Torsional Strength of the Screw Root

An important requirement for the extruder screw is the ability to transmit the torque required to turn the screw. The most critical area of the screw in this respect is the feed section. In the feed section, the cross-sectional area of the root of the screw is generally the smallest and, thus, the torsional strength the lowest. Also, in the feed section, the entire torque has to be transmitted, while further downstream only a fraction of the total torque has to be transmitted. The torque that is transmitted can be determined from the power to the screw, Zj rew, and the screw rpm, N. 

If Z is expressed in horsepower and N in rev/min., the constant C must equal 7120.9 to give a torque expressed in Newton-meter. If Z is expressed in kilowatt, constant C equals 9549.3. This formula is based on the relationship between torque, angular 

From Eq. 8.1, it can be seen that the transmitted torque is directly proportional to the horsepower and inversely proportional to the screw speed. The power to the screw is related to the motor power by  

The total efficiency is generally around 0.75. Thus, the power to the screw will be about 75% of the motor power. The stresses in the screw shaft as a result of the torque on the screw are shown in Fig. 8.1. 

The shear stress in the shaft resulting from torque T can be expressed as 2Tr Tr 

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