ISSN 10683712, Russian Electrical Engineering, 2012, Vol. 83, No. 11, pp. 609612. Allerton Press, Inc., 2012.Original Russian Text A.G. Shcherbinin, A.E. Terlych, E.V. Subbotin, 2012, published in Elektrotekhnika, 2012, No. 11, pp. 2831.

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Singlescrew plasticating extruders enjoy wideapplication in processing of polymers. (Fig. 1). Theextruders are meant to obtain products of unlimitedlength by continuous extrusion the polymer meltthrough the forming tool.

The basic working part of the extruder is the heated(cooled) casing (cylinder), within which the screwrotates. The polymer material comes to the plasticating extruder from a special loading device in the formof grains; then, it is grabbed by the screw thread andmoves along the screw channel. In the process ofadvancing the material, it is compacted, melted, andhomogenized. Up to the output, the extruder createsthe pressure, which is necessary for extrusion of thepolymer melt through the forming instrument.

The power consumed by the extruder for the bulkmaterial motion, its melting and extrusion, is one ofthe main operation parameters, as are the perfor

mance, pressure, and polymer temperature at the output. Power Q needs to be known on the shaft of theextruder motor in addition to power Nm. This power isconducted (disposed) through the inner surface of acylinder providing the given distribution of the casingtemperature. The value of these characteristics of theextruder operation and their relationship mainlydepend on different initial parameters: the geometricdimensions of the screw, polymer material, and technological processing modes. Any change in the technological process of extrusion leads to a change inextruder power consumption.

The power on the motor shaft of the plasticatingextruder is calculated by the following formula [3, 4]:

(1)Nm Q Q0Pk+ SdS

zd

0

L

Q0Pk,+= =

Extruder Power ConsumptionA. G. Shcherbinin, A. E. Terlych, and E. V. Subbotin

Received October 22, 2012

AbstractA way to estimate the power characteristics of a plasticating extruder is proposed, and numericalexperiments are carried out to investigate them. The regularities of extruder power consumption are found.

Keywords: extruder, power consumption, extruder screw, numerical simulation

DOI: 10.3103/S1068371212110132

H1

H2

Loading hopper

Heated (cooled) casing (cylinder)

Heaters

Solid polymers Screw Polymer meltz

D W

x

Fig. 1. Scheme of a plasticating extruder

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where Q is the power of dissipative heat source; Q0Pkis the power consumed to the polymer materialmotion along the extruder channel and the pressureinjection, z is the longitudinal coordinate of the channel, S is the current area of the transverse cross section of the channel (Fig. 1), is the specific dissipativeheat source defined by the work of the viscous forces ofthe polymer, Pk is the pressure at the output from theextruder, Q0 is the given volume flow of the polymermaterial, and L is the length of the screw channel.

The polymer material moving along the extruderscrew channel is heated, turned from the solid stateinto the plastic state, and reaches the temperatureneeded for formation at the output. A change in theinternal energy of the polymer Qi during its advancingalong the channel is due to the heat injection (rejection) though the walls of the channel Q and the workof viscous forces in the polymer melt Q [5, 6]:

(2)

Up to the output from extruder,

(3)

where G0 is the given mass flow of the polymer material, T is the temperature, Tin is the temperature at theinput to the extruder, Tout is the temperature at theoutput from the extruder, and C(T) is the specific heatcapacity of the polymer.

Qi Q Q.+=

Qi G0 C T( ) T,d

Tin

Tout

=

Numerical investigations of the energy characteristics of the plasticating extruder operation were carriedout by using a mathematical model [79].

Polyethylene was the object under investigation.The table gives the values of the following thermalcharacteristics: density , heat capacity factor , andmelting temperature Tm. Subscript s in the table corresponds to the solid state of the polymer, while m corresponds to the melting one. Figure 2 shows the relationship between the specific heat capacity and thetemperature.

The effective viscosity of the polyethylene melt wascalculated by the following formula:

(4)

where is the temperature viscosity coefficient, n isthe index of viscosity anomaly, I2 is the second invariant of the strain rate tensor, and 0 is the consistencycoefficient at temperature T0.

The values of the rheological properties of the polyethylene melt are given in the table below.

The change in the extruder cylinder temperaturewith length is shown in Fig. 3. A dotted line denotespolyethylene melting temperature Tm. The temperature in the screw was estimated by the model of [8] taking the dissipative heat source defined by the model of[7] into account.

Initial temperature of the granulated material Tin is20C.

During conducting numerical experiments, thenumber of screw turns was changed from 40 to 80 rpm,while the mass performance of the extruder waschanged within the range of 0.020.12 kg/s.

Geometric parameters of a screw and a cylinder

Inner diameter of a cylinder (casing) D is 160 mm

Outer diameter of a screw is 159.4 mm

Screw thread step is 160 mm

Width of a channel W is 137.3 mm

Width of a screw thread ridge s is 15.3 mm

Lengths of the geometric areas of loading, compression, and dosing are 10/10/7 turns

Total length of a screw is 27 turns

Depth of a channel in the loading area H1 is 16 mm

Depth of a channel in the dosing area H2 is 4 mm

Lifting angle of a screw line is 1739

Radial clearance between the screw ridge and the casing is 0.3

E 0 T T0( )( )expI22

n 1

2

,=

Rheological and thermal properties of the polyethylene

n 0 T0 Tm s m s m

Pa sn C 1/C C kg/m3 W/(m C)

0.44 10825 160 0.018 110 919.0 779.0 0.335 0.182

6.0

4.0

0 200100 T, C

C, kJ/(kg C)

2.0

Fig. 2. Relationship between the specific heat capacity andthe temperature.

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EXTRUDER POWER CONSUMPTION 611

Figure 4 presents a change in polymer internalenergy Qi, as well as the heat components that are dissipative and injected (rejected) through the channelwalls, which are Q and Q, respectively, per time unitalong the channel length at number of screw turnsNscr = 60 rpm and mass performance of the extruderG0 = 0.06 kg/s. It is evident from Fig. 4 that the heatinjection through the casing is implemented at the firstfour turns, namely, in the very area where the polymeris in a solid state. After the appearance of melt, thematerial is heated in the channel only due to the dissipative energy, whereas the casing operates in the modeof heat rejection. For the above technological mode,the power consumed by the electric motor Nm was70 kW. Here, 5.6 kW passed on to the transport ofmaterial Q0P, which is 8% of the power on the shaft,and 64.4 kW (92%) was consumed to overcome theviscous forces, i.e., the mechanical energy dissipationQ, from which 40 kW was for heating the materialfrom 20 to 226C and 24.4 kW was rejected throughthe extruder casing.

Figure 5 shows the dependence of melt averagetemperature Tav at the output from the extruder andpeak temperature Tmax on the extruder performanceand the number of screw turns. It is seen from Fig. 5that Tav and Tmax rise with an increasing number ofturns and fall with increasing performance.

Figure 6 portrays the relationships between powercomponents of the plasticating extruder and its performance G0 and number of screw turns Nscr. It should benoted that the power on the electric motor shaft Nm isdetermined by (1). Figure 6 shows that power Q0Pkconsumed for the mass transition and pressure injection is no more than 10% of the electric motor power,while the rest of the energy is converted into heat as aresult of acting viscous forces. The value of Q significantly depends on the number of screw turns. The heatexcess extracted due to mechanical energy dissipationis rejected through the extruder cylinder wall, wheretemperature Tc remains constant.

With a number of screw turns of 40 rpm and a massflow of more than 0.065 kg/s, Q is a positive magni

200

100

0 2010 z, turns

T, C1

2

Fig. 3. A change in the temperature of the extruder cylinder: (1) is Tch and (2) is Tp.

6.0

2.0

0 189 z, turns

Q 104, W

4.0

0

2.0

4.0

Qi

Q

Q

Fig. 4. A change in the internal energy of the polyethyleneQi, as well as the dissipative Q and injected (rejected)through the channel walls Q heat components, per timeunit along the channel length.

240

220

2000.100.080.060.040.02

T, C

G0, kg/s

Tav

Tmax

Fig. 5. Dependences of average temperature Tav at theoutput from extruder and peak temperature Tmax on massflow G0 and number of screw turns Nscr: () is 40 rpm,() is 60 rpm, and ( ) is 80 rpm.

40

40

800.100.080.060.040.02

Q, kW

G0, kg/s

Q

Q

0

80

QiQ0 Pk

Fig. 6. Relationships between the power componentsof the extruder and its performance G0 at different numbers of screw turns Nscr: () is 40 rpm, () is 60 rpm,and ( ) is 80 rpm.

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tude; i.e., heating of the polymer material under theseconditions is partly implemented at the expense of theheat energy of casing walls. In other instances, theextruder casing operates in the mode of heat rejection.

The change of internal energy Qi, which is estimated by (3), is practically in linear dependence onchange in mass flow G0. The difference between thevalues of Qi for various screw turns and at fixed flow G0is determined by the difference between average temperatures of the polymer at the output (Fig. 5).

Thus, the results of numerical investigations showthat no more than 90% of the electric power consumedby the extruder motor is consumed to overcome theviscous forces of the polyethylene melt, while themotion of the polymer material and pressure injectionuse under 10%. The casing of the extrusion machineoperates in the mode of heat rejection practicallythroughout the whole length, apart from the initialportions at the loading area. During design of plasticating extruders, it is necessary to account for theobtained regularities of power consumption to providethe extruder casing with an effective system of heatrejection.

REFERENCES

1. Rauwendaal, C., Polymer Extrusion, New York: HanserPubl., 1990; St. Petersburg: Professiya, 2008.

2. Tadmor, Z. and Gogos, C.G., Principles of PolymersProcessing, New York: John Wiley & Sons, 1979; Moscow: Khimiya, 1984.

3. Trufanova, N.M., Shcherbinin, A.G., and Yankov, V.I.,Plavlenie polimerov v ekstruderakh (Polymers Meltingin Extruders), MoscowIzhevsk: NITs Regulyarnaya ikhaoticheskaya dinamika, 2009.

4. Syrjl, S., Numerical Simulation of NonisothermalFlow of Polymer Melt in a SingleScrew Extruder: aValidation Study, Numer. Heat Transfer A, 2000, vol. 37,no. 1, pp. 897915.

5. Shcherbinin, A.G. and Trufanova, N.M., StationaryProblem on Liquid Heat Mass Transfer in RectangularChannel, Informatsionnye upravlyayushchie sistemy:Sb. Nauch. Tr. Perm. GTU (Collection of ScientificPapers of Perm State University National ResearchInformation Control Systems), 2001, pp. 3136.

6. Shcherbinin, A.G., Trufanova, N.M., and Yankov, V.I.,Energy Characteristics of Extruder Operation, Informatsionnye Upravlyayushchie Sistemy: Sb. Nauch. Tr.Perm. GTU (Collection of Scientific Papers of PermState University National Research Information Control Systems), 2003, pp. 7477.

7. Shcherbinin, A.G., Trufanova, N.M., and Yankov, V.I.,Spatial Mathematical Model of Single Screw Plasticising Extruder. Part 1. Mathematical Model of PolymerHeat Mass Transfer in Extruder Channel, Plast. Massy,2004, no. 6, pp. 3841.

8. Shcherbinin, A.G., Trufanova, N.M., and Yankov, V.I.,Spatial Mathematical Model of Single Screw Plasticising Extruder. Part 2. Mathematical Model for Determining Screw Temperature, Plast. Massy, 2004, no. 8,pp. 3840.

9. Shcherbinin, A.G., Trufanova, N.M., and Yankov, V.I.,Spatial Mathematical Model of Single Screw Plasticising Extruding Press. Part 3. Mathematical Model Verification, Plast. Massy, 2005, no. 5, pp. 4345.