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PERIODICA POLYTECHNICA SER. MECH. ENG. VOL. 45, NO. 2, PP.
to ensure a controlled operating pressure modulated at a high accuracy and high temporal resolution.
effects and flow fluctuations expected from a realistic pneumatic pipe performing high velocity flow.
a high accuracy and high temporal resolution, according to the application demands.
thus increasing the actuator pressure if prescribed by the control. The LOAD valve offers a potential for loading the actuator chamber. Functional representation of the electro-pneumatic modulator . The modulator is connected to the actuator with a flexible pneumatic pipe. The EXHAUST valve offers a potential for exhausting the actuator chamber towards the atmosphere. which is long enough that the wheel movement does not stress the pipe walls too much. • A LOAD solenoid valve connecting the air supply (SUPPLY) and the internal chamber (CH). the EPM consists of the following components.240 V. as illustrated in Fig. LOAD EXHAUST PS SUPPLY OUT CH MODULATOR ATM Fig. SZENTE et al. and the modulator is located on the chassis. device on the wheel body (e. The output port (OUT) is connected to the actuator chamber via a pneumatic pipe (see also Fig. thus reducing the actuator pressure if prescribed by the control. • A pressure sensor (PS) measuring the pressure in the internal chamber (CH). a disc brake).g. The measured pressure signal serves as a feedback signal for the pressure control loop electronics supplying the solenoids with appropriate commands. • An EXHAUST solenoid valve connecting the internal chamber (CH) and the atmosphere (ATM). In a simplified layout. 1: • A small-scale internal chamber (CH) connected to the output port (OUT) of the EPM. 2 later). 1.
then applying a short (10 ms) impulse-like EXHAUST command (interrupted before the full exhaust of the actuator chamber). 2. This is the reason why the pressure measured in the internal chamber (CH) is used as feedback signal. respectively. Pipe length and diameter are 3 m and 10 mm. EX- HAUST) and the pressure sensor (PS) are physically integrated in the same EPM unit and are connected to the same integrated circuit panel included in the EPM casing. an EPM modulator unit. The appropriateness of the simulation tool is illustrated in a simplified case study. This setup aims to represent the gas dynamic pipe flow and control problem described in the introductory section. In the past years. The pressure supply is set to an absolute pressure of 11 bar. The test cases presented herein for representation of fluid dynamic behavior of the system are as follows: • Test case 1: loading the actuator chamber using a step-like LOAD solenoid command. respectively. The set-up consists of a pressure source supply. GAS DYNAMIC PIPE FLOW EFFECTS 241 The electro-pneumatic components such as the solenoid valves (LOAD. 2. and simulating the interaction of these elements. all other components are filled in the initial state to the absolute atmospheric pressure of 1 bar. including also their con- trol aspect . then exhausting the actuator chamber using a step-like EXHAUST solenoid command. This compromise necessitates the consideration of dynamics of the pipe connecting the modulator output port (OUT) and the actuator chamber in design of the pressure control loop. a number of investigations has been carried out on the dy- namic behaviour and modelling of solenoid valves  . The modulator internal chamber (CH) and actuator chamber volumes are 10 cm3 and 1000 cm3 . The initial temperature in the pneumatic components as well as the ambient temperature is 293 K. Case Study Set-Up and Test Cases The case study set-up presented in the paper is outlined in Fig. • Test case 3: applying a short (10 ms) impulse-like LOAD command on the fully deflated actuator chamber. an actuator chamber of fixed volume. no detailed pressure control models are presented in- corporating realistic solenoid valve models (resolving mechanical. . The present paper aims to introduce a novel simulation tool for investigation of EPM dynamics. with special regard to gas dynamic pipe flow effects. and a pipe connecting the modulator and the actuator chamber. The pipe wall roughness is as usual for a flexible pneumatic pipe. • Test case 2: loading the actuator chamber using a step-like LOAD solenoid command. Strategies have been elaborated for consideration of gas dynamic pipe flow effects in pressure control . electro-dynamic and fluid mechanical phenomena) and realistic pneumatic pipe models (resolving gas dynamic flow effects). However. The gas dynamic behavior of pneumatic pipes is well-understood . although the pressure control aims to realize a controlled pressure in the actuator chamber. The other parameters are based on .
242 V. Given that the cited version of the AMESim software does not contain a realistic solenoid valve model. it had to be developed by the authors . this software proved its appropriate- ness in simulation of systems related to automotive industry . Most sub-element models have been built up using the commercially available AMESim sub-models taken from the mechanical. . 3. 2. and hydraulic model libraries. SZENTE et al. Therefore. extension. control. pneumatic. . in a topology similar to that of Fig. Including a number of ready-made submodel elements structured in libraries. the temporary development of sonic pipe flow is anticipated for the tests. For . . 2. giving an opportunity for comparison of pipe models based on different assumptions on com- pressibility. Fig. Simulation Tool and Modelling The study of dynamic behavior of the system outlined as above has been carried out using AMESim (Advanced Modeling Environment for Simulations of engineering systems) version 3. Scheme of case study set-up The pressure ratio (ratio between the pressures downstream and upstream of the pipe) takes instantaneously subcritical values for each test case. this simulation environment makes possible a con- venient and effective modification. Among several application fields. 3 represents the AMESim model of the test case presented herein. Budapest Univer- sity of Technology and Economics. and improvement of the case study simulation. Fig.01 at the Department of Fluid Mechanics.
i. AMESim model of case study set-up pneumatic pipes there are several different models included in AMESim. As a consequence. M > 0. Solenoid valve models considering magneto-dynamic and mechanical effects are not available in the 3. GAS DYNAMIC PIPE FLOW EFFECTS 243 Fig. . pulsed fluid transmission between enclosures of relative pressures in the order of magnitudes of 10 bar and 0 bar within a time period in the order of magnitude of 0. pressure signal for relay valves.  is capable for realistic consideration of valve body position-dependent inductance. Given that a pneumatic pipe performs the physically possible entire Mach number range (up to sound speed) above the critical pressure ratio. but their documentation explicitly states that they should not be used when the gas velocity is high. The solenoid is energised by DC voltage. the self-developed AMESim models deserve a more detailed description in the next chapter.01 version of the AMESim environment. solenoid current. The resultant magnetic force displaces the valve body against the return spring. the valve body is kept at its closed end-position by the return spring. Self-Developed AMESim Models Solenoid Valve Model Solenoid valves are applied in fast-response pneumatic systems as control valves providing e.3 . and magnetic force.e. Due to their special characteristics. 3. In absence of solenoid excitation. a novel AMESim gas dynamic pipe model had also to be developed by the authors.g.01 s. a flow cross-section develops through the orifice. Such miniature valves must provide rapid. 4. The self-developed pipe and solenoid models were irreplaceable in the case study presented herein. The fully self- developed solenoid valve model .
flexible collision of the valve body is suitably modelled. such forces are: gravity force. This model is capable for resolution of valve body position-dependent magnetic resistance. Resolving the effect of flexible seal and contact surfaces at the end of the valve body. The mechanical subsystem comprises the valve body representing a mass. and the valve body. and fluid dynamic subsystems. SZENTE et al. the clearance between the valve body and the jacket internal bore. and the valve body. and forces of collision of the valve body at the end-positions. The valve body position controls the cross-section of the throughflow ori- fice forming the fluid mechanical subsystem. The complex system of a solenoid valve can be generally decomposed to interacting magneto-dynamic. • The frame. the air clearance. The equation of motion of valve body expresses that the temporal derivative of valve body linear momentum must be equal to the forces acting on the valve body.244 V. the jacket. acting as a magnetic exciter and also representing ohmic resis- tance. The output variables are the magnetic force acting on the valve body and the solenoid current. The input variables of the magneto-dynamic subsystem are the excitation voltage and the valve body position. the jacket. With numerical treatment of the equation of valve body motion. and the return spring. Gas Dynamic Pipe Model This model is capable for resolution of pipe flow in the entire physically possible Mach number range. magnetic force. Fluid mechanical forces acting on the valve body. These elements represent together a mag- netic circuit with magnetic resistance depending on valve body position. Heat transfer through the pipe wall . The magnetic force model is based on the achievement of magnetic energy minimum. on the basis of a detailed and accurate modeling of the magnetic circuit. return spring force. The magnetic field line loops are closed through the frame. including jet forces. At the present state of investigation. Without going into detail of the self-developed complex mechatronic solenoid valve model. including wave phenomena such as shock waves  and pipe oscillations between the connected chambers. mechanical. pressure forces and viscous drag forces. the valve body position is computed. It considers unsteady electro-dynamic effects in an accurate manner. The magneto-dynamic subsystem comprises the following elements: • The solenoid. are neglected for the present case study focusing on gas dynamic pipe behavior. authors refer to  and  where the coupled electro-dynamic and mechanical subsystem models and the fluid mechanical aspects of valve operation are presented and verified by experiments. The following section gives a summary on solenoid valve modelling.
. This calls attention again to control aspects given that the aim of the EPM is to ensure a suitably controlled pressure in the actuator chamber. The maximum time step needed for stable run was derived from the Courrant–Friedrich– Lévy criteria . 1). since appearing also on the output port of the EPM). Discontinuities caused by shock waves were treated with the method of artificial viscosity . In this method the local pressure has been increased according to the shock wave pressure ratio. the following diagrams presented for the three test cases contain the time function of modulator chamber (CH) absolute pressure (p_out. Test Results As discussed above. For test case 1. in realistic systems the pressure sensor PS is integrated into the modulator chamber (CH in Fig. also reflecting pipe flow phenomena in a lifelike manner. Therefore. . (5) 2 v2 h = cp · T + . Thus the modulator chamber pressure is considered to be the most representative measure of this system. GAS DYNAMIC PIPE FLOW EFFECTS 245 and wall deformations are neglected. (2) ∂t ∂x Equation of motion: ∂(ρ · v) ∂(ρ · v 2 ) ∂ p ρ·λ + + =− · v · |v|. The descriptive equations for the pipe model are as follows: Ideal gas law:   p cp = R·T κ= = const. the time function of the actuator chamber pressure (p_ch) is also presented in order to illustrate the difference between the development of actuator and modulator chamber pressures. (4) ∂t ∂x v2 e = cv · T + . Pipe friction is based on wall roughness and the local Reynolds number. (1) ρ cv Continuity: ∂ρ ∂(ρ · v) + = 0. (3) ∂t ∂x ∂x 2·d Energy equation: ∂(ρ · e) ∂(ρ · v · h) + = 0. (6) 2 Two-step Lax-Wendroff scheme   was used to solve the equations. 5. This flattens the numerical oscillations at the cost of slightly decreased accuracy.
In this case the advantages of the self-developed gas dynamic pipe model are obvious. The differences between the standard and self-developed pipe modelling are minor. respectively. but without going into heavy oscillations. SZENTE et al. Fig. 7) the gas dynamic pipe submodel proves its advantage over the standard model again. which is. 4. Test case 1 Test cases 2 and 3 are more realistic from the viewpoint of pneumatic control. its application is recommended to be restricted to low-velocity pipe flow of M < 0. The gas dynamic model successfully . 6 and 7 present the comparative diagrams of p_out functions obtained with use of the self-developed gas dynamic pipe model as well as the most sophisticated standard AMESim pipe model. 4. with subscripts ‘gd’ and ‘wave’.246 V. Fig.01 pneumatic library. physically impossible. although it can be seen that these differences concentrate around the wave and throttled expansion effects (at the beginning of the load phase). It resolves the same wave effect as the built-in model. At the bottom of each graph the solenoid valve commands are indicated (dark bars: excitation of the LOAD valve. For test case 3 (Fig. 6 shows the simulation results for test case 2. Figs. As a basis of comparison. for which no controlling intervention occurs in the pipe flow. Besides. It is clearly visible in Fig. It can be concluded that for such a simple operational state. However. the simulation tests have also been carried out with use of the most sophisticated wave equation pipe model available in the stan- dard AMESim 3. Fig. the standard model does not even finish this test run. of course. grey bars: excitation of the EXHAUST valve). 5 that the larger actuator chamber filters out almost totally the differences caused by the different pipe flow calculation methods. 4 presents the simulation results for test case 1. also the standard low flow velocity AMESim pipe model supplies satisfactory results.3 (condition of incompressibility). Modulator chamber pressure. This distributed parameter pipe model is recommended for the most demanding use resolving wave effects. as because of the heavy oscillations the absolute pressure becomes negative.
Actuator chamber pressure. The gas dynamic pipe model resolves such phenomena in a realistic manner. The results also . although some oscillations can be observed in the first quarter of the graph. 6. Modulator chamber pressure. 5. Conclusions The simulation studies reveal that the pneumatic pipe performs wave effects and flow fluctuations between the modulator chamber and the actuator chamber. Fig. GAS DYNAMIC PIPE FLOW EFFECTS 247 Fig. Test case 1 finishes this test as well. Test case 2 6.
In that case the gas dynamic model performs much better since it resolves the same effect without heavy oscillations. Fig. strong numerical oscillations can be observed for test case 2. also leading to a considerable reduction of solenoid valve life cycle. Modulator chamber pressure. 7. It is concluded that an advanced gas dynamic pipe model is irreplaceable if a reliable pneumatic control is to be designed by numerical simulation for systems comprising pneumatic pipes. where the flow velocity change is sudden and drastic.248 V. although some numerical oscillations can be observed here as well. experiments will be carried out for verification of simulation results obtained using the pneumatic pipe models presented in the paper. as in test case 1. The simulations forecast unsteady pipe flow effects that may lead to a harmful resonance in the pressure control loop. In the near future. The wave model performed even worse in the pulsed flow of test case 3. showing similar effects as in case 2. Nomenclature cp constant-pressure specific heat cv constant-volume specific heat . Results show that because of the oscillation the modulator chamber pressure ran into a physically impossible region with use of the standard AMESim pipe model (negative absolute pressure). as it could not finish the simulation. However. The gas dynamic model performs better again. SZENTE et al. Such resonance manifests itself in oscillation of pressure around the value prescribed by the control. Test case 3 demonstrate that the standard AMESim pipe model performs quite well when the pipe flow velocity does not change drastically.
. SAE’2000 paper 2000-01-0292. C. Modelling and Simulation of a Cooling System. 2001 IEEE/ASME International Conference on Advanced Intelligent Mechatronics. M. (submitted in 2000)... Detroit. No.  Da S ILVA . Series C. Electronic Control of Braking Systems – Legislation (ECE R. A. ABS – TCS – VDC: Where Will the Technology Lead Us? Published by Society of Automotive Engineers. 1. 4. Linköping. 13). No.– BASCO . Series C. 1995. Longman Scientific & Technical. SICFP’01.  K AJIMA . An Introduction for Engineers. 1995. Como.. IEEE Transactions on Industrial Electronics. Dynamics Control Robotics Design and Manufacturing.  S ZENTE . T. ISBN 1-56091-750-4. 42. July 2001. M. Feb. Development of a High-Speed Solenoid Valve – In- vestigation of Solenoids. 40 No. C. IEEE Transactions on Industrial Electronics.– L EBRUN . JSME International Journal. S. No. Aug.– VAD . B. abstract accepted for the 7th Scandinavian International Conference on Fluid Power. Computational and Experimental Investi- gation on Dynamics of Electric Braking Systems. 1993. 1997.  A SAKURA . 3. V.  A BOT. USA.– S AMUEL . Sweden. J.  Takashi K AJIMA . T.–F RIES .  S ZENTE . G.. GAS DYNAMIC PIPE FLOW EFFECTS 249 d diameter of pipe e total energy h total enthalpy M Mach number of pipe flow p gas pressure p_ch actuator chamber pressure p_out modulator chamber pressure R perfect gas constant t time T gas temperature v gas velocity λ pipe friction coefficient x longitudinal pipe co-ordinate κ specific heat ratio ρ gas density Subscripts wave most complex standard AMESim pneumatic pipe model gd gas dynamic pipe model developed by the authors References  S TRAUB . J. L. JSME International Journal. D.– YAMADA . 3. S. V. March 2000. T... 1996. Stabilization of Electropneumatic Valve Positioner Using Sim- plified Smith Method. Development of a High-Speed Solenoid Valve – Investigation of the Energizing Circuits. G. MI. Italy. K. Inc. A... 38.. R. 40. PA.– VAD .  S HIH .– H WANG . 1989. 2001. Fuzzy PWM Control of the Positions of a Pneumatic Robot Cylinder Using High Speed Solenoid Valve.– K AWAMURA .– L ÓRÁNT. Y. Computational and Experimental Investigation on Solenoid Valve Dy- namics. Computational Fluid Dynamics. M.
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