Braking

Brake componentsDisk brakes (HSW)Drum brakes (HSW)Master cylinders (HSW)

Braking performance (Eng. Char., SEP)

Equilibrium forces Weight shift confounds analysis! Sequence of events during braking Brake pedal/cylinder forces Method of calculating

Braking Performance Measures

Deceleration rate, Dx

Stopping time, ts

Stopping distance, SD

Energy (braking)Power (braking)

FBD of vehicle during braking

)loads hitch includes(sin

0sin

WDFFRDg

W

Dg

WDWRFRFRF

aDletMaF

Axfxrhxx

xAxfbfxrbrhxx

xxxx

θ

c Wf

Fbf

Rxf

Wr

Fbr

Rxr

x

z

ha

DA

W/g Dx

Wcosθ

Wsinθ

W

Rhz

Rhxhh

h

L

dh

b

Axle Loads during Braking

sin...cos WLh

LAh

ADLhd

hzRLh

hxRxDLh

gW

WLc

fW h

sin...cos WLh

Lh

ADLLd

hzRLh

hxRxDLh

gW

WLb

rWAhh

xDLh

gW

WfW fs

xDLh

gW

WrsrW

On level road, with no hitch or drag loads…

To find the axle loads we need to know the deceleration … but we can’t calculate the deceleration without the braking force on the tires and the braking forces can’t be calculated until we know the axle loads! Huh? A different approach is required! ASSUME deceleration rate Dx

Stopping time, ts

xtxfxrxx FFFDgW

Ma

forces grade and drag hitch, rolling, small for

MFVV

t

ttt

VVttMF

dVdtMF

dtdV

MF

D

xt

fs

sf

ffxt

xt

xtx

0

0

00

time stopping

and0 let

)(

rearrange and force brake constant Assume

Stopping Distance

x

20

xt

20

0

0

20

2

2DMF

2SD distance stopping

and 0 and 0x ..stopping.. When

)(2

g..rearrangin and rule, chain the Using

VV

V

xxMFVV

dxMF

VdV

VdxdV

dtdx

dxdV

dtdV

MF

D

f

fxtf

xt

xtx

Stopping distance w/drag

b

b

Vb

SD

bxt

xt

FCVF

CM

CVFVdV

Mdx

CVFF

VCF

20

0

2

2

ln2

SD distance stopping

and , factor drag on depends When

0

Energy and power dissipated

stVM

fVM

20

20

20

2tEnergy

Power

)(2

Energy

See examples on pages 57-58

What really happens during braking?

Driver pushes on brake pedal (and brake lever) Brake lever pushes on push rod of master

cylinder Hydraulic fluid becomes pressurized Hydraulic line pressure pushes on caliper piston Caliper piston pushes on brake pads Pads clamp rotor/drum causing friction forces &

torque Brake torque causes braking force at contact

patch Weight is shifted to front axle Tires grab and slow vehicle, OR One or more tires skid (too much braking,

“brakes locked”), also slowing vehicle, not as much though.

Brake Pedal / Master Cylinder Forces

a b

pedalpedF

MCF

pedal andlever brake

MCF

cylinder master

pedMC

pedMC

pedMC

pivot

FPRF

ratio" pedal"PRb

alet

Fb

aF

aFbF

M

)(

0

:

psip

lbsFassume

Fp

sqinAandPRletA

FPR

A

Fp

ApF

F

h

ped

Ph

pedMCh

hMC

x

1200

100

)12(

5.06

)(

0

:

ApF hpiston

Calculating brake force, Fb & brake gain G

psi

lbinG

in

1

inlblb

in in

in

lb

lbin in ArG

in A

in r

2

2

2

2

calpad

2cal

pad

pad

2.19

2.19)3(4.0)8(22

3

4.0

8

32

surfaces) (2)( acalf PANF

tire) (one )2(2

)(2

2

t

a

t

acalpad

t

acalpadb

acalpadbt

fpadbt

fw

rGP

r

PAr

r

PArF

PArFr

FrFr

TT

fF

tr

padr

bF

)(roughlyis

tires2.19for

ab pF

in

Skidding= F(brake)>F(road friction) ME485/585 Vehicle Design S2009

xrsr

xfsf

DgWLhWW

DgWLhWW

)/)(/(

)/)(/(

ractxrfactxf WFWF )( and)(

ractxrbxr

factxfbxf

WFF

WFF

)()(

)()(

Recall actual axle loads during deceleration And available road friction forces: Will brake forces be greater than those the road can provide?

Rear wheel lockup

1. Front wheels turning and steering2. Little braking force on rear wheels

“unstable equilibrium”

“spin out”

Braking forces, coefficients, efficiency (handout)ME485/585 Vehicle Design S2009

W

FFD xrxf

x

r

PGF

r

PGF r

rbxrf

fbxf 2)( and2)(

for )(

for

1121

1

KPKPKKP

KPPP

PP

aar

aar

af

1. Given changeover pressure K1, and pressure proportion K2, determine front and rear

application pressure:

2. Calculate the estimated front and rear braking forces, assuming no skidding:

3. Calculate vehicle deceleration:

K1

Pf, Pr

Pa

Pr

Pf

Braking forces, coefficients, efficiency cont’dME485/585 Vehicle Design S2009

xrsr

xfsf

DgWLhWW

DgWLhWW

)/)(/(

)/)(/(

ractxrfactxf WFWF )( and)(

actxrbxr

actxfbxf

FF

FF

)()(

)()(

),max( rf

xb

r

xrr

f

xff

D

W

F

W

F

4. Calculate actual axle loads

5. Assume friction static road and calculate actual front and rear braking forces

6. Test for skidding, i.e. are estimated brake forces greater than those the road can provide?

7. If no skidding, calculate braking coefficients rf and and braking efficiency b

(see web page)

ME 485/585 Vehicle Design Braking Efficiency RJE 2/8/2009

Variable symbol value unitswheelbase L 108.5 inCG height h 20.5 intire radius rt 12.11 in

front axle wt Wfs 2210 lbsrear axle wt Wrs 1864 lbs

total wt W 4074 lbsBrake gain front Gf 20 in-lb/psiBrake gain rear Gr 14 in-lb/psivalve change P K1 290 psi

rate K2 30% n/askid number sn, μ 0.9

Decel.Pa Pf Pr Fxf Fxr Dx Wf Wr μWf μWr μf μr

pedal front rear front rear front rear front rear front rear Braking E(3-27) E(3-28)100 100 100 330 231 0.138 2316 1758 2084 1582 0.143 0.132 0.966 2444 1386200 200 200 661 462 0.276 2422 1652 2180 1487 0.273 0.280 0.985 2491 1338300 300 293 991 677 0.410 2525 1549 2273 1394 0.392 0.437 0.936 2535 1290400 400 323 1321 747 0.508 2601 1473 2341 1326 0.508 0.507 0.999 2550 1242500 500 353 1652 816 0.606 2676 1398 2409 1258 0.617 0.584 0.982 2564 1194600 600 383 1982 886 0.704 2752 1322 2477 1190 0.720 0.670 0.977 2578 1146700 700 413 2312 955 0.802 2827 1247 2545 1122 0.818 0.766 0.981 2592 1098800 800 443 2642 1024 0.900 2903 1171 2613 1054 slip 0.875 slip 2606 1050900 900 473 2973 1094 0.998 2978 1096 2680 986 slip slip slip 2621 10021000 1000 503 3303 1163 1.096 3054 1020 2748 918 slip slip slip 2635 954

Pressure Brake force Axle loads Braking CoefficientMax Brake force

),max(

)( and)(

)/)(/(

)/)(/(

2)( and2)(

for )(

for

1121

1

rf

xb

r

xrr

f

xff

ractxrfactxf

xrsr

xfsf

xrxfx

rrbxr

ffbxf

aar

aar

af

D

W

F

W

F

WFWF

DgWLhWW

DgWLhWWW

FFD

r

PGF

r

PGF

KPKPKKP

KPPP

PP

Braking forces change due to weight shift

0.000 0.200 0.400 0.600 0.800 1.000 1.2000

500

1000

1500

2000

2500

3000

Front Rear

Deceleration (g's)

Brak

ing

Forc

e (lb

s)

Conclusions

Non-skid deceleration affected by weight shift

If tires skid, use μkinetic/sliding

Skidding deceleration may be unstable