Technical Note on Design of Suspension Parameters for FSAE

car suspension parameters related to the vertical dynamics of the car as a basic point in tuning up the suspension on the car itself in real operating conditions KEYWORDS: Suspension parameters, spring rate, damping rate, Formula Student/SAE 1 INTRODUCTION Suspension is one of the most important pieces of equipment on each car It has different

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Technical Note on Design of Suspension Parameters for FSAE Vehicle

O. Suchomel*

CULS Prague, Technical Faculty, Department of Vehicles and Ground Transport, Prague, Czech Republic

B. Ruzicka

University of Technology Brno, Faculty of Mechanical Engineering, Institute of Machine and Industrial Design,

Brno, Czech Republic

* Corresponding author: suchomel@tf.czu.cz ABSTRACT: Correct suspension parameters determination is one of the most important design issues in the development of each type of car. The aim of the suspension design in the field of race cars is to provide ideal operating conditions for the tire and to allow it to generate the maximum amount of traction, braking and lateral forces which determine a vehicle's acceleration capabilities. This article describes the determination of the Formula Student/SAE car suspension parameters related to the vertical dynamics of the car as a basic point in tuning up the suspension on the car itself in real operating conditions. KEYWORDS: Suspension parameters, spring rate, damping rate, Formula Student/SAE.

1 INTRODUCTION

Suspension is one of the most important pieces of equipment on each car. It has different functions: it carries all the vehicle's loads; maintains the correct wheel alignment to the ground; reduces the effect of shock forces when passing ground disturbances; controls the vehicle's longitudinal and lateral speed, and maintains the tire contact patch in contact with the ground for the maximum time possible. The mentioned requirements are provided by different suspensions parts divided into the guiding elements and force generating elements.

In the following articles, the procedure for the

determination of the spring rate and damping rate is presented. The numerical values of the mentioned constants are computed for a Formula Student/SAE car and later used when building the real Formula Student/SAE car at CULS

Prague.

2 DETERMINATION OF SPRING RATES

The described approach for the determination of all the necessary suspension parameters related to the vertical dynamics is based on a quarter-sized car model. The basic points

for the suspension design parameters are the mass properties of the vehicle (see tab.1). VOLUME 3TRANSACTIONS ON TRANSPORT SCIENCESNUMBER 4 2010197

Table 1: Vehicle mass properties.

Constant Value Unit Signification

300 [ kg ] overall vehicle mass

w F R w 45 / 55 [ % / %] mass distribution related to front / rear axis mw=m FF

135 [ kg] overall mass on front axis

mw=m RR

165 [ kg] overall mass on rear axis

uF m 27.78 [ kg] overall unsprung mass on front axis uR m 29.11 [ kg] overall unsprung mass on rear axis UFFsF mm=m 107.22 [ kg] overall sprung mass on front axis URRsR mm=m 135.89 [ kg] overall sprung mass on rear According the suggestions from literature (Milliken & Milliken 1995) for low-downforced racing cars, the initial choice of ride fr equencies is as follow: front ride frequency nF f = 2.1 Hz, rear ride frequency, nR f = 1.9 Hz Then ride rates for front rF

K and rear

rF K end of the vehicle, with respect to corner (either left or right which equals). 22
221
,2 ,RsF

RnFRrF

RsFRrF

RnF mʌf=K,mK

ʌ=f

9333,672107,22.2,12

Nm=ʌ=K

rF 12

9683,612135,89.1,92

Nm=ʌ=K

With spring rate

125000

Nm=K t of chosen tire Hoosier 20x7.5x13 - pressure 14 PSI (Honzík , 2008)

RrFttRrF

RwF

KKKK=K

10086,849333,6712500050009333,67.12

Nm==K wF 1

10496,789683,6112500050009683,61.12

Nm==K wR VOLUME 3TRANSACTIONS ON TRANSPORT SCIENCESNUMBER 4 2010198

Final real spring rates

RsF K must be recalculated using the so-called "installation ratio" IR (Milliken & Milliken, 1995) defined as rate of change of spring compression with wheel movement. To slightly simplify the non-linear function for pull-rod type suspension, installation ratios have to be dealt with as a constant

1,50=IR=IR

FF and

1,40=IRIR

RR . Then 1 22

4483,041,510086,84

Nm==IRK=K

FwF sF 1 22

5355,51,410496,78

Nm==IRK=K

RwR sR

3 CALCULATION OF ANTI-ROLL BAR PARAMETERS FOR DESIRED ROLL

GRADIENTS

Roll gradient

gdegRG/ gives information on how much the body rolls due to the lateral acceleration of the whole car. The desired set up is up to 1.5° / 1g, referred to by suggestions given in (Milliken & Milliken, 1995) as the Formula Student/SAE car achieved a max. lateral acceleration of about 1.5g. At first, roll stiffness is computed using front and rear track m=t F

1,230,m=t

1,205), spring rates

RwF K degNm=radNm==tK=K

FwFĳF

133,177630,1984.1,2300,5.10086,21

22
degNm=radNm==tK=K

RwRĳR

133,017620,878.1,2050,5.10496,21

22
The next step in the determination of anti-roll bars is the computation (Milliken & Milliken,

1995) of the height of the center of gravity of the sprung mass

S h, sprung mass distribution S a and rolling moment lever arm RM h (with the help of used variables: height of the center of gravity of the whole car m=h0,38 , wheel radius m=r F

0,26 , m=r

0,26, and front / rear

roll center heights m=z F

0,04 , m=z

0,06).

m=+=m+mrmrmmh=h sRsFRuRFuF s

0,44135,89107,22107,22=+=m+mm=a

sRsFsF S m==azzzh=h

SFRFSRM

0,3190,4410,040,060,040,3471

VOLUME 3TRANSACTIONS ON TRANSPORT SCIENCESNUMBER 4 2010199

For anti-roll bars stiffness

B K, the calculation of the rolling moment per 1g of lateral acceleration, yĳ AM/ and the computation of the overall desired roll stiffness

Kis required.

Nm=+=gmsR+mh=AM

sFRM yĳ

762,9.9,81135,89107,220,319.

degN.m==RGAM=K yĳ /508,61.5762,9 degNm==KKK=K

RĳFĳĳB

/242,42133,01133,17508,6 The recommendation (Milliken & Milliken, 1995) is to start with a total lateral load distribution to be 5% more than the weight distribution wF at the front axle. Based on this fact, the required anti-roll bar stiffness for the front and rear axle

RFĳB

K is determined from the overall desired roll stiffness

K as follows

FĳB

K = K. ( 1005
F w F

K = 508.6 . (

100545

) - 133.17 = 121.13 Nm / deg

RĳB

K = B K -

FĳB

K = 242.42 - 121.13 = 121.29 Nm / deg

Because the anti-roll bar installation ratio

RFAB IR (the rate of anti-roll bar displacement / roll with body roll) is expected to be the same as the ratio for the springs

[PDF] Technical Note on Design of Suspension Parameters for FSAE

O. Suchomel*

B. Ruzicka

Brno, Czech Republic

1 INTRODUCTION

In the following articles, the procedure for the

Prague.

2 DETERMINATION OF SPRING RATES

Table 1: Vehicle mass properties.

Constant Value Unit Signification

300 [ kg ] overall vehicle mass

135 [ kg] overall mass on front axis

165 [ kg] overall mass on rear axis

K and rear

RnFRrF

RsFRrF

ʌ=f

9333,672107,22.2,12

Nm=ʌ=K

9683,612135,89.1,92

Nm=ʌ=K

With spring rate

125000

RrFttRrF

KKKK=K

10086,849333,6712500050009333,67.12

10496,789683,6112500050009683,61.12

Final real spring rates

1,50=IR=IR

1,40=IRIR

4483,041,510086,84

Nm==IRK=K

5355,51,410496,78

Nm==IRK=K

3 CALCULATION OF ANTI-ROLL BAR PARAMETERS FOR DESIRED ROLL

GRADIENTS

Roll gradient

1,230,m=t

1,205), spring rates

FwFĳF

133,177630,1984.1,2300,5.10086,21

RwRĳR

133,017620,878.1,2050,5.10496,21

1995) of the height of the center of gravity of the sprung mass

0,26 , m=r

0,26, and front / rear

0,04 , m=z

0,06).

0,44135,89107,22107,22=+=m+mm=a

SFRFSRM

0,3190,4410,040,060,040,3471

For anti-roll bars stiffness

Kis required.

Nm=+=gmsR+mh=AM

762,9.9,81135,89107,220,319.

RĳFĳĳB

RFĳB

K as follows

FĳB

K = 508.6 . (

100545

RĳB

FĳB

K = 242.42 - 121.13 = 121.29 Nm / deg

Because the anti-roll bar installation ratio

1,50=IR=IR

FABFAB

1,40=IR=IR

RABRAB

RFĳAB

FĳAB

K 53,831,5121,13

FABFĳB

Nm / deg

FĳAB

K 61,881,4121,29