外文翻譯----阻尼溢流閥的建模與動(dòng)態(tài)響應(yīng)

1、Nonlinear Dynamics (2005) 40: 119–147 c ? Springer 2005Modelling and Dynamic Response of a Damper with Relief ValveR. D. EYRES?, A. R. CHAMPNEYS, and N. A. J. LIEVENBristol Laboratory for Advanced Dynamic Engineering, Un

2、iversity of Bristol, Queens Building, University Walk, Bristol, BS8 1TR, U.K.; ?Author for correspondence (e-mail: richard.eyres@bristol.ac.uk; fax: +44-117-927-2771)(Received: 26 April 2004; accepted: 23 September 2004)

3、Abstract. This paper outlines several possible methods of modelling a passive hydraulic damper with a bypass tube that is opened by a precompressed relief valve. Initially a simple algebraic model is derived which is dev

4、eloped into a more computationally complex model incorporating the dynamics of the internal spring valve and fluid compressibility. Numerical simulations indicate realistic dynamical phenomena and suggest key design para

5、meters.Key words: compressibility, hydraulic damper, nonlinear, relief valve1. IntroductionVibration dampers are used in many applications such as car shock absorbers [1], bridge stabilisation[2], helicopters [3–5] and e

6、arthquake-resistant buildings [6, 7]. A model is essential if changes are tobe investigated without reconstructing the system. This paper will concentrate on a damper as a stand alone module within a larger mechanical sy

7、stem. Hence it is assumed that a simple, time dependentinput displacement produces a force. The damper modelled is essentially a plunger in hydraulic fluid.The plunger has a small orifice that connects either side throug

8、h which the fluid flows, as in Figure 1.There is an added complication on the damper studied. When the pressure difference between the twosides of the plunger is high enough, a conical valve opens that allows fluid to fl

9、ow through an alternativetube as in Figure 2. When this occurs the damper is said to ‘blow-off ’. The blow-off valve is connected to the damper’s casing via a spring. The precompression of the spring against the alternat

10、ive ‘bypasstube’ determines the pressure difference at which the valve will open. The blow-off system is the same for negative pressure differences with the valve resting against a second bypass tube preventing fluid flo

11、wing freely in the opposite direction.Such a damper is indicative of that used in applications where a nonlinear model applies where thedamping of small amplitude or low frequency motion is most important. The piecewise

12、nature of thedamper means that it can be used in applications where there is more than one mode of operation. The damper can be tuned to the different operational modes. Examples of this would be an automobile thatis use

13、d on high speed flat roads as well as off-road. Other applications are on aircraft landing gears and blade dampers. The damper could act differently when starting up on the ground than it would in cruise when the damper

14、would be in full operation.This study has been motivated by the attempt to reproduce some proprietary test data that showsa hydraulic damper configured as in Figures 1 and 2. The broad features of this data are: hysteres

15、is; delayed response; and chattering oscillations in the blow-off region. Figure 3 is a plot of a typicalinput to the system. The plot shows the damper piston’s displacement against time. Time has been normalised to 1 pe

16、riod and the displacement has been nondimensionalised as in Section 4.3. The mainModelling and Dynamic Response of a Damper 121Figure 3. A typical nondimensionalised input displacement as in Section 4.3 against normalise

17、d time for one cycle.Figure 4. The required normalised force output against normalised time and velocity for one cycle.[8–11], to our knowledge the effects of the passive blow-off valve have not been treated in the liter

18、ature (although relief valves treated on their own have been shown to lead to nonlinear [12, 13] and chaoticdynamics [14].) The resulting model can be used to predict the effect of changing the properties of the damper o

19、n the dynamic response. The key features investigated are the sizes of the orifice and bypass tube along with the stiffness and discharge characteristics of the spring and valve respectively. In thispaper a simple lumped

20、 mass parametric model is derived that incorporates all these effects.The rest of this paper is outlined as follows. Section 2 describes the modelling process used byprevious researchers to model Figure 1 as a simplifica

21、tion of an automobile shock absorber. Sections 3 and 4 investigate several possible extensions to the model in Section 2 to take into account the blow-off.First an explicit model is derived to give the force for a given

22、displacement input. The relief valve and compressibility of the fluid are then considered separately. A model for the whole system is then derived. Section 5 gives some results using the different models. There is also a