Available online at ScienceDirect. Procedia Engineering 129 (2015 ) International Conference on Industrial Engineering

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1 Available online at ScienceDirect Proceia Engineering 19 (15 ) International Conference on Inustrial Engineering Coparative evaluation of the vibration isolation properties of a suspension with ifferent ywheel ynaical absorbers of the car boy oscillations I.M. Ryabov a,.v. Chernyshov b, Poeev c, * a Departent of Autoobile Transportation, Volgogra State Technical University, Volgogra, Russia b Departent of Operation an Maintenance of Autoobiles, Volgogra State Technical University, Volgogra, Russia c Departent of Autoatic Units, Volgogra State Technical University, Volgogra, Russia Abstract The article is researching the vibration isolation properties of a ywheel ynaical absorber of the vehicle boy oscillations. It is note that the authors have previously propose aitional ywheel ynaical absorbers with echanical rives an it is prove that they have iprove the vibration isolation properties of the suspension syste. However, such ynaical absorbers are heavy. That is why there is being evelope a ywheel ynaical absorber with hyraulic rive containing a hyraulic cyliner an a hyraulic achine with a ywheel. The theoretical research ientifies the paraeters of the hyraulic rive, proviing the iniu value of the sprung ass oscillation aplitue in the area of low-freuency resonance, an it is foun out that the ywheel ynaical absorber with the hyraulic rive features a lower suspension ass an better vibration isolation properties than the ywheel ynaical absorber with a echanical transission The The Authors. Authors. Publishe Publishe by by Elsevier Elsevier Lt. Lt. This is an open access article uner the CC BY-NC-ND license ( Peer-review uner responsibility of the organiing coittee of the International Conference on Inustrial Engineering (ICIE- Peer-review 15). uner responsibility of the organiing coittee of the International Conference on Inustrial Engineering (ICIE-15) eywors: ynaical vibration absorber; ywheel; hyraulic achine; hyraulic cyliner; vibration isolation properties; car. 1. Introuction In the onograph [1] publishe in 1976, it s referre to the using appropriateness of the ynaical vibration absorbers of the car wheels in the for of aitional spring-loae weight. Conucte theoretical an experiental research of such absorbers [-1] showe their effectiveness. However, for aping car boy oscillations such the ynaical absorbers are not applicable ue to their large ass. * Corresponing author. Tel.: The Authors. Publishe by Elsevier Lt. This is an open access article uner the CC BY-NC-ND license ( Peer-review uner responsibility of the organiing coittee of the International Conference on Inustrial Engineering (ICIE-15) oi:1.116/j.proeng

2 I.M. Ryabov et al. / Proceia Engineering 19 ( 15 ) E-ail aress: avp4897@ail.ru The ywheel ynaical absorbers of the boy oscillations in which the ywheel is riven in rotation by a echanical transission (Fig. 1, a) are propose an stuie in [1-4]. To avoi locking of the suspension at high freuencies in such a rive the clutch with optial paraeters is use [13-]. In [3, 4] it is shown that to reuce the ass of the ywheel it s necessary to increase the gear ratio of the echanical transission. However, it s also increases the ass of the transission, which liits the possibility of reucing the ass of the absorber as a whole. Fining ways to reuce the ass of the ywheel absorber of the boy oscillations has le to the iea of using hyraulic achine, connecte by pipelines with a hyraulic cyliner (Fig. 1, b) as a ywheel rive [16, 5-3]. a b 1 1 k c i g k c 5 3 l Fig. 1. (a) esign schees of suspensions containing ywheel ynaical vibration absorbers: with echanical transission of otion to the ywheel, (b) esign schees of suspensions containing ywheel ynaical vibration absorbers with hyraulic transission of otion to the ywheel This article is evote to coparative evaluation of the vibration isolation properties of the consiere ywheel ynaical absorbers.. Matheatical oel Any hyraulic achines have voluetric leakages. If we assue that the voluetric leakages of the working ui in hyraulic otors an pups are not available, so a constant volue (volue of ui passing through the hyraulic achine uring one revolution of the shaft) of the hyraulic achine is connecte with the stroke of the piston in the cyliner by the epenence: Q F x a t (1) where Fa is the cross sectional area of the annular cavity in the hyraulic cyliner of the vibration absorber, xt is the stroke of the piston for one revolution of the ywheel. The epenence of the ywheel rotation angle fro suspension eforation x can be eterine by the forula x Fa xt Q We enote a tranfer coefficient fro the suspension eforation to the ywheel rotation: ()

3 48 I.M. Ryabov et al. / Proceia Engineering 19 ( 15 ) Q b (3) Fa Suspension ynaics with hyraulic ywheel vibration absorber without regar to leakages looks as follows: either k( ) ( ) (4) b k( ) ( ) ( ) (5) b Here an are the inertia oent an the ywheel rotation angle; an are the sprung ass an its isplaceent; c stiffness of the elastic eleent; k coefficient of the shock absorber resistance (aping factor); kineatic perturbation. We ivie left an right part of (5) on an get: h (6) In this euation: c (7) k h (8) b F Q (9) Euations (4), (5) an (6) coincie in for with the corresponing euations of the suspension with the echanical rive of the ywheel without the haning over link an have the sae solution [16]. So the solution of euation (6) in the for of the ynaic factor represents the following expression (1 ) 4 (1 ) 4 (1) When accounting for the voluetric leakages in a hyraulic achine, a atheatical oel escribing the ynaics of the vibrating syste, is coplicate. When the ywheel is stoppe uring the oveent of the ropiston in the hyraulic shock absorber ui ows through the gaps in hyraulic achine, foring hyraulic resistance, which in linear for is: F.h. x st./. x st./. (11) where x st./. is a spee of the ro-piston oveent in the hyraulic cyliner when the ywheel is stoppe; is a aping coefficient of the hyraulic rive.

4 I.M. Ryabov et al. / Proceia Engineering 19 ( 15 ) Locking the ywheel oes not lea to the stillness of the oscillating syste in the presence of the voluetric leakages. Thus, the presence of the voluetric leakages provies an aitional freeo egree of vibrating syste. As an aitional generalie coorinate we can consier the ywheel rotation angle. When the ywheel rotates, power of the hyraulic resistance to the ro-piston oveent in the cyliner epens on the ifference between the spee of the ro-piston oveent an angular velocity of the ywheel rotation:.h. F b Then the euality conition of the forces acting on the center of the sprung ass, an the euality conition of the oents on the axis of a ywheel constitute a syste of ifferential euations: (1) k( ) c( ) b, b b. (13) The secon euation of the syste aits a lower orer. Consiering this an the expressions (7), (8), (9), an as well as proucing replaceent (14) we get: h( ) ( ) ( ) b, ( ). b (15) The ynaic factor of the syste ating to the sprung ass is eual to (h ) h 3 h h (16) In ative paraeters it is eual to ( ) 1 ( ) 1 (17) where: h (18)

5 484 I.M. Ryabov et al. / Proceia Engineering 19 ( 15 ) (19) The analysis of oscillatory systes with the ywheel absorber having the hyraulic rive without leakages (analogue of the echanical rive), shows that the aplitue-freuency characteristics of this oscillatory syste have the freuency at which the vibration aplitue of the vibration protection object (sprung ass) is eual to ero. When eviation fro this freuency is in the irection of increasing or ecreasing the vibration aplitues increase consierably. This circustance leas to the necessity of application in echanical rives gearboxes with variable gear ratio or the introuction in the rive to the ealer links, for exaple, a clutch. We exaine an oscillating syste with a hyraulic rive of the ywheel for the existence of the invariant points at which all of the aplitue-freuency characteristics of the syste with ifferent values of the aping coefficient of the hyraulic rive intersect. In the absence of aping: () 4 (1 ) 4 (1 ) (1 ) (1) The consiere syste has two invariant points: 1 1 inv1, 1 1 inv. () The coefficients in the invariant points are eual, respectively: inv1 an 1 1 inv. (3) 1 1 Invariant points break the whole range of ative freuencies into three intervals: (; i inv1 ), (i inv1 ; i inv ) an (i inv ;). Oscillation aplitues of the sprung ass are reuce with increasing aping in the hyraulic rive on the secon interval, an are increase on the first an thir intervals. 3. Siulation results Fig. presents the aplitue-freuency characteristics of the consiere syste in coparison with the aplitue-freuency characteristics of the syste without ywheel absorber an the syste with the ywheel absorber having the echanical rive.

6 I.M. Ryabov et al. / Proceia Engineering 19 ( 15 ) a b c Fig.. (a) aplitue-freuency characteristics of oscillatory syste at,5 ;,15 ;,5 ;(b) aplitue-freuency characteristics of oscillatory syste at,5 ;,15, 1;(c) aplitue-freuency characteristics of oscillatory syste at,5,,5 ; () aplitue-freuency characteristics of oscillatory syste at,5, 1 Fig. shows that the increasing a ative inertia oent lowers the natural (resonant) freuency of the syste an reuces the oscillation aplitues in the first two ranges (up to the secon invariant point), an increases the in the thir range. The existence of a stanar shock absorber also reuces the oscillation aplitues in the first two ranges, an increases the in the thir range. The aping in the hyraulic rive also affects the oscillation aplitue of the sprung ass. The oscillation aplitues of the sprung ass are reuce on the secon range by increasing the aping in a hyraulic actuator, an are increase on the first an thir ranges. The aplitue of the sprung ass at resonance epens on aping of the hyraulic rive. The iniu value of this aplitue is for the paraeters: an, 5, an with the for the paraeters:, 1. reache with the ative aping factor, 5 ative aping factor, 4 4. Conclusion Conucte research have shown that the ynaical ywheel absorber with hyraulic rive provies better vibration isolation properties of the suspension than the ynaical ywheel absorber with a echanical transission, because it provies saller aplitue of the vehicle boy oscillations in the area of low-freuency resonance an at high freuency perturbations in the area after resonance. References [1] A.A. hachaturov, V.L. Afanasiev, S.V. Vasiliev, The ynaics of the syste roa tyre vehicle river, Engineering Publ., Moscow, 1976.

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