Class - 5 Bounce and Pitch

8/17/2019 Class - 5 Bounce and Pitch

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Vehicle Ride


2/29

Dynamic System & Excitations

Vehicle Excitations:

1. Road profile & roughness2. Tire & heel excitation!. Dri"eline excitation

#. Engine excitation


3/29

Road Excitation

$ Road excitation is the road profile or the road ele"ation along theroad and includes e"erything from smooth roads% potholes to'urang'an la(u)

$ Road ele"ation profiles are measured using high speed

profilometers

V

* + distance ,m- R o a d

E l e " a t i o n , m m -


4/29

Statistical Road rofile

/0, - /3415,36-276,28-2

9here

/0,- SD amplitude ,feet26cycle6foot- a"e numer ,cycle6ft-

/3 roughness parameter

1.2; x 13; + rough roads 1.2; x 13< + smooth roads

3 cut=off a"e numer

3.3; cycle6foot + asphalt road 3.32 cycle6foot = concrete road


5/29

Road Surface oer Spectral DensitySD


6/29

Tire&9heel >ssemly Excitation

$ ?ass imalance m r @2

$ Tire6heel dimensional "ariation

$ Tire radial stiffness "ariation


7/29

Dri"eline Excitation

$ ?ass imalance + >symmetry of rotating parts + Shaft may e off=center on its supporting flange + Shaft may not e straight + Shaft is not rigid and may deflect


8/29

Engine Excitation

$ TorAue output to the dri"e shaft from thepiston engine is not uniform. Bt has 2components + Steady state component + Superimposed torAue "ariations


9/29

Ride Bsolation

Road roughness

excitation

9heel6tire%Dri"eline excitation

Engine excitation


10/29

Suspension arameters

? + Sprung mass% 'g ,ody% frame% engine% transmission% etc.-m + Cnsprung mass% 'g ,dri"eline% heel assemly% chassis% etc.-

s + Suspension stiffness% 6mm ,spring stiffness-

t = Tire Stiffness% 6mm ,tire stiffness-

Fs = Suspension damping% .sec6m ,damper-

G + sprung mass displacement

Gu + unsprung mass displacement

Gr = road ele"ation

H + Horce on the sprung mass ,engine excitation-

H + Horce on the unsprung mass ,heel6tire or dri"eline excitation-


11/29

Ride roperties

Ride Rate% RR sIt6,s 5 t- 6mm

Ride HreAuency f n JRR6?6,2I8- K0

Damped HreAuency% f d f n J1=L2 K0

9here

L damping ratio Fs6J#s? M


12/29

Suspension Tra"el

Static suspension deflection 96s ?g6s ,mm-Ride HreAuency 3.1;NJs6?

Kence%

Ride freAuency 3.1;NJg6static deflection ,K0-


13/29

Vehicle ResponseEAuations of ?otion

?IG) 5 FsIGO 5 sIG FsIGOu 5 sIGu 5 H ===================== ,1-

mIG)u 5 FsIGOu 5,s5t-IGu FsIGO 5 sIG 5 tIGr 5 H= === ,2-

Dynamic HreAuency Responses:

G)6G)r Kr ,f- ,>r 5 ( Pr -6,D 5 ( E- ============================ ,!-

?G)6H K,f- ,> 5 ( P-6,D 5 ( E- ======================= ,#-

?G)6H K,f- ,> 5 ( P-6,D 5 ( E- ======================= ,;-

9here ( J=1 = complex operator


14/29

Vehicle Response

>r 1I2 Pr 1IFI28f

> 2I,28f-2 P FI,28f-

!

> QI,28f-#

+ ,152-I,28f-2

P FI,28f-!

D QI,28f-# + ,152IQ52-I ,28f-2 5 1I2

E 1IFI,28f- + ,15Q-IFI,28f-!

>nd Q m6?% F Fs6?% 1 t6?% 2 s6?


15/29

Vehicle Response

K , f -


16/29

ser"ations$ >t lo freAuency% gain is unity. Sprung mass mo"es as the road input

$ >t aout 1 K0% sprung mass resonates on suspension ith amplification$ >mplitude depends on damping% 1.; to ! for cars% up to ; for truc's$ >o"e resonant freAuency% response is attenuated$ >t 13=12 K0% un=sprung mass goes into resonance ,heel hop-

$ Sprung mass response gain to heel excitation is 3 at 3 freAuency asthe force on the axle is asored y the tire$ Resonance occurs at heel hop freAuency% gain is 1 and axle force

"ariation is directly transferred to sprung mass$ Sprung mass response gain to engine excitation reaches maximum at

sprung mass resonance$ >t higher freAuencies gain ecomes unity as displacements ecome

small% suspension forces do not change and engine force is asoredy sprung mass acceleration


17/29

Bsolation of Road >cceleration/0,f- Kr ,f-

2I/0r ,f-

9here: /0,f- acceleration SD of the sprung mass

K,f- response gain for road input

/0r ,f- acceleration SD for the road input

R?S acceleration sArt 4area under /0,f- "s f cur"e7


18/29

R?S >cceleration FalculationRoad profile acceleration poer spectral density SD

/ /0r ,f- =!.;2! hen /,f- U 3

/ /0r ,f- =!.;2! 5 /,f- hen /,f- 3

HreAuency Response Hunction K,f-

Sprung mass acceleration poer spectral density SD

/0s ,f- K,f-2 /0r ,f-

R?S acceleration area under the cur"e

/ 0 r

/ 0 s

K , f -

f

f

f


19/29

R?S >cceleration Falculation

Step 1 : Falculate road surface SD for each freAuency from 3.1 K0 to 23 K0

Step 2 : HreAuency response function for each freAuency from 3.1 K0 to 23 K0

Step ! : Falculate "ehicle acceleration SD for each freAuency from 3.1 K0 to 23 K0

Step #: Falculate area under the cur"e found in Step !.

Step ;: That is R?S acceleration. NNM confidence that the "ehicle

acceleration ill not exceed !IR?S


20/29

>lloale "iration le"els


21/29

Suspension Stiffness

> c c e l e r a t i o n

. S D

ote: softer suspension reduces acceleration le"el


22/29

Suspension Damping

ote: higher damping ratio reduces resonance pea'% ut increases gain at higher freAuencies


23/29

Suspension Design


24/29

9heel Kop Resonance

9heel hop resonant freAuency

f a 3.1;NJ,t5s-6m


25/29

Pounce6itch HreAuencies

EAuations of ?otion

G) 5 WG 5 XY 3

Y) 5 XG6Z2 5 [Y 3

9here% W ,f 5r -6?

X ,r Ic=f I-6?

[ ,f I25

r Ic2-6?Z2

f front ride rate

r rear ride rate

as shonc as shon

By pitch inertia

Z radius of gyration

sArt,By6?-


26/29

Pounce6itch HreAuencies

@12 ,W5[-62 5 ,W=[-26#5 X2Z2

@22 ,W5[-62 = ,W=[-26#5 X2Z2

f 1 @1628 K0

f 2 @2628 K0


27/29

Cncoupled HreAuenciesHront Ride HreAuency Jf 6? 6,28- K0

Rear Ride HreAuency Jr 6? 6,28- K0

itch HreAuency JY6By 6,28- K0

Roll HreAuency J\6Bx 6,28- K0

9here

Y ,f I25r Ic

2- pitch stiffness

\ ,f 5r -It262 roll stiffness

By 3.21;#?2 pitch moment of inertia

Bx 3.1#];?t2 roll moment of inertia


28/29

lleyOs criteria for good ride

$ Spring center should e at least "oid spring center at F./.% poor ride due to uncoupled motion

$ DB Z26c 1% happens for cars ith sustantial o"erhang. itchfreAuency U ounce freAuency% front ride freAuency U rear ridefreAuency% good ride


29/29

Suspension System Design

Vehicle

$Spring Rate$Tire Rate$Jounce/Rebound Clearance$Shock Rate$Unsprung Mass

Mass, C.G.

Roll Inertia

itch Inertia

!heelbase, Tread

RMS "cceleration

RMS Susp Tra#el

$re%uencies

&lle'(s Criteria

Road S)

Documents

Class - 5 Bounce and Pitch