ME481 Course Notes 4AH

7/22/2019 ME481 Course Notes 4AH

1/39

Mechanical Engineering

ME 481

Vehicle Design

Fall 2000

Lecture Notes

By

Richard B. Hathaway, Ph.D., PE

Professor

Mechanical and Aeronautical Engineering


2/39

Section 1

Energy Consumption

and

Poer !e"uirements in Design

2


3/39

Aerodynamics and Rolling Resistance

#E$E!%& F'!M(&%S ) %E!'D*$%M+C

Dynamic Pressure,

2

2

1vP

d =

Drag Force,

-.2

1 2 REfAvFd

=

ACvF dd2

2

1= 20 -.-2/1.

2

1vvACF dd +=

%ero Poer

f(RE)AV(2)=P 3

Cd coeicient o drag air density 1/2 g3m

% pro5ected rontal area .m2- f(RE) = Reynolds number6 6ehicle 6elocity .m3sec- V0 headind 6elocity

ENGLISH UNITS

VAC)10X(6.93=HP3

d-6

aero

where: A = area (f!) " = #elo$%y (&'H) d= dra $oeff%$%en


4/39

SI UNITS

W

kW

ACV

(2)=Pd

3

KW1000

1

1000

4700

2/1

4

-.872 02

VVVAC)10.(1=P d-6

aero +

P poer .- % area .m2-

V 6elocity .p9- V0 headind 6elocity

Cd drag coeicient 1/2 g3m

#E$E!%& F'!M(&%S : !'&&+$# !ES+S;%$CE

E$#&+S9 ($+;S

3!"

VWC=HP rrrr

here, Crr coeicient o rolling resistance < eight .l=s- V 6elocity .MP9-

S+ ($+;S

V#C)10(2.!2=P

V#C3600

9.$1=P

rr3-

rr

rrrr

here, P poer .- Crr coeicient o rolling resistanceM mass .g- V 6elocity .p9-

4


5/39

RA!"#E $%R!E RE&'"REMEN(.

Vehicles re"uire thrust orces> generated at the tires> to initiate and maintain motion/ ;hese

orces are usually reerred to as tracti6e orces or the tracti6e orce re"uirement/ + the re"uired

tracti6e orce .F- is =roen into components the ma5or components o the resisting orces to

motion are comprised o acceleration orces .Faccel ma ? +orces-> #radea=ility re"uirements

.Fgrade-> %erodynamic loads .Faero- and chassis losses .Froll resist-/

F Faero@ Froll resist@ Fgrade@ Faccel

.32- Cd% 62 @ Crrm g @ Aslope mBg @ m a

.32- Cd% 62 @ m gCrr @ A slope @ a3g

in S+ units,

% rontal area .m2- 6 6elocity .m3s- m mass .g-Crr coeicient o roll resistance .$3$- usually appro /01

Cd coeicient o aero drag or most cars / ) /7

A slope !ise3!un ;an o the roaday inclination angle

Steady state orce are e"ual to the summation o Faero@ Froll resist@ Fgrade

FgraderesistFrollFaero ++=%%F

;ransient orces are primarily comprised o acceleration related orces here a change in

6elocity is re"uired/ ;hese include the rotational inertia re"uirements .F+- and the translational

mass .Fma- re"uirements> including steady state acceleration/

VE9+C&E E$E!#* !EG(+!EME$;S/

;he energy consumption o a 6ehicle is =ased on the tracti6e orces re"uired> the mechanical

eiciency o the dri6e train system> the eiciency o the energy con6ersion de6ice and the

eiciency o the storage system/ Eamples o the a=o6e might =est =e demonstrated ith theolloing/

Storage eiciency,% lyheel used or energy storage ill e6entually lose its total energy stored due to

=earing and aerodynamic losses/ % storage =attery may e6entually discharge due to

intrinsic losses in the storage de6ice/ ;hese losses can =e a unction o the A o the totalsystem capacity at hich the system is currently operating/ % li"uid uel usually has

etremely high storage eiciency hile a lyheel may ha6e considera=ly les storage

eiciency/ Hoth hoe6er ha6e the storage eiciency a unction o time/


6/39

100E

EEEff&'&e'*+or,e

&&+&a

f&a&&+&a

%+ore

==

Con6ersion eiciency,

%n internal com=ustion engine changes chemical energy to mechanical energy/ ;hesystem also produces unanted heat and due to mo6ing parts has internal riction hich

urther reduces the system eiciency/ % storage =attery has an eiciency loss during the

discharge cycle and an eiciency loss during the charge cycle/ ;hese eiciencies may =ea unction o the rate at hich the poer is etracted/

100E

PEEff&'&e'Cover%&o

fe

de&veredfe

'ov

==

/e'a&'a+er/a'ov =

Dri6e system Eiciency,

Con6ersion o chemical or electrical to mechanical energy does not complete the poerlo to the heels/ Dri6e train ineiciencies urther reduce the poer a6aila=le toproduce the tracti6e orces/ ;hese losses are typically a unction o the system design

and the tor"ue =eing deli6ered through the system/

100P

PPEff&'&e'#e'a&'a

%or'eoer

+ra'+&ve%or'eoer

dr&ve/e'

==

redredreddr&ve/e' //////

21=

7


7/39

Reasona)le Efficiencies to use for cycle com*arisons

.Eiciencies shon are only approimations-

Electric Motor .Pea- IA

Electric Motor Eiciency .%6g i 1 spd ;rans- JA

Electric Motor Eiciency .%6g i CV;- IA

;ransmission Eiciency (0.9")= 1)-(R

Hattery Eiciency .!egen- J)8A

Hattery ? #enerator Eiciency .!egen- = 0)A

Hattery ? Motor Eiciency .%ccel- 80A

Solar Cell Eiciency 1A

+C Engine .Pea Eiciency- 0A

Flyheel Eiciency

(Storage and Conversion Average) = 70%

J


8/39

E+*erimental !oast Down esting

1- Perorm a high speed and a lo speed test ith an incremental .m3hr- 6elocity change at

each 6elocity/

2- 9igh Speed &o Speed

Va1 70 m3h Va2 20 m3h

V=1 m3h V=2 1 m3h

- !ecord the times o6er hich the 6elocity increments occur/

;h 4 sec ;l 7 sec

4- Determine the mean speed at each 6elocity/

- Determine the mean deceleration at each 6elocity/

7- Determine the drag coeicient

J- Determine the coeicient o rolling resistance/

8

k/vvv 3a =+=

2

111

k/vvv 3a =+=

2

222

%

k/

+

vva 3a

3

1

111 =

=

%

k/

+

vva 3a

3

2

222 =

=

-.

-.72

2

2

1

21

vv

aa

A

/'d

=

-.

-.

10

2/28

22

21

2

21

2

12

vv

vava

'rr

=


9/39

Section 2


10/39

E"-H and R%A"%NAL "NER"A E$$E!(

;hrust orce .F-> at the tire ootprint> re"uired or 6ehicle motion,

F Faero@ Froll resist@ Fgrade@ Faccel .32- Cd% 62 @ Crrm g @ Aslope mBg @ m a

F .32- Cd% 62 @ m gCrr @ A slope @ a3g

in S+ units,% rontal area .m2- 6 6elocity .m3s- m mass .g-

Crr coeicient o roll resistance .$3$- usually appro /01

Cd coeicient o aero drag or most cars / ) /7

A slope !ise3!un ;an o the roaday inclination angle

+ rotational mass is added it adds not only rotational inertia =ut also translational inertia/

r

a=k/=4=

d+

d4=5

+&re

ve&'eee'o/

2'o/&

angular acceleration radius o gyration t time ; ;or"ue m mass

ratio =eteen rotating component and the tire

;hereore i the mass rotates on a 6ehicle hich has translation>

a6/17r

k=F R

2+&re

22

& +8r

F Faero@ Froll resist@ Fgrade@ Faccel .32- Cd% 62@ Crr


11/39

;he PoerPlant ;or"ue is,

:

rF=5

+&re&

PP+)8(r

;he speed o the 6ehicle in m3h is,

)(r:

RP#=k/ +&re

PPJJ/03

rtire ;ire !olling !adius .meters- $ $umerical !atio =eteen P/P/ and ;ire

11


12/39

WEIGHT PROPAGATION

+t might simply =e said that eight =egets eight in any designK

$early all 6ehicle systems are aected =y a change in eight o any one component/

Poer increases and3or perormance decreases are associated ith eight increases/

L!ule o ;hum= approimations can =e made to predict the eects o eight increases/

For a-+era+e 1o2er %%+e/% ('o%&der&, +0e 1o2er %%+e/ a% a .&+)

< due to eight 22A total eight increment

[ ]*;*# WWW = 22/1mod

< due to poer increase 4/A total eight poer increment

+= 104/01mod

P*;

P*#

3a%eP

PWW

Com=ining the a=o6e actors into a single e"uation,

[ ]*;*#P*;

P*#

3a%e WWP

PWW +

+= 22/1104/01mod

12


13/39

Section

Poer ;rain Systems and Eiciencies

1


14/39

E$E!#* S;'!%#E in VE9+C&ES

+/ &+G(+D F(E&S .9eat Energy-

Fossil

$on)Fossil .%lcohol-

++/ #%SE'(S F(E&S .9eat Energy-

Fossil .largely-

$on)Fossil 9ydrogen

+++/ F&* Volume-

P'


15/39

ENERGY CONVERSION

+/ +$;E!$%& C'MH(S;+'$ E$#+$ES,

'tto cycle

Diesel cycle

Hrayton cycle

++/ EN;E!$%& C'MH(S;+'$ E$#+$ES,

Stirling cycle

Rak&e ''-e

+++/ MEC9%$+C%&,

Flyheel

9ydraulic motors

+V/ E&EC;!+C,

Electric motors

ENERGY STORAGE

+/ &+G(+D F(E&S,

@ &ong ;erm Storage Possi=le@ 9igh Energy 3


16/39

+++/ F&* $oise

V/ Hattery,

@ !echarge 3o Fossil Fuels

@ ;otal on)demand Energy Con6ersion@ &imited %tmospheric Pollution

) Finite Storage &ie

) &o Energy 3


17/39

Hybrid Vehicles Power System Matching

P!'H&EM,

+/ ;he 6arious poer systems pro6ide tor"ue and poer cur6es hich are considera=lydierent in shape/

++/ ;he dierent poer systems pea in eiciency at dierent speeds in their operating

range/

+++/ ;he dierent poer systems pea in eiciency at dierent loads)speed points/

+n &ight o +> ++> and +++ a=o6e a method must =e de6ised to optimiQe or maimiQe,

1/ ;or"ue 'utput

2/ Pea Eiciency

/ ;ransition rom one Poer System to the otheror

Phasing in o the Second Poer System in a Parallel System/

% S;!%;E#* M(S; HE DEV+SED ;' P!'V+DE P!'PE! ;+M+$# 'F E%C9 S*S;EM

H%SED '$,

a/ Demand

=/ Eiciency

c/ Perception o the operator

d/ System State

) ;otal Energy !eser6e

) ;otal System Capacity

) Energy !e"uired or Completion o Mission

e/ Energy State o each +ndi6idual System

1J


18/39

Gearbox: Transmission

1/ Manual transmission,;he types o manual transmission are,

Sliding mesh type

Constant mesh type Synchromesh gear =o

;he 6arious components o a manual gear=o and their respecti6e design considerations are

listed,

Design considerations for shaft

;here are shats in the gear=o> namely, +nput or clutch shat> +ntermediate or lay

shat and 'utput or main shat/

+nput or clutch shat,

Design consideration,Shear and torsional stresses as ell as the amount o delection under ull load/ ;his

should not only =e designed or maimum engine tor"ue> =ut also or a=sor=ingtor"ues as high as i6e times the maimum engine tor"ue hich can =e generated =y

Rclutch snapping in the loer gear/

+ntermediate or lay shat,

Design consideration,

Shear and torsional stresses should =e calculated/ %mount o delection should =e

calculated using the load on the internal gear pair> hich is nearest to the hal ay=eteen the intermediate shat mounting =earings/ For shats ith splines and

serrations> it is common to use the root diameter as the outside diameter in the stresscalculations/

'utput or main shat,

Design consideration,

Shear and torsional stresses should =e calculated/

#eneral e"uations,

1/ Maimum shear stress or shat> sor a solid circular shat,

here> d diameter o shat ;or"ue in l=)in

18

4

17

d

5or>e

f%

=


19/39

2/ %mount o delection,

here>

a distance =eteen point o delection and irst support

= distance =eteen point o delection and second support

1 total eight o shat @ gear at the point o delection

l length o shat =eteen supports

Gears:

Current cars use 6arious inds o Synchromesh units> hich ensure a smooth gearchange> hen the 6ehicle is in motion/ ;he Synchromesh unit essentially consists o

=locing rings> conical slee6es and engaging dog slee6es/

;he Synchomesh system is not "uic enough due to the pause in the =locing ring

reaction in =ringing the to engaging components in phase/ Most racing cars> thereore

use gear=o itted ith acedog engagement system instead o a Synchromesh hichpro6ides a "uicer and more responsi6e gear change and a closer eel or engine

perormance/

Design consideration for gears

Engine speed 6s Vehicle speed graph is plotted or determining the gear ratios/

Various important gear design parameters are calculated as ollos,

$ormal tooth thicness

;ooth thicness .at tip-

Proile o6erlap Measurement o6er =alls

Span measurement o6er teeth etc/>


20/39

Bearings:

Hearings ha6e to tae radial and thrust loading .hich is dependent on the heli angle o gearteeth- hen helical gears are used/ Hearings must =e capa=le o coping ith the loads that ill =e

encountered hen the transmission unit is in use/ Calculations can =e done =y straightorard

ormulas/

Dieren!ia" gears:

;he unctions o the inal dri6e are to pro6ide a permanent speed reduction and also to turn the

dri6e round through I0o/ % Rdierential essentially consists o the olloing parts,

1/ Pinion gear

2/ !ing gear ith a dierential case attached to it/ Dierential pinions gears and side gears enclosed in the dierential case/

Pinion and ring gears,

;he pinion and ring gear can ha6e the olloing tooth designs,

1/ He6el gears :a- Straight =e6el

=- Spiral =e6el : ;eeth are cur6ed

More /uiet o*eration, )ecause, cur0ed teeth ma1e sliding contact."t is stronger, )ecause, more

than one tooth is in contact all times.

2/ 9ypoid gears ,

+n this> the centerline o the pinion shat is =elo the center o the ring gear/

Adva+a,e? +t allos the dri6e shat to =e placed loer to permit reducing the

hump on the loor/

;erms used in gear design,

1/ Pitch circle,

%n imaginary circle> hich =y pure rolling action ould gi6e the same motion as theactual gear/

2/ Pitch circle diameter,

;he diameter o the pitch circle/ ;he siQe o the gear is usually speciied =y the pitchcircle diameter/ +t is also called as pitch diameter/

/ Pitch point,;he common point o contact =eteen to pitch circles/

20


21/39

4/ Pitch surace,

;he surace o rolling discs> hich the meshing gears ha6e replaced> at the pitch

circle/

/ Pressure angle or angle o o=li"uity,

;he angle =eteen the common normal to to gear teeth at the point o contact andthe common tangent at the pitch point/ +t is usually denoted =y / ;he standard

pressure angles are 14 T 0and 200/

7/ %ddendum,

;he radial distance o a tooth rom the pitch circle to the top o the tooth/

J/ Dedendum,

;he radial distance o a tooth rom the pitch circle to the =ottom o the tooth/

8/ %ddendum circle,

;he circle dran through the top o the teeth and is concentric ith the pitch circle/

I/ Dedendum circle,

;he circle dran through the =ottom o the teeth/ +t is also called root circle/

!oot circle diameter Pitch circle diameter cos

here> is the pressure angle/

10/ Circular pitch,;he distance measured on the circumerence o a pitch circle rom a point on one

tooth to the corresponding point on the net tooth/ +t is usually denoted =y p c/

Mathematically>

Circular pitch> pc D 3 ;

here> D Diameter o pitch circle ; $um=er o teeth on heel

11/ Diametrical pitch,

;he ratio o num=er o teeth to the pitch circle diameter in millimeters/ +t is denoted=y pd/ Mathematically>

Diametrical pitch>

here> ; $um=er o teeth D Pitch circle diameter

21

'

d@

5

==


22/39

12/ Module,

+t is ratio o pitch circle diameter in millimeters to the num=er o teeth/ +t is usually

denoted =y m/ Mathematically>

Module> m D 3 ;

1/ Clearance,

;he radial distance rom the top o the tooth to the =ottom o the tooth> in a meshing

gear/ ;he circle passing through the top o the meshing gear is non as the clearancecircle/

14/ ;otal depth,

;he radial distance =eteen the addendum and dedendum o a gear/ +t is e"ual to thesum o the addendum and dedendum/

1/


23/39

24/ Fillet radius,

;he radius that connects the root circle to the proile o the teeth/

2/ Path o contact,

;he path traced =y the point o contact o to teeth rom the =eginning to the end o

engagement/

27/ &ength o path o contact,

;he length o the common normal cut)o =y the addendum circles o the heel andpinion/

2J/ %rc o contact,

;he path traced =y a point on the pitch circle rom the =eginning to the end oengagement o a gi6en pair o teeth/ ;he arc contact consists o to parts> i/e/>

.a- %rc o approach, ;he portion o the path o contact rom the =eginning o

engagement to the pitch point/

.=- %rc o recess, ;he portion o the path o contact rom the pitch point to theend o engagement o a pair o teeth/

2


24/39

Section 4

Hrae System Design

+n con6entional hydraulic =rae systems the apply orce at the =rae pedal is con6erted to hydraulicpressure in the master cylinder/ %pply orce rom the dri6er is multiplied through a mechanical

ad6antage =eteen the =rae pedal and the master cylinder to increase the orce on the master

cylinder/ 9ydraulic pressure is a typical orce transer mechanism to the heel =rae as the luid can=e routed through lei=le lines to the heels hile the heels under comple heel motions/

M%S;E! C*&+$DE! P!ESS(!E .3o poer assist-,

dB

.#.AF=P 2

/'

edaeda

/'

Poer assist may =e added to a con6entional hydraulic =rae system to assist the dri6er in =rae

apply/ Poer assist utiliQes a system hich may use air pressure> atmospheric36acuum pressure

hydraulic pressure or other means to apply direct orce to the master cylinder/

M%S;E! C*&+$DE! P!ESS(!E .3 poer assist-,

dB

F7).#.AF(

=A

F

=P 2/'

oo%+eredaeda

/'

/'

/'

;he pressure rom the master cylinder is typically modiied =y a series o 6al6es =eore reaching theheel cylinders/ ;he 6al6es modiy pressure to proportion pressure as a unction o eight transer>

6ehicle static load and load location> and the heel =rae characteristics/ Val6es may also =e placed

ithin these lines to pro6ide or anti)loc =raing> traction control and3or ya sta=ility control/

;he modiied master cylinder pressure is deli6ered to a hydraulic heel cylinder hich utiliQes the

hydraulic pressure to create a mechanical apply orce/


25/39

acts at the mean radius o the =raing surace/ For an internal or eternal epanding =rae the mean

radius o the =raing surace is the radius o the =raing surace/

For a dis =rae the mean radius .rm- o the =raing surace is

D+SC H!%E ME%$ !%D+(S

;he heel tor"ue the =rae system creates during =raing .;- is a unction o the heel cylinder

orce .Fc-> the coeicient o riction =eteen the riction pad and the =rae surace .-> the mean

radius o the =raing surace .rm-> the num=er o =raing suraces .$-> and the multiplication actor.eecti6eness actor- o the =rae .E-/

compound and 6endor identiication/ %n eamplemight =e FF)20)%H/ FF identiies the riction coeicient and the 20)%H identiy the compound and

6endor respecti6ely/ ;he olloing ta=le identiies the coeicient o riction 6alues/ ;he irst letter

in the code pro6ides inormation as to the moderate .normal- temperature characteristics> the second

letter pro6ides inormation as to the high temperature characteristics o the lining/

2

2

22&o

/

rrr +=

/ad' rE:F5 =


26/39

Edge &etter Code Friction coeicient

C 0/1

D 0/1 0/2

E 0/2 0/

F 0/ 0/4

# 0/4 0/

9 O 0/

unclassiied

;he =raing orce a6aila=le at the tire)to)road interace is the heel tor"ue di6ided =y the rolling

radius o the tire/

i the =raes are properly propotioned> is,

,

a

2

D

,

aW-W

=F

R

rakeR

27

==

+

/ad'

+

rrE:F

r5F

[ ] [ ]

=

+

/1ad2

/'

'

3oo%+er1eda-1eda-3r

rE:

d

dF7).#.AF(F

2


27/39

&+M+;+$# H!%+$# F'!CE,

;he limiting =raing orce o6er hich heel slide ill occur at each ront heel is,

road-+&re

F

rake2

)D

W7W(

=F F

;he limiting =raing orce o6er hich heel slide ill occur at each rear heel is,

road-+&re

R

rake2

)D

W-W(

=F R

+ the =raes are properly proportioned the =raing orce maimum is,

2

)D

W-W(

2

)D

W7W(

=F road-+&re

RF

r 2maE

+

r-++o+r-+rfrake

W=)W7W(=F maE

2J


28/39

Section 4

Suspension Design Considerations

28


29/39

ENPE!+ME$;%& DE;E!M+$%;+'$ 'F ;9E S;!(C;(!%& +$;E#!+;*

'F VE9+C&ES

Vehicle stiness is an important parameter hich inluences ride "uality> handlingproperties> and 6ehicle aesthetics/

Vehicle stiness determines the "uality o it o many eternal panels and the interaction o

the surace panels as uniorm and asymmetric loads are applied/

!oad noise transmission and dynamic response is inluenced =y the 6ehicle stiness/

Vehicles typically are called upon to meet delection criteria in design/

a- meeting delection criteria ill esta=lish designs that inherently meet stress related

criteria/

=- Chassis design ill re"uire the engineer assure that ey delection limits are imposedor critical locations on the chassis> rame and =ody/

c- Vehicles modeled to meet crash standards may also meet delection standards in the

design process/

d- %ll measuresU delection> stress and yield> and impact must =e 6eriied in the designprocess/

STI##NESS IS $EAS%RED IN A N%$BER O# $ODES.

a- Torsiona" ri&gi&i!'is commonly used as measure o the o6erall stiness "uality/

1/ Fundamentally this is a measure o the delection that occurs i all the loadere place on diagonally opposite tires o the 6ehicle/ %s delection occurs in

this mode the "uality o it o the surace components on the =ody is altered/

2/ ;orsion o the chassis also occurs due to the diering roll stiness o the rontand rear suspension systems/

=- H(beamingis used to determine the leural stiness o the chassis/

1/ =asically =ending a=out the rocer panels o the 6ehicle/2/ measured as leure along the longitudinal ais o the 6ehicle as a 6ertical

load is applied at speciic locations along the longitudinal ais/

/ Vertical delection o the chassis is measured at critical points/4/ ;his mode may inluence glass =reaage and aect ride "uality/

c- Co)" "oa&ingis the term used to deine the stiness as it might =e 6ieed =y theoperator/

1/ ;his stiness criteria is esta=lished such that the operator does not percei6e

ecessi6e delection o the steering column and related interior components/

2I


30/39

d- Rear en& beamingis a term used to deine =ending due to the rame Lic)ups that

are present in rear heel dri6e and dependent rear suspension 6ehicles/

1/ ;his is measured ith the rame supported and eight added to the rearetremities o the 6ehicle at or near the rear =umper location/

2/ ;he measure as to assure ade"uate stiness as the rame as shaped to

allo clearance or rear ale mo6ement/

% parameter that is commonly used to esta=lish the stiness is the re"uency o the system/

Minimum 6alues are alays ar a=o6e those anticipated in the suspension or sprung

and un)sprung natural re"uencies/

;his usually sets minimum 6alues at approimately 1 9Q hile most current

designs ill eceed 20 9Q/

&oad actors are the percentage o the maimum torsional rigidity the 6ehicle might see in

ser6ice hich is the maimum diagonal moment/

&oad Factor Determination/1/ !aise the 6ehicle and place the cali=rated ero reerenced scales under each

heel/ Veriy the tires are properly inlated/

2/ !ecord the eight at each heel location/

/ Determine the load actor =ya/ taing the sum o the eights on the let and right ront suspensions

and multiplying the sum =y T the heel trac/

=/ taing the sum o the eights on the let and right rear suspensions andmultiplying the sum =y T the heel trac/

c/ taing the smaller o a and = and it is to =e called a load factor of one.d/ ;ypically to T load actor> incrementally applied> ill =e used to

esta=lish the torsional rigidity or the chassis/

0


31/39

ANA*YSIS o #RONT S%SPENSION *OADS

+#OR DESIGN,

&%;E!%& C'!$E!+$# @ +MP%C;

&'$#+;(D+$%&

H!%+$# @ +MP%C; VE!;+C%&

S;%;+C @ +MP%C;

H!%+$#, use 1)2 g =raing load-

[ ]D;A@@:A#4CD;A@*5A54CD +=2

2

+

=

D

a/

D

WD r3

+= D

,aW

DWD r3

here> h C/# 9eight &


32/39

&%;E!%& commonly considered as 2g load

+=

D,

a,WD r

2


33/39

$R%N ('(PEN("%N L%AD(

%P #"E

F&

MPS% 0

0=+ %FHD*** r'FFdF

( )Fr'Fd

F*%FHD**

+= 1

+= -.-. '3a'r

dF %

FH*

F9)&at 0

F(C9@ FSH: F&C9: F&%; 0

F&C9 F(C9 @ FSH) F&

F9)&ong 0

F(S: F&S@HF9 0 or HF9 F&S) F(S

Pro5ected Steer %is .PS%-

FSH

d

F&C9

(pper Hall Woint to PS% .=-Scru= !adius .rs-

&oer Hall Woint to PS% .c-

F(S

F&SHraing Force 9oriQontal .HF9-

&ateral Force .F&%;-F(C9


34/39


("DE #"E

F(S

F&S

MH 0aF FH* =

=

aF FH*

FN 0

F(S: F&S @ HF9 0

F&S F(S@ HF9

+= 1

aF FHD*

4

hSH

&H

(H

HF9

a


35/39


REAR #"E

M&H 0

F(CVh tan @ F(C9h @ FSHe @ F&a : V .rs@ c- 0

sinCCV FF =

cosCCH

FF =

( )

( )

aFeF'rVF D*%C

costansin ++

=

( ) ( ) DC%FH

DCH FF'

a'r

d

F +

+= cos

FV 0

V : F&CV @ F(C 0

F&CV V @ F(C sin

F(C

V

F&C9

FSH

&H

F(CV

F(C9

F&

(H

F&HV

e h


36/39

SUMMARY

+= 1a

F FHD*

+= -.-. '3

a'r

d

F %

FH*

( )

( )

aFeF'rVF D*%C

costansin ++

=

( ) ( ) DC%FH

DCH FF'

a'r

d

F +

+= cos

F&CV V @ F(C sin

'PPER !%NR%L ARM

F(FM

F(&F

F(C

g F(S

FEDR

F(!9 F(C lu

F(C

7


37/39

M(FP 0

F(C.- @ F(S .lu- : F(&!.@g- 0

F(&! F(C.- @ F(S.lu- +n the direction o F(C @g

F%N+S 0

F(&F@ F(&! F(CF(&F F(C ) F(&!;o determine F(F9and F(!9the geometry and the understanding that all loads pass through (H

can =e used,

g3 lu F(!93 F(&!F(!9 F(&!.g-

lu

FEFH7 FERH= FE*F(F9 F(S: F(!9

LOWER CONTROL ARM

Spring orce and =ump stop orce need =e determined

F&S

i F&C

5

FH F&CV FSP l= ls F&C9

ll

J


38/39

LOGARITHMIC !CR!M!"T

&ogarithmic decrement can =e used to eperimentally determine the amount o damping present in aree 6i=rating system/

For damped 6i=ration the displacement .- is epressed as e"uation 1/

7-1eX= +

2+- Sin

;he logarithmic decrement is then deined as the natural log or the ratio o any to successi6e

amplitudes as shon in e"uation 2/

=

2

1ln

( )

7)7+(-1e

7+-1e=

d1

2)7+(-

1

2+-

d1

1

Sin

Sinln

E"uation 2 can =e reduced to e"uation =ased on the act that the 6alue o the sines are e"ual or

each period at t t1@d/

e=e

e= d

d1

1

)7+(-

+-

lnln

d=

Since the damped period is

2

d

-1

2=

e"uation can =e reduced to e"uation /

2-1

2=

8


39/39

;hereore the amplitude ratio or any to consecuti6e cycles is as shon in e"uation 7/

e=

2

1

+t can also =e sho that or n cycles the olloing relationship eists

1=

0ln

ME481 Course Notes 4AH

Documents

Transcript of ME481 Course Notes 4AH