外文翻译--履带车辆的半主动液气悬架系统.doc

译 文学 院： 机电与汽车工程学院 专 业： 机械设计制造及其自动化 学 号： 09455- 姓 名： 吴欣洋 指导教师： 张建 Semi-active hydro-gas suspension system for a tracked vehicleU. Solomon, Chandramouli PadmanabhanMachine Design Section, Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai 600 036, IndiaReceived 18 June 2010; received in revised form 12 November 2010; accepted 11 January 2011 Available online 4 March 2011Abstract A semi-active hydro-gas suspension is proposed for a tracked vehicle to improve ride comfort performance, without compromising the road holding and load carrying capabilities of the passive suspension. This is achieved through an active damper used in parallel with a gas spring. The suspension damper parameters are varied by a control mechanism based on sky-hook damping theory, which alters the flow characteristics. A damper prototype has been developed, tested for its flow characteristics, after which it has been integrated into an existing hydro-gas suspension system. An analytical model has been proposed from first principles rather than developing a phenome-nological model based on experimental characteristics. This model is validated with experiments carried out on a suspension test rig. In order to compare the performance with the original passive system, an in-plane vehicle model is developed and the simulations clearly show that the semi-active system performance is superior to the passive system.2011 ISTVS. Published by Elsevier Ltd. All rights reserved.Keywords: Semi-active hydro-gas suspension; Sky-hook damper; Variable orifice damper1.Introduction The damping in a passive suspension system is chosen to provide optimal performance at low frequencies. However ,the higher damping chosen makes the performance to degrade at higher frequencies. A semi-active suspension ,with variable damper characteristics offers a low cost solution to improve the ride comfort without compromising road holding and load carrying performance of the suspension. One of the most popular semi-active damping strategies has been the “sky-hook damper originally proposed by Karnopp et al. The performance of this damper has been investigated in detail by Karnopp and Emura et al. have highlighted the limitations in realizing such a damper in a practical scenario. Oueslati and Sankar studied the performance of passive, active and semi-active suspensions using single degree-of-freedom (DOF) and four DOF vehicle models. They proposed three types of control schemes for a semi-active suspension. The first scheme is based on the idea of modulating the passively generated damper forces using feed-back control while using a small amount of external power. This alternative suspension approached the performance of an active suspension with the significant advantage that it requires only a fraction of the power used by an active suspension. The second control strategy was originally suggested by Rakheja and Sankar . They observed that, in a passive damper, the damping force increases the sprung mass acceleration when the spring and damper force have the same sign. The active damper does not provide a force during this part of the cycle. When the spring force and dam-per force are in opposite directions, the active damper generates a force having the same magnitude as the spring force but acting in the opposite direction, so that a net zero resultant force is obtained. The attractiveness of this control scheme is the need to measure only the relative dis-placement and velocity across the suspension. The power requirements of this scheme depend on the choice of the gain. As desired, at higher frequencies the isolation provided by the active damper is superior to the passive damper but at frequencies around the natural frequency of the suspension system, a high root mean square (rms) acceleration transmissibility occurs, which is a significant drawback of the control strategy. To overcome this a third control scheme, where a passive damper is placed in parallel with the active damper and spring, is proposed. While the introduction of the passive damper significantly reduces the rms acceleration ratio around the natural frequency, it increases the rms acceleration ratio at higher frequencies. Tseng and Hedrick demonstrated that modulated dampers can provide excellent vibration isolation at low frequencies (around 1 Hz). They also proved that optimal semi-active suspension parameters can be obtained by minimization of a quadratic performance index. Cheok showed that the clipped-optimal solution (where a quadratic performance index is minimized subject to road holding, suspension working space and damper maximum value constraints) is optimal in minimizing the “ model following error ” but not in minimizing the unconstrained quadratic performance index. Youn and Hac developed a 2-DOF model of a vehicle incorporating a semi-active suspension with adaptive capability. In addition to a vari-able damper, a spring in which the stiffness can be discretely varied among the three different levels was proposed by them. They concluded that the adaptive sys-tem showed significant improvement in controlling vehicle vibration when compared to a semi-active suspension with a modulated damper and fixed stiffness. The literature reviewed in the previous paragraphs primarily deal with control strategies for semi-active suspensions in wheeled vehicles. Use of active dampers in off-road wheeled/tracked vehicles has also been investigated by several authors. Nell and Steyn developed and experimentally evaluated a two-state semi-active translational damper on a high mobility off-road vehicle. They modified the passive damper by adding a bypass assembly and a controllable valve and demonstrated significant improvement in both handling and ride comfort. Giliomee and Els described the development and characterization of a semi-active hydro pneumatic suspension with a two-state pneumatic spring and a two-state hydraulic damper. Tests were conducted on a single DOF test rig and the semi-active damper control strategies were evaluated. It was shown that the acceleration levels were much lower with the semi-active mode. Els and Holman developed a two-state discrete adjustable semi-active rotary damper for heavy off-road wheeled vehicles. They carried out a full vehicle simulation using DADS commercial software and demonstrated that the semi-active rotary damper performance was better than both the passive rotary damper and traditional damper. Use of electro-rheological (ER) fluids in dampers have also been attempted. Choi et al. have proposed ER dampers for ride comfort improvement in tracked vehicles. Initially the damping characteristics are established with respect to the electric field using a Bingham plastic model and this is incorporated in a linearized state-space model of the vehicle dynamics. An optimal controller with a Kal-man filter has been used to demonstrate the reduction in vertical acceleration of the vehicle. Most of the semi-active dampers reported in the literature for tracked vehicles are two-state dampers (onoff type) which require complex control strategies. In this paper, the sky-hook damper strategy (onoff type) is used in a quarter-car model to arrive at an optimal damping co-efficient. Based on this a continuously variable damper, with a standard PID controller, is proposed for damping control. Using an analytical model of the suspension, validated with experiments on a suspension test rig, an in-plane simulation model is prepared. Comparisons with the passive suspension clearly demonstrates the superior performance of the semi-active damper.2. Passive hydro-gas suspension Tracked vehicles fitted with torsion bar suspensions are limited in their ability to achieve high mobility due to their linear characteristics. Hydro-gas suspensions due to their inherent non-linear behavior can provide higher mobility and better ride comfort performance. The hydro-gas suspension model has usually been developed from experimental forcedisplacement characteristics, which requires availability of suspension hardware. A typical hydro-gas suspension system, shown in Fig. 1a, consists of a stationary accumulator and accumulator cylinder, damper, crank pin, road wheel and axle arm. The crank, connecting rod and piston form a four link slider crank mechanism as shown in Fig. 1b to convert the rotary movement of the axle arm to linear piston displacement for compressing the gas medium. A damper is animportant sub-system of a suspension located between and linking the actuator and accumulator cylinders. Applying loop closure along the X0 and Y0 -axes for the slider-crank mechanism as shown Fig. 1 b yields for rebound position:velocity of the piston, with x being the angular velocity of the axle arm (crank), is given by To obtain the stiffness of the suspension, it is assumed that the gas pressure under compression/expansion is given by a polytropic law, pVn = constant, where n is the poly-tropic co-efficient. The volume of the gas V is calculated from the slider position (Eq. (3) and the force on the cylinder block is computed by multiplying the pressure p with the piston cross section area. The forcedeflection relation-ship yields the gas spring characteristics corresponding to the permissible travel limits of the piston. To validate the stiffness calculations using the polytropic law, an experimental set-up, as shown in Fig. 2, is used. Note that the same set-up is used for both passive and semi-active suspension experiments. The suspension test set-up has a capability to test a single station suspension with a maximum stroke of 600 mm. The displacement is sensed by a LVDT and the load is measured using a load cell with a rating of 250 kN. The test rig is capable of carrying out both static and dynamic tests at various conditions. The wheel is on a platform connected to an actuator. For varying the spring characteristics, the platform is moved from 0 to 500 mm in steps of 50 mm. the force at the fixed end of the suspension is measured for each position. The forcedeflection curve obtained from experiment is compared with the analytical model. As seen from Fig. 3 the agreement is excellent indicating the validity of the theoretical model. 2.1. Damper characteristics using electrical analogy The hydraulic conductance of the damper is calculated from the pressure drops for different piston velocities using an electrical analogy. Kirchhoffs laws are used to relate the flow rate and the pressure drop across an orifice, analogous to an equivalent electric circuit. The analogy maps flow rate to current, pressure to voltage but hydraulic resistance is used with care, as it is nonohmic. Therefore, hydraulic conductance (gi) of an orifice, proportional to the orifice area, is defined. The instantaneous rate of flow through a damper orifice can also be written as where Cd is the co-efficient of discharge, q is the mass density of the fluid, Ao is the area of the fixed orifice. Eq. (4) can be written as, Conductances in parallel add like electrical capacitances. However, conductances in series add as reciprocal squares, with the effective conductance ,gp given by where g1, g2. gn, are the conductances of the various orifices/passages in the damper. The hydraulic circuit of the damper with complex passages and orifices can be visualized to be arranged in parallel, or series, from which the effective conductance can be calculated. This analogy is used in the semi-active suspension for finding the variable orifice damping characteristics. The head loss for any restriction is given by where HL is the head loss, KL is a factor which depends on the type of restriction and to orifice length to diameter ratio. This can be re-arranged in terms of the flow rate as:Substituting Eq.(8) in Eq. (4) one gets It may be noted that, in deriving the above expressions (i.e. flow rate versus pressure) for bounce and rebound operations of the hydro-gas suspension, the assumptions are that the fluid behaves ideally and that steady-state conditions prevail. The KL factors of fluid flow for orifices are selected from Yeaple . Substituting KL in Eq. (5) yields the following expressionThe pressure drop as a function of flow rate is calculated using the effective conductance and flow rate values in the Eq. (5). To verify the proposed hydraulic conductance based model for the damper, an experiment is carried out using the test bench shown in Fig. 4. The hydraulic test bench consists of a 100 HP AC motor, a vane pump, an oil tank of 1000 l capacity, control and throttle valves, sys-tem oil inlet and outlet ports with a capacity to deliver 350 lpm. The measured quantities are flow rate, pressure and temperature. During damper testing, the damper is connected to the hydraulic test bench at the inlet and the outlet of the dam-per is returned to the sump as seen in Fig. 4. The testing was conducted for various differential pressures and the corresponding flow rates were measured. The non-linear flow characteristics of experimental and theoretical of the damper are shown in Fig. 5. The experimental and theoretical damper characteristics match very well, thus validating the damper model. Finally, the assembled passive hydro-gas suspension characteristics are obtained using the set-up shown in Fig. 2. The input to the platform is a sinusoidal displace-ment with amplitude of 100 and 150 mm from a mean position of 300 mm. The frequency of the displacement is varied from 0.1 to 0.8 Hz and both input displacement and suspension force are measured .Fig. 6 shows a comparison at 0.8 Hz excitation frequency with displacement amplitude of 150 and 100 mm from 300 mm mean posi-tion. For the wheel displacement between 220 and 250 mm for the 0.8 Hz excitation case, there is a bump, which is due to the opening of the pressure relief valve. It can be seen that the simulation result also exhibits this phenomenon; however, the displacement at which this happens is slightly lower than what is observed in the experiment. This difference is possibly due to additional friction in the actual hardware. 3. Semi-active hydro-gas suspension 3.1. Sky-hook damping control for semi-active suspension For a semi-active suspension, the sky-hook control strategy is first implemented in a quarter-car model and is shown in Fig. 7a. The sky-hook damper is a variable damper where the force is controlled by the product of sprung mass absolute velocity and relative velocity between sprung and unsprung masses as shown below: In the quarter-car, model the damping co-efficient Csky has been varied to study the effect of sprung mass, acceleration, road force and suspension travel. From this study, a semi-active control strategy for the damper is implemented as shown in Fig. 7 b. The road input for evaluating the semi-active suspension is one wavelength of a sine wave. In a semi-active suspension, the damping co-efficient ( Cs) for various road inputs at any instant is arrived based on the Csky value through sky-hook logic of the system. The parameter C sky is varied and the value which leads to the desired rms acceleration level of the sprung mass while satisfying the suspension working space constraints is chosen for further studies/implementation. The parameters considered are, sprung mass, ms ,of 4100 kg and an unsprung mass, mu , of 380 kg. The damping co-efficient Cs for various road inputs at any instant is arrived based on the Csky value through sky-hook logic of the system. The Csky is an imaginary value that can result in the desired acceleration level for the sprung mass and is primarily estimated based on acceleration level of the sprung mass and suspension working space. The damping co-efficient Cs is available for the suspension system to effect the necessary damping force based on relative velocity between sprung and unsprung masses, which is equivalent to the sky-hook damping force. To find out the optimum C sky , the methodology adopted is to simulate the quarter-car model of the hydro-gas suspension system with various road wavelengths, amplitudes and vehicle speeds. In the simulation, seven similar continuous sinusoidal inputs have been given. The rms acceleration levels and suspension working space have been generated for preset C sky values. The input variables considered for the simulation is wave length of 4 m and amplitude 150 mm 1060 kmph speed. Fig. 8 shows rms acceleration for 20, 40 and 60 kmph at 4 m wavelength, It can be seen that lower rms acceleration is exhibited at a Csky value of 15,000 N s/m. The rms acceleration levels are shown in Table 1.From the table, it is observed that the rms acceleration levels are smaller when C sky value is at least 15,000 N s/m. Next, the suspension working space for various C sky values has been simulated and shown in Fig. 9 for 40 kmph and 4 m wavelengths respectively. Lower the Csky value higher the suspension travel and hence larger the suspension working space required. For C sky values between 15,000 and 18,000 N s/m, the suspension travel is within limits for this hydro-gas suspension system.If one were to map the rms acceleration data to the ISO 2631 reduced comfort curves for 2 and 4 h fatigue-decreased proficiency boundary requirement for the tracked vehicle as shown in Fig. 10, it can be seen that a C sky of 15,000 N s/m and 18,000 N s/m result in lower level of vibrations. However, considering the critical damping co-efficient Cc , which is estimated to be around 20,000 N s/m at the static position, it is preferable to choose C sky as 15,000 N s/m. Also, the practical realiz