Theoretical Analysis of the compacting (vibrating) system
The principle of the concrete (vibrator-compactor) block making machine is the eccentric weight. The eccentric weight, based on calculation for size, was fastened on the compactor drive shaft (cds). The cds was also based on design as carried out below. The attachment of eccentric to the cds caused an out-of-balance rotation that sets the long face of the mould to vibrate, a process which compacted the wet block mix.
a).
b).
Figure 4.4: a) Eccentric weight Attached to Compactor Drive Shaft and b) free body diagram of the system.
The rotation of the shaft gave rise to centrifugal force, Fc, which acted radially outwards in a direction that is perpendicular to the axis of rotation of the compactor drive shaft, and through the centre of gravity, G.
Centripetal force is defined as a force that pulls a rotating or spinning object toward a center or axis [Encarta Dictionary]. According to Newtons third law of motion, every action must have a reaction. Therefore the reaction to centripetal force is called centrifugal force [6]. Centrifugal force is defined as the force that pulls an object away from the center point. However, since an object would only move tangentially away from the center on a linear path (force of velocity), and not continue around a center point, centrifugal force is actually not a force at all, but rather a concept that represents an effect. Some definitions even describe this as an imagined force. This is interesting to keep in mind when applying these ideas to vibrator-compactor system.
The centripetal force Fp, was equal to Fc but in the opposite direction towards the centre of rotation. There were four forces that were relevant in design of the vibrator-compactor system of the machine. They were the centrifugal force, Fc, the spring force, Fs, the force due to flexural rigidity, Ff, and the force due to the wet block mix, Fwb. The point O (fig 4.4) was the geometric centre of the eccentric weight, G was the centre of gravity of the cds and eccentric, me was mass of eccentric, mwb was mass of wet block mix, y1 was the length OD and was the additional deflection of the centre of the cds when it rotated at rad/s, e was the length OG which was the initial distance of the centre of the eccentric from the combined centre of gravity of the cds and eccentric weight, K was the stiffness of cds, it is the ability of a material to resist deformation under stress. The modulus of elasticity is the measure of stiffness, EI was the flexural rigidity of the cds, E was th youngs Modulus of the cds, was the moment of inertia of the cds, Ls was taken as the length of the compactor drive shaft, Le as the length of the eccentric, y2 was half the diameter of cds and line of action of the flexural rigidity and g as acceleration due to gravity.
The design required that the following quantities were known:
The forces activated in the system,
The mass of the cds and eccentric,
Force due to wet block Fwb,
Operating stress,
The diameter of the cds and eccentric,
The length of the cds and eccentric,
The lengths of y and e for the cds and eccentric.
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