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Development of performance simulation technology of cylindrical hydraulic shock absorber

Abstract: various modeling methods of automotive cylindrical shock absorber are summarized and analyzed, which are summarized into parametric model, equivalent parametric model and non parametric model, and their basic principles and existing problems are described respectively. The current situation of domestic shock absorber performance simulation technology is introduced, and the future development trend is put forward

key words: shock absorber, performance, simulation, simulation, solid-liquid coupling

Chinese figure classification number: u463331, tp391.9 document identification code: a

Article Number: (2006)

I. classification of mathematical model of shock absorber

shock absorber is a damping element in automotive suspension system, and its performance has a direct impact on ride comfort, handling performance, etc, The establishment of its mathematical model has always been an important research topic in the field of vehicle dynamics at home and abroad. As far as the research of cylindrical hydraulic shock absorber is concerned, three kinds of mathematical models have been established, namely parametric model, equivalent parametric model and non parametric model. The parametric model considers the real working conditions such as the flow of oil in the shock absorber and the deformation of the elastic element of the throttle valve, and establishes the coupling dynamic model of fluid and structure. This model can be used not only for the prediction and analysis of the characteristics of the shock absorber, but also for the simulation and analysis of automotive system dynamics and vibration. The equivalent parametric model abstracts the shock absorber into a combination system of some typical physical elements with certain mechanical properties, and establishes an equivalent mechanical property analysis model. The nonparametric model is a kind of model based on the experimental test and analysis of the shock absorber. It does not consider the actual structure and internal working process of the shock absorber, but only adopts the appropriate mathematical function expression in form to approximate the experimental results

II. Parametric model

shock absorber is usually composed of piston and piston rod, flow valve, compression chamber, recovery chamber, compensation chamber, bottom valve, etc. When establishing the parametric model, the equations expressing the parameter relationship of fluid pressure flow should be established for each chamber and throttle valve, and then the equations should be connected according to the fluid mass conservation relationship. The characteristics of throttle valve have a decisive influence on the characteristics of shock absorber. The throttle valve inside the shock absorber includes elastic valve plate combination type, elastic valve plate and coil spring combination type, plate valve and coil spring combination type, etc. There is a strong dynamic coupling relationship between the deformation of the elastic element and the flow field in the throttling area. The correct description of this coupling relationship is the key to establish the parametric model of the shock absorber. The parametric model of shock absorber can be divided into lumped parameter model and distributed parameter model. At present, the physical parameter model established mostly belongs to lumped parameter model

The lumped parameter model of a double barrel suspension shock absorber established by Lang in the late 1970s contains 83 parameters, which is used to study the high-frequency characteristic distortion of the shock absorber. He uses simplified vaporization and liquefaction models to describe the physical changes of the gas mixed in the studio, and uses analog circuits to simulate the characteristics of the shock absorberin the lumped parameter model, it is necessary to express the characteristics of the valve as a function of the flow of the valve and the pressure difference at both ends of the valve. The relationship between the flow through each throttling pore and the pressure difference on both sides is usually established by using the semi empirical formula in engineering fluid mechanics. The relationship between the oil pressure in the chamber and the kinematic parameters of the piston must be expressed in the models of the compression chamber and the recovery chamber. Usually, the compressibility of the oil should be considered, which is an important reason for the hysteresis of the speed characteristics of the shock absorber. The model of the compensation chamber must express the relationship between its internal oil pressure and volume. If considering the problem that gas mixed with oil causes the distortion of shock absorber characteristics, it is necessary to establish a model in which the physical change of oil-gas mixture in each chamber causes the change of pressure volume characteristics. According to the fluid mass conservation equation, the flow models of each chamber and throttle valve are connected to form a complete shock absorber model

when establishing the above lumped parameter model, it is assumed that the oil pressure distribution in each chamber is uniform. But in fact, it is generally non-uniform, especially in the area near the throttle valve, which will inevitably lead to model error. Some key model parameters, such as the deformation and flow coefficient of the elastic valve group, must also be obtained by experimental testing. Most of the established models use the experimental results to obtain some or all of the model parameters, so it is not convenient to predict the characteristics of the shock absorber in the design stage

with the development of computing technology, it is gradually possible to establish and solve the distributed parameter model of shock absorber by using numerical methods. If FFA method and CFD method are used to analyze the dynamic and hydrodynamic characteristics of elastic structures respectively, and the liquid-solid coupling dynamic problem is decomposed into a multi-step uncoupled problem, the accuracy of the model can be improved to reduce the dependence on experimental tests. With the development of fluid solid coupling dynamic analysis theory and calculation technology, it is possible to use the finite element analysis tool with FSI (fluid ID structure interaction) analysis function to solve the fluid solid coupling nonlinear dynamic problems of shock absorbers

III. equivalent parametric model

in the late 1980s, Karadayi and Masada believed that Lang's modal spring fatigue testing machine was a reciprocating type of connecting rod driven by electromechanical and reducer connecting cam. Although it could better express the nonlinear characteristics of shock absorber, it was too complex to be used for automotive system dynamics and vibration simulation analysis. In order to establish a simple model that can express the hysteresis characteristics of the shock absorber, they adopted the mechanical model that equivalent the shock absorber to the combination of elastic elements, damping elements, clearance and friction elements. The actual structure of the shock absorber is not considered in the model, including sending GH technicians to accompany the solar race team and the internal working process. The mechanical characteristics of the components can be linear or nonlinear, and its combined system can express the nonlinear dynamic characteristics of the shock absorber. Karadayi's modeling method explores an effective way to establish a few parameter nonlinear model of the shock absorber, but its model simulation results are only in good agreement with the experimental results under the condition of low 4 and sudden increase in frequency of data test of the shock absorber

besinger and Cole applied this modeling method to the modeling of heavy vehicle suspension shock absorber in the middle and late 1990s, using nonlinear elastic and damping elements. The model simulation results are in good agreement with the experimental results in the range of piston motion frequency less than 10Hz and speed less than 1m/s

Figure 1 shows several equivalent parameterized models composed of physical elements with different mechanical properties: (a) it is only composed of linear elastic element K and linear damping element C in series; (b) A friction element is added ψ； (C) A clearance element is added on the basis of (b) ε。 There is a certain correspondence between the physical elements in the equivalent parametric model and the actual factors that affect the characteristics of the shock absorber: the elastic elements correspond to the combined effects of the elastic elements of the throttle valve system, the compressibility of the oil or oil-gas mixture, the elasticity of the cylinder barrel and the elasticity of the rubber bushing connecting the hinges at both ends of the shock absorber; The damping element corresponds to the damping effect produced by the oil flowing through the throttling pore; The friction element corresponds to the friction between the moving pairs; The clearance element corresponds to the movement lag of the throttle valve and the oil and the possible idle distance when the direction of the shock absorber movement changes. The parameter values of each physical element in the model can be fitted by the experimental measurement data

for different shock absorbers, different combinations of elements can be used, and different mechanical characteristic parameters of elements can be taken to establish models - when the influence of friction is significant, for example, for shock absorbers bearing lateral forces, the combinations shown in (b) and (c) should be used. For the suspension shock absorber of commercial vehicles, the influence of friction and clearance is not significant, and the model shown in (a) can also achieve high accuracy. It should be pointed out that the nonlinear characteristics of the damping characteristics of the shock absorber under different working speeds and different excitation frequencies are quite different. Usually, there are two obvious stages with the opening state of the throttle valve, and the hysteresis phenomenon increases with the increase of excitation frequency. Therefore, the value of mechanical characteristic parameters of components under low-frequency and low-speed working conditions is often not suitable for high-frequency and high-speed working conditions. Mechanical components can be selected according to the actual damping characteristics of shock absorbers, and parameters can be fitted according to specific working conditions. This is also a difficult problem in equivalent parametric modeling

IV. nonparametric model

there are many kinds of nonparametric models (also known as black box models) of shock absorbers. The simplest method is to fit the curve of the experimental measured damping force piston displacement or speed relationship data (indicator diagram and speed characteristic diagram) or arrange the measurement results into a table. However, because the damping force of the shock absorber is actually related to many motion state parameters (such as displacement, velocity, acceleration, etc.), the above expression method is not comprehensive. Restoring force surface (RFs) method is a relatively successful non parametric modeling method. The key point is that the damping force of the shock absorber is expressed as a function of multi motion state parameters, and the characteristics of the shock absorber are intuitively expressed in a two-dimensional surface diagram. This modeling method has certain special requirements for the test method of shock absorber. At present, the more mature method is to change the excitation amplitude under a certain excitation frequency, so that each grid on the state plane contains enough data. Because the characteristics of the shock absorber are related to its vibration frequency, it is necessary to carry out laser vibration experiments on the shock absorber at many frequencies to obtain a series of equal frequency restoring force surface diagrams. This requires a large number of experimental tests, which is the main disadvantage of this kind of modeling method at present. At present, the RFs modeling method based on harmonic excitation is relatively mature, and the RFs modeling method based on non harmonic excitation (such as random excitation) is under further research

v. current situation of domestic shock absorber simulation technology

in the field of shock absorber modeling and simulation analysis, some domestic scholars have established some simplified parametric models, equivalent parametric models and non parametric models. However, the physical parameter model established greatly simplifies the actual structure of the shock absorber, and does not deeply consider the influence of medium working temperature, friction and other factors. Reference [6] used the liquid-solid coupling finite element method to simulate the throttling characteristics of the bottom valve compression valve. The bottom valve and compression valve adopt slide valve structure, so it is easy to directly solve their pressure difference flow characteristics by liquid-solid coupling finite element method. The solution results are generally in good agreement with the test results, but due to the complex shape of the throttling pore of the bottom valve compression valve, appropriate structural simplification is carried out when establishing the solid-liquid coupling model, resulting in certain errors. The research on the equivalent parametric model of shock absorber mainly applies foreign modeling methods to the modeling of domestic automotive suspension shock absorber. At present, the modeling process of this kind of method has been mastered, but its application research needs to be further carried out. At present, the research on non parametric modeling method is limited to the simple fitting of experimental test results. (end)

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