Study of the simulation model of a displacementsensitive shock absorber of a vehicle by considering the fluid force

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1 Study of the simulation model of a displaementsensitive shok absorber of a vehile by onsidering the fluid fore Choon-Tae Lee1 and Byung-Young Moon2* 1Department of Mehanial and Intelligent Systems Engineering, Pusan National University, Busan, Republi of Korea 2Department of Aerospae Engineering, Pusan National University, Busan, Republi of Korea The manusript was reeived on 19 Otober 2004 and was aepted after revision for publiation on 30 Marh DOI: / X Abstrat: In this study, a new mathematial dynami model of a displaement-sensitive shok absorber (DSSA) is proposed to predit the dynami harateristis of an automotive shok absorber. The performane of a shok absorber is diretly related to the vehile behaviour and performane, for both handling and ride omfort. The proposed model of the DSSA is onsidered as two modes of the damping fore (i.e. soft and hard) aording to the position of the piston. In addition, the DSSA is analysed by onsidering the transient zone for more exat dynami harateristis. For the mathematial modelling of the DSSA, flow ontinuity equations at the ompression and rebound hamber are formulated. The flow equations at the ompression stroke and rebound stroke respetively are formulated. Also, flow analysis of the reservoir hamber is arried out. Aordingly, the damping fore of the shok absorber is determined by the fores ating on both sides of the piston. The harateristis of the damping fore are observed by the proposed method. The analytial results of the damping fore harateristis are ompared with the experimental results to prove the effetiveness. In partiular, the effets of the displaement-sensitive orifie area on the damping fore and the effets of the displaement-sensitive orifie length on the damping fore are observed. The results reported herein will provide a better understanding of the shok absorber. Keywords: shok absorber, damping fore, displaement-sensitive orifie, flow ontinuity equations, stroke-dependent, piston valve, mathematial model 1 INTRODUCTION Reybrouk [4] proposed a mathematial model of a monotube-type gas-harged shok absorber. Herr The shok absorber is an important part of an et al. [5] proposed a mathematial model of a twinautomotive whih has an effet on ride haragated tube-type shok absorber. Simms et al. [6] investi- teristis suh as ride omfort and driving safety. the influene of damper properties on luxury There have been several studies arried out on the vehile dynami behaviour through simulation and shok absorber. First, Lang [1] proposed a simple tests. Liu et al. [7] reported the harateristis of mathematial model of passive shok absorber. the non-linear dynami response for the twin-tube Subsequently, many studies have been performed to hydrauli shok absorber. Nevertheless, there have analyse the performane of a shok absorber [2]. been few studies arried out on the displaement- Cherng et al. [3] reported the effet of the noise of a sensitive shok absorber (DSSA). There have been no shok absorber using the aousti index method. studies on the mathematial modelling of the DSSA. Reently, a study of the DSSA was reported. * Corresponding author: Department of Aerospae Engineering, However, it was insuffiient to understand the Pusan National University, ILIC (Industrial Liaison Innovation dynami harateristis of the DSSA ompletely Cluster), Engineering Building, 30 Changjeon-dong, [8, 9]. Therefore, in this study a new mathematial Keumjeong-ku, Busan , Republi of Korea. and simulation model for the DSSA is proposed and moonby@pusan.a.kr analysed, whih onsiders the transient range of

2 966 Choon-Tae Lee and Byung-Young Moon the displaement-sensitive orifie. A typial twin- pression hamber. The volume whih surrounds the tube-type passive shok absorber of an automotive ylinder is known as the reservoir hamber. The vehile is onsidered in order to study the operating reservoir hamber is partially filled with fluid and priniples of a DSSA. For the mathematial modelling partially filled with a gas phase, normally air. The of the DSSA, flow ontinuity equations for the om- fluid flow between the ompression and reservoir pression and rebound hambers are formulated. The hambers passes through the body valve assembly flow equations for the ompression stroke and the at the bottom of the ompression hamber. Figure 2 rebound stroke respetively are obtained. Also, flow illustrates the typial onfiguration of a DSSA. As an analysis of the reservoir hamber is arried out. be observed in Fig. 2, the DSSA has additional flow Aordingly, the damping fore of the shok absorber passages in the ylinder wall of a typial passive is determined by the fores ating on both sides of shok absorber. This displaement-sensitive orifie the piston. an be divided into three zones, namely the soft, The effets of the displaement-sensitive orifie transient and hard zones. Here, the transient zone area on the damping fore of the DSSA and the has a tapered sheme to avoid abrupt hanges in effets of the displaement-sensitive orifie length the damping fore. Eah valve and orresponding on the damping fore are observed. hamber are desribed aording to the fluid flow. Figure 3 illustrates the analytial model of the DSSA, whih desribes a fluid flow pattern aording to piston movement. 2 GENERAL CONFIGURATION AND OPERATING The fluid flows at the ompression stroke an be PRINCIPLES OF THE DSSA divided into two flows with flowrates Q and Q. Q r r is the flowrate from the ompression hamber to the Figure 1 illustrates a typial twin-tube-type passive rebound hamber through the piston valve (1), and automotive shok absorber. As shown in Fig. 1, Q is the flowrate from the ompression hamber to basially the shok absorber onsists of a piston the reservoir hamber through the body valve (2), whih moves up and down in a fluid-filled ylinder. where the valve numbers are shown in Fig. 2(a). Q, r The ylinder is fastened to the axle or wheel suspeninto the flowrate through the piston valve, an be divided three: Q, Q, and Q. Q is the flowrate ri ro rd ri sion, and the piston is onneted via the piston rod to the frame of the vehile. As the piston is fored through the bleed valve (4), Q the flowrate through ro to move with respet to the ylinder, a pressure the intake valve (6), and Q the flowrate through the rd differential is developed aross the piston, ausing displaement-sensitive orifie (9) of the piston valve. the fluid to flow through orifies and valves in the Q, the flowrate through the body valve (2) at the piston. The portion of the ylinder above the piston ompression stroke, an be divided into two: Q and i is known as the rebound hamber, and the portion Q. Q is the flowrate through the bleed valve, f i of the ylinder below the piston is known as the om- and Q the flowrate through the blow-off valve. f Fig. 1 Typial onfiguration for the twin-tube-type passive automotive shok absorber

3 Displaement-sensitive shok absorber 967 Fig. 2 Typial onfiguration and fluid flow pattern of the DSSA On the ontrary, at the rebound stroke the fluid 3 MATHEMATICAL MODELLING OF DSSA flow an be divided into two flows with flowrates Q* r and Q*.Q* is the flowrate from the rebound hamber 3.1 Flow ontinuity equations for the r to the ompression hamber through the piston ompression and rebound hambers valve (1), and Q* the flowrate from the reservoir The flow ontinuity equations for the ompression hamber to the ompression hamber through the hamber at the rebound stroke, as desribed in Fig. 3, body valve (2). Q*, the flowrate through the body an be expressed as valve (2) an be divided into two: Q and Q. Q is i o i the flowrate through the bleed valve, and Q the o flowrate through the sution valve (7). Also, Q*, the r flowrate through the piston valve (1), an be divided into three: Q,Q, and Q. Q is the flowrate through ri rf rd ri the bleed valve (4), Q the flowrate through the rf blow-off valve (5), and Q the flowrate through the rd displaement-sensitive orifies. V K qp qt = A p ẋ+(q* r +Q* ) (1) where K is the bulk modulus of elastiity of the working fluid, V is the volume of the ompression hamber, P is the pressure of the ompression hamber, A is the area of the piston, and ẋ is the veloity p

4 968 Choon-Tae Lee and Byung-Young Moon Here, the flowrates an be obtained as Q ri A pbs 2 r (P P d1 ) A d1s 2 r (P d1 P r ) (6) Q ro A d2s 2 r (P P d2 ) P P =Q d2 ir (7) im P P im ir (when P <P,Q beomes zero) and d2 ir ro Q rd A ds (x)s 2 r (P P r ) (8) where Fig. 3 Shemati diagram of the fluid flow and pressure during the ompression and rebound strokes A (x)=gwc h (x+z )+h D z <x (z +z ) z wh z <x z ds 1 1 w C h z 2 (x z 1 )+h D (z 1 +z 2 )<x z 1 of the piston. The flow ontinuity equation for the (9) ompression hamber at the ompression stroke an be expressed as where C is the oeffiient of disharge, r is the d oil density, A is the bleed valve (4) orifie area of V qp pb the piston valve, A and A are the areas of the d1 d2 K qt =A p ẋ (Q r +Q ) (2) piston valve port restrition (3), P and P are d1 d2 the pressures at the piston valve port restrition (3), In a similar way, the flow ontinuity equation for Q is the maximum flowrate of the intake valve the rebound hamber at the rebound stroke an be im (6), P is the raking pressure of the intake valve (6), expressed as ir and P is the pressure of the intake valve (6) at the im maximum flowrate Q. Figure 4 shows the detailed im V r K qp r qt =(A p A rod )ẋ Q* r (3) The flow ontinuity equation for the rebound hamber at the ompression stroke an be expressed as V r K qp r qt = (A p A rod )ẋ+q r (4) where V r is the volume of the rebound hamber, P r is the pressure of the rebound hamber, and A rod is the area of the piston rod. 3.2 Flow equations at the ompression stroke The flowrate Q r of the piston valve between the rebound and ompression hambers at the ompression stroke an be expressed as Q r =Q ri +Q ro +Q rd (5) Fig. 4 Detailed onfiguration of the displaementsensitive orifie

5 Displaement-sensitive shok absorber 969 where Q is the maximum flowrate of the blowoff valve (5) at the piston valve, P is the raking pr pm pressure of the blow-off valve at the piston valve, and P is the pressure of the blow-off valve at the maxi- pm mum flowrate of the piston valve. Q beomes zero rd when the displaement of the piston is outside the displaement-sensitive zone. The flowrate Q* of the body valve between the reservoir and ompression hambers at the rebound stroke an be expressed as Q* =Q +Q (17) i o with onfiguration of the displaement-sensitive orifie. A is the area of the displaement-sensitive orifie ds shown in Fig. 4, where w is the width of the displaement-sensitive orifie, h is the height of the displaement-sensitive orifie, z is the soft-zone 1 length, z is the transient-zone length, and x is the 2 stroke of the piston. The flowrate Q beomes zero rd when the piston detahes from the displaementsensitive orifie. The flowrate Q of the body valve between the reservoir and ompression hambers at the ompression stroke an be expressed as Q A d3s 2 r (P P d3 ) Q i A bbs 2 r (P a P d3 ) =Q i +Q f (10) The flowrates in equation (10) an be obtained as A d3s 2 r (P d3 P ) (18) Q i A bbs 2 r (P d3 P a ) (11) Q o A d4s 2 r (P a P d4 ) Q f =Q bm P d3 P br P bm P br (12) =Q sm P d4 P sr P sm P sr (19) (when P <P, Q beomes zero) where A is the d3 br f bb (when P <P, Q beomes zero) where A is the bleed valve orifie area of the body valve (2), A is d4 sr f d4 d3 port restrition (8) area of the body valve, P is the port restrition area (8) of the body valve, P d4 d3 the pressure at the body valve port restrition (8), is the pressure at the port restrition of the body Q is the maximum flowrate of the sution valve (7), valve (2), P is the air pressure in the reservoir sm a P is the raking pressure of the sution valve, hamber, Q is the maximum flowrate of the blow- sr bm and P is the pressure at the maximum flowrate of off valve at the body valve, P is the raking sm br the sution valve. pressure of the blow-off valve at the body valve, and P is the pressure of the blow-off valve at the bm maximum flowrate at the body valve. 3.4 Flow analysis of the reservoir hamber 3.3 Flow equations at the rebound stroke Beause the piston rod passes through the rebound hamber and is onneted to the rebound side of the piston, the area of the rebound side is less than The flowrate Q* of the piston valve between the the area of the ompression side of the piston. r rebound and ompression hambers at the rebound Aordingly, as the piston moves, the ombined stroke an be expressed as volume of the ompression and rebound hambers Q* =Q +Q +Q r ri rf rd (13) hanges by an amount equivalent to the inserted or withdrawn piston rod volume. The amount of fluid with equivalent to the inserted (or withdrawn) piston rod volume must be transferred to (or from) the reservoir Q =C A ri d pbs 2 r (P d1 P ) (14) hamber whih normally surrounds the ylinder. The air pressure of the reservoir hamber an be expressed as an ideal gas equation as P P Q =Q d1 pr (15) P V =m RT (20) rf pm P P a a a pm pr where P is the air pressure of the reservoir hamber, a (when P <P, Q beomes zero) and d1 pr rf V is the air volume of the reservoir hamber, m is a a the air mass of the reservoir hamber, R is the gas onstant, and T is the temperature of the air in the Q =C A rd d ds (x)s 2 r (P r P ) (16) reservoir hamber.

6 970 Choon-Tae Lee and Byung-Young Moon Generally, the mass of air is assumed onstant beause the hamber is sealed, and the temperature T of the reservoir hamber is assumed onstant to simplify the analysis. Aordingly, the air of the reservoir hamber an be expressed as an ideal gas equation as P a V a =onstant (21) The time variation in the air volume V a of the reservoir hamber an be expressed as with A =A A (25) r p rod where F is the damping fore and F is the damping frition fritional fore ating on the piston rod. Here, the fritional fores are another fator that determines the damping fore but, in this study, the fritional fores are ignored to simplify the analysis. 4 RESULTS OF THE ANALYSIS AND DISCUSSION V a (t)=v a0 P Q dt (22) 4.1 Analysis results where V is the initial air volume of the reservoir a0 A simulation model of DSSA is shown in Fig. 6. The hamber. Therefore, the variation in the air pressure simulation model is strutured by using AMESIM of the reservoir hamber an be obtained from ver4.0 of Imagine Co. The input exitation in the equations (20) and (22) as simulation model is omposed of a displaement veloity transformer, whih transforms the displae- P = m a RT a V P (23) ment input into the veloity. The reservoir hamber Q a0 dt is modelled with the real air properties by using the pneumati module of AMESIM. The displaementsensitive orifie is modelled with the funtion blok 3.5 Damping fore of the shok absorber f (x) and variable hydrauli restritor. The funtion The damping fore of the shok absorber is deterrestritor blok alulates the opening area of variable hydrauli mined by the fores ating on both sides of the by using the piston stroke. piston. Figure 5 shows the free-body diagram of The main physial properties of the simulation the piston. model are listed in Table 1. By onsidering the fores ating on the piston, the As an exitation fore of the system, the simple damping fore an be obtained as sinusoid displaement input ±40 mm, 0 4 Hz, is applied, as desribed in Fig. 7. F =P A P A ±F damping r r p frition (24) Figure 8 shows simulation results of the stroke damping fore diagram for various exitation veloities: 0.1, 0.2, 0.3, 0.6 and 1.0 m/s. The damping fore hanges from the soft mode to the hard mode owing to the displaement-sensitive harateristis around the stroke at ±20 mm, as shown in Fig. 8. In partiular, as an be seen in Fig. 8, the damping fore hanges smoothly around the transient zone. This Table 1 Simulation parameters Fig. 5 Free-body diagram of the piston Diameter of the piston 30 mm Diameter of the piston rod 16 mm Inner diameter of the reservoir hamber 32 mm Outer diameter of the reservoir hamber 42 mm Initial oil height in the reservoir hamber 100 mm Sinusoid displaement input ±40 mm Hz Initial rebound hamber volume 63 m3 Initial ompression hamber volume 88.4 m3 Initial reservoir hamber volume 65.9 m3 Perfet gas onstant J/g K Absolute visosity of gas N s/m2 Density of the hydrauli oil 850 kg/m3 Bulk modulus of the hydrauli oil 1700 MPa Kinemati visosity of the hydrauli oil m2/s Temperature of the hydrauli oil 40 C

7 Displaement-sensitive shok absorber 971 Fig. 6 Simulation model of the DSSA using AMESIM ver4.0 Fig. 7 Exitation fore of the DSSA

8 972 Choon-Tae Lee and Byung-Young Moon Fig. 8 Analytial results for the DSSA: stroke damping fore harateristis Effets of the soft-zone length of the displae- ment-sensitive orifie on the damping fore diagram illustrates well the funtion of transient zone, whih prevents abrupt hanges in the damping fore. To verify the reliability of the simulation results of the proposed model, the experimental results are presented in Fig. 9. As an be observed in Fig. 9, the experimental results show very similar tendenies to the results of this study. Figure 10 shows the variation in the damping fore harateristi for various displaement-sensitive orifie areas. The exitation veloity is 1 m/s and the width of orifie is 2 mm. Figure 10 shows the stroke damping fore harateristis when the height of the displaement-sensitive orifie is varied and equal to 0.5, 1.0, 1.5, 2.0, and 2.5 mm respetively. As shown in this figure, it an be observed that the inreasing rate of damping fore inreases gradually with derease in the orifie height. Figure 11 shows the variation in the damping fore harateristi for various soft-zone lengths of the displaement-sensitive orifie. The exitation veloity is 1 m/s. Figure 11 shows the stroke damping fore harateristis when the soft-zone length is varied and equal to 12, 14, 16, and 18 mm respetively. As Fig. 10 Fig. 11 Effets of the displaement-sensitive orifie area on the damping fore diagram Fig. 12 Flowrate through the displaement-sensitive Fig. 9 Experimental results for the DSSA: stroke orifie for various displaement-sensitive damping fore harateristis orifie areas

9 Displaement-sensitive shok absorber 973 shown in this figure, it an be observed that the exitation frequeny. The pressure in the ompression damping fore varies in a transient range with the hamber beomes nearly zero during the variation in orifie length. Nevertheless, there is no rebound stroke. The results show well the harateristis hange in damping fore in the soft zone. of pressure variation for various exitation Figure 12 shows the variation in the flowrate veloities in both the rebound and the ompression through the displaement-sensitive orifie for various hambers. The pressure of the ompression hamber displaement-sensitive orifie areas. beomes nearly zero during the rebound stroke. Figure 13 shows the variation in the pressures of the rebound and ompression hambers for various exitation veloities. In this figure, the solid urves 5 CONCLUSIONS show the variation in pressure of the rebound hamber and the dashed urves show the variation In this study, a new mathematial non-linear dynami in pressure of the ompression hamber. Here the model is proposed to predit the performane of exitation veloity of 1.0 m/s orresponds to the 4 Hz the DSSA. A typial twin-tube-type passive shok Fig. 13 The variation in the pressure of the rebound and ompression hambers for various exitation veloities

10 974 Choon-Tae Lee and Byung-Young Moon absorber of an automotive vehile is onsidered in 4 Reybrouk, K. G. A nonlinear parametri model of order to study the operating priniples of the DSSA. an automotive shok absorber. SAE paper , For the mathematial modelling of the DSSA, flow 1994, pp Herr, F., Malin, T., Lane, J., and Roth, S. A shok ontinuity equations for the ompression hamber absorber model using CFD analysis and Easy 5. In and the rebound hamber are formulated. The flow Proeedings of the 1999 SAE International Congress equations at the ompression stroke and the rebound and Exposition, SAE paper , stroke are also formulated. Also, flow analysis of the 6 Simms, A. and Crolla, D. The influene of damper reservoir hamber is arried out by onsidering properties on vehile dynami behavior. SAE paper the real properties of the air and working fluid , 2002, pp Aordingly, the damping fore of the shok absorber 7 Liu, Y., Zhang, J., Yu, F., and Li, H. Test and is determined by the fores ating on both sides of simulation of nonlinear dynami response for the the piston. twin-tube hydrauli shok absorber. SAE paper , 2002, pp The analytial results of the DSSA in the form of 8 Park, J., Joo, D., and Kim, Y. A study on the stroke stroke damping fore harateristis are ompared sensitive shok absorber. J. Korean So. Preision with the experimental results to prove the effetive- Engng, 1997, 14, ness of the proposed simulation model. The effets 9 Cho, K. and So, S. A study of the new typed stroke of the displaement-sensitive orifie area on the dependent damper. J. Korean So. Automot. Engrs, damping fore of the DSSA and the effets of 1999, 7(3), displaement-sensitive orifie length on the damping fore are observed. The variation in flowrate through the displaement-sensitive orifie with displaementsensitive orifie area shows the effiieny of the APPENDIX proposed method. The pressures of the rebound hamber and ompression hamber are analysed Notation reasonably aording to the proposed method. The results reported herein will provide better undervalve (2) A bleed valve orifie area of the body bb standing of the shok absorber. Moreover, it is believed that those properties of the results an be A area of the displaement-sensitive ds utilized in the dynami design of an automotive orifie system. A,A areas of piston valve port restrition (3) d1 d2 A port restrition area (8) of the body d3 valve ACKNOWLEDGEMENTS A port restrition (8) area of the body d4 valve This work was supported by Grant R A area of the piston p from the Basi Researh Program of the A bleed valve (4) orifie area of the piston pb Korea Siene and Engineering Foundation and the valve authors are grateful for this support. A area of the piston rod rod C oeffiient of disharge d F damping fore REFERENCES damping F fritional fore frition h height of the displaement-sensitive 1 Lang, H. H. A study of the harateristis of orifie automotive hydrauli dampers at high stroking K bulk modulus of elastiity of the frequenies, PhD thesis, Department of Mehanial Engineering, University of Mihigan, Ann Arbor, working fluid Mihigan, USA, Deember m air mass of the reservoir hamber a 2 Duym, S. W., Stiens, R., Baron, G. V., and P air pressure of the reservoir hamber a Reybrouk, K. G. Physial modeling of the hystereti P raking pressure of the blow-off valve behavior of automotive shok absorbers. SAE paper br at the body valve , 1997, pp P pressure of the blow-off valve at the 3 Cherng, J. G., Ge, T., Pipis, J., and Gazala, R. bm maximum flow-rate at the body valve Charaterization of air-borne noise of shok absorber by using aoustis index method. In Proeedings of P pressure of the ompression hamber the 1999 SAE International Congress and Exposition, P,P pressures at the piston valve port d1 d2 SAE paper , restrition (3)

11 Displaement-sensitive shok absorber 975 P pressure at the port restrition of the Q flowrate from the ompression hamber d3 r body valve (2) to the rebound hamber through the P pressure at the body valve port piston valve (1) d4 restrition (8) Q* flowrate from the rebound hamber to r P raking pressure of the intake valve (6) the ompression hamber through ir P pressure of the intake valve (6) at the piston valve (1) im maximum flowrate Q Q flowrate through displaement sensitive im rd P raking pressure of the blow-off valve orifie (9) of piston valve pr at the piston valve Q flowrate through the blow-off valve (5) rf P pressure of the blow-off valve at the pm Q flowrate through the bleed valve (4) ri maximum flowrate of the piston valve Q flowrate through the intake valve (6) ro P pressure of the rebound hamber r Q maximum flowrate of the sution valve P raking pressure of the sution valve sm sr (7) P pressure at the maximum flowrate of sm R gas onstant the sution valve T temperature of the air in the reservoir Q maximum flowrate of the blow-off valve bm hamber at the body valve V air volume of the reservoir hamber Q flowrate from the ompression hamber a V initial volume of the air in the reservoir to the reservoir hamber through the a0 hamber body valve (2) V volume of the ompression hamber Q* flowrate from the reservoir hamber to V volume of the rebound hamber the ompression hamber through body r w width of the displaement-sensitive valve (2) orifie Q flowrate through the blow-off valve f x stroke of the piston Q flowrate through bleed valve i ẋ veloity of the piston Q flowrate through the sution valve (7) o z soft-zone length Q maximum flowrate of the intake valve 1 im z transient-zone length (6) 2 Q maximum flow-rate of the blow-off pm r oil density valve (5) at the piston valve