Strojniški vestnik - Journal of Mechanical Engineering 52(2006)1, 41-51 UDK - UDC 629.11.012.1:519.61/.64+006(430) Strokovni članek - Speciality paper (1.04) Primerjalna analiza preračuna prednje preme po metodi končnih elementov in standardu DIN743 The Difference Between a Front-Axle Stress Calculation Using the Finite-Element Method and the Same Calculation According to DIN743 Ivan Okorn1 - Tomaž Bešter1 - Petar Orbanič2 - Matija Fajdiga1 (1Fakulteta za strojništvo, Ljubljana; 2 Cimos, Koper) Prednja prema je sklop elementov, prek katerih se prenašajo obremenitve s prednjih koles na sasijo vozila. Glavni elementi preme so most, krmilni sornik in krmilna os. Obremenitve elementov so odvisne od sil na kolesih. Velikosti in smeri sil so odvisne od okoliščin vožnje (vožnja naravnost, neravna cesta, vožnja v ovinku, sunkovito zaviranje). Dinamične sile so bile določene na podlagi mase vozila in dinamičnih koeficientov. Za bolj natančno določitev sil na kolesih bi morali opraviti meritve obremenitvenega kolektiva. Na primeru preme avtobusa so bili ugotovljeni kritični elementi in definirana kritična mesta na njih pri različnih obremenitvenih primerih. Preračun elementov je bil izveden po standardu DIN743, ki se v praksi uporablja za preračun osi in gredi, in z metodo končnih elementov (MKE). Primerjani so varnostni faktorji, dobljeni po obeh metodah. © 2006 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: preme sprednje, osi krmilne, sile dinamične, metode končnih elementov) The front-axle assembly is used to transmit forces from the wheels to the chassis of a vehicle. The main parts of the front-axle assembly are the I beam, the knuckle extension and the bolt. The loads on the elements depend on the road and the driving conditions (straight driving, bumpy road, cornering and panic braking). The dynamic forces were calculated with regard to the vehicle mass and the dynamic coefficients. To more accurately determine the wheel forces, measurements of the load spectrum need to be carried out. The first calculation, according to DIN743, was carried out for critical spots on the assembly. Later, a finite-element analysis was carried out, which confirmed the positions of the critical spots. A comparison of the safety coefficients obtained by both methods was also made. © 2006 Journal of Mechanical Engineering. All rights reserved. (Keywords: front axles, knuckle extensions, dynamic forces, finite-element methods) 0 UVOD 0 INTRODUCTION Prednja prema je vitalni sklop vozila. V primeru poškodbe kateregakoli elementa preme so posledice lahko usodne. Obremenitve elementov so naključno dinamične. Dolčitev nosilnosti preme je zahtevna naloga, saj navadno ne poznamo dejanskih dinamičnih obremenitev. Te lahko natančno določimo le z meritvami obremenilnih kolektivov pri dejanskih obratovalnih razmerah. Pri praktičnih preračunih dinamične obremenitve določimo na podlagi statične obremenitve in dinamičnih koeficientov. Zavedati se moramo napak, ki se pri tem pojavijo, in uporabiti pri The front-axle assembly is a vital part of a vehicle, although damage to any part of the assembly can have fatal consequences. Determining the load capacity is a demanding task, because we do not know the exact dynamic loads in the early design stages. Exact dynamic loads can only be determined from a load-spectrum measurement in real operating conditions. The dynamic forces used for calculations in the early design stages are obtained from static loads and dynamic coefficients. We have to realize the deviations that occur as a result of such an 41 Strojniški vestnik - Journal of Mechanical Engineering 52(2006)1, 41-51 določanju nosilnosti ustrezno velike varnostne faktorje. Napetosti v kritičnih prerezih lahko določimo po običajni metodi z uporabo enačb trdnosti ali z metodo končnih elementov. V kritičnih prerezih (prehodi, krčni nased) se pojavijo koncentracije napetosti, ki so odločilne za nastanek in širjenje razpoke pri dinamični obremenitvi. Pri običajni metodi koncentracije napetosti ocenimo na temelju vrste, oblike in izmer kritičnega prereza. Z metodo končnih elementov dobimo porazdelitev napetosti po elementu. Določimo lahko največje napetosti v kritičnem prerezu. Pri znani masi vozila m lahko izračunamo sile na kolesu. Cesta, po kateri pelje vozilo ni nikoli idealno ravna, zato v navpični in bočni smeri nastajajo sunki. Ti so posebej izraziti pri vožnji prek ovire in pri vožnji po luknjasti cesti. Dinamične sile določimo z ustreznimi koeficienti. Vrednosti preberemo iz diagramov [4], ki so določeni na podlagi meritev in izkušenj. Natančno je dinamične sile mogoče določiti le s preizkusi. Za trdnostno kontrolo je treba izračunati tako najmanjše kakor tudi največje napetosti in zato tudi najmanjše in največje sile, ki se pojavljajo pri vožnji. Navpična sila: Dinamični koeficient k je odvisen od vzmetne konstante pnevmatike, statične sile in načina obremenitve (spremenljiva, sunkovita). Pri spremenljivi obremenitvi upoštevamo koeficient k1, pri sunkoviti obremenitvi pa k2 [4]. Na obremenitev preme ne vplivata teža kolesa in pesta Gk. Bočna sila: Pri vožnji naravnost se bočna sila na kolo pojavi zaradi neravnosti tal. Njena smer se med vožnjo spreminja. Če je obremenitev spremenljiva, upoštevamo koeficient stranskega sprijema « pri sunkoviti obremenitvi pa M2 [4]. approximation, and use the appropriate safety factors. Stresses can be determined by a static calculation of the critical cross-sections or by the finite-element method. In critical cross-sections stress peaks occur. These peaks are decisive for the origin and the propagation of cracks under a dynamic load. In a calculation according to DIN743 we estimate the stress peak with regard to the type, the shape and the size of the cross-section. The finite-element method allows us to obtain the stress distribution over the whole part and determine the maximum stress in the critical cross-section. If the total mass of the vehicle is known, the approximate wheel forces can be calculated. Roads are never completely flat, therefore vertical and horizontal shocks can be expected. The most significant shocks occur when the vehicle is driving over an obstacle or on a bumpy road. The dynamic forces for the calculations are determined with the coefficients from diagrams [4] that were established from previous measurements and experience. For stress control we need the maximum and minimum stress, therefore we need the maximum and minimum wheel force. Vertical force: (1) The dynamic coefficient depends on the tyre spring rate, the static force and the load mode (variable load, shock load). For the variable load coefficient, k1 is used, while for the shock load coefficient, k2 is used [4]. The weights of the wheel and hub do not influence the axis assembly loads, Gk. Lateral force: (3) During straight driving the road roughness causes a lateral force on wheel. The direction and magnitude of this force is changing during the drive. For the variable load friction coefficient, ms1 is used, and for shock load friction coefficient, ms1 is used [4]. 1 SILE NA KOLESU 1 WHEEL FORCES Fzmax =-----xxxxk-Gk F zmin = mmin g -G k m max ' g 2 m min ¦g F (4). (2). 42 Okorn I. - Bešter T. - Orbanič P. - Fajdiga M. Strojniški vestnik - Journal of Mechanical Engineering 52(2006)1, 41-51 Zavorna sila: F Braking force: (5). Koeficient trenja med pnevmatiko in cesto ms je odvisen od vrste pnevmatike, globine profila, vrste cestišča in hitrosti vozila pred zaviranjem. Pri močnem zaviranju lahko doseže koeficient trenja vrednost ms = 1,25 [4]. Vrednosti sil na kolesu pri določeni najmanjši in največji obremenitvi so podane v preglednici 1. The friction coefficient between the road and the tyre depends on the tyre type, the profile depth, the road conditions and the vehicle speed. During intensive braking a friction coefficient ms=1.25 can be achieved [4]. The wheel force magnitudes for the minimum and maximum loads are given in Table 1. Sl.1. Sile na kolesu Fig.1. Forces on the wheel Preglednica 1. Sile na kolesu pri osni obremenitvi m = 3200 kg in m in = 2650 kg Table 1. Forces on the wheel at axial load mmax = 3200 kg and mmin = 2650 kg Vožnja naravnost Straight ride Fzmin N Fzmax N Fxmax 0 N 11208 11208 11208 19901 35597 19901 F ymin 2860 2860 N F ymax 3095 3095 N Vožnja preko ovire Ride over obstacle Sunkovito zaviranje Shock braking 0 0 19620 Primerjalna analiza preračuna prednje preme - The Difference Between a Front-Axle Stress Calculation 43 Strojniški vestnik - Journal of Mechanical Engineering 52(2006)1, 41-51 Sl.2. Krmilna os Fig.2. Knuckle extension 2 PRERAČUN KRMILNE OSI Za znano geometrijsko obliko krmilne osi na sliki 2 smo izvedli kontrolo napetosti v kritičnem prerezu 1. 2.1 Preračun na trajno dinamično trdnost Pri okoliščinah, ki veljajo za vožnjo naravnost, preračunamo elemente preme na trajno dinamično trdnost. Upoštevamo navpično silo F, ki se spreminja med FZmi in FZm in bočno silo F . Bočna sila se spreminja po velikosti in tudi po smeri. Največja upogibna napetost v kritičnem prerezu se pojavi pri FZm in delovanju F navzven, najmanjša upogibna napetost pa pri FZmin in delovanju F in navznoter. Za izračun varnostnega faktorja smo uporabili standard DIN743, ki se v praksi uporablja za preračun osi in gredi. Na sliki 3 je prikazan splošen algoritem preračuna na trajno dinamično trdnost. V našem primeru se preračun poenostavi, saj so za preračun krmilne osi odločilne upogibne napetosti. Natezne in tlačne napetosti zaradi bočne sile ter strižne napetosti zaradi navpične sile so zanemarljive. Napetosti lahko določimo po znanih enačbah iz trdnosti ali z metodo končnih elementov. Trajne dinamične trdnosti za različne materiale so določene s preizkusi in jih dobimo v [2]. Vrednosti so podane za določeno izmero preizkušanca. Pri izračunu trajne dinamične trdnosti elementa, ki ga oblikujemo, moramo upoštevati velikost prereza s tehnološkim faktorjem velikosti prereza K [2]. Oblikovna trajna dinamična trdnost je odvisna od hrapavosti površine, oblike in izmer kritičnega prereza, velikosti prereza in toplotne obdelave površinskega sloja. Navedeni vplivi so zajeti v konstrukcijskem faktorju, ki je določen z enačbo: 2 KNUCKLE EXTENSION CALCULATION For the knuckle extension in Figure 2 stress control was performed. 2.1 Endurance limit calculation Endurance limit control is performed for all axle-assembly elements with straight-drive loads. The vertical force FZ and the lateral force FY are used in the calculation. The vertical force varies between FZmin and FZmax, while FY is alternating. The maximum bending stress is caused by the maximum vertical force FZmax and the maximum lateral force FYmax. The minimum bending stress is achieved with the minimum vertical force FZmin and the minimum lateral force FYmin. A safety-factor calculation was performed according to DIN743, which is used for shaft and axle calculations. Figure 3 shows the general calculation procedure. In our case the procedure can be simplified, because the bending stresses are much greater than the tension stress due to the lateral force and the share stress due to the vertical force, which can therefore be neglected. The stresses can be determined with static theory or with the finite-element method (FEM). The endurance limits were obtained with measurements and are available in the literature [2]. The values in the literature are given for a certain specimen size. In the calculation of the endurance limit the cross-sectional size is considered with a technological size factor. The endurance limit depends on the surface roughness, the shape, the cross-sectional dimensions and the surface hardness. The stated influences are captured with the equation: K b kb K K V g oa J K (6). 44 Okorn I. - Bešter T. - Orbanič P. - Fajdiga M. Strojniški vestnik - Journal of Mechanical Engineering 52(2006)1, 41-51 Koncentracijo napetosti v kritičnem prerezu upoštevamo s faktorjem zareznega učinka R , velikost prereza s K, hrapavost površine s K in toplotno obdelavo površinskega sloja površinskega sloja s Kv [2] . Na utrujanje materiala odločilno vpliva amplitudna napetost, zato pri izračunu varnostnega faktorja računamo z amplitudnimi napetostmi. Za R=a /a = konst določimo oblikovno amplitudno napetost po enačbi: s The stress concentration is captured with the notch effect factor pkb, the cross-sectional size with K, the surface roughness with K and the surface-hardening treatment with K [2]. " The decisive factor for material fatigue is the stress amplitude, which is used in the calculation as a criterion for the calculation of the safety factor. For R=a /a =const. the modified amplitude endurance limit is calculated according to the following equation: bGW 1 + ys (7), ba kjer je V fator občutljivosti na srednjo napetost. Odvisen je od vrste materiala in njegove natezne trdnosti Rm. Za jeklo znaša: ys=0,00035-R-0,1 Hkrati z običajnim izračunom napetosti smo določili napetosti v krmilni osi z metodo končnih elementov (MKE). Izkazalo se je, da je bil kritični where V is the middle stress factor, which depends on the material and its tensile strength R . For steel this factor is: (8). Parallel with this calculation, the FEM stress analysis was performed. With the FEM analysis we obtained a stress-distribution picture that confirmed L I Start [ _L 7 / GmH* Tfww Kt i Kotila ' K i G&ti/Ka *tGW " K TtWH'Kpf Amplitudne in srednje napetosti Amplitude and mean stresses Izmenična trajna dinamična trdnost Endurance limit (R=-1) Konstrukcijski faktor Design factor Oblikovna trajna dinamična trdnost Modified endurance limit (R—1) Faktor občutij iwsti na srednjo napetost Mean stress sensitivity factor Primerjalna srednja napetost Equivalent mean stress (von Mises) Oma- *tw r*V<7 »*/<*<» I Tm' ~W I VI'bmJ Lt,^J Oblikovna amplitudna napetost Modified amplitude endurance limit Tff'U-R0uH-Kl/T&~ S,- ItF J When driving over an obstacle, during panic braking and when driving over a bumpy road, shock loads appear. In such cases the safety factor with regard to the yield stress was calculated. The calculation procedure for the safety factor is presented in Figure 5. In the calculation of the safety factor the maximum stresses are taken into consideration. The safety factors for the wheel forces in Table 1are presented in Table 3. The safety factors with regard to the yield strength are much higher than necessary. The shock stresses, therefore, are not critical. The safety factors calculated with the FEM are lower than those calculated with the conventional static calculation. Največja upogibna napetost Maximum bending stress Največja strižna napetost Maximal shearstress Meja plastičnosti (nateg) Yield strenght (tension) Meja plastičnosti (upogib) Yield strenght (bending) Meja plastičnosti (strig, torzija) Yield strenght (shear) Varnostni faktor glede na mejo plastičnosti Safety factor with regard to yield strenght Sl.5. Določitev varnostnega faktorja glede na mejo plastičnosti Fig.5. Determination of the safety factors with regard to the yield strength Preglednica 3. Varnostni faktorji glede na mejo plastičnosti Table 3. Safety factors with regard to the yield strength sbmax MPa Rp0,2N 9 MPa Kt Vožnja prek ovire Ride over obstacle običajni izračun classical calculation 191 MKE FEM Sunkovito zaviranje Shock braking običajni izračun classical calculation 207 185 224 900 900 900 900 0,876 0,876 0,876 0,876 SF 4,97 4,57 5,11 4,22 MKE FEM Primerjalna analiza preračuna prednje preme - The Difference Between a Front-Axle Stress Calculation 47 Strojniški vestnik - Journal of Mechanical Engineering 52(2006)1, 41-51 saj z običajnim izračunom ne zajamemo koncentracij napetosti. Pri sunkovitem zaviranju največje napetosti se ne pojavijo v prerezu 1, ampak ob spodnjem ušesu. 3 PRERAČUN MOSTU This is expected since the FEM analysis shows stress peaks. During panic braking the maximum stress does not appear at cross-section No. 1, but at the bolt hole. 3 I BEAM CALCULATION Po enakem postopku, kakor smo preračunali The same procedure that was used for the krmilno os, smo preračunali tudi most preme. knuckle extension was used for the I beam as well. 3.1 Preračun na trajno dinamično trdnost Kritični prerez je ob ušesu, v katerega vstavimo krmilni sornik. V preračunu smo upoštevali navpično silo FZ, ki se spreminja med FZmin in FZmax, Preglednica 4. Napetosti in varnostni faktor SD Table 4. Stresses and safety factor SD 3.1 Endurance limit calculation The maximum stresses on the I beam occurred by the bolt hole. In the calculation of the vertical forces Fz and FY the lateral force was taken into account. sm MPa s ba 83 92 MPa K sbGA MPa Običajni izračun Classical calculation 126 182 s bWN 550 550 MPa bkb 1,2 1 1,978 s bGW 241 272 MPa 169 SD 2,02 1,9 MKE FEM 1,748 174 Sl.6. Porazdelitev napetosti v mostu Fig.6. Distribution of stresses in I-beam 48 Okorn I. - Bešter T. - Orbanič P. - Fajdiga M. Strojniški vestnik - Journal of Mechanical Engineering 52(2006)1, 41-51 in bočno silo F. Največja upogibna napetost v kritičnem prerezu se pojavi pri FZm in delovanju F navzven, najmanjša upogibna napetost pa pri f ymax in delovanju F i navznoter. Porazdelitev napetosti prikazuje sliki 6, vrednosti napetosti in varnostnih faktorjev pa preglednica 4. Varnostni faktorji so bistveno manjši kakor pri preračunu krmilne osi. Most preme je bistveno bolj kritičen element kot krmilna os. 3.2 Varnost glede na mejo plastičnosti Iz preglednice 5 je razvidno, da je sunkovito zaviranje kritična obremenitev. Med ušesom mostu in pritrditvijo na nadgradnjo je most obremenjen na upogib in torzijo, med pritrdiščema na nadgradnjo pa na upogib. Pri običajnem preračunu po DIN 743 smo predpostavili členkasto pritrditev mostu na nadgradnjo, zato so največje napetosti večje od napetosti, dobljenih z MKE. 4 SKLEPI V prispevku je podan preračun krmilne osi in mostu preme pri spremenljivih in sunkovitih obremenitvah. Omejili smo se na vožnjo naravnost. Pri spremenljivi obremenitvi računamo z obremenitvami, ki se pojavijo pri navadni vožnji po srednje dobri cesti. Te obremenitve mora material trajno prenesti, zato smo elemente oblikovali na trajno dinamično trdnost. Pri sukovitih obremenitvah, ki se pojavijo pri vožnji prek ovire in sunkovitem zaviranju največje napetosti, ne smejo prekoračiti meje plastičnosti materiala. Določili smo varnostne faktorje glede na mejo plastičnosti. Napetosti smo določili po običajnih trdnostnih enačbah in z metodo končnih elementov ter izračunali The maximum bending stress in the critical cross-section occurs when FZmax and FYmax are applied, while the minimum bending stress occurs when FZmin and FYmin are applied. The stress map is presented in Figure 6. The safety factors are presented in Table 4. Since the safety factors of the I beam are much smaller than the safety factors of the knuckle extension. The I beam is a much more critical element than the knuckle extension. 3.2 Yield stress safety The results in Table 5 show that panic braking is the most critical load. In this load case the I beam between the bolt hole and the spring is subjected to bending and torsion, while the I-beam section between the springs is subjected only to the bending stress. For the DIN 743 calculation the knuckle fastening to the springs was assumed, while in the FEM analysis the rotation in a lateral direction was omitted. 4 CONCLUSIONS This article presents part of the axle-assembly calculation for variable and shock loads. The article does not consider straight driving. In the variable-loads calculation we consider the loads that occur when driving on normal or moderately bumpy roads, where the axle assembly must permanently endure these loads and the endurance limit is the dimensioning criterion. Shock loads, like driving over an obstacle or panic braking, do not occur frequently, therefore, it is sufficient if no plastic deformations occur and the yield stress can be the dimensioning criterion. The stresses were calculated with conventional static equations and the FEM. The Preglednica 5. Varnostni faktorji glede na mejo plastičnosti Table 5. Safety factors with regard to the yield strength sbmax MPa Vožnja prek ovire Ride over obstacle običajni izračun classical calculation 476 420 907 781 MKE FEM Sunkovito zaviranje Shock braking običajni izračun classical calculation MKE FEM Rp0,2N 9 MPa 900 900 900 900 Kt 0,908 0,908 0,908 0,908 SF 2,06 2,33 1,08 1,26 Primerjalna analiza preračuna prednje preme - The Difference Between a Front-Axle Stress Calculation 49 Strojniški vestnik - Journal of Mechanical Engineering 52(2006)1, 41-51 varnostne faktorje po DIN743. Izkazalo se je, da krmilna os ni kritični element niti pri spremenljivih niti pri sunkovitih obremenitvah. Bistveno bolj kritičen je most preme, posebno pri sunkoviti obremenitvi, ki se pojavi zaradi močnega zaviranja. Rezultati, ki jih dobimo z metodo končnih elementov, se dobro ujemajo z rezultati, dobljenimi po običajni metodi. Ker je običajna metoda bistveno hitrejša je smiselno najprej izvesti preračun po običajni poti. Za elemente, ki se izkažejo za kritične, je smiselno uporabiti še metodo končnih elementov. V našem primeru se izkaže, da krmilna os ni kritičen element, zato preračun z MKE ne bi bil nujno potreben. Upravičena pa je uporaba MKE pri preračunu mostu preme. Krmilna os in most preme sta povezana prek krmilnega sornika, ki je prav tako kritičen element. Če bi želeli ugotoviti dejanske mejne nosilnosti, bi bilo treba s preizkusom ugotoviti dejanska obremenilna stanja med obratovanjem (obremenilni kolektivi), ugotoviti dejanske trdnostne lastnosti materialov s preizkušanjem, z numeričnimi simulacijami izdelati preračune trenutnega in utrujenostnega loma vseh ključnih elementov in z vidika zanesljivosti s preizkusi ugotoviti največjo mogoče nosilnost. Naslova avtorjev: dr. Ivan Okorn Tomaž Bešter prof.dr. Matija Fajdiga Univerza v Ljubljani Fakulteta za strojništvo Aškerčeva 6 1000 Ljubljana ivan.okorn@fs.uni-lj.si tomaz..bester@fs.uni-lj.si. matija.fajdiga@fs.uni-lj.si safety factors were, in both cases, calculated according to the DIN 743 standard. The results showed that the knuckle extension is not the critical element, neither for variable nor for shock loads. Much more critical is the I beam, especially with a shock load due to panic braking. The results obtained by both methods are in good agreement. Since the conventional static calculation is much faster than the finite-element method it is reasonable to use this method and then apply the FEM analysis to the most critical elements. In our case the knuckle extension was not the most critical element, therefore the FEM analysis was not necessary, while the I beam is more critical and the FEM analysis is more suitable. The knuckle extension and the I beam are connected by a bolt that is a more critical element as well. In the event that we want to establish the actual limit load capacity, it would be necessary to establish with an experiment the actual loading states during operation, establish the actual material properties with tests, carry out the calculation of the temporary and fatigue fracture of all the vital elements with numerical simulations and by testing establish the major potential load capacity from the reliability point of view. Authors’ Addresses: Dr. Ivan Okorn Tomaž Bešter Prof.Dr. Matija Fajdiga University of Ljubljana Faculty of Mechanical Eng. Aškerčeva 6 1000 Ljubljana, Slovenia ivan.okorn@fs.uni-lj.si tomaz..bester@fs.uni-lj.si. matija.fajdiga@fs.uni-lj.si 5 LITERATURA 5 REFERENCES [1] Muhs, D. et al. (2003) Roloff/Matek Maschinenelemente - Normung, Berechnung, Gestaltung, 16. Auflage. Vieweg Verlag, Wiesbaden, p.p. 37-69. [2] Muhs, D. et al. (2003) Roloff/Matek Maschinenelemente - Tabellen, 16. Auflage, Vieweg Verlag, Wiesbaden, p.p. 1-3, 36-51. [3] Haberhauer, H. et al. (2001) Maschinenelemente - Gestaltung, Berechnung, Anwendung, 11. Auflage. Springer Verlag, Berlin Heidelberg, p.p. 277-291. [4]Goljar, M. (1977) Motorna vozila. Fakulteta za strojnitvo, Ljubljana, p.p.195-200, 212-228. [5] DIN 743 (2000) Tragfahigkeitsberechnung von Wellen und Achsen. Beuth Verlag, Berlin. 50 Okorn I. - Bešter T. - Orbanič P. - Fajdiga M. Strojniški vestnik - Journal of Mechanical Engineering 52(2006)1, 41-51 dr. Petar Orbanič Cimos d.d. C. Marežganskega upora 2 6000 Koper petar.orbanic@cimos.si Dr. Petar Orbanič Cimos d.d. C. Marežganskega upora 2 6000 Koper, Slovenia petar.orbanic@cimos.si Prejeto: Received: 5.10.2005 Sprejeto: Accepted: 16.11.2005 Odprto za diskusijo: 1 leto Open for discussion: 1 year Primerjalna analiza preračuna prednje preme - The Difference Between a Front-Axle Stress Calculation 51