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Journal of Electrical and Electronics Engineering69rebound=4c=Clrn=2c=lc/4n=3n=4c=:ixa6.i -comprssion ;oe; JLaJn=4 Hrixc=cic/i6 o,ppnn=3- i r 4c=cic/9 cmi Pressure -IHHIn=l , V J_=CJc EXTENSrCCYCtEa) ft;Fig. 1. VZN (B) and DSA (b) shock absorbersIf the force developed is inversely proportional to thenumber of assets in the square holes 3:F =Shock Absorbers Multi-Modeling and Suspension OptimizationLUPU Ciprian, TABACU Ciprian, CAMPAN Dan Lucian TERTISCO Mihai University POLITEHNICA of Bucharest, Romania,Postal address, Splaiul Independentei 313, sect.6, Bucharest, Romania Department of Automatics and Systems Engineering, Faculty of Automatics and Computers Department of Autovehicles, Faculty of Transport EngineeringE-Mail: lcD: E-Mail: tabacu_ciprian;E-Mail: Iudan840808:E-Mail: tertisco.mihaiAbstract - The standard dampers used by more 90% ofvehicles have damping coefficients constant alongstroke, so they cant solve simultaneous all of them,situation solving practically using a relative dampingcoefficient able to made compromise between them.This paper design and simulation testing multi-modelsof two types of Damp (DSA and VZN). To compare thetwo types of suspension they are simulated in variousroad and load conditions. Analysis of simulationresults is presente a new VZN shock absorber. This isan invention of the Institute of Mechanics of theRomanian Academy, and patented at European andU.S. 1, 2. This is Called VZN shock absorber, iscoming from Variable Zeta Necessary acronym, forwell moving in all road and load Conditions, Wherezeta Represents the relative damping. Which isAdjusted automatically, stepwise. According to thepiston positions 3,4,5. Suspension systems are used inall air and ground transportation to protect thatbuilding transportation and cargo transported aroundagainst shocks and vibrations induced in the systemfrom the road Modifying damping coefficients (Zeta)function piston position, being correlated with vehicleload and road unevenness.Keywords: shock absorbers, simulation, damper.I. INTRODUCTIONThe paper design and testing multi-models of twotypes of Dampers (DSA and VZN To highlight thepeeulia- rities of the new VZN shock absorber he iscompared to a classic DSA shown in Fig.l. Principlewith VZN difference between DSA and is generated byplacing spatial factor of a section through the oil in thecylinder piston is pushed by:- DSA hole is made in the piston and the compressionstroke, the piston displacement piston oil under strainover the plunger through the hole in the piston;- the VZN are executed several vertical holes in thecylinder wall (fig.2). Oil under the piston is pushed intothe outer cylinders holes, reaching above the piston.This small difference has major consequences inconstructive behavior modifying static buffers principleof operation.(1)where C| the damper factor one active port and n is thenumber of active ports (through which the oil out of thecylinder pushing the piston). The DSA damping factorCi does not depend on the piston position.He has the same value throughout a race (SK-suspenssion or SR-rebound strokes). In Fig.l observethat if C, respectively VZN force F changes Both racesalong a progressive and at RK or SK biggest strength isobtained towards the end of the race, becoming the bestwhen only one port is active. Regarding VZN weremany theoretical articles on quality and performancesuspension containing VZN damper 2, 3, 4. But, noneof the papers did not address multi-modeling andoptimization of VZN-shock absorber.The objective of this paper is to develop a multi-model VZN damper on this base simulation optimizationof spatial distribution of holes in order to ensureefficient behavior as random perturbations in terms ofthe way.Section II contains the results of their scientificresearch on a shock absorbers multimodeling andsimulation. In Section III presents suspensionparameters and optimization criteria. The IV sectionpresents the results on the design of an appropriatecriterion and optimization procedures for suspensionsystem in a random road conditions. Section 5 containssome conclusions and comments on MM new type ofsuspension based on a VZN damper type.70Volume 6, Number 1, May 2013II. MULTI-MODELING OF STATICSIn all scientific work which refers to themathematical model of suspension shock absorber isconsidered to be no crashes, no delay which is reltiva Vspeed input piston and the output force F developed forautovehicle chassis suspension, and keeping it, ifpossible in the same position y = 0, given a randomdisturbance u (t) induced by the entry road suspension,producing a the piston displacement, S (t) = y (t)-u (t),called, piston stroke.OMPtESSlON STRCI=828.055Fig. 2. DSA F(V) damper-curve, for n=l3Piston displacement in the cylinder to travel theentire length 1 of two areas (lo and l-lo): lo is the free movement (no mechanical brake butviscous friction of oil to push , by holes); l-lo breaking the motion, made by rubber padsdesigned to absorb the impact of blows produced at theends of the strokes.Most of the works published in the literature referonly to the free movement of the piston model. Thismodel is called the F (V) damper curve. In Figure 2 isrepresented (bold line) experimental F (V)-curve damperfor n = 1 and all there is is represented, linearapproximation of the curve obtained by the least squaresmethod 5,6,7,8.For all race speed as positive (up) called RS featurehas a slope of about 2 kN/s. and in the negative (runCS-down) has a slope of more than two times lower (0.8kN/s ).2 :modelFig. 3. Block diagram for MM of DSA - simulationIn Fig. 3 is shown by simulation in Matlab blockdiagram of multimodel for n=l. The relativedisplacement of the piston S (t), applied to the inputblock 1 is a S(t) = S sin(yf) where So = 50 mm isthe amplitude and a = 27if is the angular frequency andf = lHz of signal test.On out to model block 1 isobtained speed signal V(t) = Sa cos( cot) Signal V(t) isapplied to input block 2 (multi-model base) and the onthe X axis of a plotter 3. The relative displacement ofthe piston S (t), applied to the input block 1 is aSt) = 5 sn(Ot) where So = 50 mm is the amplitudeand CO = 27tf is the angular frequency and f = 1 Hz ofsignal test.On out to model block 1 is obtained speedsignal V(i) = Sicos(iyf) Signal V(t) is applied toinput block 2 (multi-model base) and the on the X axisof a plotter 3.Fnl:CF-Icui-vFig. 4. S(t) and F(t) and F(S) curve for n=lIn Fig. 4 is shown test results of the dampere forn=l. For VZN damper type (Fig,la) with four holes inthe cylinder wall to obtain a fooPdamper-curves shownin Figure 5. In this case n = 4 static feature available onall distnta ste that the piston does not pass the first hole.Piston passes after the first hole, it remains active only n= 3 holes. When the piston passes the penultimate holeuntil the end of stroke and therefore n = 1, C = Cj andforce F has a maximum value. The four staticcharacteristics in Figure 5 aferente four areas betweenholes refiect changing progressive shock absorberdamping force generated by the piston position.COMPRESSION STROKEClc=828.0255 :Vreipertmentil piston rdadye velocity m/s :Fig. 5. F(V) damper-curve, for n=l, n=2, n=3, n=4By simulating a static shock absorber with a featurethat gradually changes as the image in Figure 5 isobtained from Figure 6. From this picture you can seethe progressive development of static behavior duringthe compression stroke and during the return stroke . Infig. 6 can see how static curves are contracted at thebeginning of the race and gradually swell depending onthe piston position.Journal of Electrical and Electronics Engineering71III. MULTI MODELING AND OPTIMIZATIONPROBLEM FORMULATION OF THE SUSPENSIONThe main elements of such a model are spring anddamper. These two elements generate forces to thechassis suspension.Fig. 6. F(S) curves for n=l ,2,3,4To illustrate the procedure and criteria to optimizevehicle suspension in random road conditions use asimplified model with a single degree of freedom, whichis the chassis vertical displacement y (t). The structuresimplified by neglecting the tire action of the suspensionsystem, is shown in figure 7.For determining analytical model, many simplifyingassumptions are made following considerations:The linear behavior of the dependence between theforce and the displacement in case of flexibleelements (Fe=k(y-u);ml:SPRUNGMASSWj-u)1VZN.ihock absortermLFig. 7. Suspension system modelThe linear dependence between the viscousfriction force and the damper piston movement speedand the speed of the oil passing through the damperpiston passing hole,p d j y - ) dtThe suspension mass m considered constant andfocused on a point (center of gravity) and the force ofinertia calculated as the product between the mass andthe accelerationFor simplicity we neglect the elastic force of the tires.The dynamic behavior of the system is:dtdtrespectively(2)(3)In what concerns the road (way) it induces randominterferences caused by the roughness of the roadrepresented in model (1) by the random signal ut). Theroad roughness is the most important disturbance for thedriver and for the vehicle structure itself More roadsurface profiles were measured, and several road modelswere discussed in the literature of specialty. In thevibration context, the road roughness is typicallyrepresented as a stationary stochastic process 12.Regarding the performance evaluation of thesuspension system, in this paper we were inspired by thetheory of automatic control systems destined formaintaining a physical size yt) to a given constantvalue, in the action terms of some external disturbances.This theory treats the problem of granting the controllerparameters in accordance with minimizing the standarddeviation of the output quantity (O from a givenprescribed value jo, in the conditions of a randqpidisturbance, u(t) given.For increasing the safety performance evaluationcriteria are proposed two functions J and .Ti suspensionoptimization in random road conditionsThe ferst proposed criterion in this papee forsuspension optimization is expressed by the ratio of theaverage square for output signal yt) centered by theaverage Miy) on the average square for input signal ut)centered by the average M(u):jm,n,u)= -yt)-My)Ydt_ou(/)- M u)fdtThe second proposed criterion in this paper is:(4) (5)From relations (4) and (5) it can be seen that in theideal case, in which suspension system filters all randomperturbations induced by road, the chassis position y isnot affected and I=I=O.The signal y (t) and u (t) for the criterion function (4)and (5) is obtained by simulating multimodel damperand suspension dynamics expressed by equation (2) and(3). This is suspension multi-model variant with a onedegree of free. Block diagram for this multimodel isshown in Figure 8 where S(t)=y(t)-u(t).In Figure 8 block called command base(CB) is amultimodel VZN damper type with four holes throughthe cylinder wall arranged in vertical line,at equal distances between them. The block called basemoder(MB) represents the dynamic of the suspensionsystem Block CB is implemented in Matlab and blockMB is implemented in Simulink.Optimization problem is formulated afternoonsuspended biparametric minimum J of m and number ofholes n in the conditions of a random disturbance, u(t)given.72Volume 6, Number 1, May 2013- cy = mra-S-y(Q) = 0VIODEX-S BA.SE5- sc/ 4/ S/16/16T.f.Fig. 8. Suspension system mult-modelIV. SUSPENSION OPTIMISATION RESULTSThe proposed procedure for solving areaoptimization problem formulated in the previous sectionof this article is an experimental method for searchingapproximate optimal criterion function. Theseexperimental methods involving response surfaceexploration (in space described by the criterion function)by changing the input variables m and n and measuringthe output quantity J(m,n) for each combination of inputquantities of m and n in the conditions of a randomdisturbance, uf) given.TABLE I. Suspension parameters and criteriasimbolsmki=var y/ var unCleClrvalues1000;700;4001000J =max y/max u1;2;3;410002000unitsKgN/mCrit.holesNs/mNs/mTable 1 contains the parameter values for simulatedand optimized suspension system by the proceduredescribed above.J (4OO;J(4OO4)O34) = O23JJOOO;4)=O43S)O.3J(4OC:4)-O47OO OOOFig. 9. Suspension experiment plane m and nModification of the input variables m and n is limitedby technological considerations, so that it can explorethe entire surface of the response, but only a portionthereof around the nominal operating point. In twoexogenous variables such data are obtained bymeasurements where. This is called factorial experimentplane m and n which is shown in the following Fig.9.From this figure it follows that the value of parameter mand n which ensure maximum criteria J are: m* = 700Kg and n* = 3 holes. From this figure it follows that thevalue of parameter m and n which ensure maximumcriteria J are: m* = 700 Kg and n* = 3 holes as in allother points surrounding the center point lower valuesare obtained criterion function.V. CONCLUSIONSAnalysis of simulation results showed substantialincrease yield by the ratio of the signals u and y variantsof DSSA than five times the compression strokecomparedThe simulations indicated that the multi-model wasquite effective over wide ranges of unmeasureddisturbances and process changes. Analysis ofsimulation results showed a substantial increase of theratio of variances yield signals u and y of DSSAcompression standard over in stroke compared withstroke rebound. Basically degree of pulsation input tothe sprung mass are null for making a Cd more apple asj. in the other three cases.L The contributions of this paper are their mainobjectives: a detailed testing scheme for the dampingcharacteristics and multimodeling of shock absorber isproposed.2. The suspension multi-modeling dampingcharacteristics are tested under random excitation3. Interpretation is given to the bank multimodel linearmodels for damper standard curve of DSA andVZNshock absorber; To deduce a linear model for aportion of the static characteristic (damper-curve) ofstandard DSA and VZN-; shock absorbers4. The bank of models and the one of commands areconceived and the whole structure MATLAB_Simulinkits presented for simulating and testing on a standardcase study.5. DSA and VZN shock absorber, anal