Accuracy, Repeatability and Resolution

There are three terms often used in precision practices and they are often used incorrectly or in a vague manner. The terms are accuracy, repeatability, and resolution. Because the present discussion is on machining and fabrication methods, the definitions will be in terms related to machine tools. However, these terms have applicability to metrology, instrumentation, and experimental procedures, as well.

Accuracy
Accuracy is the ability of a machine to move to a commanded position which it has not visited before. This implies the machine must calculate the new position in terms of its feedback system parameters, or lack thereof, and then move to that position. This does not mean the machine is "shown" or "taught" the position and the feedback parameters are stored, as is often done in robotic applications. Accuracy brings the entire machine, hardware and controls, to bear on the task at hand and is therefore a demanding specification placed on the machine.

In the area of measurements, the quantity to be measured is never known therefore instrument accuracy is extremely important. Here, accuracy is the ability of the instrument to provide a quantitative value for the unknown parameter. This has implications beyond that of accuracy in a machine tool where the "unknown" is the true position of a cutting tool, for example, which was computed and where the phenomena (the machine tool performance) should be known and understood with some level of confidence. In instrumentation, the resolution of the output (how many decimal places are shown) is often mistakenly taken as the instrument accuracy. The accuracy of the instrument is best quantified by comparison with fundamental standards and careful.

Repeatability
Repeatability is the ability of the machine to re-visit a location and has other implications including from which direction is the movement made. If the point is repeatedly approached from the same direction, the term used is repeatability. If the point is approached from two directions, such as the work table on an ordinary milling machine, then the term is bi-directional repeatability. Good bi-directional repeatability is more difficult to achieve than repeatability because it involves hysteresis of mechanical motions, among other possible factors such as feedback deadband.

In instrumentation measurements, the repeatability is again perhaps more complex than in machine tools. The quantity to be measured with an instrument is always influenced by the presence of the instrument and this can change the unknown parameter, especially over time which can have a significant effect on repeatability. This is not to say that metrology tools do not affect machine tools in a similar way. In the figure above, the distribution of the data points is due to repeatability errors associated with the phenomena and the instrument.

Resolution
Resolution is the least increment of movement the machine is capable of making. Because machines use digital controllers and motors with discrete feedback, such as encoder slits or interferometer fringes, the resolution represents the quantity upon which all motions are made. If the system resolution is n, then all motions are integer multiples of n. This is not to imply the resolution is the least of any system component but rather the largest. A machine controller which can calculate a movement of 0.1 micrometers will not be able to reliably move the machine an increment of 0.1 micrometers if the feedback encoder only has a resolution of reliably 1 micrometer. The control system will never "see" such a small movement. Therefore, one must be very careful in interpreting machine performance figures.

As mentioned above, resolution is the least count of output of an instrument. Because instrumentation is mostly digital, it is very easy to display with many insignificant digits and the user must be very careful when interpreting such data. If a temperature recorder, for example, outputs to one-hundredth of a degree, there is no assurance that it is reporting the correct temperature! One may know the reported temperature with high resolution, but it may be the entirely wrong temperature! Equipment manufacturers and users often use the term "precision" to describe resolution which can lead to a false conclusion about the instrument accuracy.

Courtesy: MTU

The Sagnac Effect

http://www.mathpages.com/rr/s2-07/2-07.htm

Ring Laser Gyroscope

There is an ever-increasing demand for accurate, yet low-cost and highly reliable guidance, control, and navigation systems for air, land, sea, and space vehicles. The heart of these systems are gyroscopes, devices which can precisely measure changes in orientation of an airplane, ship, tank, or satellite as it moves. The familiar mechanical gyroscope with its rotating wheels is now seeing competition from the laser gyroscope, another application of the versatile laser. For this reason, military readers may find it helpful to know how the laser gyroscope works, its advantages and disadvantages, the current status of laser gyroscope technology, and what it all means in terms of future military system capability.

How a Laser Gyroscope Works
The laser gyroscope works on a physical principle discovered by the French physicist G. Sagnac in the first decade of this century. In simple terms, Sagnac found that the difference in time that two beams, each traveling in opposite directions, take to travel around a closed path mounted on a rotating platform is directly proportional to the speed at which the platform is rotating. This principle is incorporated in a laser gyroscope. Although Sagnac and other scientists demonstrated the concept in the laboratory, it was not until the 1960s, with the advent of the laser beam with its unique properties, that the principle could be used in a practical gyroscope. The key properties of the laser that make the laser gyroscope possible are the laser's coherent light beam, its single frequency, its small amount of diffusion, and its ability to be easily focused, split, and deflected.

In the laser gyroscope, the two counterrotating laser beams travel around a closed circuit or ring, which is usually rectangular or triangular. Such a laser gyro is referred to commonly as a ring laser gyroscope.

Mirrors are located at each corner to turn the beams. At one corner, there is a detector or an output sensor. However, rather than detecting time-of-travel differences, the detectors measure differences in frequency, using the Doppler principle which is the basis of range-finding radars. The beam that is traveling in the direction of rotation of the platform has a longer distance to travel and thus a lower frequency. Conversely, the beam traveling against the direction of motion has a shorter path and a higher frequency. The difference in frequency is directly proportional to the rotation rate.

In an actual application Such as an aircraft autopilot, three laser gyroscopes would be used to sense changes in pitch, roll, and yaw. In addition, there would be three accelerometers to measure longitudinal, lateral, and vertical motion.

Advantages and Disadvantages

There are many characteristics desired in a gyroscope for military applications. These include accuracy, long-term stability, low cost, high reliability, low maintenance, high tolerance to accelerations and vibration, small size and light weight, minimum start-lip time, and low power requirements.

One of the significant attributes of the laser gyro is its use of very few moving parts. Indeed, it is theoretically possible to build laser gyros without any moving components. Unlike the conventional spinning gyroscope with its gimbals, bearings, and torque motors, the laser gyroscope uses a ring of laser light, together with rigid mirrors and electronic devices. Thus the laser gyroscope is more rugged than conventional gyros, offering the obvious advantages of much greater reliability and lower maintenance requirements. Typically, laser gyros have a mean-time between failures about twice that found in conventional gyros [1]. Not only does the greater reliability of the laser gyro mean lower life-cycle costs, but such gyros potentially could be less costly to produce in the first place. Current technological efforts are under way to get production costs down. Indeed, some of the advanced work on very small solid-state devices portends substantial reduction in cost and increases in reliability. The miniature laser gyros that may result could be used in such applications as low-cost tactical missiles and even "guidance" systems issued to the individual foot soldier to replace his compass.

Because the laser gyro uses solid-state components and "massless" light, it is insensitive to variations in the earth's magnetic and gravity fields. Likewise, shock and vibration have little impact. The laser gyros are especially attractive for high-performance aircraft, remotely piloted vehicles, and missiles. High-speed turns, dives, and jinking maneuvers do not represent a real problem to a laser gyro. Unlike a conventional gyro that requires a finite time for wheels to spin up and bearings to come up to operating temperatures, the laser gyro is essentially ready instantaneously when turned on. Again, because of the absence of moving parts and solid-state components, a typical laser gyro has much lower power requirements than a conventional laser and requires half as much cooling [2].

In regard to the important matter of accuracy, the laser gyro has the potential to provide accuracy equivalent to that offered by mechanical gyroscopes, even to the accuracy levels required for the ballistic missile role [3].

Today, accuracy levels of laser gyros in production are in the range of slightly less than one nautical mile per flight hour––about the minimum required for typical aircraft missions and for use in tactical cruise missiles. Short-range tactical missiles such as the AIM-7 and AIM-9 can do very well with rate gyros in the 10-nm/hr to 100-nm/hr class.

One of the inherent difficulties of the laser gyro is the problem of frequency "lock-in." As previously mentioned, the laser gyro measures turning rate by sensing frequency differences. When the rate of turn is very small and thus the frequency difference between the two beams is also small, there is a tendency for the two frequencies to couple together, or "lock-in," and a zero turning rate is indicated. Lock-in limits the accuracy of the laser gyro at important low turn rates. Fortunately, there are several ways to overcome the problem of lock-in. The approach currently used in production devices is to "dither," or vibrate, the gyroscope, either mechanically or electromagnetically. This dithering of the laser gyroscope adds to the complexity, weight, and size of the device, and, in the case of mechanical dithering, adds moving mechanical parts. Another approach is to rise a passive ring laser gyro. In a passive system the laser itself is located outside the actual ring. This is in contrast to an active laser gyro, where the laser is an integral part of the ring (Fig. 3). To date, passive laser gyros are still in the experimental stage; the laser gyros in production are all active devices.

Applications and the Future of the Laser Gyroscope
Laser gyroscopes are more than a laboratory experiment. A laser gyroscope system built by Honeywell is used on the Boeing 757 and 767, the new generation of commercial transports. The European A310 Airbus uses a laser gyro unit built by Litton. Honeywell's laser gyro navigation systems are now being installed in business jets such as the Gulfstream. Other prototype laser gyros have been test flown on commercial aircraft, military fighters such as the A-7E and F-14, and helicopters, giving good accuracy and outstanding reliability.

The future for the laser gyroscope is a bright one. A recent marketing survey has shown that in the last half of this decade about 50 percent of the dollars spent on gyros for military aircraft will go for the laser variety. In the 1990s, the amount will jump to 75 percent. According to this study, laser gyros should start appearing in tactical missiles during the late 1980s or early 1990s. By the mid-1990s, they will capture a predominant share of the market. The laser gyroscope is a viable contender for almost all military and commercial applications, including military and commercial aircraft, tactical and strategic missiles, naval and marine vehicles, land vehicles and weapon platforms, and spacecraft [4].

References
[1] John C. Patterson, "Laser Gyros, Supplanting Inertial Navs," Defense Electronics, May 1981, pp. 106-09.

[2] Jerry Lockenour and John J. Deyst, Jr., "Aerospace Highlight 1980, Guidance and Control," Astronautics and Aeronautics, December 1980, pp. 58-59.

[3] W. Kent Stowell, Robert W. McAdory, and Robert Ziernicki," Air Force Applications for Optical Rotation Rate Sensors," Proceedings of the SPIE Laser Inertial Rotation Sensors, vol. 157, 30-31 August 1978, pp. 66-71.

[4] Robert G. Brown, "Growing Role Predicted for Inertial Technology," Military Electronics/Countermeasures, December 1980, pp. 40-46.

Reservation at IITs

"The HRD Ministry in India, led by Minister Arjun Singh, is proposing to impose a 49.5% reservation for backward classes at IITs and IIMs. This is a significant increase from the current 22.5% reservation policy. Interestingly, but perhaps not coincidentally, this anouncement by the HRD Ministry comes just before elections are on in five states."

As if that 22.5% reservation was not enough already to deprive the talented lot of getting admission to the most prestigious institute. The brand name that IIT has gained over the past few decades is based on the exceptional quality of students the IIT system has produced and the work done by them in various fields of engineering and management. The toughest screening level of IIT-JEE allows only the cream-de-la-cream. Increase the reservation and that image will be gone in no time.

It looks like the basic purpose of introducing the reservation system after independence is lost with the illiterate and criminal-turned-politician leaders forcing caste-based selection procedure and depriving capable people of what they deserve. It is supposed to bring in the reserved castes into the main stream, not to create another yet category full of menacing ignorant engineers and doctors. I mean, how many of these politicians would actually go to a scheduled-caste doctor to cure his ailing knee or something?

US is better off that way. At least every child gets the basic education. The government should rather emphasis on the level of primary education in India. Have reservations there, reservations on admission, not performance. Once in, all that should matter is the performance based on identical level of competition.

Personal Web-page

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