Rotation around a fixed axis is a type of rotation in which a body is rotating around its center of mass. It is important in the engineering field to avoid vibration of rotating systems by balancing. In practical machines such as electric generators and gas turbines, vibration can cause breakdown, noise and discomfort. For in the instance of a narrow wheel, balancing involves moving the gravity center towards the rotation center so that the system achieves full balance, force couple is supposed to be closed. When this is achieved the body is said to be rotating around a fixed axis. However, there are challenges in achieving this. A fixed axis rotation is accomplished through the following formula;
Where ∑M is the total mass of the rigid body around the center pin, I the moment of inertia around the center pin, and α is the angular acceleration of the particle. However, some problems are encountered in ensuring a uniform rotation around a fixed axis.
Two types of Problems are majorly encountered based on a body having angular acceleration, α, but may or may not have a linear acceleration aG, depending on the location of their mass center G. Classes of fixed axis rotation problems, depending on the location of the mass center, G include:
1. If the mass center is at the pin, G doesn’t move.
2. If the mass center is not at the pin, G moves in a circle about the pin and is thus resolved into tangential acceleration and normal acceleration components.
Some of the examples of the challenges encountered due to these unbalanced rotating systems include:
1. Washing machine; When washing clothes wet one’s shifts to one side of the, and the entire machine shakes dramatically. It is due to the composite mass center of the drum plus the clothes have moved well away from the fixed axis of rotation.
2. Automobile Tires; Tires even new ones are not perfectly balanced. When one buys new tires, after fixing them on their rims, the mechanic balances the rim-tire assembly on a balancing machine. The device rotates the tires while determining the dynamic loads and evaluates the particular places on the rim to fasten on lead weights of different sizes to balance the tire. Automobile crankshaft and fishing reels are other examples.
Rotation And Dynamic Balancing:
Dynamic rotation, however, plays a significant role in ensuring a balance in a system of rotating bodies.
Balancing is the procedure of trying to enhance the mass spread of a body so as to rotate in its bearings without the unbalanced centrifugal forces acting on it.
Dynamic balance is said to have been achieved in a system of rotation in case a rotation doesn’t give a resultant
centrifugal force. In this case, a system spins without the need of an external force acting on it, other than that needed to sustain its mass. If a rotating system is not balanced initially, counterbalancing weights are added to bring back the system to a dynamic balance to avoid the stress on the bearings caused by the centrifugal couple.
It’s evident when a wheel of a bicycle gets bent. The stationary wheel will rotate itself due to gravity because it still has static balance, it won’t spin smoothly because the center of weight is towards the edge of the center bearing. Thus, in this case, the bicycle wheel has to be tuned to avoid it and allow the wheel to operate normally.
Dynamic balancing is a balancing achieved due to the activity of inertia forces acting on a rotating body. Benefits of dynamic balancing include; Increasing the quality of operation, minimizes vibration, reduces structural fatigue stresses, reduces signal noises, reduce power loss, and increase the bearing life.