Static imbalance

In static imbalance, the only force involved is weight. For example, assume that a rotor is perfectly balanced and, therefore, will not vibrate regardless of the speed of rotation. Also, assume that this rotor is placed on frictionless rollers or knife edges. If a weight is applied on the rim at the center of gravity line between two ends, the weighted portion immediately rolls to the 6 o clock position due to the gravitational force. 

When rotation occurs, static imbalance translates into a centrifugal force. As a result, this type of imbalance is sometimes referred to as force imbalance and some balancing machine manufacturers use the word force instead of static on their machines. However, when the term force imbalance was just starting to be accepted as the proper term, an American standardization committee on balancing terminology standardized the term static instead of force. The rationale was that the role of the standardization committee was not to determine and/or correct right or wrong practices, but to standardize those currently in use by industry. As a result, the term static imbalance is now widely accepted as the international standard and, therefore, is the term used in this chapter. 

Visualize a rotor that has only one imbalance in a single plane. Also, visualize that the plane is not at the rotor s center of gravity, but is off to one side. Although there is no other source of couple, this force to one side of the rotor not only causes translation (parallel motion due to pure static imbalance), but also causes the rotor to rotate or wobble end-over-end as from a couple. In other words, such a force would create a combination of both static and couple imbalance. This again is dynamic imbalance. 

In addition, a rotor may have two imbalance forces exactly 180° opposite to each other. However, if the forces are not equal in magnitude, the rotor has a static imbalance in combination with its pure couple. This combination is also dynamic imbalance. 

An important point to remember is that static imbalance is always removed first. In static and couple balancing, remove the static imbalance first and then remove the couple. 

So far, there has been no consideration of the angular positions of the usual two points of imbalance relative to each other or the distance between the two correction planes. For example, if the residual Imbalances in each of the two planes were in-phase, they would add to each other to create more static imbalance. 

Mechanical imbalance is one of the most common causes of machinery vibration and is present to some degree on nearly all machines that have rotating parts or rotors. Static, or standing, imbalance is the condition when there is more weight on one side of a centerline than the other. However, a rotor may be in perfect static balance and not be in a balanced state when rotating at high speed. 

Couple imbalance is caused by two equal non-colinear imbalance forces that oppose each other angularly (i.e., 180° apart). Assume that a rotor with pure couple imbalance is placed on frictionless rollers. Because the imbalance weights or forces are 180° apart and equal, the rotor is statically balanced. However, a pure couple imbalance... 

Another way of looking at it is to visualize the usual rendition of dynamic imbalance - imbalance in two separate planes at an angle and magnitude relative to each other not necessarily that of pure static or pure couple. 

Note that whenever you hear the word imbalance, mentally add the word dynamic to it. Then when you hear dynamic imbalance, mentally visualize a combination of static and couple imbalance. This will be of much help not only in balancing, but in understanding phase and coupling misalignment as well. 

In actual fact, both approaches have considerable merit, and it would appear that the two schools are describing the actual physical mechanism from two different points of view. Certainly, a steady-state condition exists in which the rate of heat generation does not exceed the rate of heat loss from the combustion zone. There are also purely dynamic conditions related to the creation of the same imbalance between heat generation and heat loss. These purely static and purely dynamic conditions can be considered as the end points for a whole range of combined static (i.e., minimum-pressure) and dynamic (depressurization) conditions by which termination can be achieved. L -termination is probably one of these intermediate conditions. 

As a result of sensor development in the automotive industry, low-priced acceleration sensors are now available. Acceleration sensors are fundamentally also suited to observing excursion (Fig. 5.57) of the suds container caused by imbalance. However, static measurement of the weight of the washing, as achieved with a distance sensor, is not possible with acceleration sensors. 

At this point we may introduce a better definition for quasi-static or reversible processes. These are changes in a system that result from an imbalance of only those forces that maintain a system at equilibrium. 

Membrane Osmometry In this technique a dilute polymer solution and a pure solvent are separately placed in two different chambers that are divided by a tightly held semipermeable membrane through which only solvent molecules can move across. Because the chemical potential of pure solvent is higher than that of the solvent in the solution, the solvent will diffuse across the membrane from the pure solvent to the solution chamber up to the point in which the osmotic pressure equals the hydrostatic pressure created by the volume imbalance between the liquids of the two chambers. The osmotic pressure (k = pgh) at equilibrium (static method) can be calculated from the difference in height (h) between the liquids in the capillaries connected to each chamber. In practice, a dynamic method is used in which a pressure (P) is applied to counterbalance (at t = 0) the osmotic pressure... 

The load imbalance resulting from a dynamic distribution of tasks is very difficult to model because the times required for the individual computational tasks are not known in advance. Provided that the number of tasks is much larger than the number of processes, however, it is reasonable to assume that the dynamic task distribution will enable an essentially even distribution of the load. For this to remain true as the number of processes increases, the number of tasks, umn, must increase proportionally to p. Although this is the same growth rate as obtained for a static work distribution, the actual value for umn needed for high efficiency for a given process count is much smaller for the dynamic distribution, and the assumption of perfect load balance is therefore adequate for our purposes. 

Processes request tasks (atom quartets) by calling the function get quartet, which has been implemented in both a dynamic and a static version. The dynamic work distribution uses a manager-worker model with a manager process dedicated to distributing tasks to the other processes, whereas the static version employs a round-robin distribution of tasks. When the number of processes is small, fhe sfafic scheme achieves the best parallel performance because the dynamic scheme, when run on p processes, uses only p - 1 processes for compulation. As the number of processes increases, however, the parallel performance for the dynamic task distribution surpasses that of the static scheme, whose efficiency is reduced by load imbalance. Wifh fhe entire Fock and density matrix available to every process, no communication is required during the computation of the Fock matrix other than the fetching of tasks in the dynamic scheme. After all ABCD tasks have been processed, a global summation is required to add the contributions to the Fock matrix from all processes and send the result to every process. 

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