Modified Campbell-Dontula Model

Forces for the Modified Campbell-Dontula Model Fi = forwarding force at the barrel wall and centered on surface. p2 = force due to pressure and centered on surface. 

Fa/= normal force that is directly proportional to the friction at the barrel 

The modified Campbell-Dontula model used a lateral stress ratio [5, 6] that is defined below  

Unfortunately, cannot be easily determined analytically, and is often either estimated using methods from the field of soil mechanics (from the normal stress ratio, K, or simply adjusted to a value which produces good fits for the experimental data. The forwarding force f, at the barrel wall is positioned in the plane of the barrel surface. This force is adjusted using as found in Eq. A5.1 and results in Eq. A5.2. This is because is the local pressure in the channel. Referring to Fig. A5.4, the forces are defined as follow  

Following the procedure in Campbell and Dontula [1], the static force balance is 0 = -f, sin V - sin61 + cosfl, - sin61 - sin (9 ) 

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Unlike the previous models by Darnell and Mol [14] and Tadmor and Klein [1], which are based upon the assumption of isotropic stress conditions, Campbell s model [20] considered anisotropic stress conditions, as suggested by Schneider [15], but it was assumed to be 1.0 due to the lack of published experimental data on the subject. Variations on the model set forth by Campbell and Dontula [20] include a modification to incorporate the lateral stress ratio [19, 22], and other modifications discussed by Hyun et al. [21, 23]. A modified Campbell-Dontula model with a homogeneous lateral stress is as follows ... 

Comparison of the Modified Campbell-Dontula Model with Experimental Data... 

The modified Campbell-Dontula model was developed using the LDPE resin friction data as applied to an empirical model. The empirical model is shown by Eq. 5.31 for the temperature range of 25 to 110 °C. The coefficients of dynamic friction using Eq. 5.31 is shown in Eig. 5.31. 

Figure 5.32 Solids conveying rate data calculate using the modified Campbell-Dontula model for the Dow solids conveying process using the shallow screw, 75 °C barrel and screw temperatures, and a screw speed of 50 rpm. The solids conveying rates measured from the experimental device are provided...

For the modified Campbell-Dontula model, Eq. 5.13, cp is calculated as follows for... 

The modified Campbell-Dontula model provides an acceptable prediction of the rate at the section exit pressure. For many cases, the coefficients of friction are adjusted until an acceptable performance is obtained. This model and the other models should always be used with caution. As previously discussed, these models use a static force balance to approximate a dynamic process. 

Figure A5.4 Force diagram for modified Campbell-Dontula model...

The modified Campbell-Dontula solids conveying model was based on screw rotation and a normal force at the pushing flight that was directly proportional to the frictional force between the solid bed and the barrel wall. The force balance on the slab is provided in Fig. A5.4... 

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