en.wikipedia.org/wiki/Delrinhttp://www.tms.org/pubs/journals/JOM/9702/Froes-9702.htmlhttp://encarta.msn.com/media_461550907_761562123_-1_1/Tony_Volpentest.htmlhttp://encarta.msn.com/media_461550907_761562123_-1_1/Tony_Volpentest.htmlhttp://en.wikipedia.org/wiki/Transtibial_prosthesishttp://www.washington.edu/research/pathbreakers/1985a.htmlhttp://documents.wolfram.com/applications/structural/BendingofCantileverBeams.htmlhttp://documents.wolfram.com/applications/structural/BendingofCantileverBeams.htmlhttp://www.oandp.org/jpo/library/2000_01_009.asphttp://en.wikipedia.org/wiki/Delrinhttp://www.tms.org/pubs/journals/JOM/9702/Froes-9702.htmlhttp://encarta.msn.com/media_461550907_761562123_-1_1/Tony_Volpentest.htmlhttp://encarta.msn.com/media_461550907_761562123_-1_1/Tony_Volpentest.htmlhttp://en.wikipedia.org/wiki/Transtibial_prosthesis

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