Post on 06-Jul-2018
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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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