Mechanics ISSN Transport issue 3, 2007 Communications article 0155

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1 Mehanis ISSN Transport issue 3, 7 Communiations artile Aademi journal ABOUT ADOPTION OF THE VERTICAL SUSPENSION PARAMETERS FOR PASSENGER WAGONS Cătălin CRUCEANU, Marius SPIROIU, Mădălina DUMITRIU _rueanu@yahoo.om, Asso. Prof. Dr. Cătălin Crueanu, let. Dr. Marius Spiroiu, assist. Mădălina Dumitriu, POLITEHNICA University of Buharest, Faulty of Transports, Rolling Stok Engineering Departmentр 33 Splaiul Independentei, setor, 77, Buharest, ROMANIA Abstrat: The suspension s projetion implies to establish the elasti and shok absorbent onstants of the onditions to ensure the rolling vehile s dynami performanes. The neessary vertial rigidities adoption implies also a ertain orrelation between the onstrutive masses. The geometrial and mehanial harateristis of the railway affet signifiantly the suspension s response. Moreover, during the braking ations, due to the frition fore between diss and brake pads, the axles suspension s shok absorption fator inreases. Key words: suspension, suspension s rigidity, shok absorption fator, braking INTRODUCTION An important role of suspension is that of ontributing to the dereasing of mutual fores between the vehile and the trak, with the view to maintain these fores into the limits that are established by the onditions of seurity of traffi and the neessity of ensuring the protetion both of the running gear and the trak. That is why the orret adoption of the suspension parameters plays a major part for safety operating and when it omes about passenger oahes, there must be onsiderate the neessity of ensuring a vibratory omfort as better as possible. In point of suspension, a railway vehile an be modeled through a omplex, osillating system, formed by ontinuously distributed and onentrated masses joined together through elasti and shok absorber elements. Suh model implies however a big number of unknown elements, situation whih makes it more diffiult the resolving of both the motion equations and extrating the onlusions that are useful in designing. That is why, onsidering the peuliarities of railway vehiles vibrations and the present engineering of the bogies, there is a model of a osillating two-liberty degrees system whih reflets, in an aeptable extent, the behavior of the studied system and whih an be adopted with a view to vertial suspension study. (see fig. ) [,]. m ρ m ρ Fig.. Elementary linear model of a vertial, two-liberty degree osillating t Generally, the suspension s design implies the establishment of elasti and shok absorber onstants in onditions onerning the insurane z z z o VІ-3

2 of rolling vehile s dynami performanes. The neessary rigidities an theoretially be determined by the ondition of imposed natural frequenies, but by onsidering also the neessary limitation of osillation amplitudes, whih the vehile box an develop on vertial diretion, and by taking notie of the elastiity repartition between the two suspension levels. Sine the suspension s state of exitation is given by the answer of unsprung masses, the value of these masses and the quality of the trak defined by its irregularities, as well as its elasti and shok absorbent harateristis, onstitute a very important aspet of projetion that must be taking into aount. One must also onsider the fat that, while braking ations, due to the frition fore that appears between the diss and brake pads, the shok absorption fator of the axles suspension inreases. CORRELATIONS BETWEEN MASSES In the ase of vertial suspension with two liberty levels, starting from the natural pulsation equation: m ( m + m + m ) ω + () mω = where m represents the bogie s sprung mass, m = ( m + mi ), m represents the box vehile s mass, m i the harge mass, and and the equivalent rigidities of the axles, respetively entral bogie s suspension levels, it follows the adequate expression of the defletion [,]: ν g ν + m f, = () 8π ν ν = ( ν + ν ) ( + m m ) ν ν In these relations, ν and ν represents the natural low, respetive high frequeny of suspension, whih, for avoiding the resonane phenomena and for omfort onditions there are reommended to be valorized, in the ase of high speed vehiles, at Hz, respetively between 7 Hz; g is gravitational aeleration s value. Considering these, the suspension s total stati defletion an be figured out with the following relation: f = f + f ν By establishing the rigidities of the suspension s levels, there are also other aspets g π ν (3) that must be onsidered, namely the ondition that the total defletion h aused by the harge not to exeed the aepted differene of elevation h max between the buffers of two suessive vehiles: mi h = h ν ( m + m ) max () and the known tehnial reommendation to ensure a ( 8...7) % (...)% ratio between the primary suspension s rigidity and the rigidity of the seondary one []. On the basis of determined points, in the ase of railway oahes having a bogie s sprung mass m =...3 t, a box mass m =... t and a harge mass m i =... t, we determinate the oherene range of the neessary equivalent rigidities of the two levels, enforing the low natural frequeny ν =Hz and the high one aording to ν =...7 Hz. From the analysis and the mathematial proessing of the obtained results it has been determined that the two levels rigidities of suspension an indeed keep all the onditions previously imposed if between the vehile s masses, expressed in tons, the following ondition is respeted: ( m + m ) m = i + () THE VERTICAL SUSPENSION S EXCITATION The exitation of vertial suspension depends on the trak s elasti system onstants, on its irregularities and on the vehile s unsuspended mass. This study limits itself at the vertial motion, supposing that the longitude leveling irregularities of the two traks are in the same phase and, for simplifying, that the osillations are harmonious. The vehile railway osillatory system was studied based on a simplified one liberty level mehanial model. (see fig. ) []. If m n is onsidered to be the unsprung mass, and ρ rigidity, respetive trak s shok absorption fators, z o and η o the amplitude of the unsuspended mass answer, respetively of the vertial irregularities, λ the pulsation disaord, the system s, answer fator in amplitude is, in simplifying hypotheses: VІ-

3 H z ηz o zo + D λ = =, () o η =η H ( λ ) D λ o + ηz. (7) m n z o ρ η the inrement of the irregularities trak s length wave, beoming smaller than. for length waves L 7. m (see fig. 3, urve ). These maximums move themselves with the inreasing of the unsuspended mass, due e.g. to the fittingout the mounted axles with brake diss. For the extreme ase of a bloked axles suspension, the transfer funtion H ηz dereases under. for wavelength L 7 m (see fig. 3, urve ). It is important to know these sizes both for the exitation s value transmitted to vehile s suspension and for the fat that it determines the dynami load s size at the wheel - rail ontat, whih influenes at the same time the adhesion fore that an affet the braking and the tration ones, the latter in the ase of driving vehiles. The influene that the main parameters have on the transfer funtion on amplitude of the vertial displaements at the level of mounted axles, whih determines the amplitude of suspension s reeived exitation, was the entral problem. Thus, it has been onsidering the trak irregularities wave length L =...3 m, unssprung masses m n =... kg (orresponding, in an extreme ase, to the bloked braking axle), various rigidities and shok absorption fators of the trak. funtie de transfer in amplitudine Fig.. Mehanial model for establishing the vehile s suspension exitation bloked axles suspension normally funtioning axles suspension 3 lungime de unda a denivelarilor aii [m] wave length of the irregularities of the trak [m] () suspensia osiilor funtionand normal () suspensia osiilor bloata Fig. 3. Dependene of transfer funtion s maxims in amplitude of vertial osillation on the trak irregularities wave length. The main results point that, in the onsidered domains, the transfer funtion on amplitude of the vertial displaements of the unsuspended masses reahes a maximum whih reedes with ABOUT THE RIGIDITY OF THE SUSPENSION S LEVELS The natural frequenies of the two suspension s levels depend on the onerned mass proportion: the bogie s suspended mass, the box mass and the harge mass, theoretially, the passengers and luggage s mass. It is obvious the fat that, observing the onditions pertinent to impose natural frequenies an be ahieved only through determinate areas of speified mass s values. Thereby, in the partiular ase of a railway arriage with a tons mass, for the 3 kg bogie s sprung masses, the possibilities of ensuring. Hz natural low frequenies, respetive of a 7 Hz high frequenies is presented in fig. and. E.g., for a kg bogie s suspended mass, the high frequeny exeeds 7 Hz value that is why it does not appear in fig.. low natural frequeny [Hz] harge mass [t] t. t t. t 3 t Fig.. Dependene of low natural frequeny on harge mass and sprung bogie mass (vehile s box mass t). VІ-

4 The imposed natural frequenies determine, in the whole suspension system, ertain values of the two levels rigidities. The high frequeny inrease realizes itself through the inrement of the rigidity of axles suspension, simultaneous with the derease of entral suspension s rigidity, as one an see in fig. (for the prior partiular ase above mentioned). high natural frequeny [Hz] Fig.. Dependene of high natural frequeny on harge mass and sprung bogie mass (vehile s box mass t). entral suspension rigidity [kn/mm] harge mass [t]. t t. t 3 t entral suspension high natural frequeny [Hz] axles suspension It might be interesting to analyze the influene that the axles suspension rigidity may have upon the phenomena during the braking ations. In the partiular ase of dis brake use, whih is a ompulsory element for the vehiles running with over km/h [3], the braking pads, whih are fixed through hangers on the bogie s frame, will have vertial diretion displaements aountable to the diss that are usually mounted on the axle. Therewith, the bogie s suspended mass will aquire vertial aeleration, determining a vertial fores development. During the braking ation, if the sum of frition fores between the braking diss and the pads exeeds the value of Fig.. Dependene of equivalent rigidities on high natural frequeny..9.8 axles suspension rigidity [kn/mm] these vertial fores, the suspension s primary level an obstrut itself, situation leading on to a substantial bigger unsprung mass []. This determines the development of ertain vertial dynami fores at the rail-wheel ontat. These fores inrease while the running speed inreases and might beome dangerous for the ssafety of running. From this point of view, as a priniple, we an say that the reession of the axles suspension level obstrution assumes the reah of some vertial dynami fores big enough at the bogie s frame level. Taking into aount the two levels mehanial suspension model (see fig. ), the vertial dynami fores at the bogie s frame level an be determined with the relation [,]: u = zo m ω A + B N, (8) where: z o represents the unsuspended mass s amplitude of osillation whih an be alulated with relation (7), A = γ λ + µ µ λ, ( ) B = λ 3 + µ δ, δ and δ the dumping ratio of the axles, respetively entral suspension levels, N = a + b, a = ( Γ λ δ δ ), γ =, b = [ Λ λ + ( γ λ ) λ ] δ, Γ = µ λ γ λ γ λ, V Λ = µ λ λ, ω = π, V [km/h] 3, L the instantaneous irulation speed, L [m] the rails irregularities wave length. On the alulus programmers ground, we observed that one with the inrease of the axles suspension s rigidity, there is also reorded an inrease of the bogie s vertial dynami fores. The perentage growth of the fore maxims, aountable to the minimum aepted value of 3 kn/mm is roughly linear, reahing almost % at the maximum aepted value of 3.9 kn/mm, how is presented in the diagram in fig. 7 []. ( ) ω m δ, λ =, µ =, m ω o ω o = ( ) ( ) m VІ-

5 growth of vertial dyn. fores [%] axles suspensions' rigidity [kn/mm] Fig. 7. Perentage growth of vertial dynami fores at the bogie s frame level in terms of axles suspension rigidity. Therefore, from this point of view too, follows the neessity of a bigger rigidity onerning the axles suspension s elasti elements and, impliitly, a natural high frequeny regarding the aeptable superior limit. We onsidered the ase of an emergeny braking ation starting at 3 km/h, at the adhesion limits. In the present ase, the use of a 3.9 kn/mm rigidity within the axles suspension would lead on a possible bloking of that suspension level at a speed about % smaller (9 km/h aountable to 3 km/h). We speify that, during a servie braking ation, ommanded with a..7 bar depression in the main brake-pipe, the effet of the axles suspension rigidities is insignifiant; theoretially, the suspension level s bloking tendeny manifests itself under km/h []. For almost the same ratio of the two suspension levels rigidities, we also observed the influene of the vehile s box mass, on the ground of 3 t. We onsidered the same harateristis of the rail and the same masses. The main alulus results are reported in the diagram presented in fig. 8. We notied that, for running speeds exeeding km/h, the box mass s influene beomes important and determines an inrease of the vertial dynami fores maxims developed at the bogie s level with 3% at a box mass growth from to 3 tons. The inrease is almost linear []. dyn. vert. fores [kn] 3 We also made a study regarding the effets of the suspension levels rigidities modifiations on the amplitude of the vertial osillations and on the vertial aeleration develpped at the vehile s box level. Within the study we onsidered a passenger vehile haraterised by a box mass of 8 t, a bogie s suspended mass of. t, a harge mass of 9 t and an. t unsprung mass for one mounted axle.the alulus presumed pairs of the suspension s levels rigidities, whih respet all the prior onditions and reommendations. The main results are summarized in the diagrams presented in fig. 9 and. amplit. transfer funtion t 3 veloity [km/h] t 8 t t Fig. 8. Dependene of vertial dynami fores at the bogie s frame on different vehile s box mass. veloity [km/h] =3 kn/mm; =.97 kn/mm =3.3 kn/mm; =.9 kn/mm =3. kn/mm; =.9 kn/mm Fig. 9. Amplitude transfer funtions of the vertial osillations of the vehile s box for different suspension s levels rigidities =3.9 kn/mm; =.9 kn/mm VІ-7

6 vert. a. of vehile's box [m/s^] veloity [km/h] =3 kn/mm; =.97 kn/mm =3.3 kn; =.9 kn/mm =3. kn/mm; =.9 kn/mm It an be observed that a inrease of the axles suspension s rigidity (impliitly a remission of the entral suspension s rigidity) does not affet in a major way the vertial osillation amplitude of the vehile s box. Overpassing km/h (in this partiular ase), we notied a vertial aeleration s inrease whih, at the maxim veloity, beomes with almost 3% bigger. ABOUT THE DUMPING RATIO OF THE SUSPENSION LEVELS As it is known, the establishment of the optimal dumping ratio rekons on the ondition of obtaining minimal values of the osillating amplitudes. In the two levels suspension, usually the dumping ratio of the axles suspension must be enough for the pithing motion vibrations and the entral suspension s dumping ratio is determined in aordane with the maximum aepted values of the osillation amplitudes or aelerations for the vehile s [, ]. During the braking ations however, the axles suspension s dumping ratio may substantially inrease and may possibly reah the bloking situation. That is why, for this partiular ase, we onsidered theoretially the influene of an axles suspension s dumping ratio between... The main results are summarized in the diagram presented in fig = 3.9 kn/mm; =.9 kn/mm Fig.. Vertial aelerations of the vehile s box for different suspension s levels rigidities. vert. dyn. fore (bogie) [kn] vert. a. of the vehile's box [m/s^] 3 3 Fig.. Vertial dynami fores at the bogie s frame level for different dumping ratios δ δ =. δ =. δ = veloity [km/h] δ =.3 3 veloity [km/h] δ=.3 δ=. bloked axle susp. level Fig.. Vertial aelerations of the vehile s box for different axle suspension s dumping ratio. We observed that one with the inrease of the dumping ratio, at high speed running an be notied a substantial vertial dynami fores inrease with more than 3% at the bogie s frame level. At the same time, in the slow speed area, it is notied a derease of these with almost %. At the vehile s box level it an be observed that inreasing the dumping ratio from.3 to. and even when the axles suspension is bloked, at least for the studied ase, there are no major influenes on the vertial osillating amplitude of the vehile s box. Instead, its vertial aelerations modify enough both as value and through an obvious displaing of the veloity orresponding to the seond maximum (see fig. 3). VІ-8 CONCLUSIONS Respeting the imposed onditions and reommendations regarding the adoption of the suspension s elasti harateristis for railway vehiles requires the existene of some

7 orrelations between the unssprung mass, the bogie s and box suspended mass and harge mass, whih have been presented in this study. Regarding the suspension funtioning during the braking ations based on the rail-wheel adhesion, there appear some hanges of the dumping ratio of the axles suspension, whih affets the vehile s vibratory regime. With a view of projeting in an optimal manner the suspension, speially in designing the high speed vehiles whih requires a quite long distane for braking and onsequently a longer time for running speed dereasing, we onsider that it would be neessary to take into onsideration suh studies of the aspets that we have been pointed out in our paper. REFERENCES [] Sebeşan, I., Dinamia vehiulelor de ale ferată, Ed. Tehniă, Buureşti, 99, 37 p. [] Sebeşan, I. Hanganu, D., Proietarea suspensiilor pentru vehiule pe şine, Ed. Tehniă, Buureşti, 993, p. [3] Fihe Nr. : FREIN Freins à haute puissane pour trains de voyageurs, e édition..97, Tirage du..98, mise à jour..983, Union Internationale des Chemins de Fer. [] Crueanu, C., Frâne pentru vehiule feroviare, Ed. MATRIXROM, Buureşti,, 7, 388 p. ОТНОСНО ПРИЕМАНЕТО НА ПАРАМЕТРИТЕ ЗА ВЕРТИКАЛНО ОКАЧВАНЕ ЗА ПЪТНИЧЕСКИТЕ ВАГОНИ Каталин Кручеану, Мариус Спирою, Мадалина Думитрию Доц. Д-р Каталин Кручеану, ас. д-р Мариус Спирою, ас. Мадалина Думитрию, Университет Политехника в Букурещ, Транспортен факултет, Катедра Подвижен състав, 33 Splaiul Independentei, setor, 77, Букурещ, РУМЪНИЯ Резюме: Проектирането на окачването прилага установени еластични и поглъщащи удара константи за условията за осигуряване на действието на динамиката на подвижния състав. За приемането на необходимата вертикална твърдост се прилага определена корелация между конструктивните маси. Геометричните и механичните характеристики на железницата оказват значително въздействие върху реакцията на окачването. Нещо повече при задействане на спирачки поради силата на триене между дисковете и подложките на спирачките се увеличава факторът за поглъщане на удара при осевото окачване. Ключови думи: окачване, твърдост на окачването, фактор на поглъщане на удара, задействане на спирачки. VІ-9