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8/18/2019 Report Report Groupe

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University of Puerto Rico

Mayagüez Campus

Department of Mechanical Engineering

Machine Component Design 1, 2!"#

#$ME %11

Shaft Design for Transmission Application

#rmy&el 'ugo (elaz)uez

*%+"+"+*1

(ictor Molina (argas

*2"2"%2*

Ela&io Pereira -roche

*%+""

May *, 2!


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Objective

Design a shaft that transmits % .P /ith a fluctuating rotation of 1 to + RPM0 -his shaft

/ill e &esigne& for an infinite live /ith a safety factor0 ther re)uirements of the &esign are

minimize the /eight of the shaft an& appropriate material selection0


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Description

Design a shaft that /ill e use& in some type of transmission application0 -his shaft is use& to

transmit a ma3imum amount of po/er of % hp at + rpm0 -his element is su4ecte& to forces

applie& /hen the gears it5s rotating0 6e have a restriction of length of 2 ft an& a minimal

thic7ness of 02 inches0 8nother important aspect of this &esign is that /e nee& choose a

material that hol&s all the stresses applie& to it an& must have a very high safety factor to assure

that the shaft /ill have infinite life0 -he material in a&&ition must e as light /eight as possile

an& &urale, en&ure other types of fatigue, although our &esign /ill ta7e into consi&eration the

critical points of the shaft an& optimize them0

-he &ata given in this &esign sumits the shaft to fluctuating stresses0 -he main i&ea is for the

shaft to /ithstan& the change in loa&s, for e3ample, rising from 1 to + RPM an& ac7

again0 -he follo/ing figure is a &escription of the shaft that /e must &esign0


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Design Details

• 9irst /e calculate the tor)ue applie& to the shaft at + RPM:

• $o/ /e calculate the force &ue to the tor)ue:

• 9or the ne3t step, /e ma&e a &iagram sho/ ho/ the forces are applie& at the point

of the spur gear, /e assume the angle of attac7 for the teeth of the spur gear is

2;:

• Diagrams:o


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o


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o ?tresses taine&:


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• Moment of #nertia for each &iameter:

• 9irst Moment of 8rea:

• ?tresses:

o ?ection /ith &iameter of 2 in:


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o ?ection /ith &iameter of %0* in:

o ?ection /ith &iameter of @ in:


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• Principal ?tresses:

o ?ection /ith &iameter of 2 in:

o ?ection /ith &iameter of %0* in:

o ?ection /ith &iameter of @ in:

Material Selection:


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• Aoun&ary Con&itions:

o

o

• ?ustituting Constants:

o


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• $o/ /e &etermine the material in&ices that minimize the mass of the shaft, so it /ill e

as light as possile:

-o minimize the mass /e have to minimize the relation 0 ?o /e ma3imize the inverse to

fin& appropriate materials in the Elasticity mo&ulus"&ensity graph0 -he graph tells us that the


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est material is A%C, ut a ceramic is not recommen&ale ecause it5s a very rittle an& small

crac7s /ill propagate very fast0 8mongst the est materials to e use& are aluminum alloys,

titanium alloys an& steel0 8lso the ceramic an& caron fier alloys, ut &ue to the fact that the

forces an& stresses are so high, it is not recommen&ale to use them0 6ith the relation

mentione& efore /e otain that aluminum has the lo/est ratio /ith 10@* follo/e& y titanium

/ith 20! an& finally steel /ith 20*0 6e foun& some recommen& materials to e use& for this

applicationB /hich are the follo/ingB 8luminum 22%"-%, 12 ?teel an& Aeta -itanium 8lloy0

9or the fluctuating stresses /e start out /ith the follo/ing graph to sho/ 9orce vs RPMB

Deflection:


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-he ma3imum &eflection occurs at B /here a an& b are the &istances et/een the

applie& force an& the supports, /here b > a0 #n our &esign a is in an& b is 1 in0

8t this point the ma3imum &eflection is otaine& y the follo/ing e)uationB /here P is

1@*0@%l, # is 0!*2++ in% an& ' is 2* in0

6e otaine& the value of E for 8l"22% -"% E F 1@2 G?#H, 8?#"12 E F 2!+2 G?#H an& -i"

1Mo>r+8l I titanium alloyH E F 1*!* G?#H0

6e can compare these values an& fin& that the least proale to have &eflection is steel follo/e&

y titanium an& finally aluminum0


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Calculating Safety Factor:


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#n each of the previous tales, /hich /e &evelop in e3cel, /e can fin& all the calculations &one

to otain the safety factor for each material an& &ifferent point on the shaft0 -he safety factor

/as calculate& y ta7en into consi&eration that /e use infinite life as a goal of the &esign0 -he

highest safety factor /as otaine& y titanium, follo/e& y steel an& aluminum respectively0


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Discussion

8fter compiling all the &ata, from the initial &imensions to the safety factor for each in&ivi&ual

material, /e foun& that et/een zero an& 1 rpm the forces are so great &ue to the fact that they

ten& to infinity, /ith this it /oul& not transfer the % hp re)uire& y the &esign0 ?o /e &eci&e& to

evaluate the &esign /ith fluctuating stresses relating from 1 rpm to + rpm0 #n the material

selection /e otaine& various materials, ut ceramics an& caron fiers /ere &iscar&e& &ue to

the fact that they /oul& not /ithstan& the forces e3erte&0 -he remaining materials /ere analyze&

to re&uce /eight an& increase the safety factors0 ?teel is the est option, even though eing the

heaviest of the materialsB the reasons out/eigh the /eight re&uction0 9or e3ample, there is a ig

&ifference et/een the &eflection of the steel /as of0 2!+@ in, an& this is appro3imately +0

smaller times that that of titanium an& that of aluminum0 -his is a &eterminant factor for &esign

a shaft since helps to re&uce the fatigue an& otaining infinite life0 8lso cost comes into effect

ecause of the fact that oth the titanium an& aluminum consi&ere& are fairly e3pensive an& rare0

8 &isa&vantage that /e confronte& &esigning the shaft /as the constants changes in &iameters0

Aecause /e have no ra&ius to &eal /ith, it ecame a challenge0


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Conclusion

-he shaft that /e &esigne& /or7s for velocities et/een 1rpm to +rpm, generating a

constant po/er of % .P0 -his shaft /as &esigne& to minimize the /eight an& the cost of

manufacturing0 -o minimize the /eight /e selecte& &iameters that /ill give small cross sections

an&, that /ay, /e use less material0

ur main o4ective /as to ma7e a shaft that /ill have infinite life0 -o achieve that, /e searche&

for materials that resist &eflection, crac7s an& fatigue0 6e selecte& an& analyze& three

preliminary materials: an aluminum alloy, a titanium alloy an& a stainless steel0 ur est option

/as the steel 8#?# 12, since it fille& etter the re)uisites0 -his material gave the lo/est

possile &eflection of the shaft, in comparison /ith the other t/o materials analyze&0 -he safety

factors /ere 20%+ for one critical section, an& @0!* for the other critical section stu&ie&0 -hese

safety factors are goo& to ma7e the shaft useful for infinite life0 6e calculate& /ith the (on

Mises e)uivalentH, amplitu&e an& mean stresses of each section0 6e foun& on tales the fatigue

limit stress ?f H an& the ultimate stress ?utH of the materials, an& /ith these )uantities /e

calculate& the safety factor, using the Joo&man mo&el0


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Appendix


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