Water Hammer Model of Shock Absorber Throttle Slice

Journal of Beijing Institute of Technology, 2008, Vol.17, No. 1Water Hammer Model of Shock Absorber Throttle SliceCHEN Yi-jie(陈轶杰)，GU Liang(顾亮)，LEI Sheng -guang(雷绳光),GUAN ji-fu(管继富)(School of Mechanical and Vehicular Engineering, Beijing Institute of Technology, Beijing 100081, China)Abstract: In alusion to easy invalidation of damping valve in vehicle shock absorber caused by the impact fromthe road surface, the importance of the study of damping valve water hammer pressure is presented. Thephysical model of damping valve with the circle throttle slice is established. The time for the thottle slice de-formation is studied by using the finite software, and the laws that how the structure parameters affect the de-formation time are obtained. Combining the theory of water hammer, the water hammer initial and boundarycondition of the damping valve is deduced, and the water hammer model of throttle slice is established. Theanalysis of simulation results indicates that the water hammer pressure amplitude and the amount of waterhammer osillation period can be reduced and the dependability of the valve can be enbanced by modifying thestructure parameters and aperture width between slice and valve body.Key words: shock absorber; throttle slice; deformation; water hammer modelCLC number: TB 123Document code: A Article ID: 1004-0579(2008)01-0014-06In the hydraulic system, the frequent openness1 Physical Model of Damping Valveand closeness of valve will cause the significant changeof the flow velocity， which is accompanied by theFirst，the physical model of the damping valvephenomenon of the hydraulic pressure ’s alternantwith the throttle slice is established, as shown inraise and fall. We call it water hammer. The alter-Fig.1. The flow flows through straight oil orifice- +nant flow pressure is called water hammer pres-circle oil orifice 十aperture between valve body andsurel1].slice +circle cavity, then to and fro between the cavi-While the vehicle runs on the highly frequentty 1 and cavity 2. The damping force is produced byroad surface， shock absorber bears the impact fromthe throttle effect of the circle aperture between thethe road, which leads to the sudden open and closeslice and valve body. Because the slice is equipped onchange of the damping valve and high water hammerthe internal surface of the oil orifice, the initial widthpressurel2l. The fact shows that the damping valveof the aperture O8o should be given in advance avoid-can be easily invalidated when it is exposed to theing the interference between slice and valve body.high hammer pressure. According to the current2 Water Hammer Model of Throttledamping devices, there are many kinds of the throttleSlicemodes of the damping valve. The most common oneAs shown in Fig. 1, when the shock absorber isis the aperture throttle of the annular slice. Based onthis situation, the systemic study of the water ham-impacted and throttle slice is deformed instantaneous-ly, the velocity of flow around it changes sharply andmer force of the throttle slice at the non- instantaneousthe flow pressure increases or decreases significantly.open and close state has been done.中国煤化工Received 2007-05-25Sponsored by the Ministerial Level Advanced Research Foundation (623010202.MYHCNMHGBiographles CHEN Y-jie(1980 - ), doctoral student, ceii8888@bit. edu. cn; GU Liang(1958- ), professor, doctoral adviser.一14-CHEN Y-je(陈轶杰) aal. 1 Water Hammer Maded of Shoce AborerThrottle Slicecircle cavitytermal diameter dn= 0.055 m, thickness of the slicestraight oil oifice.δ=5X 10~4 m，elasticity modulus E = 2.06 xoilcavityIoilcavity2105 MPa, density p,=7 830 kg/m', Poisson's ratio .u=0.3, the impacts P=0.2 MPa, 0.4 MPa areloaded respectively. The initial step of simulation isvalve bodyOt=2.5X10~s，the amount of the stepsis n=circle oil orifice / \ throtle slice100, the simulation results are shown in Fig. 3. Un-Fig.1 Damping valve physial modelder the condition that the structure parameters of theThis kind of change is transferred to the oil orifie,slice and the characteristic of the material are fixed,which causes water hammer wave. As the wavechanging the impact load, the largest deformation'sreaches the oil cavum, because of the unequal pres-time of slice are the same, in spite that the deforma-sure at the end of the oil orifice, the reverse watertions are different. When the thickness is 5 xhammer wave is caused and passes to the valve. It re-10~4 m, the time needed to reaches the largest defor-verses after it bumps into the valve and goes roundmation for the throttle slice is l =0.9x 10-3 s,and round. However, in fact, because of frictionalwhich is an important parameter for analyzing theloss and local head los, the energy of the water ham-change of the water hammer pressure while the valvemer will be reduced. On the other hand, it takesopens and closes non- instantaneously.some time for the slice to deform. Thus, the utmoststate of the valve' s instantaneous open and close will1.2一load 0.2 MPa- - load 0.4 MPanot happen.1.02.1 Time for Slice Deformation.8-It's very dificult to calculate the exact time.6which is needed for the slice to reach the largest de-formation caused by instantaneous impact through the.2-theoretical method, and it isn' t suitable for the appli-0.04 0.08 0.12 0.16 0.20cation in the project. Thus, the instantaneous re-sponse of the throttle slice is analyzed by using soft-Fig.3 Deformation of slice thicknessAssume that the thickness of the throttle slice isware Ansys, and the laws that how the structure sizesaffet the deformation are studied in detail.δ=1X 10~3 m and the impact load is P=0.4 MPa,The established finite model of the throtle sliceThe itial load step of simuationis Ot=1.25x10-*s，is shown in Fig.2. The free gridding is carved up onother parameters are the same as the above example.the model suriace, and the even impact is loaded.The simulation result is shown in Fig. 4.The inside circle is totally leashed.0.16ANSYS0.12-MAR 21 200720-53:030.08L，0.040.020.040.060.08 0.10 0.12中国煤化工Fig.2 Finite element model of thottle sliceJYHCNMH G ..=0.09 m, theAssume that: outside diameter d. =0.08 m, in-thicknessof the thottle sliceis 8≈5x 10~4 m and--15-Journal of Beijing Institute of Technology, 2008, Vol.17, No.1the impact load is P = 0.4 MPa, the initial load stepequation group of the water hammer pressure and ve-of simulation is Ot=5X10~+ s, other parameters arelocity is obtained asthe same as the above example. The simulation resultp:-p11- paV{+is shown in Fig. 5.pV}(a+ gosin0 - 1V2到)=0, (2)p- p:+ ρaV?-3-pV={(a-gOtin9 - 41V1)=0, (3)where the subscript i(2,3,.",m - 1) stands for theposition of the orifice, the superscript j(2,3,"",N)stands for time step, Eq. (2) presents the characteris-0.1 0.2 0.3 0.4 0.5tic equation in the direction opposite to the wave.ime/msEq. (3) presents the characteristic equation in theFig.5 Deformation of sliceAccording to Figs. 3 - 4，under the conditionsame direction as the wave.As shown in Fig. 6，the lines AP and BP arethat the thickness is δ=1x10-3 m, the time for theslice to reach the largest deformation is t =0.97 xknown as the characteristic lines of the s- t plane,10~4 s. It indicates that the largest deformation ofthe Eqs.(2) - (3) are tenable only along the respec-tive characteristic line. The initial and boundary con-the slice is reduced as the thickness increases.ditions are given in advance to the established damp-According to Figs. 3 - 5，under the conditionthat the outside diameter is dw =0.09 m, the timeing valve model. If the water hammer pressure andvelocity are known at the pre-time grid point, the pa-for slice to reach the largest deformation ist=0.38Xrameters of water hammer can be obtained at any cur-10~4 s, which indicates that the time for slice torent grid point[3-6].reach the largest deformation increases as the outside14diameter increases.+12.2 Water Hammer Mathematic Model of ThrottleSlice-1「he mathematic model is mainly based on theolunsteady flow differential equation. It is modified ac-Fig.6 Difference element sketchcording to the real stateAssuming that when the initial time t = 0, the?+p V+ povV+pVlVl=0,as+ P- 2d(1)fluid average velocity through the oil orifice cross sec-tionis V{= Vo, the initial pressure is p!= po; thev然+时+pgVsinθ+pa2 ￥=0,asboundary condition of the pressure at the left end ofwhere p is the water hammer pressure; V is the av-the straight orifice is Pl。= po; the dynamic width oferage velocity of fluid flowing through the oil orifice;the aperture caused by the deformation of slice isp is the density of the fluid; a is the velocity of theO8;. In order to be convenient for analyzing, assumewater hammer; 0 is the angle insluded between thethat the change of the dynamic width is linear afterdamping device axes and horizontal line; t is the timethe slice is impacted instantaneously. As shown inthat water hammer lasts, s= at; λ is the pressureFig.7, the width of the circle aperture changes alongloss on the way; g is the acceleration of gravity; d is中国煤化工the equivalent orifice diameter.YHCNMHGt;).(4)According to the characteristic line method tosolve the differential equation group, the differenceAccording to Eq. (2) and the given pressureCHEN Yi-jie(陈轶杰) et al. / Water Hammer Model of Shock Absorber Throttle Slicep.= [ +内h- pa(V,h-吃)-s8 hpgOtsin0(V1;+1+ v,1)+哈会(whl V，hl- IV:2)], (10)v.=去[+a(V,;1+ v71)-Fig.7 Closed curve of throttle sliceboundary condition, the fluid velocity through the leftside of the straight orifice is obtained as验(V,hNV,h1+ v,H1V1)]. (11)vn.=[pn- p%z'+pV%:"(a+As the straight orifice and circle orifice are in se-ries, at the boundary, the flow rate conservationglsin. -会1V:1)]/x.(5)principle should be obeyed. Combining Eqs. (8) andAccording to the aperture flow rate formula,Eq. (10), the fllwing equation is obtained as[A,(C1+C2)+A,(S,-Sz)]when the slice is close non instantaneously the changePm,=ρ，(12)(A,+ Ax)of the fluid velocity through the circle orifice can bewhereexpressed byC1= /(pa),v. = ropd.W,. (6)12μ8AxC2= Bv-:1,(- Otsin9 -分v=1l),where Ax is the area of the circle orifice; μ is the dy-(13)amic viscosity. According to Eqs. (3)(6), the waterSi= ph'/(pa),hammer pressure expression at the valve when it clos-es non- instantaneously iss2= 8V3公(。+ Otsin0 - Ad°1vz"l),2gdpm.=(14)以+ pV=+n( a- goSsin0 -where A, is the area of straight orifice.The local head loss between straight and circle(7)orifice is2d'ph=pm,- Opi.(15)According to Eqs. (2)(3), the solution expres-sion of the water hammer pressure and fuid velocityAs the fluid flows to the valve, the local headat the straight orifice is obtained asloss is .p=L听+在- pa(V,A-V75)-sp=p(1-创兴(16)pgOtsin0(Vi,+1+ V;,)+As the fluid flows to the oil cavum, the local(V，;1V,1- vh1)], (8)|head loss is57]2d(V.)21[啞_ 堕Op=Eρ2(17)V.=zaL-+a(V,H1+ Vj,H)-The frictional loss in the orifice isgOtsin0( v.hi- Vi+)-L (V,)2Opz=λa2 P(18)4(V;h1 v,21+ v,21V,41)], (9)中国煤化工water hammer inand the solution expression of the water hammerthe fpressure and fluid velocity at the circle orifice is ob-YHCNMHGtained asa=↓p/N1+Eh'(19)Journal of Beijing Institute of Technology, 2008, Vol.17, No. 1where the elasticity modulus of the orifice wall isdw=0.09 m, the thicknessis δ=5X10~4 m, otherE;= 2X 10' MPa, the width of the orifice wall is h=parameters are the same as the above, the simulation0.02 m, and the volume modulus of the fluidis K=result is shown in Fig.10. The highest water hammer1 670 MPa.pressure at the valve is 2.13 MPa. Compared withCombining Eqs. (3) - (18) and the given initialFig. 8, the highest pressure at the valve is reduced.and boundary condition, the water hammer mathe-matical model of the throttle slice is established. Inaddition, the establishing of the valve model whileopen is the same as the above, and the caused water1.5-hammer pressure is the same as that while close, thedirection is opposite.0.52.3 SimulationThe related parameters are: θ=一，the length-0.5200 400500 800 1000of straight orifice L,= 0. 007 m, the outside diameterd,=0.01 m, the numbers n=6, the length of circleFig.8 Water hammer pressure when thickness is5X10~*morifice Lx= 0.008 m，the internal diameter dm =3.50.055m，the oil density ρ= 890 kg/ m', the initial2.5-velocity of the fluid Vo= 1 m/s, the dynamic viscosi-ty μ=8.9X10 -3 kg/(m's)，the initial pressure in1.the oil cavum po = 0.4 MPa, the initial aperturewidth Oδo=0.5X 10-5 m. To be easy for compar-ing，assume that the dynamic aperture width is08,=1X10-3 m.-1.5 200400 600 800 1000The iterative calculating is done by programmingwith Matlab. The amount of gridding point ofFig.9 Water hammer presure when thicknes is5x10~ 'mstraight orifice is n,= 7, the length of the griddingunit is Os,=L。/ng, the time interval is Ot,= Os./a.f 2.0The amount of gridding point of circle orifice is nx=.5-8, the length of the gridding unit is Osx= Lx/ nx,the time interval is Otx=Osx/a; the time stepj=2,.03, ..1000.First, assuming that the thicknesses of the sliceare5X10~4 m and 1X 10~ 3 m respectively, the sim-ulation result is shown in Figs. 8 - 9. When the00thickness of slice is 1 x 10~ 3 m，the highest waterhammer pressure at the valve is 3.3 MPa; when theFig. 10 Water hammer pressure when outside diameter is 0.09 mAgain assuming that the initial aperture widththickness of slice is 5x 10-4 m， the highest waterhammer pressure at the valve is 2.5 MPa. It indicatesbetween the slice and valve body is Oδo=1X10 5 m,that with the thickness of slice reduced, the highestthe slice thickness is δ=5x 10-+ m, other parame-water hammer pressure decreases and the amount ofters a中国煤化工imulation result iswater hammer oscillation period is also reduced.;YHC N M H Gter hammer pres-Then assuming that the slice outside diameter issure at the valve is 0.49 MPa. Compared with Fig. 8,一18--CHEN Yi-jie(陈轶杰) etal. 1 Water Hammer Model of Shock Absorber Throttle Slicethe highest pressure at the valve is reduced signifi-decayed and the amount of water hammer oscillationcantly, and the amount of water hammer oscillationperiod can be reduced by modifying the structure pa-period also decreases rapidly, the curve is quite simi-rameters of slice, and the initial aperture width,lar to over damping oscillation.thereby the slice invalidation caused by instantaneous.s- -impact can be avoided and the application life can beprolonged. These provide an important base for de-sign of damping valve and the feasibility of the struc-0.3-ture parameters are validated theoretically.0.2-References:[1] Wang Shuren. The water hammer theory and calculating[M]. Beijing: Tsinghua University Press, 1981:223 -°b 200006008001 000230. (in Chinese)[2] Lu Jinpu, Guan Zhi. The numerical solution of partialFig.11 Water hammer pressure when initial eperturediferential equation [M]. Beijing: Tsinghua Universitywidth is1X10~5 mPress, 1987 :40- 80. (in Chinese)[3] Kaliatka A, Uspuras E. Uncertainty and sensitivity anal-3 Conclusionsysis of parameters affecting water hammer pressure wave①The study about the time needed for slice de-behavior [J]. Kerntechnik, 2006, 71(5):270- 278.formation through finite element software Ansys indi-[4] Husaini Syed M, Arastu, Asif H. Analysis of passive wa-ter hammer. American Society of Mechanical Engineerscates: under the condition that the structure parame-[J]. 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