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Figure 2. Dynamic Balancing of the Car

Figure 3. Braking Distance Versus Tyre-GroundFriction Coefficient

2.2. Brake Selection Analysis

Lets assume that brake is optimized for tyre -groundfriction coefficient equal to =0,8 (see fig. 2) then:

Ft =16720

2=8360 N

F p =46212

2

=23106 N

FHt =*F t=6688 N

FHp =*F p=18485 N

r =0,426 m

Mht =F Ht*r=2850 Nm

Mhp =F Hp *r=8300 Nm

m =MhtMhp

=2,91

Lets assume, that every braking pressure will give us

constant braking moment ratio m=const

Kinetic energy of the vehicle with mass

ms = 6400 kg and speed V=60km

h=16,67 m

s is equal

to

E=ms*V

2

2=888888,9 J

Second parameter is a braking distance.Vehicle braking test shown that braking distance from

velocity V =60km

h is equal to h =30 m

For vehicle stop in desired distance (assuming constantdecelerated motion) we need braking force equal to:

Fh =Es

=29629 N

or total braking moment equal to:

M=F h*r =12622 Nm

assuming that

m =MHtMHp

=2,91

result is

MHt =1262 2

2*(1+2,91)=161 4 Nm

MHp =2,91*161 4 =4697 Nm

2.3. Braking Pressures Estimation

After front brake tests, it turned out, (despite firstsuggestions) that pressure in braking system can bearound 3[MPa] and pressure needed to achieve brakingmoment at level of 3000[Nm] is around 9 10[MPa].According to results of the tests for front and rear brakesdistribution of the rear and front braking moments can

be checked in assumption that pressures in both frontand rear brakes are equal. Initial parameters are takenfrom previous chapterVehicle energy at the start of braking process:

Es=mV 2

2 =888888,9 Nm

All wheels braking force:

Fch=Essh

=29629,63 N

According to dynamic tests linear interpolation of frontaxle braking moment (disc brake) versus braking

pressure was made:

Mhpr =342,01*p hp +28,329 Nm

y=342,01*x+28,329

0

10000

2000030000

40000

50000

60000

0 0,2 0,4 0,6 0,8 1 F p ;

F t [ N ]

Fp( ); Ft( )

Fp( ) Ft( ) Liniowy (Ft( ))

0

50

100

150

200

250

300

0,00 0,20 0,40 0,60 0,80 1,00

s [ m ]

s()

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Fhpr =342,01*p hp+28,329

R kp N

Figure 4. Front Axle Braking Moment Versus BrakingPressure Linear Interpolation

For rear axle drum brake, two braking moments versus braking pressure two interpolations were made. One islinear as in the case of front brake while the second isnon linear. Such analysis was made because of nonlinear drum brake M h(ph) relation caused by drum brakeoperating principle.

Figure 5. Rear Axle Braking Moment Versus BrakingPressure Interpolations

Linear interpolation:

Mhtr =217,59*p ht-239,2 Nm

y=217,59*x-239,2

Fhtr =217,59*p ht- 239,2

R kt N

Non -linear interpolation:

Mhtr 2=8,0975* pht2+127,92*p ht-44,657 Nm

Fhtr 2=8,0975* pht

2+127,92*p ht-44,657

R kt N

Overall braking force is equal to:

For linear interpolation:

2* 342,01 * php + 28,329

R kp +

2 * 217,59 * pht - 239,2

R kt - Fhc = R = 0

R =0,731872718

ph =11,655[MPa]

For nonlinear interpolation:

2* 342,01 * php + 28,329

R kp +

2 * 8,0975* pht2+127,92*p ht-44,657

R kt -Fhc= R = 0

R =1,978344 ph =11,275[MPa]

verification

Fhc =29629,62963

Fhpr *2+F htr *2= 29630,36153

SummaryCar (mass m s = 6400 kg ) braking from speed

Vs=60km

h, will stop within s h=30 m when braking

pressure is equal to p h =11,655[MPa] (linearinterpolation) or p h =11,275[MPa] (non linearinterpolation) what gives us average braking pressure

ph 11,5[MPa]

2.4. Braking With Constant Tyre-groundFriction C oefficient ( = 0,8)

Aviation regulations (ex. FAR, JAR) recommend taking = 0,8 tyre-ground friction coefficient for permissibleside loads.Where permissible loads are the ones which can be

present during standard operation.Lets take an assumption that analyzed car uses frictiontyre-ground coefficient = 0,8 Rest of the parameters are the same as in previouschapters (repeated below for better overview).ms = 6400 kg car mass

Vs=60km

h=16,66667

m

s car speed

sh=30 m braking distanceR kp=0,426 m front wheel radiusR kt=0,426 m rear wheel radius

Es=mV2

2=888888,9 Nm car energy in the beginning

of brakingFch=

Essh

=29629,63 N all wheels braking force

ph=11,5 Mpa average braking pressure from chapter2.3

0

1000

2000

3000

4000

5000

0 5 10 15

Mhp(ph)

M h p

[ N m

]

p h [MPa]

-5000

50010001500200025003000

0 5 10 15

Mht(ph)

Braking moment versus braking pressure -linear interpolationBraking moment versus braking pressure - nonlinear interpolation

M h p

[ N m

]

p h [MPa]

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4. REFERENCES

Reski A. 2004 Budowa samochodw Ukadyhamulcowe i kierownicze, Oficyna wydawniczaPolitechniki Warszawskiej

Institute of Aviation Landing Gear Report, 2009, Laboratory tests of armored cars brake lining sectorswith termovision made with IL-68 test rig ,26/LW/2009, Institute of Aviation

Institute of Aviation Landing Gear Report, 2009,Armored Car Drum Brake Laboratory Tests ,27/LW/2009, Institute of Aviation

Institute of Aviation Landing Gear Report, 2009, CarBraking System Dynamics Analysis , 36/BZ/2009,Institute of Aviation

AMZ-Kutno sp. z o.o. website, http:/ /www.amz,plLanding Gear Department website,

http://www.cntpolska.pl/index.php/landing-gears-department/about-us

Institute of Aviation website, http://www.ilot.edu.pl

AUTHOR BIOGRAPHIES

WOJCIECH KOWALSKI, born inWarsaw, Poland and went to the WarsawAcademy of Technology, received hisM.Sc. in Engineering in 1970, Faculty ofPower and Aeronautical Engineering in

Applied Mechanics and 2000 PhD from WarsawUniversity of Technology, Faculty of Automotive andConstruction Machinery Engineering. Now he isworking at Warsaw Institute of Aviation. His current

professional area are: load and stress analysis,

construction dynamics, test parameters determination,results analysis and interpretation of tests andcalculationsE-mail: wojciech.kowalski@ilot.edu.pl

ZBIGNIEW KONRAD SKORUPKA, born in 1977 in Warsaw, Poland. FinishedWarsaw Academy of Technology, wherehe studied Shaping Machines Design andSteering. He received his M.Sc. in 2004.

Currently he is working at Landing Gear Department ofWarsaw Institute of Aviation. His current professionalarea are: use of smart materials in landing gear, general

design and testing of landing gear, brakes and teststands.E-mail: zbigniew.skorupka@ilot.edu.pl

RAFA KAJKA born in 1977, receivedhis M.Sc. in Engineering (2000) fromWarsaw University of Technology,(Poland). Directly after graduation hestarted his doctoral studies and in 2005 he

received PhD from Warsaw University of Technology,Faculty of Automotive and Construction MachineryEngineering. Since 2001 he is working at Institute ofAviation, Warsaw initially as a strength engineer and

from 2007 as a Manager of Landing Gear Department,Institute of Aviation, Warsaw, Poland.E-mail: rafal.kajka@ilot.edu.pl

JAN AMBORSKI born in 1972 receivedhis M.Sc. in Engineering in 1999 fromWarsaw University of Technology, Facultyof Power and Aeronautical Engineeringand 2006 PhD from Warsaw University of

Technology, Faculty of Automotive and Construction

Machinery Engineering. Now he is working at WarsawInstitute of Aviation.E-mail: jan.amborski@ilot.edu.pl

http://www.amz%2Cpl/http://www.cntpolska.pl/index.php/landing-gears-department/about-ushttp://www.cntpolska.pl/index.php/landing-gears-department/about-ushttp://www.ilot.edu.pl/mailto:wojciech.kowalski@ilot.edu.plmailto:wojciech.kowalski@ilot.edu.plmailto:wojciech.kowalski@ilot.edu.plmailto:zbigniew.skorupka@ilot.edu.plmailto:zbigniew.skorupka@ilot.edu.plmailto:zbigniew.skorupka@ilot.edu.plmailto:rafal.kajka@ilot.edu.plmailto:rafal.kajka@ilot.edu.plmailto:rafal.kajka@ilot.edu.plmailto:jan.amborski@ilot.edu.plmailto:jan.amborski@ilot.edu.plmailto:jan.amborski@ilot.edu.plmailto:jan.amborski@ilot.edu.plmailto:rafal.kajka@ilot.edu.plmailto:zbigniew.skorupka@ilot.edu.plmailto:wojciech.kowalski@ilot.edu.plhttp://www.ilot.edu.pl/http://www.cntpolska.pl/index.php/landing-gears-department/about-ushttp://www.cntpolska.pl/index.php/landing-gears-department/about-ushttp://www.amz%2Cpl/