VOLUME 3 TANSATIONS ON TANSPOT SIENES NUMBE 4 00 Technical Note on Design of Suspension Paraeters for FSAE Vehicle O. Suchoel* ULS Prague, Technical Faculty, Departent of Vehicles and Ground Transport, Prague, zech epublic B. uzicka University of Technology Brno, Faculty of Mechanical Engineering, Institute of Machine and Industrial Design, Brno, zech epublic * orresponding author: suchoel@tf.czu.cz ABSTAT: orrect suspension paraeters deterination is one of the ost iportant design issues in the developent of each type of car. The ai 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 axiu aount of traction, braking and lateral forces which deterine a vehicle s acceleration capabilities. This article describes the deterination of the Forula Student/SAE car suspension paraeters related to the vertical dynaics of the car as a basic point in tuning up the suspension on the car itself in real operating conditions. EYWODS: Suspension paraeters, spring rate, daping rate, Forula Student/SAE. INTODUTION Suspension is one of the ost iportant pieces of equipent on each car. It has different functions: it carries all the vehicle s loads; aintains the correct wheel alignent to the ground; reduces the effect of shock forces when passing ground disturbances; controls the vehicle s longitudinal and lateral speed, and aintains the tire contact patch in contact with the ground for the axiu tie possible. The entioned requireents are provided by different suspensions parts divided into the guiding eleents and force generating eleents. In the following articles, the procedure for the deterination of the spring rate and daping rate is presented. The nuerical values of the entioned constants are coputed for a Forula Student/SAE car and later used when building the real Forula Student/SAE car at ULS Prague. DETEMINATION OF SPING ATES The described approach for the deterination of all the necessary suspension paraeters related to the vertical dynaics is based on a quarter-sized car odel. The basic points for the suspension design paraeters are the ass properties of the vehicle (see tab.). 97
VOLUME 3 TANSATIONS ON TANSPOT SIENES NUMBE 4 00 Table : Vehicle ass properties. onstant Value Unit Signification 300 [ kg ] overall vehicle ass w F / w 45 / 55 [ % / % ] ass distribution related to front / rear axis F wf 35 [ kg ] overall ass on front axis w 65 [ kg ] overall ass on rear axis 7.78 [ kg ] overall unsprung ass on front axis uf 9. [ kg ] overall unsprung ass on rear axis u 07. [ kg ] overall sprung ass on front axis s F UF 35.89 [ kg ] overall sprung ass on rear U According the suggestions fro literature (Milliken & Milliken 995) for low-downforced racing cars, the initial choice of ride frequencies is as follow: front ride frequency f nf. Hz, rear ride frequency, f n.9 Hz Then ride rates for front rf and rear rf end of the vehicle, with respect to corner (either left or right which equals). f nf, rf,,, rf, πf nf,, π 07, 35,89 rf π., 9333,67N π.,9 9683,6N r With spring rate (Honzík, 008) t 5000N of chosen tire Hoosier 0x7.5x3 - pressure 4 PSI wf, rf, t t rf, wf 9333,67.5000 0086,84N 5000 9333,67 w 9683,6.5000 0496,78N 5000 9683,6 98
VOLUME 3 TANSATIONS ON TANSPOT SIENES NUMBE 4 00 Final real spring rates, ust be recalculated using the so-called "installation ratio" (Milliken & Milliken, 995) defined as rate of change of spring copression with wheel oveent. To slightly siplify the non-linear function for pull-rod type suspension, installation ratios have to be dealt with as a constant F F 0,5 0. Then and,4 0086,84 N wf 4483,04 F,5 s 0496,78 N w 5355,5,4 3 ALULATION OF ANTI-OLL BA PAAMETES FO DESED OLL GADIENTS oll gradient deg g G / gives inforation on how uch the body rolls due to the lateral acceleration of the whole car. The desired set up is up to.5 / g, referred to by suggestions given in (Milliken & Milliken, 995) as the Forula Student/SAE car achieved a ax. lateral acceleration of about.5g. At first, roll stiffness is coputed using front and rear track ( t F,30, t,05 ), spring rates wf,. N F wftf 0,5.0086,84.,30 7630,9 33,7 rad N deg N N wt 0,5.0496,78.,05 760,8 33,0 rad deg The next step in the deterination of anti-roll bars is the coputation (Milliken & Milliken, 995) of the height of the center of gravity of the sprung ass h S, sprung ass distribution a S and rolling oent lever ar h M (with the help of used variables: height of the center of gravity of the whole car h 0,38, wheel radius r F 0,6, r 0,6, and front / rear roll center heights z F 0,04, z 0,06 ). h ufrf ur 300.0,38 7,78.0,6 9,.0,6 hs 0,37 + 07,+ 35,89 s a S + s 07, 0,44 07,+ 35,89 z z z a 0,347 0,04 0,06 0,04 0,44 hm hs F F S 0,39 99
VOLUME 3 TANSATIONS ON TANSPOT SIENES NUMBE 4 00 For anti-roll bars stiffness acceleration, B M / Ay and the coputation of the overall desired roll stiffness, the calculation of the rolling oent per g of lateral is required. M A y h M +sg 0,39. 07,+ 35,89.9,8 76,9N M / Ay 76,9 508,6N. / deg G.5 B F 508,6 33,7 33,0 4,4N / deg The recoendation (Milliken & Milliken, 995) is to start with a total lateral load distribution to be 5% ore 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 B F, is deterined fro the overall desired roll stiffness as follows B F. ( w F 5 00 45 5 ) - F 508.6. ( ) 33.7.3 N / deg 00 B B - B F 4.4.3.9 N / deg Because the anti-roll bar installation ratio, (the rate of anti-roll bar displaceent / roll AB F with body roll) is expected to be the sae as the ratio for the springs,5 and,4 AB F AB AB 0, then the final front and rear anti-roll bar stiffness AB F, is : AB F 0 AB F,3,5 B F AB F 53,83 N / deg AB F,9,4 B AB 6,88 N / deg 00
VOLUME 3 TANSATIONS ON TANSPOT SIENES NUMBE 4 00 4 DETEMINATION OF DAMPING OEFFIIENTS The baseline ean ride daping coefficients for each wheel of the front brf and rear axle br result fro the critical daping values brfcrit, brcrit (the critical daping coefficients of the sprung ass) ultiplied by the recoended (Milliken & Milliken, 995) daping ratios for the front and rear axle ζ F 0,4, resp. ζ 0,45. 07, wf 0008,84 brfcrit 470,73 s 35,89 w 0496,78 brcrit 689,05 brf ζ FbrFcrit 0,4.470,73 588,9 br ζ brcrit 0,45.689, 05 760,07 To obtain the final values of the ean daping coefficients set-up on the dapers,,, these ust be corrected by the corresponding installation ratio again F brf 588,9 F 6,46,5, br 760,07 387,79,4 For better control of resonance and the energy released by the spring, ore daping force is required by the daper during the rebound (bilinear odel). This asyetry for copression and extension E daping is expressed by the copression/extension ratio E with a typically value 0.4 as recoended fro (Dixon, 999). E 0
VOLUME 3 TANSATIONS ON TANSPOT SIENES NUMBE 4 00 Then, the odified daping coefficients, as a starting point for the next suspension tuning for the linear progressivity of copression and extension, are calculated for both axles as follows EF F E.6,46 0,4 373.5, F E EF 49.4 E E.387,79 0,4 553.99, E E.59 5 ONLUSIONS This paper presents an approach for the deterination of basic suspension paraeters - spring stiffness, anti-roll bar stiffness and daping coefficients. The approach is based on linear vibrations dynaics and sei-experiental recoendations for the choice of basic constants. The presented approach can be applied for any road racing vehicle. ANOWLEDGEMENTS This paper was supported by the Internal Grant Agency of the Technical Faculty at the zech University of Life Sciences. The paper was created in the Forula Student/SAE project at TF ULS. EFEENES Milliken, W., Milliken D., 995. ace ar Vehicle Dynaics. SAE, 995. Honzík T., 008. Front Axle Design for Forula SAE. VUT Brno ill, G. : Vehicle dynaics. Lecture notes, October 007. Fachhochshule egensburg. Available on http://hoepages.fhregensburg.de/~rig3965/skripte/vehicle_dynaics.pdf Dixon, J. : 999, The Shock Absorbers Handbook, SAE 999 0
VOLUME 3 TANSATIONS ON TANSPOT SIENES NUMBE 4 00 Index of Titles Volue 3/ 00 Abdoinal Finite Eleent Model for Traffic Accidents Injury Analysis, 69-78 Acceptance of Train Delays by Passengsers, 83-9 An Application for the Ipendance Spectroscopy Metod and Building Material Trstiny, 7-76 Assessent of Heavy Metal Pollution (d, u, Pb, Hg) in Urban Soils of oadsides in Brno, 47-56 Bioechanical esponse of Head Dutiny Ipact Loading, 53-66 ritical Infrastructure Safety Manageent, 57-68 Decarbonisation of Transport and Modal Split, 07-4 Dynaic Tests: Passenger ar vs. hild Pedestrian, 57-96 Fast Ipedance Spectroscopy Method for Insulating Layers with Very High Ipedance, 9-38 Influences of Utility Networks on Measuring, 39-44 Interaction between yclist and ar during Broadside and onfortation with Pedestrian Throw Forulas Multibody Siulation, 99-06 Methods of Safety Estiation in oad Traffic with Taking Pedestrian Traffic Probles into onsideration, 77-8 Modeling Traffic Inforation using Bayesian Networks, 9-36 Modelling of Price Deand Elasticity for Entry to Bus Terinals, 67-70 Non-linear Ultrasonic Spectroscopy as an Assessent Tool for the Structure Integrity of oncrete Specien, 7 - Optiizing the Location of Piezoelectric Senzore, 3-8 Pedestrian Model for Injury Prediction for Laterál Ipact, 45-5 Proposal for a Wheel Suspension Mechanis with ontrolled haracteristics, 5-0 Study of the Developent of racks Accopanying Mechanical Loading of Solids, - 8 03