ISSN 1068�798X, Russian Engineering Research, 2010, Vol. 30, No. 8, pp. 779–780. © Allerton Press, Inc., 2010.Original Russian Text © S.N. Grigor’ev, A.A. Gribkov, 2010, published in Vestnik Mashinostroeniya, 2010, No. 8, pp. 41–42.

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Optimal synthesis of dosing systems entails ensur�ing the required dosing parameters (productivity ortotal dosing time and permissible error) with minimalrequirements on the precision of system components.Minimizing the precision of system components per�mits cost reduction, which is of great importance.

In this context, we need to assess the precision ofthe dosing�system components. Generalized assess�ment of the precision for the whole set of componentswould be ideal.

For this purpose, we propose the reduced error K ofthe dosing time, which declines with increase in theprecision of system components

(1)

Here α = Qsw/Q; Qsw is the mean supply rate of thematerial after switching, under the condition of con�stant supply Q; Δt1 is the maximum error in the trigger�ing time of the device regulating the supply; Δt2 is theerror in dose measurement (in time units)

(2)

where ΔM1 is the error in dose measurement, kg; Δt3 =ΔM2/Q is the change in the quantity of the materialbetween the feeder and the intake device (for example,a tank), expressed in time units; ΔM2 is the maximumerror in the mass of material between the feeder andthe intake device.

Note that the reduced error K of the dosing timedoes not characterize the precision of dosing butrather the precision of the dosing system. With identi�cal precision of the dosing system but different dosingconditions, the dosing precision may vary consider�ably.

The distinguishing feature of K is that it is expressed(for a given dosing system) in units of time and doesnot much depend on the supply rate. This facilitatesthe development of a mathematical model of the dos�ing system, for its subsequent optimization.

Thus, one possibility is optimization in terms of theproductivity. This involves minimization of the total

K αΔt1( )2

Δt2( )2

Δt3( )2+ + .=

Δt2 ΔM1/Q,=

dosing time for a portion, with specified dosing preci�sion, portion size, and reduced error of the dosing time.

Another option is optimization of the reduced errorof the dosing time, so as to obtain the maximumreduced error of the dosing time with specified dosingprecision, portion size, and productivity. As a result,we obtain a dosing system that functions with specifiedparameters. The optimal dosing system will then becharacterized by minimum complexity, precision ofthe components, and cost. Of course, at the end ofsuch optimization, an additional task remains: toestablish the requirements on the type and precision ofthe system components (within the framework of therequired reduced error and dosing time).

We now consider the elements of some componentsemployed in dosing by weighed portions.

A wide range of devices may be used to supplymaterial to the dosing units. In dosing friable materi�als, gates are often used; for liquids, valves may beemployed. The error in the triggering time is low forsuch devices, and so Δt1 makes a small contribution tothe reduced error of the dosing time.

The error in dose measurements in dosing by massis determined by the error of the weighing system,whose calculation will depend on the operating prin�ciple adopted. Thus, the error of a beam weighingmechanism is determined by factors such as variationin the time at which the rotary bearings of the beammechanism begin to move and error in the triggeringtimes of the switches [1].

It seems more promising to use tensometric [2] andmagnetoelastic [3] force sensors, whose electrical out�put signal determines, after appropriate processing,the control signal for the unit that regulates the supply.In this case, the error of dose measurement is signifi�cantly reduced. In most cases, moreover, the systemdesign may be considerably simplified, its cost may bereduced, and its size may be reduced.

The error of a measuring system based on tenso�metric sensors is determined by the variable resistanceof the tensoresistors and the fluctuations in the powersupply. The latter factor may often be eliminated by

Precision of Dosing�System ComponentsS. N. Grigor’ev and A. A. Gribkov

Stankin Moscow State Technical Universitye�mail: rector@stankin.ru

Abstract—Basic types of dosing�system components are considered. The reduced error of the dosing time isproposed as the basis for estimating the error of the dosing�system components.

DOI: 10.3103/S1068798X1008006X

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RUSSIAN ENGINEERING RESEARCH Vol. 30 No. 8 2010

GRIGOR’EV, GRIBKOV

introducing a current stabilizer in the dosing system.Thanks to modern means of stabilizing the tensomet�ric effect, the error of mass�produced tensometric sen�sors has been reduced to 0.1%. In recent years, thedevelopment of semiconductor tensometric resistorshas offered further scope for improved performance.

In the case of small and moderate doses (up to a fewhundred kg), the error of the system based on magne�toelastic sensors is significantly greater than for tenso�metric sensors. For large doses (up to several tons),however, magnetoelastic sensors are preferable, onaccount of their more stable operation. The error ofmagnetoelastic measurements is determined by thevariation of the magnetic elasticity in the sensor. Fac�tors with a considerable influence on the magneticelasticity include temperature variation and fluctua�tion in grid current and voltage. In addition, the mag�netoelastic properties vary over time. The error of cur�rent mass�produced magnetoelastic sensors is at least0.4–0.5%.

The error of dosing systems that is most difficult toeliminate is the variation in the quantity of materialbetween the feeder and the intake device, especially inthe case of friable materials. This error is related to theproperties of the dosed material, which cannot easilybe monitored. Significant increase in the qualityrequirements on the dosed material implies increase inits cost and reduction in manufacturing efficiency. Theuse of additional equipment to condition the mate�rial—mixers, dryers, loosening and compaction sys�tems based on vibration and aeration, etc.—is alsoexpensive. Nevertheless, additional equipment mustbe used in some cases.

In dosing liquids, this error also has a pronouncedinfluence on the reduced error of the dosing time. Inparticular, the mass of the dosed material between thefeeder and the intake device depends on the liquidviscosity, which, as a rule, depends on the tempera�ture and the impurity content. In addition, the vol�ume of some liquids depends considerably on thetemperature.

As well as the variable physicomechanical proper�ties of the dosed material, the fluctuation in the quan�tity of material between the feeder and the intakedevice is determined by error in the triggering time ofthe device regulating the supply.

Extensive research shows that the reduced error ofthe dosing time is 0.02–0.2 s for most dosing systems.

The figure of 0.02 s corresponds to more complexand hence more expensive dosing systems, usuallywith additional equipment for conditioning the dosedmaterial and with fast, precise measurement, moni�toring, and control instruments. For friable materials,whose physicomechanical properties fluctuate rela�tively widely, it is very difficult—and sometimesimpossible—to achieve such errors.

Dosing systems of moderate complexity are char�acterized by reduced error of the dosing time in therange 0.07–0.12 s. This is sufficient in the case of cor�rect system design to ensure high speed (a few secondsper portion) and high dosing precision (errors of lessthan 0.1 wt %). Moreover, there is great scope for fur�ther increase in productivity and precision withoutimpairing the reduced error of the dosing time.

A dosing error of 0.2 s or more is typical of simplesystems for preliminary dosing, with a permissibleerror of more than 1%.

The reduced error of the dosing time may be usedin mathematical simulation of dosing systems and forgeneralized assessment of the precision of systemcomponents during the design process.

REFERENCES

1. Isaakovich, E.G., Vesy i vesovye dozatory: metrolog�icheskoe obespechenie (Weighing and Dosing Systems:Metrological Considerations), Moscow: Izd. Standar�tov, 1991.

2. Datchiki: Spravochnik (Sensors: A Handbook),Gotra, Z.Yu. and Chaikovskii, O.I., Eds., L’vov:Kamenyar, 1995.

3. Zainutdinova, L.Kh. and Tureiskii, G.G., Reducing theNonlinear Error of Magnetoelastic Mechanical�ForceConverters, Datchiki Sist., 2008, no. 4.