Knife-edge balance

Equation 9.1 is the basic equation for unbalance. For such a simple arrangement, balancing (referred to as static balance) could be done by placing the shaft on knife edges. Initially, the location of the mass would rotate the disk gravitationally until the mass was on the bottom. If... 

The first moment and synonyms is the location at which the curve, if cut out, would balance on a knife-edge. 

Dreh-. rotatory, rotary, rotating, rotational, revolving, turning, torsional, -achse, /, axis of rotation (or of revolution) knife edge (of a balance) pin, -bank, /, lathe, drehbar, a. capable of being turned or twisted. 

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. 

My immediate fate balanced on a knife edge. If she had summoned me just to see what I looked like, she could now jettison me and carry on with her day. 

Balance Design. The principle underlying the design of technical chemical and analytical equal-arm balances is the same. A metal beam (equal-arm lever) is provided with three knife edges—two at its ends and one at its middle (Fig. 22b). 

The middle knife edge rests on a plate on the central column of the balance and is the point of support. In an analytical balance, the knife edges and plate are made from agate or synthetic sapphire. The stirrups carrying the balance pans rest on the side knife edges. The beam is provided with a long pointer that indicates the deviation of the beam from a horizontal position on a scale. When the beam is horizontal, the pointer is opposite zero of the scale. 

When a balance is not being used, all its moving parts should be lifted and the knife edges separated from their bearing surfaces by means of a device called an arrester. In this position of the balance, the beam cannot rock. This prevents excessive wear of the knife edges. 

The beam is the sensitive element of a balance because its position is determined by the load at both sides of the central knife edge. Some balances are outfitted with a special device called a damper. The latter shortens the time needed for the beam to come to rest in a stable state of equilibrium. Such a balance is called damped. 

A mechanical balance should be in its arrested position when you load or unload the pan and in the half-arrested position when you are dialing weights. This practice minimizes wear on the knife edges, which degrades sensitivity. 

Two other manufacturers have produced balances with the single pan design.27 In these balances, as in the Mettler, the counter weights are loaded in such a fashion that the knife edges are protected during the coarse weighing process. These balances also feature semicircular, clear front panels for better visibility and numerous additional features which provide for simpler operation. 

The instrument that Lavoisier used with the greatest success to demonstrate the truth of his system was the balance, an instrument with a beam pivoting on a central knife-edge, with a scale pan at each end. Chemical substances are neither created nor destroyed during reactions, and this truth can be shown to hold for any substance that has weight. We shall see later that Lavoisier needed a different instrument to try to show that caloric, the matter of heat, behaved as a simple substance in chemical reactions. This was a problem precisely because caloric had no weight. 

According to Gorbach, Weber (24) in 1892 was the first to substitute a quartz fused-on fiber for the knife-edge support of a microbalance beam. He also experimented with fused-on metal fibers. There is little information about the performance of these balances except that they possessed the extremely small capacity of about 1 mg. and were very fragile. Nevertheless the principle of the torsion fiber support of the beam is the basis of most contemporary precision microgravimetry. 

If A] = A2 then it is not difficult to show that coexistence is possible. This is a knife-edge effect - exactly balanced parameters - and cannot be expected to be found in nature. 

The analytical balance has undergone a dramatic evolution over the past several decades. The traditional analytical balance had two pans attached to either end of a lightweight beam that pivoted about a knife edge located in the center of the beam. The object to be weighed was placed on one pan sufficient standard masses were then added to the other pan to restore the beam to its original position. Weighing with such an equal-arm balance was tedious and time consuming. 

The two knife edges in a mechanical balance are prism-shaped agate or sapphire devices that form low-friction bearings with two planar surfaces contained in stirrups also of agate or sapphire. 

To avoid damage to the knife edges and bearing surfaces, the arrest system for a mechanical balance should be engaged at all times other than during actual weighing. 

A second knife edge (B) is located near the left end of the beam and support as a second planar surface, which is located in the inner side of a stirrup that couples the pan to the beam. The two knife edges and their planar surfaces are fabricated from extraordinarily hard materials (agate or synthetic sapphire) and form two bearings that permit motion of the beam and pan with a minimum of friction. The performance of a mechanical balance is critically dependent on the perfection of the.se two bearings. 

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