Angle of Wall Friction

This is the simplest powder failure property to test as it depends little on the state of consolidation of the powder. The equipment required includes a shallow, open-ended ring or a square frame 

There is a simple Wall Friction Tester available commercially, (from Ajax Equipment (Bolton) Ltd.), which uses a round plastic cell 160 mm in diameter and 25 mm in height, with a stainless 

Evaluation of results from wall friction tests is very simple. The shear force necessary to move the loaded cell is plotted against the applied normal load (note that both axes should have the same modulus and that it does not matter whether forces or stresses are plotted as the area on which they apply is the same) and a straight line is drawn through the plot - see Fig. 16. The angle of the line with the x-axis (normal load axis) is the angle of wall friction. 

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SB Tan, JM Newton. Influence of capsule dosator wall texture and powder properties on the angle of wall friction and powder-wall adhesion. Int J Pharm 64 227-234, 1990. 

Example 8.1 Three sets of yield loci under different consolidation conditions are obtained for a sample of powder of bulk density 1,500 kg/m3, as shown in Fig. E8.1. If a conical hopper is to be designed, determine the wall slope of the hopper and the opening size necessary to ensure a steady mass flow. The angle of wall friction is 15°. The design diagram for mass flow conical hoppers is given in Fig. E8.2 [BMHB, 1988]. 

Figure E8.2. Design diagram for mass flow conical hopper (from BMHB, 1988) (a) Flow factor (b) Angle of wall friction.

A cohesionless material of weight density 12 kN/m3 and an angle of internal friction of 30° is stored in a tall cylindrical bin of diameter 1.8 m and an angle of wall friction 22°. Use Janssen s formula to determine the depths at which the radial stress in the material reaches 70 percent of its maximum value for both active and passive cases. 

A conical hopper of a half angle 20° and an angle of wall friction 25° is used to store a cohesionless material of bulk density 1,900 kg/m3 and an angle of internal friction 45°. The top surface of the material lies at a level 3.0 m above the apex and is free of loads. Apply Walker s method to determine the normal and shear stresses on the wall at a height of 1.2 m above the apex if the angle between the major principal plane at that height and the hopper wall is 30°. Assume a distribution factor of 1.1. 

Determine the half angle of the hopper and the minimum outlet diameter for the two cases where the hopper wall material has an angle of wall friction of (i) 10° and (ii) 30°. 

The angle of wall friction is the simplest of the five failure properties it is equivalent to the angle of friction between two solid surfaces except that one of the two surfaces is now a powder. It describes the friction between the powder and the material of construction used to confine the powder, e.g. the hopper wall. The wall friction causes some of the powder weight to be supported by the walls of a hopper. 

In this chapter, we address in considerable depth empirical methods and models found in the literature, as well as variables that affect compressibility such as moisture, temperature, and particle size and shape. Compressibility can be used in feeder designs to calculate loads that act on a feeder or gate and angle of wall friction to calculate the pressures acting perpendicular to the hopper wall. Furthermore, it can be used for quality control to determine the resistance of materials to breakage, from the production process to the consumer. 

The kinematic angle of friction between powder and hopper wall is otherwise known as the angle of wall friction, This gives us the relationship between normal stress acting between powder and wall and the shear stress under flow conditions. To determine it is necessary to first construct the wall yield locus... 

The kinematic angle of wall friction is given by the gradient of the wall yield locus (Figure 10.17), i.e. 

Figure 10.16 Apparatus for the measurement of kinematic angle of wall friction,...

Kinematic angle of wall friction on mild steel, = 16°... 

Shear cell tests are carried out on a powder for which a stainless steel conical hopper is to be designed. The results of the tests are shown graphically in Figure 10E4.1. In addition it is found that the friction between the powder on stainless steel can be described by an angle of wall friction of 11°, and that the relevant bulk density of the powder is 900kg/m. ... 

The results of shear cell tests on a powder are given in Figure 10E5.1. An aluminium conical hopper is to be designed to suit this powder. It is known that the angle of wall friction between the powder and aluminium is 16° and that the relevant bulk density is 900 kg/m. ... 

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