DESIGN AND ANALY ANALYSIS OF DISC BRAKE ROTORS R OTORS A Major Major Project Report Submitted in partial fulfillment of the requirements for the Award Award of the degree of
BACHELOR OF TECHNOLOGY IN MECHANICAL ENGINEERING Submitted by ROHAN AR!H"# $$%$$A&%'(
Under the guidance of !Ra"iKanth
Dr!A!#uru$hotha%
STO& 'CAD(CA)
#rof! of ech!Engg
CI#ET& Cher*a+a**,&
SNIST& Ya%na%+et&
-,dera.ad!
-,dera.ad!
'E 'E/terna* Guide)
'Interna* Guide)
De+art%ent of echanica* Engineering Sreenidhi In$titute of Science and Techno*og, echno*og, 'An Autono%ou$ In$titution under 0a1ahar*a* Nehru Techno*og, echno*og, Uni"er$it, -,dera.ad) Ya%na%+et& Ghat2e$ar& R!R! Di$trict& -,dera.ad 3 456 756
1
Central Institute of Plastics Engineering & Technology echnology
Certifcate
This is to certify that Mr. Mr. Rohan Karthik Karthik bearing Roll No. 11311A0367 a bona de stdent of !reenidhi "nstitte of !cience and Technology# Technology# $hatkesar# %yderabad & Telangana Telangana has ndergone a 'ro(ect for a 'eriod of ) *onths fro* )1st +anary# )01, to )1st March# )01, in flll*ent of his -.Tech&Mechanical -.Tech&Mechanical ngineering sccessflly. sccessflly. /ring the 'ro(ect 'eriod# he as fond to be reglar# hardorking and diligent. The re'ort sb*itted by hi* is fond releant. 2e ish hi* all the ery best for his ftre endeaors. 2ith best regards
M.RaiKanth !T# 45A/5AM 5"8T# 5herla'ally# %yderabad. 49ternal $ide
CIDA Phase-II, Post Bag No. 3, Cherlapally, C! Post, y"era#a" $ % %'.
)
SREE NIDHI INSTITUTE OF SCIENCE AND TECHNOLOGY DEPAR DEPARTMENT TMENT OF MECHANICAL ENGINEERING
CERTIFICATE
This is to certify that the 'ro(ect re'ort on :/!"$N AN/ ANA;
/"!5
-RAK
RTR!”#
sb*itted
-y
Roha Ro han n
art arthi hi! !
"##$##A%$&'( "##$##A%$&'()) is a bona de ork that has been carried ot by the* as 'art of their Pro*ect +,rin- B.Tech "Mechanica/( Fo,rth Year Year Secon+ Se0e1ter# Se0e1ter # nder or gidance. This re'ort has not been sb*itted to any other institte or niersity for the aard of any degree.
INTERNAL INTERN AL GUIDE2
Dr. Dr. T. CH. SI3A
REDDY 8rofessor 8rofessor > %ead of the /e'art*ent# /e't /e't.. of Mechanical ngineering
!N"!T
E4TERNAL E4AMINER2
3
ACKNO8LEDGEENT !his project report is the outcome of the efforts of many people) who ha*e dri*en our passion to e+plore into ,oncept and -esign regarding our project. /e ha*e ha*e recei*ed great guidance) encouragement and support from them and ha*e learned a lot because of their willingness to share their 0nowledge and e+perience. Primarily) we should e+press our deepest sense of gratitude to our e+ternal guide Mr. Sri !Ra"i2anth 'S!T!O& CAD(CA) . His guidance has been of immense help in surmounting *arious hurdles along the path of our goal. /e are are deep deeply ly inde indebt bted ed to Dr!T! Profes esso sorr 1 Head Head of Dr!T!Ch!Shi"a Ch!Shi"a Redd,) Prof -epartment of Mech. 2ngg) and Dr! A! #uru$hotha%& Professor & & "nternal guide who spared his most *aluable time without any hesitation whene*er we wanted. /e record with a great feeling of gratitude) the contributions of all the faculty members members)) Princi Principal pal and managem management ent who encour encourage aged d us during during this this project project by rendering their help when needed. 3inally we than0 our parents and adore Almighty 4od who has made us come in contact with such worthy people at the right time) pro*ided us with all the necessary resources and made us accomplish this tas0.
ROHAN AR!H"# $$%$$A&%'(
?
ABSTRACT
!he !he main main obj objec ecti* ti*ee of the the project is to design of bi0e5s disc rotors and analy an aly6e 6e th thee str struc uctu tural ral pe perfo rform rman ance ce by us usin ing g fin finit itee el eleme ement nt me meth thod od 7A 7ANS NS8S 8S Software9. -isc bra0e technology used for bi0es has impro*ed significantly as high performance is most desirable now days. Rotor design is *aries from company to company. Some companies still use the same initial rotor designs that were introduced o*er a decade ago. /ith the finite element analysis and optimi6ation process) it is possible to understand the difficulties of designing disc bra0e rotors. /ith ,A- technology the *alidity of new design tends is pursued quic0ly. More specifically specifically) the proje project ct deals with analysis of three different different disc rotor rotorss that is a*ailable on commercial two wheelers. !he 32A analysis determines) the stresses de*eloped in three different disc rotors. !hen the structural performance of all three selected rotors is compared in terms stresses de*eloped.
,
CONTENTS Tit*e$
#age! No
Ac0nowledgement
7
Abstract
9
:ist of figures
:
:ist of tables
;
Nomenclature
65
,hapter $;"ntroduction
66
$.$
"ntroduction
66
$.<
=ra0ing Requirements
66
$.%
,lassification of =ra0es
6<
$.>
-isc =ra0e
6<
$.?
Principle
6<
$.'
Main ,omponents
67
$.(
Applications Of -isc =ra0e
69
$.@
Assumptions
69
,hapter <;Problem Statement 1 Methodology
64
<.$
Problem Statement
64
<.<
Methodology
6=
,hapter %;-esign Parameters of -isc =ra0e
6:
%.$
Steel
6:
%.<
Specifications of Steel
6:
%.%
-imensions of -isc =ra0e
6:
%.>
2ngine Specifications
6> 6
%.?
3orce ,alculation
6>
,hapter >; %- Modeling of Rotor -isc in Pro#2
<6
>.$
"ntroduction
<6
>.<
History
<6
>.%
ey 3eatures 1 =enefits
<<
>.>
Main modules
<<
>.?
3low process in Pro#2
<7
>.'
Sequential steps followed for building rotor disc in pro#e
<9
,hapter ?;3inite 2lement Analysis of Rotor -isc /ith ANS8S
75
?.$
"ntroduction
75
?.<
2ngineering Applications of 3inite 2lement Method732M9
75
?.%
arious Applications of 32M
76
?.>
Ad*antages of 32M
76
?.?
-isad*antages of 32M
76
?.'
Procedure for ANS8S Analysis
7<
?.'.$ =uild the model
7<
?.'.< Material Properties
7<
?.'.% Solution
7<
".
Pre#Processor
77
Solution
74
Post Processing
7=
Structural Analysis in ANS8S
7=
"". """. ?.(
,hapter '; Results 1 -iscussions
46
,hapter (; ,onclusions 1 3uture scope of studies
4<
7
References
47
LIST OF FIGURES Fig! No
De$cri+tion
#age! No
$.$
-isc =ra0e Rotor
66
$.<
-isc =ra0e Assembly
66
$.%
arious Parts of -isc =ra0e
67
<.$
3ig<.$; -isc Rotor $ 7old model9
64
<.<
3ig<.<; -isc Rotor < 7proposed model9
64
<.%
3ig<.%; -isc Rotor % 7proposed model9
64
>.$
Rotor -isc 3low ,hart
<7
>.<
Sequential steps followed for building rotor disc in Pro#2) step $
<9
>.%
Step <
<9
>.>
Step %
<4
>.?
Step >
<4
>.'
Step ?
<=
>.(
Step '
<=
>.@
Step (
<:
>.B
Step @
<:
>.$&
pro#e model of rotor disc $
<>
>.$$
pro#e model of rotor disc <
<>
>.$<
pro#e model of rotor disc %
<;
?.$
"mporting model
7:
?.<
2lement selection
7:
?.%
Material type selection
7>
?.>
Meshing
7> @
?.?
Appling load
7;
?.'
-eformed C un deformed
7;
?.(
-isplacement *ector sum
95
?.@
-of in D#direction
95
?.B
-of in 8#direction
96
?.$&
Stress in D#direction
96
?.$$
Stress in 8#direction
9<
?.$<
ector plot
9<
?.
%$on Mises stress
97
?.$>
-"S, RO!OR#<;
97
?.$?
-eformed C un deformed -isplacement *ector sum
99
?.$'
Stress in D#direction
99
?.$(
Stress in 8#direction
94
?.$@
Stress in E#direction
94
?.$B
ector plot
9=
?.<&
on Mises stress
9=
?.<$
-"S, RO!OR#%;
9:
?.<<
-eformed C un deformed -isplacement *ector sum
9:
?.<%
Stress in D#direction
9>
?.<>
Stress in 8#direction
9>
?.
Stress in E#direction
9;
?.<'
ector plot
9;
?.<(
on Mises stress
45
LIST OF TABLES Ta.*e no
De$cri+tion
#age! No
?.$
-escription of Steps followed in 2ach phase
77
'.$
Results
46
10
NOENCLATURE
Symbol 2 P : I J L
B h / / b Mt * " 0 m
-escription 8oung5s modulus 7NFmmG9 load 7N9 -isplacement 7mm9 ,oefficient of friction Poisson5s ratio -ensity 7gFmK9 Angular *elocity 7radFsec9 Angle 7radians9 /heel height 7m9 /eight of the *ehicle 70gs9 /heel base 7m9 !orque 7N#m9 Ma+imum *elocity of *ehicle 7mFsec9 Moment of inertia 70g# m<9 Radius of gyration 7m<9 Mass of disc rotor 70g9
C-A#TER 6 INTRODUCTION
6!6 INTRODUCTION
11
A bra0e is an instrument or equipment that ma0es use of artificial frictional resistance to stop the motion of a mo*ing member. /hile performing this function) the bra0es imbibe potential energy or 0inetic energy of the mo*ing member. !he energy that is absorbed by the bra0es is dissipated in the form of heat. !he dissipated heat is in turn liberated into the surrounding atmosphere.
3ig $.$ -isc =ra0e Rotor
3ig $.< -isc =ra0e Assembli e$
6!< BRAKING RE?UIREENTS@
=ra0es of a *ehicle should be strong enough to stop the *ehicle in a minimum time 1 distance.
/hile bra0ing the dri*er should ha*e good control o*er the *ehicle i.e. the *ehicle should not s0id.
=ra0es should be a good anti wear resistant.
=ra0es should ha*e good anti fade characteristics.
1)
6!7 CLASSIFICATION OF BRAKES@
=ased on mode of operation bra0es are classified as follows;
Hydraulic =ra0es.
2lectrical =ra0es.
Mechanical =ra0es.
!he mechanical bra0es according to the direction of acting force may be sub di*ided into the following two groups;
Radial =ra0es
A+ial =ra0es.
Radial =ra0es. "n these bra0es the force acting on bra0e drum is in radial direction for Radial bra0es. !hese bra0es are of two types; "nternal =ra0es and e+ternal bra0es A+ial =ra0es. "n these bra0es the force acting on the bra0e drum is in a+ial direction for a+ial bra0es.
6!9 DISC BRAKE@ A disc bra0e is a de*ice) composed of cast iron or ceramic composites that are connected to the wheel hub or a+le and a caliper. "n order to stop the wheel hub) friction material is automatically or hydraulically forced on both sides of the bra0e in the form of bra0e pads. !his friction in turn originates the wheel hub and the disc to slow down and stop. -ifferent *iews of -isc =ra0e Rotor are shown in the figure $7a9 and $7b9.
6!4 #RINCI#LE@ -isc bra0e is a *ery essential bra0e application de*ice in a *ehicle. !his part of the bra0e helps in the slowing and stopping the motion of the *ehicle. !he principle of
13
disc bra0e is to produce a bra0ing force on the bra0e pads which in turn compresses the rotating disc.
6!= AIN CO#ONENTS OF A DISC BRAKE ;
Rotor
=ra0e Pads
,aliper
3ig$.% *arious parts of disc bra0e
Rotor; !he disc rotor is connected to the wheel and it rotates with respect to the wheel. /hen bra0es are applied) the bra0e pads come in contact with the rotor in order to stop or slow down the *ehicle.
Bra2e +ad$; =ra0e pads are present in the disc which scrapes against the disc that rotates with the wheel hub and creates high friction.
Ca*i+er; A caliper is a motionless housing which is clipped to the frame of a *ehicle containing a piston. !his piston forces the pads onto the rotor in order to stop or slow down the *ehicle. "n order to bring the *ehicle to a slow or stop position) the dri*er applies pressure on the bra0e pedal which acti*ates the caliper that in turn compresses the bra0e pads against the disc rotor. !he Rotor is then connected to the wheel which halts
1?
the *ehicle. /hen the bra0es are applied the 0inetic energy of the mo*ing *ehicle is con*erted into heat and dissipated into the surrounding atmosphere.
6!: A##LICATIONS OF DISC BRAKES
,ars
Motorcycles
=icycles
6!> ASSU#TIONS
=ra0es are applied on two wheels.
!hic0ness of %.?mm is considered for all the models.
Only ambient cooling is considered for dissipation of heat.
!his analysis does not determine the life of the disc bra0e
!he disc bra0e model used is of solid type.
!he thermal conducti*ity of the material is uniform throughout.
!he specific heat of the material is constant throughout and does not change with the temperature.
!he 0inetic energy of the *ehicle is lost through disc bra0es i.e. there is no heat loss between the tire and the road side.
1,
C-A#TER < #ROBLE STATEENT ET-ODOLOGY
16
=ig).1C /isc Rotor 1 4old *odel
=ig).)C /isc Rotor
) 4'ro'osed *odel
=ig).3C /isc Rotor 3 4'ro'osed *odel
!he objecti*e of the problem is to adopt proposed models by pro*ing minimum on Mises stress compared to old model.
sing the standard dimensions of rotor discs) %- model is de*eloped using Pro#2.
2+porting Pro#2 model on to ANS8S) finite element model is de*eloped.
=ra0ing load is calculated with road conditions and speed of the *ehicle.
Minimum on Mises stress is e+tracted after applying boundary conditions and bra0ing load.
A table is drawn comparing stresses and deformations in each disc rotor.
Among the three discs) the on Mises stresses found minimum is considered structurally good performance.
17
C-A#TER 7 DESIGN #ARAETERS OF DISC BRAKE
7!6 STEEL@ Steel is an alloy of iron) with carbon) which may contribute up to <.$ of its weight. ,arbon) other elements) and inclusions with in iron act as hardening agents that pre*ents the mo*ement of dislocations that naturally e+ist in the iron atom crystal lattices. arying the amount of alloying elements) their form in the steel either as solute elements) or as precipitated phases) retards the mo*ement of those dislocations that ma0e iron so ductile and so wea0) and so it controls qualities such as the hardness) ductility) and tensile strength of the resulting steel. Steel can be made stronger than pure iron) but only by trading away ductility) of which iron has an
1@
e+cess.
7!< S#ECIFICATIONS OF ATERIAL Mechanical properties of structural steel that are important to the designer include; Modulus of elasticity) 2 <$&)&&& NFmmG Shear modulus) 4 2F<7$ C I9Q NFmmG) often ta0en as @$)&&& NFmmG Poissons ratio) I &.% ,oefficient of thermal e+pansion) $< + $&#'FT, 7in the ambient temperature range9. -ensity @.&?gFcm%.
7!7 DIENSIONS OF DISC BRAKE !he dimensions of bra0e disc used for static structural analysis are gi*en bellow -iameter of -isc bra0e <>&mm !hic0ness %.?mm
7!9 ENGINE S#ECIFICATION -isplacement 7cc9 ,ylinders
$
Ma+ Power
(.>
Ma+imum !orque =ore 7mm9
?&
Stro0e 7mm9
>B
al*es per ,ylinder
B(
@
<
3uel -eli*ery System ,arburetor
1
3uel !ype
Petrol
"gnition
,.-."
Spar0 Plugs 7Per ,ylinder9 ,ooling System
$
Air ,ooled.
7!4 FORCE CALCULATIONS@ -ata A*ailable; d&.<>m) t&.&&%?m) !ime for deceleration td $.?sec) Ma+imum *elocity of *ehicle * $>&0mFhr. Outer radius of disc pad R o$&&mm) "nner radius of disc pad R i '&mm) /eight of the *ehicle /$&&0gs 7Assume9) /heel diameter - >?(&
&.'>mm) /heel height h &.&$?mts) /heel =ase / b &.>?(FU &.$>?? mts.
Stopping distance : $&mts. ,o#efficient of friction of pads V &.%. -ensity of material W @&&& 0gFm % X *FR ) %@.@@F&.$<) %<> radFsec. L 9 D 79) %&'?.?> rpm. inetic 2nergy) .2 [7"ZX <9) " mZ0 <) < m Ud D >ZtZdensity of material)
)0
7%.$>Z7.<>< D 9Q >Z.&&%?Z@&&&) $.<'0g. 0 <d<99 >('.$( \.
B 7X$F<9Ztd 7%<>F<9Z$.? <>% rad. Mt .2FB >('.$(F<>% $.B?N#m. 3riction radius) R f
Mt $.B?F< &.B(B N#m 7torque on one pad9 Mt VZPZR f V &.% P 7&.B(BZ$& %9F7&.%Z@$.''9 %B.B'<> N 7%B.B'<>FB.@$9 0gs >.&(0gs. Static weight on front wheel / fs /F?#&.&$?Z$&9F$& '.?
)1
$??.
C-A#TER 9 7D ODELING OF DISC ROTOR IN #ROE SOFT8ARE 9!6 INTRODUCTION ProF2N4"N22R /ildfire is the standard in %- product design) featuring industry#leading producti*ity tools that promote best practices in design while ensuring compliance with your industry and company standards. "ntegrated ProF2N4"N22R ,A-F,AMF,A2 solutions allow you to design faster than e*er) while ma+imi6ing inno*ation and quality to ultimately create e+ceptional products. ,ustomer requirements may change and time pressures may continue to mount) but your product design needs remain the same # regardless of your projects
))
scope) you need the powerful) easy#to#use) affordable solution that ProF2N4"N22R pro*ides.
9!< -ISTORY ,reo 2lementsFPro 7formerly ProF2N4"N22R9) P!,s parametric) integrated %- ,A-F,AMF,A2 solution) is used by discrete manufacturers for mechanical engineering) design and manufacturing. ,reated by -r. Samuel P. 4insberg in the mid#$B@&s) ProF2N4"N22R was the industrys first successful rule#based constraint 7sometimes
called
]parametric]
or
]*ibration]9 %-
,A- modeling
system.
?Q
!he parametric modeling approach uses parameters) dimensions) features) and
relationships to capture intended product beha*ior and create a recipe which enables design automation and the optimi6ation of design and product de*elopment processes. !his design approach is used by companies whose product strategy is family#based or platform#dri*en) where a prescripti*e design strategy is fundamental to the success of the design process by embedding engineering constraints and relationships to quic0ly optimi6e the design) or where the resulting geometry may be comple+ or based upon equations. ,ero 2lementsFPro pro*ides a complete set of design) analysis and manufacturing capabilities on one) integral) scalable platform. !hese required capabilities include Solid Modeling) Surfacing) Rendering) -ata "nteroperability) Routed Systems -esign) Simulation) !olerance Analysis) and N, and !ooling -esign. ,ompanies use ,ero 2lementsFPro to create a complete %- digital model of their products. !he models consist of <- and %- solid model data which can also be used downstream in finite element analysis) rapid prototyping) tooling design) and ,N, manufacturing. All data is associati*e and interchangeable between the ,A-) ,A2 and ,AM modules without con*ersion. A product and its entire bill of materials 7=OM9 can be modeled accurately with fully associati*e engineering drawings) and re*ision control information. !he associati*ely functionality in ,ero 2lementsFPro enables users to ma0e changes in the design at any time during the product de*elopment process and automatically update downstream deli*erables. !his capability enables concurrent engineering ^ design) analysis and manufacturing engineers wor0ing in parallel ^ and streamlines product de*elopment processes.
9!7 KEY FEATURES AND BENEFITS@
)3
3ully integrated applications allow you to de*elop e*erything from concept to manufacturing within one application.
Powerful parametric design capabilities for superior product design.
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,omplete *irtual simulation capabilities.
Automated generation of associati*e tooling design and manufacturing deli*erables.
9!9 T-E AIN ODULES Part -esign Assembly
-rawing
9!4 FLO8 #ROCESS IN #ROE @ NE8 FILE
#ART DESIGN
SKETC-
)?
ETRUDE
SAE 'IN IGES FORAT)
E#ORT TO ANSYS
3ig >.$ Rotor -isc 3low ,hart
9!= SE?UENTIAL STE#S FOLLO8ED FOR BUILDING ROTOR DISC IN #ROE Sequential steps followed for building rotor disc in Pro#2 are shown from fig. no >.< to >.B. Proposed rotor models also de*eloped in Pro#2 with change of number of spo0es and shown in fig no >.$$1>.$<%
),
3ig >.< step $
3ig >.% step <
)6
3ig >.> step %
3ig >.? step >
)7
3ig >.' step ?
3ig >.( step '
)@
3ig >.@ step (
3ig >.B step @
)
#ROE ODEL OF ROTOR DISC 6@
3ig >.$& pro#e model of rotor disc $
#ROE ODEL OF ROTOR DISC <@
3ig >.$$ pro#e model of rotor disc <
30
#ROE ODEL OF ROTOR DISC 7@
3ig >.$< pro#e model of rotor disc %
31
Cha+ter 4 FINITE ELEENT ANALYSIS 4!6INTRODUCTION 3inite 2lement Method 732M9 is also called as 3inite 2lement Analysis 732A9. 3inite 2lement Method is a basic analysis technique f o r r e s ol * i ng a n d s u b st i t ut i n g c o m p l i ca t e d p r o bl e m s b y s i m pl e r o n e s) obtaining appro+imate solutions 3inite element method being a fle+ible tool is used in *arious industries to sol*e se*eral practical engineering problems.
AN S8 S
is
g en er al
p ur po se
3 2A
s of tw ar e
d e* el op ed )
s u pp or t ed 1 m a r0 e te d b y A N S8 S " n c. AN S 8S a r e u s ed b y s e *e r al c o m pa n i es t o p r od u c e a w i d e r a n g e o f p r o du c t s
,
automobile engines
including aircrafts 1
4enerally there are three methods to sol*e any
.
engineering problems such as analytical method) Numerical method) 1 2 + pe r i me n t a l m e t h o d i n w h i ch n u me r i c al m e t ho d i s m o s t c o m m o n ly u se d.
= ec au se
it
is
t he
m at he ma ti ca l
r ep re se nt at io n
o f p hys ic al
problems 1 it gi*es the appro+imate solut ion 1 als o applicable e*en if phys ical prototype is not a*ailable. Numerical methods li0e 3inite e le me nt a na ly si s a re b as ed o n d is cr it i6 at io n o f i nt eg ra l f or m o f equation. =asic theme of all numerical method is to ma0e calculations at only limited numbers of points 1 then interpolate the results for entire domain. "t is now used to sol*e problems in the following areas# s tr uc tu ra l
s tr en gt h
d es ig n)
t he rm al
a na l ys is )
* ib ra ti on )
1
c ra sh
simulations etc.
4!< ENGINEERING A##LICATIONS OF FINITE ELEENT ET-OD@ "nitially 32M method was used for only structural mechanics problems but o*er the years researches ha*e successfully applied it to *arious engineering problems. "t has been *alidated that this method can be used for other numerical solution of ordinary and partial differential equations.
3)
!he finite element method is applicable to three categories of boundary *alue problems
2quilibrium or steady state or !ime#"ndependent problems
2igen *alue Problems
Propagation or transient problems.
4!7 ARIOUS A##LICATIONS OF FE@ ,i*il 2ngineering Structures Aircraft Structures Heat ,onduction 4eo mechanics Hydraulic and /ater Resource 2ngineering Nuclear engineering =io#Medical 2ngineering Mechanical 2ngineering 2lectrical Machines and 2lectromagnetic.
4!9 ADANTAGES OF FEA(FE@ Non#linear problems are easily sol*ed. Se*eral types of problems can be sol*ed with easy formulation. Reduces the costs in the de*elopment of new products. "mpro*es the quality of the end product. :ife of the product is increased. Rapid de*elopment of new products. High product reliability. Product fabrication process is enhanced.
4!4 DISADANTAGES OF FEA(FE@
33
2+treme aspect ratios can cause problems. Not well suited for open region problems.
4!= #ROCEDURE FOR ANSYS ANALYSIS Static analysis is used to determine the displacements stresses) stains and forces in structures or components due to loads that do not induce significant inertia and damping effects. Steady loading in response conditions are assumed. !he 0inds of loading that can be applied in a static analysis include e+ternally applied forces and pressures) steady state inertial forces such as gra*ity or rotational *elocity imposed 7non#6ero9 displacements) temperatures 7for thermal strain9. A static analysis can be either linear or non linear. "n our present wor0 we consider linear static analysis. !he procedure for static analysis consists of these main steps
=uilding the model
Obtaining the solution
Re*iewing the results.
4!=!6 BUILD T-E ODEL "n this step we specify the job name and analysis title use PR2P( to define the element types) element real constants) material properties and model geometry element type both linear and non# linear structural elements are allowed. !he ANS8S elements library contains o*er @& different element types. A unique number and prefi+ identify each element type.
4!=!< ATERIAL #RO#ERTIES 8oung5s modulus 72D9 must be defined for a static analysis. "f we plan to apply inertia loads 7such as gra*ity9 we define mass properties such as density 7-2NS9. Similarly if we plan to apply thermal loads 7temperatures9 we define coefficient of thermal e+pansion 7A:PD9.
4!=!7 SOLUTION "n this step we define the analysis type and options) apply loads and initiate the finite element solution. !his in*ol*es three phases; Pre#processor phase Solution phase
3?
Post#processor phase
I!
#RE#ROCESSOR Pre processor has been de*eloped so that the same program is a*ailable on
micro) mini) super#mini and mainframe computer system. !his slows easy transfer of models one system to other. "t in*ol*es the preparation of finite element data such as nodal coordinates) element connecti*ity) boundary conditions 1 loading 1 material information.
Ta.*e No@ 4!6
The fo**o1ing Ta.*e 4!6 $ho1$ the .rief de$cri+tion of $te+$ fo**o1ed in each +ha$e@
GEOETRICAL DEFINITIONS@ !here are four different geometric entities in pre processor namely 0ey points) lines) area and *olumes. !hese entities can be used to obtain the geometric representation of the structure. All the entities are independent of other and ha*e unique identification labels.
3,
ODEL GENERATIONS@ !wo different methods are used to generate a model;
-irect generation.
Solid modeling
/ith solid modeling we can describe the geometric boundaries of the model) establish controls o*er the si6e and desired shape of the elements and then instruct ANS8S program to generate all the nodes and elements automatically. =y contrast) with the direct generation method) we determine the location of e*ery node and si6e shape and connecti*ity of e*ery element prior to defining these entities in the ANS8S model. Although) some automatic data generation is possible 7by using commands such as 3"::) N42N) 242N etc9 the direct generation method essentially a hands on numerical method that requires us to 0eep trac0 of all the node numbers as we de*elop the finite element mesh. !his detailed boo0 0eeping can become difficult for large models) gi*ing scope for modeling errors. Solid modeling is usually more powerful and *ersatile than direct generation and is commonly preferred method of generating a model.
ES- GENERATION@ "n the finite element analysis the basic concept is to analy6e the structure) which is an assemblage of discrete pieces called elements) which are connected) together at a finite number of points called Nodes. :oading boundary conditions are then applied to these elements and nodes. A networ0 of these elements is 0nown as Mesh.
FINITE ELEENT GENERATION@ !he ma+imum amount of time in a finite element analysis is spent on generating elements and nodal data. Pre processor allows the user to generate nodes and elements automatically at the same time allowing control o*er si6e and number of elements. !here are *arious types of elements that can be mapped or generated on *arious geometric entities. !he elements de*eloped by *arious automatic element generation capabilities of pre processor can be chec0ed element characteristics that may need to be *erified before the finite element analysis for connecti*ity) distortion#inde+ etc. 4enerally) automatic mesh generating capabilities of pre processor are used rather than defining 36
the nodes indi*idually. "f required nodes can be defined easily by defining the allocations or by translating the e+isting nodes. Also on one can plot) delete) or search nodes.
BOUNDARY CONDITIONS AND LOADING@ After completion of the finite element model it has to constrain and load has to be applied to the model. ser can define constraints and loads in *arious ways. All constraints and loads are assigned set "-. !his helps the user to 0eep trac0 of load cases.
ODEL DIS#LAY@ -uring the construction and *erification stages of the model it may be necessary to *iew it from different angles. "t is useful to rotate the model with respect to the global system and *iew it from different angles. Pre processor offers these capabilities. =y windowing feature pre processor allows the user to enlarge a specific area of the model for clarity and details. Pre processor also pro*ides features li0e smoothness) scaling) regions) acti*e set) etc for efficient model *iewing and editing.
ATERIAL DEFECTIONS@ All elements are defined by nodes) which ha*e only their location defined. "n the case of plate and shell elements there is no indication of thic0ness. !his thic0ness can be gi*en as element property. Property tables for a particular property set $#- ha*e to be input. -ifferent types of elements ha*e different properties for e.g. =eams; ,ross sectional area) moment of inertia etc Shell; !hic0ness Springs; Stiffness Solids; None !he user also needs to define material properties of the elements. 3or linear static analysis) modules of elasticity and Poisson5s ratio need to be pro*ided. 3or heat transfer) coefficient of thermal e+pansion) densities etc. are required. !hey can be gi*en to the elements by the material property set to $#-.
II!
SOLUTION !he solution phase deals with the solution of the problem according to the problem definitions. All the tedious wor0 of formulating and assembling of matrices are done by the computer and finally displacements are stress *alues
37
are gi*en as output. Some of the capabilities of the ANS8S are linear static analysis) non linear static analysis) transient dynamic analysis) etc.
III!
#OST #ROCESSING !he post processing stage deals with the presentation of the results. !ypically)
the deformed configuration) mode shapes) temperature 1 stress distribution are computed 1 displayed at this stage. /hile solution data can be manipulated many ways in post processing) the important objecti*e is to apply sound engineering judgment in determining whether the solution results are physically reasonable.
4!: STRUCTURAL ANALYSIS IN ANSYS Structural analysis is the commonly used application of the 32A. /e can perform the se*en types of structural analysis in ANS8S such as
Static Analysis
Modal Analysis
=uc0ling Analysis
Spectrum Analysis
Harmonic Analysis
!ransient dynamic Analysis
2+plicit dynamic analysis
A static analysis is performed o*er a structure when the loads 1 boundary conditions remain stationary 1 do not change o*er time it is assumed that the load or field conditions are applied gradually) not suddenly. !he system under analysis can be linear or nonlinear. "nertia and damping effects are ignored in structural analysis. Static analysis is used to determine displacements) stresses 1 so on. "n structural analysis following matrices are sol*ed K F& /here K is stiffness matri+) is displacement matri+) 1F is the force matri+. !he abo*e equation is called the force balance equation for the linear system. Nonlinear systems include large deformation) plasticity) and creep and so on.
3@
ROTOR DISC ODEL 6@ STRESS NODAL DEFLECTION Sequential steps followed in modeling rotor disc in ANS8S are gi*en from fig. no ?.$ to ?.$%. Similarly ANS8S analysis carried out on proposed rotor disc models and the results are shown from fig no ?.$>to ?.<(.
3ig ?.$ "mporting model
3ig ?.< 2lement selection
3
3ig ?.% Material type selection
3ig ?.> Meshing
?0
3ig ?.? Applying :oads
3ig ?.' -eformed C un deformed
?1
3ig ?.( -isplacement ector sum
3ig ?.@ -of in#D direction
?)
3ig ?.B -of in# 8 direction
3ig ?.$& Stress in _ D direction
?3
3ig ?.$$ Stress in#8 direction
3ig ?.$< ector Plot
??
3ig ?.$% on Mises stress
ROTOR DISC ODEL <@ STRESS NODAL DEFLECTION
3ig ?.$> -eformed C un deformed
?,
3ig ?.$? -isplacement ector sum
3ig ?.$' Stress in _ D direction
?6
3ig ?.$( Stress in#8 direction
3ig ?.$@ Stress in#E direction
?7
3ig ?.$B ector Plot
3ig ?.<& on Mises stress
?@
ROTOR DISC ODEL 7@ STRESS NODAL DEFLECTION
3ig ?.<$ -eformed C un deformed
3ig ?.<< -isplacement ector sum
?
3ig ?.<% Stress in#D direction
3ig ?.<> Stress in#8 direction
,0
3ig ?.
3ig ?.<' ector Plot
,1
3ig ?.<( on Mises stress
,)
C-A#TER = RESULTS DISCUSSIONS S "n chapter ' simulation studies are made on three rotor discs) using ANS8S software. !he resultant displacements undergone by each disc and the resultant stresses de*eloped in each disc are determined and tabulated in table no '.$
Ta.*e No@=!6 Rotor /iscs /"!8;A5MNT Model E5TR !FM s 4** 1 ).601 ) [email protected] 3 0.0)3,
!TR!!! "N !TR!!! "N <& G&/"R5T"N /"R5T"N4M 4M8a 8a @.60@ 30.0? @.1? 7.71 0.?1? 0.)00)
EN M"!! !TR!! ! 4M8a )).@3, @.663 ).1)@
3rom the table no '.$ it is obser*ed that the displacement and on Mises stresses are *ery low for the rotor disc of model #%. nder the high speed of $>&mph and retardation time of $.? sec) the rotor disc shows good structural displacement and stresses. "t is obser*ed from the simulation studies that the weight of disc#% is less than the weight of disc#< 1$) because of only ' spo0es) instead of $< spo0es in model#<. !he material used for model#% is steel ha*ing compressi*e strength of %&&Mpa. !herefore) the factor of safety for the design is ?'.>B. !he main ad*antage obser*ed in rotor disc model#% is that) it undergoes &.&<%?mm radial deformation) so that the bearing life of disc drastically increases.
,3
C-A#TER : CONCLUSIONS FUTURE SCO#E OF STUDY
CONCLUSIONS "n this project) three disc rotor models with same outer dimensions but with different design parameters ha*e been modeled using Pro#2 and analy6ed using ANS8S to determine structural performance. =ased on the results of the ANS8S simulation which are tabulated abo*e in table no '.$) "t is concluded that the on Mises stresses de*eloped in disc model no#% are minimum compared to other two models. So "t is suggested that the use of %rd disc model instead of $ st and &MPH with bra0e time $.?seconds.
SCO#E FOR T-E FURT-ER STUDY "n the present in*estigation of structural analysis of disc rotor) a simplified disc bra0e without considering any thermal stresses) is analy6ed by 32M pac0age ANS8S. As future wor0) a model considering thermal factors can be underta0en in the analysis. !he analysis still becomes complicated by considering *ariable thermal conducti*ity) *ariable specific heat and non uniform deceleration of *ehicle. !his can be considered for the future wor0.
,?
