Weight (W) is a force created by the acceleration of gravity (g) acting on the mass of an object. The simple formula becomes W = m x g. The acceleration of gravity, which is nominally 32.2 feet per second per second, is directed towards the center of gravity of the earth. This is what makes the leveling of a scale so very important, in order that the full effect of the gravitational acceleration acts on the object being weighed. In addition, the acceleration of gravity is not constant over the surface of the earth for a variety of reasons. Just think of the variation in altitude from place to place and how that varies the distance from the center of gravity. This variation in gravity must be compensated for in the calibration of any precision weighing device if weight is to be measured accurately from location to location. The weight we use for calibrating a scale has been carefully adjusted to match a weight which has been defined to be a primary or secondary standard weight. These standard weights are kept under carefully controlled conditions at very specific locations and are very rigidly defined and controlled. Calibration weight should be traceable to these tightly controlled standard weights. The need for cleanliness and careful handling of calibration weights should be quite obvious by now. When we become involved in weighing very small objects and the weighing resolution becomes micrograms we face a new set of problems. The amount and density of the air being displaced by the object being weighed must be compensated for accurate measurements. The density of the air varies with the barometric pressure and the humidity. Once again the location gets into weighing. Add to these factors the reality that modern electronic scales drift with both time and temperature (for a variety of reasons), and the need for frequent re-calibration of the scale when doing fine weighing becomes apparent. This need has led to the introduction of scales which are self calibrating based upon automatic internal calibration mechanisms and weights. These scales must calibrate based upon temperature changes and the passage of defined time periods. Scale Calibration and why it is necessary in high accuracy scales One common mistake that scale users make it to confuse checking a scale with a precision weight to see if is within its accuracy limits with actually calibrating the scale. Many times you will hear technicians say "Oh, I checked the scale and it was calibrated" in response to the question "Did you calibrate the scale?" Using a precision weight to verify that the scale is within its accuracy limits is certainly better than doing nothing but it allows the scale to be more inaccurate than it would be if it were re-calibrated. Why do these modern marvels that we call digital scales require calibration? Let’s look at the high accuracy scales where force restoration load cells are used to convert the weight into a proportional current that can then be converted to a digital equivalent and measured using computer techniques. The load cell uses a very strong permanent magnet and an iron based magnetic keeper path to generate a high magnetic field across a small air gap. A circular coil attached to the weight restoration mechanism ( a Roberval structure with many flexures used to eliminate any side loading effects) is used to generate the restorative force to bring the weigh pan back to a vertical center null position (as detected by an electro optical sensor) by passing an electrical current generated by a servo amplifier through the coil. This current is measured by an Analog to Digital converter and from that point on the computer has control. Unfortunately nature does not always follow our nice simple linear equations and throws in a few complications. This is especially true in magnetic circuits which contain iron. They have problems associated with temperature, problems associated with magnetic flux density, problems with air gaps, and others. The computer does its best to compensate for the linearity and drift problems. The plot of force versus current shows that the motor gain (force generated per ampere of current) slumps as the current is increased. The same plot run at different ambient temperatures show that motor gain is changed by temperature. Things such as mechanical vibration can cause changes in motor gain. Do anything to affect the level position of the scale and it causes an apparent change in motor gain. The computer knows the temperature (usually measured in the magnetic core) and the current flowing in the force coil and tries to compensate for the non-linearity. Calibration gives the computer a known anchor point, usually at full scale, which allows the computer to reset its various parameters based upon a certified mass. Calibrate often, or better yet, buy a scale with automatic internal calibration. These scales have a known reference weight built in, and periodically, based upon time and temperature, perform an automatic calibration. The Importance of Leveling a Weigh Scale The force we call weight is directed to that center and follows the simple formula; force = mass x acceleration, where the acceleration is that of gravity which is approximately 32 feet per second per second. In order to measure weight accurately the weight sensor, usually a force motor type load cell in the case of Laboratory and Analytical Scales, must have its weigh axis aligned with the gravitational field. In most scales the weigh pan must be orthogonal (90 degrees) to the gravitational field in all directions. The base plate is made to be orthogonal to the weigh axis of the force motor by internal adjustment, and must not be changed. A bubble type level adjustment indicator is mounted carefully on the base plate and is used to trim the base plate to a level condition. Scales are designed to be leveled in this way. The best and most common system for level adjustment involves a 3 point stance for the base plate (in order to eliminate rocking). Two legs are adjustable and one is fixed. Leveling bubbles are made with different angular sensitivities. Generally speaking the bubble in an analytical balance must be about ten times as sensitive as that in a laboratory scale because of the higher resolution of the analytical balance (1 part in 1,000,000 for the analytical and 1 part in 100,000 for the laboratory). The reduction in weight as we deviate from the orthogonal axis to the base plate follows a cosine curve shape. If the angle of error is 0 degrees (perfect alignment) the cosine of 0 degrees = 1.000…) there is no weight error. If the angle of error is 0.0833 degrees (5 minutes of angle) then the cosine = 0.9999989, or 1.1 parts per million of force reduction, about the max we would tolerate for an analytical scale. If the angular error is o.25 degrees (15 minutes) the cosine = 0.9999904, or close to 1 part per 100,000 of force reduction, the max we would tolerate for a laboratory scale. These are very small angles and care should be taken to center the bubbles when leveling the scale. After leveling do not move the scale on the surface of the bench. If it is moved the level indicator must be checked before using the scale. Most surfaces that people use precision scales upon are not of the quality of surface plates and moving the scale can introduce weighing errors in many instances. Be warned. Be wise. The Importance of Leveling a Balance or Scale It is important that the modern digital electronic scale be properly leveled on whatever is used for the weighing surface (the surface upon which the scale is placed). Quite often analytical scales and balances are placed on what essentially is table top or shelf like work station. It is very important that this surface is vibration and draft free. Many of these surfaces are not truly flat. They may appear to be flat to the naked eye, but a level will show them to have uneven surfaces. Almost all modern precision scales use a Bubble (or Spirit) Level to indicate the level condition. Scales usually have two adjustable legs that allow the user to level the balance. These scales have three legs in all, one of them being fixed. The triangular stance is the most stable and easiest to adjust. Some scales have four legs and all four are adjustable. These scales are much harder to level, and have a definite tendency to rock. The level usually is circular when viewed from above, and has a circular bull's eye to indicate a level condition when the bubble is centered in the eye. The feet of the precision scale should be adjusted in such a way as to cause the bubble to move to the center of the eye. Many users level the scale once and assume that will keep the scale level as long as it is on that same surface. However, scales frequently are moved small distances when in use or by accident. Even a small movement can cause a significant change in the scales calibration, if the surface is uneven or warped. It is necessary that the weight vector be in line with the force restoration vector in order to achieve maximum accuracy. An angular change of 0.1 degrees (6 minutes) can create an error 2.mg in a 100.g weighing. An angular change of 1.0 degrees can create an error of 15.2mg in a 100.g weighing. A good level will allow the user to find level within three minutes of arc if he is careful and discerning. The time spent reconfirming the level status may avoid serious errors when doing work which requires high accuracy weighing. Care should be taken that nothing is placed near the adjustable legs that might accidentally touch and turn them. If the scale is accidentally bumped the level should be checked immediately. The level itself requires zero maintenance unless it becomes dirty and, therefore, hard to read.
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How are these three things; the weight of an object, the location of that object, and the calibration of the scale used to weigh that object, all related? The one thing that remains constant about the object (provided it is not mechanically altered) is its mass. The mass of an object is the same any where on earth, or in space, or on the moon, or any other location. The simple equation, F = m x a, states that Force (F) on an object is equal to the product of the mass (m) of that object ...
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