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7/22/2019 ME481 Course Notes 4AH
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Mechanical Engineering
ME 481
Vehicle Design
Fall 2000
Lecture Notes
By
Richard B. Hathaway, Ph.D., PE
Professor
Mechanical and Aeronautical Engineering
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Section 1
Energy Consumption
and
Poer !e"uirements in Design
2
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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
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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
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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/
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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
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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
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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
=
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Section 2
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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
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;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
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WEIGHT PROPAGATION
+t might simply =e said that eight =egets eight in any designK
$early all 6ehicle systems are aected =y a change in eight o any one component/
Poer increases and3or perormance decreases are associated ith eight increases/
L!ule o ;hum= approimations can =e made to predict the eects o eight increases/
For a-+era+e 1o2er %%+e/% ('o%&der&, +0e 1o2er %%+e/ a% a .&+)
< due to eight 22A total eight increment
[ ]*;*# WWW = 22/1mod
< due to poer increase 4/A total eight poer increment
+= 104/01mod
P*;
P*#
3a%eP
PWW
Com=ining the a=o6e actors into a single e"uation,
[ ]*;*#P*;
P*#
3a%e WWP
PWW +
+= 22/1104/01mod
12
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Section
Poer ;rain Systems and Eiciencies
1
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E$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-
$on)Fossil 9ydrogen
+++/ F&* Volume-
P'
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ENERGY CONVERSION
+/ +$;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
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+++/ F&* $oise
V/ Hattery,
@ !echarge 3o Fossil Fuels
@ ;otal on)demand Energy Con6ersion@ &imited %tmospheric Pollution
) Finite Storage &ie
) &o Energy 3
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Hybrid Vehicles Power System Matching
P!'H&EM,
+/ ;he 6arious poer systems pro6ide tor"ue and poer cur6es hich are considera=lydierent in shape/
++/ ;he dierent poer systems pea in eiciency at dierent speeds in their operating
range/
+++/ ;he dierent poer systems pea in eiciency at dierent loads)speed points/
+n &ight o +> ++> and +++ a=o6e a method must =e de6ised to optimiQe or maimiQe,
1/ ;or"ue 'utput
2/ Pea Eiciency
/ ;ransition rom one Poer System to the otheror
Phasing in o the Second Poer System in a Parallel System/
% S;!%;E#* M(S; HE DEV+SED ;' P!'V+DE P!'PE! ;+M+$# '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
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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%
=
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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/>
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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
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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> ; $um=er o teeth D Pitch circle diameter
21
'
d@
5
==
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12/ Module,
+t is ratio o pitch circle diameter in millimeters to the num=er o teeth/ +t is usually
denoted =y m/ Mathematically>
Module> m D 3 ;
1/ Clearance,
;he radial distance rom the top o the tooth to the =ottom o the tooth> in a meshing
gear/ ;he circle passing through the top o the meshing gear is non as the clearancecircle/
14/ ;otal depth,
;he radial distance =eteen the addendum and dedendum o a gear/ +t is e"ual to thesum o the addendum and dedendum/
1/
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24/ Fillet radius,
;he radius that connects the root circle to the proile o the teeth/
2/ Path o contact,
;he path traced =y the point o contact o to teeth rom the =eginning to the end o
engagement/
27/ &ength o path o contact,
;he length o the common normal cut)o =y the addendum circles o the heel andpinion/
2J/ %rc o contact,
;he path traced =y a point on the pitch circle rom the =eginning to the end oengagement o a gi6en pair o teeth/ ;he arc contact consists o to parts> i/e/>
.a- %rc o approach, ;he portion o the path o contact rom the =eginning o
engagement to the pitch point/
.=- %rc o recess, ;he portion o the path o contact rom the pitch point to theend o engagement o a pair o teeth/
2
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Section 4
Hrae System Design
+n con6entional hydraulic =rae systems the apply orce at the =rae pedal is con6erted to hydraulicpressure in the master cylinder/ %pply orce rom the dri6er is multiplied through a mechanical
ad6antage =eteen the =rae pedal and the master cylinder to increase the orce on the master
cylinder/ 9ydraulic pressure is a typical orce transer mechanism to the heel =rae as the luid can=e routed through lei=le lines to the heels hile the heels under comple heel motions/
M%S;E! C*&+$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*&+$DE! P!ESS(!E .3 poer assist-,
dB
F7).#.AF(
=A
F
=P 2/'
oo%+eredaeda
/'
/'
/'
;he pressure rom the master cylinder is typically modiied =y a series o 6al6es =eore reaching theheel cylinders/ ;he 6al6es modiy pressure to proportion pressure as a unction o eight transer>
6ehicle static load and load location> and the heel =rae characteristics/ Val6es may also =e placed
ithin these lines to pro6ide or anti)loc =raing> traction control and3or ya sta=ility control/
;he modiied master cylinder pressure is deli6ered to a hydraulic heel cylinder hich utiliQes the
hydraulic pressure to create a mechanical apply orce/
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acts at the mean radius o the =raing surace/ For an internal or eternal epanding =rae the mean
radius o the =raing surace is the radius o the =raing surace/
For a dis =rae the mean radius .rm- o the =raing surace is
D+SC H!%E ME%$ !%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 .$-> and the multiplication actor.eecti6eness actor- o the =rae .E-/
compound and 6endor identiication/ %n eamplemight =e FF)20)%H/ FF identiies the riction coeicient and the 20)%H identiy the compound and
6endor respecti6ely/ ;he olloing ta=le identiies the coeicient o riction 6alues/ ;he irst letter
in the code pro6ides inormation as to the moderate .normal- temperature characteristics> the second
letter pro6ides inormation as to the high temperature characteristics o the lining/
2
2
22&o
/
rrr +=
/ad' rE:F5 =
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Edge &etter Code Friction coeicient
C 0/1
D 0/1 0/2
E 0/2 0/
F 0/ 0/4
# 0/4 0/
9 O 0/
unclassiied
;he =raing orce a6aila=le at the tire)to)road interace is the heel tor"ue di6ided =y the rolling
radius o the tire/
i the =raes are properly propotioned> is,
,
a
2
D
,
aW-W
=F
R
rakeR
27
==
+
/ad'
+
rrE:F
r5F
[ ] [ ]
=
+
/1ad2
/'
'
3oo%+er1eda-1eda-3r
rE:
d
dF7).#.AF(F
2
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&+M+;+$# H!%+$# F'!CE,
;he limiting =raing orce o6er hich heel slide ill occur at each ront heel is,
road-+&re
F
rake2
)D
W7W(
=F F
;he limiting =raing orce o6er hich heel slide ill occur at each rear heel is,
road-+&re
R
rake2
)D
W-W(
=F R
+ the =raes are properly proportioned the =raing orce maimum is,
2
)D
W-W(
2
)D
W7W(
=F road-+&re
RF
r 2maE
+
r-++o+r-+rfrake
W=)W7W(=F maE
2J
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Section 4
Suspension Design Considerations
28
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ENPE!+ME$;%& 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
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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
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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!%+$#, use 1)2 g =raing load-
[ ]D;A@@:A#4CD;A@*5A54CD +=2
2
+
=
D
a/
D
WD r3
+= D
,aW
DWD r3
here> h C/# 9eight &
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&%;E!%& commonly considered as 2g load
+=
D,
a,WD r
2
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$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
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$R%N ('(PEN("%N L%AD(
("DE #"E
F(S
F&S
MH 0aF FH* =
=
aF FH*
FN 0
F(S: F&S @ HF9 0
F&S F(S@ HF9
+= 1
aF FHD*
4
hSH
&H
(H
HF9
a
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$R%N ('(PEN("%N L%AD(
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
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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
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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
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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
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;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