Model identification and simulation of function of the amortization in context of functioning characteristics.

Pajaziti, Agron ; Latifi, Ahmet ; Geca, Ahmet 等

1. INTRODUCTION

In this paper is included development and identification of the extinguisher model that is foreseen the force of extinction as a function of speed displacement of the extinguisher for the given controlling parameters. In order to compare the coefficients of the model directly with controlling components of the extinguisher the approach of the model of black box, as neural nets (latifi, 2007) or force-state maps (Karnopp, 1991), is issued in the favor of so called models of the white box that offer contact to the physicality of the extinguisher. Even though the actual model is based in the previous physical models (Duym, 1997), it should be emphasized that are grouped in the global coefficients in that way that they can be identified only by dynamometer measurements. This is very important for many vehicle producers that want to have their identity that are obstructed by the other physical models where it is required detail measurements of the components but these are not always possible e.g. the measurement of the depressor, as well if the measurement is done only with dynamometer, it isn't necessary to avoid the extinguisher ant to obtain time and money.

The model of pressure entirely determines the conduct of the extinguisher dynamic through equations system that have physical adiabatic relations of the gas that is in the spare tube in low frequencies and in the oil pressure and in accordance to the cylinder faces in high frequencies. Undesired effects, as it is the mixture of gas with oil in pressure tube (Margolis, 1982), that can cause the increase of the pressure that usually refers if it isn't considered the ventilation. If it is considered the ventilation, the extinguisher efficacy can be obviously reduced because of the low module the effect produces impediments or membranes in order to separate the gas from fluid and as a consequence there is the avoidance of the oil and air mixture.

2. PHYSICAL MODEL OF THE ABSORBER

The quicklime hydrator (extinguisher) model can be classified in the model of pressure and in the model of bearing. The model of pressure consists of the group of differential equations of indoor pressure in the chamber, although the bearing model calculates the bearing oil Q through the chambers in function of the pressure change [DELTA]p with help of nonlinear equations (statistic). The extinguishing force is calculated for the pressure chamber in the pressure and attraction, friction and possible striking force, i.e.,

F = ([A.sub.pt] - [A.sub.rod]) [P.sub.reb] - [A.sub.pt][P.sub.com] + Friction + [F.sub.bumper] (1)

To the absorber with two pipes, the geometrical change of the turning chamber volume because of the piston movement is equilibrated after the fluid bearing through piston valve as well with the pressure or attraction of oil in that chamber. On the other hand, the geometrical change of the volume of pressure chamber as well because of piston movement is equilibrated by geometrical amount with the quantity of flow through piston and basic valve and pressure or attraction of oil in pressure chamber. These preserving laws direct us to the differential equations system which expects the pressure increases in pressure pipe.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

[FIGURE 1 OMITTED]

Regarding to the spare pipe (tube), the pressure of oil is insignificant comparing to gas so the spare pressure can be expected by polytrophic pressure or attraction respectively by turning strike.

[P.sub.rt] = [P.sub.rt,0] [([V.sub.rt,gas,0]/[V.sub.rt,gcs,0] + [A.sub.rod]x).sup.[gamma]] (4)

If the adiabatic condition is completed, i.e., it isn't transmitted the heating from the volume of gas, that is typical for high frequencies and is equal to Y = 1.4 for nitrogen gas. For volume change without temperature change that is usually for slowly changes, should be taken exponent Y = 1.

The bearing model has to do with bearing through valves for the appropriate pressure decline. In fig. 1 is showed a typical piston with valve. When the absorber moves to the width (turning), the oil will flow down through the indoor diameter of the entering valve, then through the port canal in the body of piston and then through the open valve determined by splitting and bending valve disks. When the flow meets the pressure extinction along the piston, so it is described as the bearing in pressure.

During the pressure the oil will begin to flow above through splitting and those are wholes in the body of piston with concentric rings around canals port.

At the end of splitting the oil will pressure and it will open the entering valve. The entering valve usually is control valve and it makes a slow resistance in oil when it moves up and it doesn't make any important pressure in order to reduce the relation of the valve. This bearing has to do with the bearing in entrance.

3. GEOMETRICAL CHARACTERISTICS

Geometrical parameters are simply determined by technical drawing. Except in the case if can't be found all geometrical parameters, the evaluation of valve parameters will compensate the appropriate no accuracy and it makes the model suitable for measurement. For BMW all relevant parameters of the model are given in the Table 1.

4. THE MODEL EVALUATION OF THE EXTINGUISHER

Up to now, all the parameters of the vehicle BMW are determined except the entering parameters which are determined as well compressibility value (compression). It can be thought in the value identification of compressibility by the oil supplying data and these don't consider the suitability of cylinder faces (walls). Thus, it is better to determine compressibility of oil from measurements of extinction.

In this section, are used the value and compressibility parameters of a = l e - 9 [Pa.sup.-1] to anticipate the force of extinction for mature irritation. In fig. 2, together the curve force-displacement and force-speed are drawn for these selected rings of irritation for speed increased values. With the given curves are shown the measured values to those anticipated values by simulations of extinction complete model. As long as non linear nature of the extinguisher should be well devised, the dynamic bearing seems to be as well satisfactory. On the other hand, nonlinear nature of the extinguisher is in the aspect of nonlinearity of the curve force-speed. On the other hand, the dynamic bearing can be seen by hysteresis aspect of the similar drawing and the road of the curve force-displacement is steep. For the elaborated application, can be said that hysteresis is created by the gas compressing in the spare tube much more than oil compressing presented in (Duym, 1997). This comes out by the fact that hysteresis seems to be present always by low frequencies and it doesn't often increase. In order to qualify the shown evaluation, the value of RMS--is mature extinctive and the value of RMS is calculated the remain between the force which is shown in Table 1 and 4 rings of fig. 2 and the global sight between 1.23 and 3.08 s, considering high speeds. The general relative error of RMS is about 5 % that also means that the average square value is about 0.25 %! The general value of RMS of the remain signal is 39 N for time unit it is comparative or better than the best quality which is obtained by using black boxes, especially with situation maps of the force where the extinction force is modulated as the function of speed and velocity (Margolis, 1982).

The actual model doesn't anticipate the effects of ventilation that are noticed as delays in the indoor pressure or of the force increase, particularly at the very beginning of the pressure (Karnopp, 1991).

As it is shown in fig. 2, there isn't an apparent delay presence (see curves force--displacement) that it means, that this absorber seems not to be sensitive in the ventilation during these tests and for this reason it is allowed to be used the model without ventilation effect.

[FIGURE 2 OMITTED]

5. SUMMARY

In this paper is included the development and identification of the extinction model that anticipates the force of extinction as a displacement function of the extinction speed for the given controlling parameters. In purpose of the comparison of the model coefficients directly to the controlling components of the extinguisher the approach of black box models, as neural nets or maps of force--situation is issued in favor of so called models of white box that offers the approach in the physicality of the extinguisher.

Even though these models are based in the previous physical models, it should be emphasized that the coefficients of model are grouped in the global coefficients in that way that they can be identified only with measurement. It is very important for many producers of the vehicles that they wish to have their identity that is obstructed by other physical where are required detail measurements of the components which are not always possible.

6. REFERENCES

Latifi, A. (2007), Modeling, Identification and Simulation of function of Shock Absorber in the connects of working diagrams, Ph. D., FME, Prishtina, 2007.

Duym, S., Stiens, R., Baron, G. & Reybrouck, K. (1997), Physical Modeling of the Hysteretic Behaviour of Automotive Shock Absorbers, SAE Transactions--Journal of Passenger Cars SAE paper 970101, 1997.

Duym, S., Stiens, R. & Reybrouck, K. (1997): Evaluation of Shock Absorber Semi--Vehicle System Dynamics 27 (2), 109-127.

Karnopp, D., Crosby, M. & Harwood, R. A. (1991), "Vibration Control Using Semi-active Force Generator, " Jnl. Eng. for Industry, Vol. 20, pp. 207-218.

Margolis, D. C. (1982), "The Response of Active and Semi-active Suspensions to Realistic Feedback Signal", Vehicle System Dynamics, Vol. 11, pp 267-282.

Table 1. Geometrical parameters of the vehicle BMW.

The length of pressure tube [L.sub.PT] (mm) 380
The static length of piston [X.sub.0] (mm) 110
The length of piston (mm) 360
Diameter of piston [d.sub.pistoneta] 25
Diameter of pressure tube ID [d.sub.PT] (mm) 36
Diameter of spare tube OD [d.sub.RT] (mm) 56
The length of low measurer up to the base [d.sub.LMPT] 15
The static length of the extinguisher (mm) 485