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METROLOGY AND INSTRUMENTATION (M602)

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Metrology (from Ancient Greek metron (measure) and logos (study of)) is the

science of measurement. Metrtrology includes all theoretical and practical aspects of

measurement.

INTRODUCTION

Metrology is defined by the International Bureau of Weights and Measures (BIPM) as

"the science of measurement, embracing both experimental and theoretical determinations at

any level of uncertainty in any field of science and technology."

Metrology is a very broad field and may be divided into three subfields:

• Scientific or fundamental metrology concerns the establishment of measurement units,

unit systems, the development of new measurement methods, realisation of

measurement standards and the transfer of traceability from these standards to users in

society.

• Applied or industrial metrology concerns the application of measurement science to

manufacturing and other processes and their use in society, ensuring the suitability of

measurement instruments, their calibration and quality control of measurements.

• Legal metrology concerns regulatory requirements of measurements and measuring

instruments for the protection of health, public safety, the environment, enabling

taxation, protection of consumers and fair trade.

A core concept in metrology is (metrological) traceability, defined as "the property of the

result of a measurement or the value of a standard whereby it can be related to stated

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references, usually national or international standards, through an unbroken chain of

comparisons, all having stated uncertainties." The level of traceability establishes the level of

comparability of the measurement: whether the result of a measurement can be compared to

the previous one, a measurement result a year ago, or to the result of a measurement

performed anywhere else in the world.

Traceability is most often obtained by calibration, establishing the relation between the

indication of a measuring instrument and the value of a measurement standard. These

standards are usually coordinated by national laboratories: National Institute of Standards and

Technology (USA), National Physical Laboratory, UK, etc.

Tracebility, accuracy, precision, systematic bias, evaluation of measurement uncertainty

are critical parts of a quality management system.

METROLOGY BASICS

Mistakes can make measurements and counts incorrect. If there are no mistakes, all

counts will be exactly correct. Even if there are no mistakes, nearly all measurements are still

inexact. The term 'error' is reserved for that inexactness, also called measurement uncertainty.

Among the few exact measurements are:

• The absence of the quantity being measured, such as a voltmeter with its leads shorted

together: the meter should read zero exactly.

• Measurement of an accepted constant under qualifying conditions, such as the triple point of

pure water: the thermometer should read 273.16 Kelvin (0.01 degrees Celsius, 32.018 degrees

Fahrenheit) when qualified equipment is used correctly.

• Self-checking ratio metric measurements, such as a potentiometer: the ratio is between steps

is independently adjusted and verified to be beyond influential inexactness.

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All other measurements either have to be verified to be sufficiently correct or left to chance.

Metrology is the science that establishes the correctness of specific measurement situations.

This is done by anticipating and allowing for both mistakes and error. The precise distinction

between measurement error and mistakes is not settled and varies by country. Repeatability

and reproducibility studies help quanitfy the precision: one common method is an ANOVA

Gauge R&R study.

Calibration is the process where metrology is applied to measurement equipment and

processes to determine confomity with a known standard of measurement, usually tracable to

a national standards board.

METROLOGY STANDARDS

Standards are objects or ideas that are designated as being authoritative for some

accepted reason. Whatever value they possess is useful for comparison to unknowns for the

purpose of establishing or confirming an assigned value based on the standard. The design of

this comparison process for measurements is metrology. The execution of measurement

comparisons for the purpose of establishing the relationship between a standard and some

other measuring device is calibration.

The ideal standard is independently reproducible without uncertainty. This is what the

creators of the 'metre' length standard were attempting to do in the 19th century. Later, we

learned that the Earth’s surface is a terrible basis for a standard. The Earth is not spherical and

it is constantly changing in shape. But the special alloy metre/meter bars that were created and

accepted in that time period standardized international length measurement until the 1950s.

Careful calibrations allowed tolerances as small as 10 parts in 1 million to be distributed and

reproduced in metrology laboratories worldwide, regardless of whether the rest of the metric

system was implemented and in spite of the shortfalls of the metre/meter’s original basis.

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Historical International Prototype Meter Bars

HISTORICAL DEVELOPMENT OF METROLOGY STANDARDS

The inhabitants of the Indus Valley Civilization (c. 3000–1500 BCE, Mature period

2600–1900 BCE) developed a sophisticated system of standardization, using weights and

measures, evident by the excavations made at the Indus valley sites. This technical

standardization enabled gauging devices to be effectively used in angular measurement and

measurement for construction. Calibration was also found in measuring devices along with

multiple subdivisions in case of some devices.

Metrology has existed in some form or another since antiquity. The earliest forms of

metrology were simply arbitrary standards set up by regional or local authorities, often based

on practical measures such as the length of an arm. The earliest examples of these

standardized measures are length, time, and weight. These standards were established in order

to facilitate commerce and record human activity.

Little progress was made with regard to proto-metrology until various scientists,

chemists, and physicists started making headway during the scientific revolution. With the

advances in the sciences, the comparison of experiment to theory required a rational system of

units, and something more closely resembling modern metrology began to come into being.

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The discovery of atoms, electricity, thermodynamics, and other fundamental scientific

principles could be applied to standards of measurement, and many inventions made it easier

to quantitatively or qualitatively assess physical properties, using the defined units of

measurement established by science.

Metrology was thus one of the precursors to the Industrial Revolution, and was

necessary for the implementation of mass production, equipment commonality, and assembly

lines.

Modern metrology has its roots in the French Revolution, with the political motivation

to harmonize units all over France and the concept of establishing units of measurement based

on constants of nature, and thus making measurement units available "for all people, for all

time". In this case deriving a unit of length from the dimensions of the Earth, and a unit of

mass from a cube of water. The result was platinum standards for the meter and the kilogram

established as the basis of the metric system on June 22, 1799. This further led to the creation

of the Système International d'Unités, or the International System of Units. This system has

gained unprecedented worldwide acceptance as definitions and standards of modern

measurement units. Though not the official system of units of all nations, the definitions and

specifications of SI are globally accepted and recognized. The SI is maintained under the

auspices of the Metre Convention and its institutions, the General Conference on Weights and

Measures, or CGPM, its executive branch the International Committee for Weights and

Measures, or CIPM, and its technical institution the International Bureau of Weights and

Measures, or BIPM.

As the authorities on SI, these organizations establish and promulgate the SI, with the

ambition to be able to service all. This includes introducing new units, such as the relatively

new unit, the mole, to encompass metrology in chemistry. These units are then established

and maintained through various agencies in each country, and establish a hierarchy of

measurement standards that can be traced back to the established standard unit, a concept

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known as metrological traceability. The U.S. agencies holding this responsibility are the

National Institute of Standards and Technology (NIST) and the American National Standards

Institute (ANSI).

The development of standards also involves individual and small group achievements.

In 1893, Edward Weston (chemist) and his company perfected his Saturated Standard Cell

design, which allowed the volt to be reproduced to 1 part in ten to the fourth power directly.

This advance made a huge practical difference at a critical moment in the development of

modern electrical devices. Groupings of saturated cells, called banks, can still be found in

some metrology and calibration laboratories today. Edward Weston did not pursue patents for

his cell design. By doing this, his superior design quickly replaced similar but inferior

patented devices worldwide without much discussion.

MODERN STANDARDS

Currently, only five independent units of measure are internationally recognized. All

measurements of all types are based on one or more of these independent units. For example,

Ohm's law is the most widely understood concept in all of electricity usage. Of the three units

of measure involved, only current (ampere) is an independent unit. Voltage and resistance

units are dependent on current units, per Ohm's law. Two supplemental independent units are

also recognized internationally, both dealing with angle measurement.

In the United States, ASTM Standard Practice E 380,replaced by IEEE/ASTM SI10[2],

adapts independent unit of measure theory to practical measurement activity.

It is believed that each of independent units of measure will be defined in terms of the other

four independent units eventually. Length (meter) and time (second) are already connected

this way. If an accurate time base is available, then a length standard can be reproduced

without a meter bar artifact. Lesser known is the relationship between the luminance (candela)

and current (ampere). The candela is defined in terms of the watt, which in turn is derived

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from the ampere. This difficult to recreate standard is supplemented by an incandescent bulb

design that is used as a secondary and transfer standard. These bulbs recreate the candela

when a specific amount of current is applied.

The development of standards follows the needs of technology. As a result, some units

of measure have much more resolution than others. The second is reproducible to 1 part in 10

to the 14th power. As this resolution capability increased, what was believed to be a constant

proved to be very slightly irregular. See leap second for an explanation and as a case study of

international cooperation under challenging conditions.

Luminance (candela) can only be reproduced to 5% of reading despite having sensors

that are capable of 50 parts per million (0.0005%) precision. Reproducibility of the standard is

the constraint.

Temperature (kelvin) is defined by accepted fixed points. These points are defined by

the state changes of nearly pure materials, generally as they move from liquid to solid.

Between these fixed points, Standard Platinum Resistance Thermometers (SPRTs)

constructed a very specific way are used to interpolate temperature values. This mosaic of

approaches produces uncertainty that is not uniform over the entire range of temperature

measurement. Temperature measurement is coordinated by the International Practical

Temperature Scale, maintained by the BIPM.

Non-commercial measurement details like these used to be academic curiosities. But

as the frontiers of science moved forward, it pulled applied science along. Engineering,

manufacturing and ordinary living now routinely challenge the limits of measurement.

For example, most owners of 'atomic clocks,' more correctly known as radio clocks,

know that there are no radioactive materials in their clocks. An unacceptably small percentage

of users know that the clocks are synchronized by internal radio receivers for broadcasted

time signals from real atomic clocks. There are too many other measurement devices used by

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people who don't have adequate comprehension of the basic principles involved. Without this

basis, the need for metrology and calibration is difficult to substantiate.

After 40+ centuries of effort, there still are many unanswered questions and a lot of

work remaining to be done. There also are plenty of surname-less units of measure waiting for

new champions. They would join Kelvin, Watt, Ampere, Hertz and, in 1971, Siemens, in the

ranks of those who received the ultimate acknowledgement of their contributions to

technology and measurement.

INDUSTRY-SPECIFIC METROLOGY STANDARDS

In addition to standards created by national and international standards organizations, many

large and small industrial companies also define metrology standards and procedures to meet

their particular needs for technically and economically competitive manufacturing. These

standards and procedures, while drawing in part upon the national and international standards,

also address the issues of what specific instrument technology will be used to measure each

quantity, how often each quantity will be measured, and which definition of each quantity will

be used as the basis for accomplishing the process control that their manufacturing and

product specifications require. Industrial metrology standards include dynamic control plans,

also known as “dimensional control plans”, or “DCPs”, for their products.

In industrial metrology, several issues beyond accuracy constrain the usability of metrology

methods. These include

1. The speed with which measurements can be accomplished on parts or surfaces in the

process of manufacturing, which must match the TAKT Time of the production line.

2. The completeness with which the manufactured part can be measured such as

described in High-definition metrology,

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3. The ability of the measurement mechanism to operate reliably in a manufacturing

plant environment considering temperature, vibration, dust, and a host of other

potential hostile factors,

4. The ability of the measurement results, as they are presented, to be assimilated by the

manufacturing operators or automation in time to effectively control the

manufacturing process variables, and

5. The total financial cost of measuring each part.

NATIONAL STANDARDS

Every country maintains its own metrology system. In the United States, the National

Institute of Standards and Technology (NIST) plays the dual role of maintaining and

furthering both commercial and scientific metrology. NIST does not enforce measurement

accuracy directly.

The accuracy and traceability of commercial measurements is enforced per the laws of the

individual states. Commercial measurement generally involves any material sold by any unit

of measure. Some intuitive or obvious measurement is generally exempted, such as selling

cloth on a cutting table that has a yardstick fastened to it. All counting-based transactions are

generally exempt also. But each state has its own rules, responding to the accumulated

concerns of the state residents.

Commercial metrology is also known as "weights and measures" and is essential to

commerce of any kind above the pure barter level. Every state maintains its own weights and

measures functionality with traceability to the national standards maintained by NIST. Large

states further divide this effort by county, where a "Sealer" or other appointee is responsible

for the validity of most common commercial measurements such as mass balances (scales) in

grocery stores and gasoline pump measurements of volume. The sealer's staff and agents

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make periodic inspections to catch merchant cheaters, maintaining the integrity of commercial

measurements.

Typical State Seal application: Even in Las Vegas, people prefer not to leave volumetric

gasoline measurements to chance.

Depending on the specific state, other state government agencies can be involved. For

example, electricity watt-hour meters and water delivery flow meters are commonly

monitored by the state's "public utilities commission" who enforces the measurement

tolerances and traceabiity to NIST through the utility providers. Highway State Police and the

State Highway Department generally run the commercial truck mass measurement programs

for safety purposes and to minimize the damage to road surfaces that overloaded trucks cause.

Nearly all states license weighmasters, weighmistresses, scale calibrators and other specialists

involved in commercial measuring equipment maintenance.

The term "commercial metrology" is also used to describe calibration laboratories that are not

owned by the companies they serve.

Scientific metrology addresses measurement phenomena not quantified in

ordinary commerce, such as the test bed pictured at the beginning of the article.

Calibration laboratories that serve scientific metrology are regulated as businesses

only. They may choose to have their work accredited by voluntary certification

organizations based on customer desires, but there is no requirement to do so.

Irresolvable disputes involving scientific metrology are generally settled in the civil

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court systems. Some federal government entities like the Federal Communications

Commission and the Environmental Protection Administration are considered to be

the final authority in their domains rather than the NIST. Disputes involving only

metrology issues with those organizations probably would not be heard in any courts.

LINE STADARDS

INTERNATIONAL PROTOTYPE METER

Historical International Prototype Meter bar, made of an alloy of platinum and

iridium, that was the standard from 1889 to 1960.

The meter was originally defined as one ten-millionth of the distance between the

North Pole and the equator at the longitude of Paris. Because of the difficulty of reproducing

this measurement, a platinum bar of that length was constructed in 1799 and housed at

Pavillon de Breteuil near Paris. This is the headquarters for the International Bureau of

Weights and Measures. Its French language acronym is BIPM.

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It was discovered that this bar was a fraction of a millimeter too long. In 1889 the

meter was redefined as the distance between precision marks on a new 'X' shaped 90%

platinum 10% iridium bar at 0 °C. This alloy was used because it is does not oxidize, is hard,

can be highly polished, and expands or contracts very little with temperature changes. The bar

is kept at the BIPM.

Selected metrologists were authorized to travel there to duplicate the marks on to their

own bars for regional prototypes The new bar served as standard until 1960 when the meter

was redefined in terms of the wavelength of a spectral line of Krypton86. The meter was

redefined yet again in 1989 in terms of the speed of light. The present speed of light is defined

as 299,792,458 meters per second and is used to indirectly calculate the length of the meter.

SYSTEMS OF MEASUREMENT

A system of measurement is a set of units which can be used to specify anything which can

be measured and were historically important, regulated and defined because of trade and

internal commerce. Scientifically, when later analyzed, some quantities are designated as

fundamental units meaning all other needed units can be derived from them, whereas in the

early and most historic eras, the units were given by fiat (See Statutory law) by the ruling

entities and were not necessarily well inter-related or self-consistent.

Although we might suggest that the Egyptians had discovered the art of measurement, it is

really only with the Greeks that the science of measurement begins to appear. The Greeks'

knowledge of geometry, and their early experimentation with weights and measures, soon

began to place their measurement system on a more scientific basis. By comparison, Roman

science, which came later, was not as advanced...

The French Revolution gave rise to a scientific system, and there has been steady

significant pressure since to convert to a scientific basis from so called customary units of

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measure. In most systems, length (distance), weight, and time are fundamental quantities; or

as has been now accepted as better in science and engineering, the substitution of mass for

weight, as a better more basic parameter. Some systems have changed to recognize the

improved relationship, notably the 1824 legal changes to the imperial system.

Later science developments showed that either electric charge or electric current must

be added to complete the minimum set of fundamental quantities by which all other

metrological units may be defined. Other quantities, such as power, speed, etc. are derived

from the fundamental set; for example, speed is distance divided by time. Historically a wide

range of units were used for the same quantity; for example, in several cultural settings,

length was measured in inches, feet, yards, fathoms, rods, chains, furlongs, miles, nautical

miles, stadia, leagues, with conversion factors which are not simple powers of ten or even

always simple fractions within a given customary system.

Nor were they necessarily the same units (or equal units) between different members

of similar cultural backgrounds. It must be understood by the modern reader that historically,

measurement systems were perfectly adequate within their own cultural milieu, and the

understanding that a better more universal system (based on more rationale and fundamental

units) only gradually spread with the maturation and appreciation of the rigor characteristic of

Newtonian physics. Moreover, changing one's measurement system has real fiscal and

cultural costs.

Once the analysis tools within that field were appreciated and came into widespread

use in the nascent sciences, especially in the utilitarian subfields of applied science like civil

and mechanical engineering, conversion to a common basis had no impetus. It was only after

the appreciation of these needs and the appreciation of the difficulties of converting between

numerous national customary systems became widespread could there be any serious

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justification for an international effort of standardization. Credit the French Revolutionary

spirit for taking the first significant and radical step down that road.

In antiquity, systems of measurement were defined locally, the different units were

defined independently according to the length of a king's thumb or the size of his foot, the

length of stride, the length of arm or per custom like the weight of water in a keg of specific

size, perhaps itself defined in hands and knuckles. The unifying characteristic is that there was

some definition based on some standard, however egocentric or amusing it may now seem

viewed with eyes used to modern precision. Eventually cubits and strides gave way under

need and demand from merchants and evolved to customary units.

In the metric system and other recent systems, a single basic unit is used for each

fundamental quantity. Often secondary units (multiples and submultiples) are used which

convert to the basic units by multiplying by powers of ten, i.e., by simply moving the decimal

point. Thus the basic metric unit of length is the metre or meter; a distance of 1.234 m is

1234.0 millimetres, or 0.001234 kilometres.

METRIC SYSTEM

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A baby bottle that measures in three measurement systems—imperial (U.K.), U.S.

customary, and metric.

Metric systems of units have evolved since the adoption of the first well-defined system in

France in 1791. During this evolution the use of these systems spread throughout the world,

first to the non-English-speaking countries, and more recently to the English speaking

countries.

Multiples and submultiples of metric units are related by powers of ten; the names for

these are formed with prefixes. This relationship is compatible with the decimal system of

numbers and it contributes greatly to the convenience of metric units.

In the early metric system there were two fundamental or base units, the metre and the gram,

for length and mass. The other units of length and mass, and all units of area, volume, and

compound units such as density were derived from these two fundamental units.

Mesures usuelles (French for customary measurements) were a system of measurement

introduced to act as compromise between the metric system and traditional measurements. It

was used in France from 1812 to 1839.

A number of variations on the metric system have been in use. These include

gravitational systems, the centimetre-gram-second systems (cgs) useful in science, the metre-

tonne-second system (mts) once used in the USSR and the metre-kilogram-second system of

units (mks) most commonly used today.

The current international standard metric system is the International System of Units

(Système international d'unités or SI) It is an mks system based on the metre, kilogram and

second as well as the kelvin, ampere, candela, and mole.

The SI includes two classes of units which are defined and agreed internationally. The first of

these classes are the seven SI base units for length, mass, time, temperature, electric current,

luminous intensity and amount of substance. The second of these are the SI derived units.

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These derived units are defined in terms of the seven base units. All other quantities (e.g.

work, force, power) are expressed in terms of SI derived units.

ENGLISH CUSTOMARY WEIGHTS AND MEASURES

DISTANCE

In all traditional measuring systems, short distance units are based on the dimensions

of the human body. The inch represents the width of a thumb; in fact, in many languages, the

word for "inch" is also the word for "thumb." The foot (12 inches) was originally the length of

a human foot, although it has evolved to be longer than most people's feet. The yard (3 feet)

seems to have gotten its start in England as the name of a 3-foot measuring stick, but it is also

understood to be the distance from the tip of the nose to the end of the middle finger of the

outstretched hand. Finally, if you stretch your arms out to the sides as far as possible, your

total "arm span," from one fingertip to the other, is a fathom (6 feet).

Historically, there are many other "natural units" of the same kind, including the digit

(the width of a finger, 0.75 inch), the nail (length of the last two joints of the middle finger, 3

digits or 2.25 inches), the palm (width of the palm, 3 inches), the hand (4 inches), the

shaftment (width of the hand and outstretched thumb, 2 palms or 6 inches), the span (width of

the outstretched hand, from the tip of the thumb to the tip of the little finger, 3 palms or 9

inches), and the cubit (length of the forearm, 18 inches).

In Anglo-Saxon England (before the Norman conquest of 1066), short distances seem to have

been measured in several ways. The inch (ynce) was defined to be the length of 3 barleycorns,

which is very close to its modern length. The shaftment was frequently used, but it was

roughly 6.5 inches long. Several foot units were in use, including a foot equal to 12 inches, a

foot equal to 2 shaftments (13 inches), and the "natural foot" (pes naturalis, an actual foot

length, about 9.8 inches). The fathom was also used, but it did not have a definite relationship

to the other units.

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When the Normans arrived, they brought back to England the Roman tradition of a

12-inch foot. Although no single document on the subject can be found, it appears that during

the reign of Henry I (1100-1135) the 12-inch foot became official, and the royal government

took steps to make this foot length known. A 12-inch foot was inscribed on the base of a

column of St. Paul's Church in London, and measurements in this unit were said to be "by the

foot of St. Paul's" (de pedibus Sancti Pauli). Henry I also appears to have ordered construction

of 3-foot standards, which were called "yards," thus establishing that unit for the first time in

England. William of Malmsebury wrote that the yard was "the measure of his [the king's] own

arm," thus launching the story that the yard was defined to be the distance from the nose to

the fingertip of Henry I. In fact, both the foot and the yard were established on the basis of the

Saxon ynce, the foot being 36 barleycorns and the yard 108.

Meanwhile, all land in England was traditionally measured by the gyrd or rod, an old

Saxon unit probably equal to 20 "natural feet." The Norman kings had no interest in changing

the length of the rod, since the accuracy of deeds and other land records depended on that

unit. Accordingly, the length of the rod was fixed at 5.5 yards (16.5 feet). This was not very

convenient, but 5.5 yards happened to be the length of the rod as measured by the 12-inch

foot, so nothing could be done about it. In the Saxon land-measuring system, 40 rods make a

furlong (fuhrlang), the length of the traditional furrow (fuhr) as plowed by ox teams on Saxon

farms. These ancient Saxon units, the rod and the furlong, have come down to us today with

essentially no change. The chain, a more recent invention, equals 4 rods or 1/10 furlong in

order to fit nicely with the Saxon units.

Longer distances in England are traditionally measured in miles. The mile is a Roman

unit, originally defined to be the length of 1000 paces of a Roman legion. A "pace" here

means two steps, right and left, or about 5 feet, so the mile is a unit of roughly 5000 feet. For

a long time no one felt any need to be precise about this, because distances longer than a

furlong did not need to be measured exactly. It just didn't make much difference whether the

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next town was 21 or 22 miles away. In medieval England, various mile units seem to have

been used. Eventually, what made the most sense to people was that a mile should equal 8

furlongs, since the furlong was an English unit roughly equivalent to the Roman stadium and

the Romans had set their mile equal to 8 stadia. This correspondence is not exact: the furlong

is 660 English feet and the stadium is only 625 slightly-shorter Roman feet.

In 1592, Parliament settled this question by setting the length of the mile at 8 furlongs,

which works out to 1760 yards or 5280 feet. This decision completed the English distance

system. Since this was just before the settling of the American colonies, British and American

distance units have always been the same.

AREA

In all the English-speaking countries, land is traditionally measured by the acre, a very

old Saxon unit that is either historic or archaic, depending on your point of view. There are

references to the acre at least as early as the year 732. The word "acre" also meant "field", and

as a unit an acre was originally a field of a size that a farmer could plow in a single day. In

practice, this meant a field that could be plowed in a morning, since the oxen had to be rested

in the afternoon. The French word for the unit is journal, which is derived from jour, meaning

"day"; the corresponding unit in German is called the morgen ("morning") or tagwerk ("day's

work").

Most area units were eventually defined to be the area of a square having sides equal

to some simple multiple of a distance unit, like the square yard. But the acre was never

visualized as a square. An acre is the area of a long and narrow Anglo-Saxon farm field, one

furlong (40 rods) in length but only 4 rods (1 chain) wide. This works out, very awkwardly

indeed, to be exactly 43 560 square feet . If we line up 10 of these 4 x 40 standard acres side

by side, we get 10 acres in a square furlong, and since the mile is 8 furlongs there are exactly

10 x 8 x 8 = 640 acres in a square mile.

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WEIGHT

The basic traditional unit of weight, the pound, originated as a Roman unit and was

used throughout the Roman Empire. The Roman pound was divided into 12 ounces, but many

European merchants preferred to use a larger pound of 16 ounces, perhaps because a 16-ounce

pound is conveniently divided into halves, quarters, or eighths. During the Middle Ages there

were many different pound standards in use, some of 12 ounces and some of 16. The use of

these weight units naturally followed trade routes, since merchants trading along a certain

route had to be familiar with the units used at both ends of the trip.

In traditional English law the various pound weights are related by stating all of them

as multiples of the grain, which was originally the weight of a single barleycorn. Thus

barleycorns are at the origin of both weight and distance units in the English system.

The oldest English weight system has been used since the time of the Saxon kings. It is based

on the 12-ounce troy pound, which provided the basis on which coins were minted and gold

and silver were weighed. Since Roman coins were still in circulation in Saxon times, the troy

system was designed to model the Roman system directly. The troy pound weighs 5760

grains, and the ounces weigh 480 grains. Twenty pennies weighed an ounce, and therefore a

pennyweight is 480/20 = 24 grains. The troy system continued to be used by jewelers and also

by druggists until the nineteenth century. Even today gold and silver prices are quoted by the

troy ounce in financial markets everywhere.

Since the troy pound was smaller than the commercial pound units used in most of

Europe, medieval English merchants often used a larger pound called the "mercantile" pound

(libra mercatoria). This unit contained 15 troy ounces, so it weighed 7200 grains. This unit

seemed about the right size to merchants, but its division into 15 parts, rather than 12 or 16,

was very inconvenient. Around 1300 the mercantile pound was replaced in English commerce

by the 16-ounce avoirdupois pound. This is the pound unit still in common use in the U.S. and

Britain. Modeled on a common Italian pound unit of the late thirteenth century, the

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avoirdupois pound weighs exactly 7000 grains. The avoirdupois ounce, 1/16 pound, is divided

further into 16 drams.

Unfortunately, the two English ounce units don't agree: the avoirdupois ounce is

7000/16 = 437.5 grains while the troy ounce is 5760/12 = 480 grains. Conversion between

troy and avoirdupois units is so awkward, no one wanted to do it. The troy system quickly

became highly specialized, used only for precious metals and for pharmaceuticals, while the

avoirdupois pound was used for everything else.

Since at least 1400 a standard weight unit in Britain has been the hundredweight,

which is equal to 112 avoirdupois pounds rather than 100. There were very good reasons for

the odd size of this "hundred": 112 pounds made the hundredweight equivalent for most

purposes with competing units of other countries, especially the German zentner and the

French quintal. Furthermore, 112 is a multiple of 16, so the British hundredweight can be

divided conveniently into 4 quarters of 28 pounds, 8 stone of 14 pounds, or 16 cloves of 7

pounds each. The ton, originally a unit of wine measure, was defined to equal 20

hundredweight or 2240 pounds.

During the nineteenth century, an unfortunate disagreement arose between British and

Americans concerning the larger weight units. Americans, not very impressed with the history

of the British units, redefined the hundredweight to equal exactly 100 pounds. The definition

of the ton as 20 hundredweight made the disagreement carry over to the size of the ton: the

British "long" ton remained at 2240 pounds while the American "short" ton became exactly

2000 pounds. (The American hundredweight became so popular in commerce that British

merchants decided they needed a name for it; they called it the cental.) Today, most

international shipments are reckoned in metric tons, which, coincidentally, are rather close in

weight to the British long ton.

VOLUME

The names of the traditional volume units are the names of standard containers. Until

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the eighteenth century, it was very difficult to measure the capacity of a container accurately

in cubic units, so the standard containers were defined by specifying the weight of a particular

substance, such as wheat or beer, that they could carry. Thus the gallon, the basic English unit

of volume, was originally the volume of eight pounds of wheat. This custom led to a

multiplicity of units, as different commodities were carried in containers of slightly different

sizes.

Gallons are always divided into 4 quarts, which are further divided into 2 pints each.

For larger volumes of dry commodities, there are 2 gallons in a peck and 4 pecks in a bushel.

Larger volumes of liquids were carried in barrels, hogsheads, or other containers whose size

in gallons tended to vary with the commodity, with wine units being different from beer and

ale units or units for other liquids.

The situation was still confused during the American colonial period, so the

Americans were actually simplifying things by selecting just two of the many possible

gallons. These two were the gallons that had become most common in British commerce by

around 1700. For dry commodities, the Americans were familiar with the "Winchester

bushel," defined by Parliament in 1696 to be the volume of a cylindrical container 18.5 inches

in diameter and 8 inches deep. The corresponding gallon, 1/8 of this bushel, is usually called

the "corn gallon" in England. This corn gallon holds 268.8 cubic inches.

For liquids Americans preferred to use the traditional British wine gallon, which

Parliament defined to equal exactly 231 cubic inches in 1707. As a result, the U.S. volume

system includes both "dry" and "liquid" units, with the dry units being about 1/6 larger than

the corresponding liquid units.

In 1824, the British Parliament abolished all the traditional gallons and established a

new system based on the "Imperial" gallon of 277.42 cubic inches. The Imperial gallon was

designed to hold exactly 10 pounds of water under certain specified conditions.

Unfortunately, Americans were not inclined to adopt this new, larger gallon, so the traditional

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English "system" actually includes three different volume measurement systems: U.S. liquid,

U.S. dry, and British Imperial.

On both sides of the Atlantic, smaller volumes of liquid are traditionally measured in

fluid ounces, which are at least roughly equal to the volume of one ounce of water. To

accomplish this in the different systems, the smaller U.S. pint is divided into 16 fluid ounces,

and the larger British pint is divided into 20 fluid ounces.

THE INTERNATIONAL SYSTEM OF UNITS (SI)

All systems of weights and measures, metric and non-metric, are linked through a

network of international agreements supporting the International System of Units. The

International System is called the SI, using the first two initials of its French name Système

International d'Unités. The key agreement is the Treaty of the Meter (Convention du Mètre),

signed in Paris on May 20, 1875. 48 nations have now signed this treaty, including all the

major industrialized countries. The United States is a charter member of this metric club,

having signed the original document back in 1875.

The SI is maintained by a small agency in Paris, the International Bureau of Weights

and Measures (BIPM, for Bureau International des Poids et Mesures), and it is updated every

few years by an international conference, the General Conference on Weights and Measures

(CGPM, for Conférence Générale des Poids et Mesures), attended by representatives of all

the industrial countries and international scientific and engineering organizations. The 23rd

CGPM met in 2007; the next meeting will be in 2011. As BIPM states on its web site, "The SI

is not static but evolves to match the world's increasingly demanding requirements for

measurement."

At the heart of the SI is a short list of base units defined in an absolute way without

referring to any other units. The base units are consistent with the part of the metric system

called the MKS system. In all there are seven SI base units:

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• the meter for distance,

• the kilogram for mass,

• the second for time,

• the ampere for electric current,

• the kelvin for temperature,

• the mole for amount of substance, and

• the candela for intensity of light.

Other SI units, called SI derived units, are defined algebraically in terms of these

fundamental units. For example, the SI unit of force, the newton, is defined to be the force

that accelerates a mass of one kilogram at the rate of one meter per second per second. This

means the newton is equal to one kilogram meter per second squared, so the algebraic

relationship is N = kg·m·s-2. Currently there are 22 SI derived units. They include:

• the radian and steradian for plane and solid angles, respectively;

• the newton for force and the pascal for pressure;

• the joule for energy and the watt for power;

• the degree Celsius for everyday measurement of temperature;

• units for measurement of electricity: the coulomb (charge), volt (potential), farad

(capacitance), ohm (resistance), and siemens (conductance);

• units for measurement of magnetism: the weber (flux), tesla (flux density), and henry

(inductance);

• the lumen for flux of light and the lux for illuminance;

• the hertz for frequency of regular events and the becquerel for rates of radioactivity

and other random events;

• the gray and sievert for radiation dose; and

• the katal, a unit of catalytic activity used in biochemistry.

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Future meetings of the CGPM may make additions to this list; the katal was added by the

21st CGPM in 1999.

In addition to the 29 base and derived units, the SI permits the use of certain additional units,

including:

• the traditional mathematical units for measuring angles (degree, arcminute, and

arcsecond);

• the traditional units of civil time (minute, hour, day, and year);

• two metric units commonly used in ordinary life: the liter for volume and the tonne

(metric ton) for large masses;

• the logarithmic units bel and neper (and their multiples, such as the decibel); and

• three non-metric scientific units whose values represent important physical constants:

the astronomical unit, the atomic mass unit or dalton, and the electronvolt.

The SI currently accepts the use of certain other metric and non-metric units traditional in

various fields. These units are supposed to be "defined in relation to the SI in every document

in which they are used," and "their use is not encouraged." These barely-tolerated units might

well be prohibited by future meetings of the CGPM. They include:

• the nautical mile and knot, units traditionally used at sea and in meteorology;

• the are and hectare, common metric units of area;

• the bar, a pressure unit, and its commonly-used multiples such as the millibar in

meteorology and the kilobar in engineering;

• the angstrom and the barn, units used in physics and astronomy.

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ACCURACY AND PRECISION

Accuracy indicates how close a measurement

is to the accepted value. For example, we'd

expect a balance to read 100 grams if we

placed a standard 100 g weight on the

balance. If it does not, then the balance is

inaccurate.

Precision indicates how close together or

how repeatable the results are. A precise

measuring instrument will give very nearly

the same result each time it is used.

There are several ways to report the precision

of results. The simplest is the range (the

difference between the highest and lowest

results) often reported as a deviation from

the average.

More preciseTrial # Mass (g)1 100.002 100.013 99.994 99.99Average 100.00Range 0.01Std. Dev. 0.05

Less preciseTrial # Mass (g)1 100.102 100.003 99.884 100.02Average 100.00Range 0.11Std. Dev. 0.09

Which of the following sets of data is more precise, based on its range?

Set A Set B

15.32 32.56

15.37 32.55

15.33 32.48

15.38 32.53

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15.35 32.55Both accuracy and precision affect how many significant digits can be reported.

Manufacturers will usually specify the accuracy and precision to be expected from their

equipment as a uncertainty.

It is quite possible for an instrument to be precise, but inaccurate. For example,

consider the chains used to measure the first down in a football game. They are supposed to

be ten yards long. But what if they were only 9 yards, 35 inches? You would certainly get

the same precise measurement each time you used the chains, but you wouldn't be getting the

correct accurate measurement. Both teams would not have to go quite ten yards to get a first

down, and the error is so small you probably wouldn't even notice it. However, there

probably have been football games played where one inch would have made a difference to

the outcome of the game. In science and in football, our measurements should be both

accurate and precise.

Of course, even precise and accurate equipment can be used incorrectly. If the chains

were the proper ten yards long, it would still be possible to get an imprecise measurement for

first downs. The chains must be stretched tightly, and they must be marked from the proper

location on the yard line markers.

The thermometers found in high school labs are often

more precise than they are accurate. It is quite easy

to read a thermometer to the nearest 0.2 oC.

However, the overall calibration can often be off by a

degree or more. The temperature shown on the

thermometer at the right can be read to 34.0 oC.

However, if the thermometer is not of high quality, it

would be easy for the real temperature to be off by as

much as a degree or more. Iin other words, the

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temperature could really be as high as 35 or as low as

33 oC, although the thermometer reads 34.0.

ERRORS OF MEASUREMENT

The true score theory is a good simple model for measurement, but it may not always

be an accurate reflection of reality. In particular, it assumes that any observation is composed

of the true value plus some random error value. But is that reasonable? What if all error is not

random? Isn't it possible that some errors are systematic, that they hold across most or all of

the members of a group? One way to deal with this notion is to revise the simple true score

model by dividing the error component into two subcomponents, random error and

systematic error. here, we'll look at the differences between these two types of errors and try

to diagnose their effects on our research.

WHAT IS RANDOM ERROR?

Random error is caused by any factors that randomly affect measurement of the

variable across the sample. For instance, each person's mood can inflate or deflate their

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performance on any occasion. In a particular testing, some children may be feeling in a good

mood and others may be depressed. If mood affects their performance on the measure, it may

artificially inflate the observed scores for some children and artificially deflate them for

others. The important thing about random error is that it does not have any consistent effects

across the entire sample. Instead, it pushes observed scores up or down randomly. This means

that if we could see all of the random errors in a distribution they would have to sum to 0 --

there would be as many negative errors as positive ones. The important property of random

error is that it adds variability to the data but does not affect average performance for the

group. Because of this, random error is sometimes considered noise.

WHAT IS SYSTEMATIC ERROR?

Systematic error is caused by any factors that systematically affect measurement of the

variable across the sample. For instance, if there is loud traffic going by just outside of a

classroom where students are taking a test, this noise is liable to affect all of the children's

scores -- in this case, systematically lowering them. Unlike random error, systematic errors

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tend to be consistently either positive or negative -- because of this, systematic error is

sometimes considered to be bias in measurement.

REDUCING MEASUREMENT ERROR

So, how can we reduce measurement errors, random or systematic? One thing you can do is to

pilot test your instruments, getting feedback from your respondents regarding how easy or

hard the measure was and information about how the testing environment affected their

performance. Second, if you are gathering measures using people to collect the data (as

interviewers or observers) you should make sure you train them thoroughly so that they aren't

inadvertently introducing error. Third, when you collect the data for your study you should

double-check the data thoroughly. All data entry for computer analysis should be "double-

punched" and verified. This means that you enter the data twice, the second time having your

data entry machine check that you are typing the exact same data you did the first time.

Fourth, you can use statistical procedures to adjust for measurement error. These range from

rather simple formulas you can apply directly to your data to very complex modeling

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procedures for modeling the error and its effects. Finally, one of the best things you can do to

deal with measurement errors, especially systematic errors, is to use multiple measures of the

same construct. Especially if the different measures don't share the same systematic errors,

you will be able to triangulate across the multiple measures and get a more accurate sense of

what's going on.

LIMITS FITS AND TOLERANCES

BASIC TERMS

It is necessary that the dimensions, shape and mutual position of surfaces of individual

parts of mechanical engineering products are kept within a certain accuracy to achieve their

correct and reliable functioning. Routine production processes do not allow maintenance (or

measurement) of the given geometrical properties with absolute accuracy. Actual surfaces of

the produced parts therefore differ from ideal surfaces prescribed in drawings. Deviations of

actual surfaces are divided into four groups to enable assessment, prescription and checking

of the permitted inaccuracy during production:

• Dimensional deviations

• Shape deviations

• Position deviations

• Surface roughness deviations

This toll includes the first group and can therefore be used to determine dimensional

tolerances and deviations of machine parts.

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As mentioned above, it is principally impossible to produce machine parts with

absolute dimensional accuracy. In fact, it is not necessary or useful. It is quite sufficient that

the actual dimension of the part is found between two limit dimensions and a permissible

deviation is kept with production to ensure correct functioning of engineering products. The

required level of accuracy of production of the given part is then given by the dimensional

tolerance which is prescribed in the drawing. The production accuracy is prescribed with

regards to the functionality of the product and to the economy of production as well.

A coupling of two parts creates a fit whose functional character is determined by

differences of their dimensions before their coupling.

where:

d=D ... basic size

Dmax , Dmin ... limits of size for the hole

dmax , dmin ... limits of size for the shaft

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ES ... hole upper deviation

EI ... hole lower deviation

es ... shaft upper deviation

ei ... shaft lower deviation

Depending on the mutual position of tolerance zones of the coupled parts, 3 types of fit can be

distinguished:

A. Clearance fit

B. Transition fit

C. Interference fit

ISO 286: ISO system of limits and fits.

This paragraph can be used to choose a fit and determine tolerances and deviations of

machine parts according to the standard ISO 286:1988. This standard is identical with the

European standard EN 20286:1993 and defines an internationally recognized system of

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tolerances, deviations and fits. The standard ISO 286 is used as an international standard for

linear dimension tolerances and has been accepted in most industrially developed countries in

identical or modified wording as a national standard (JIS B 0401, DIN ISO 286, BS EN

20286, CSN EN 20286, etc.).

The system of tolerances and fits ISO can be applied in tolerances and deviations of

smooth parts and for fits created by their coupling. It is used particularly for cylindrical parts

with round sections. Tolerances and deviations in this standard can also be applied in smooth

parts of other sections. Similarly, the system can be used for coupling (fits) of cylindrical

parts and for fits with parts having two parallel surfaces (e.g. fits of keys in grooves). The

term "shaft", used in this standard has a wide meaning and serves for specification of all outer

elements of the part, including those elements which do not have cylindrical shapes. Also, the

term "hole" can be used for specification of all inner elements regardless of their shape.

Note: All numerical values of tolerances and deviations mentioned in this paragraph are given

in the metric system and relate to parts with dimensions specified at 20 °C.

BASIC SIZE

It is the size whose limit dimensions are specified using the upper and lower deviations. In

case of a fit, the basic size of both connected elements must be the same.

Attention: The standard ISO 286 defines the system of tolerances, deviations and fits only for

basic sizes up to 3150 mm.

TOLERANCE OF A BASIC SIZE FOR SPECIFIC TOLERANCE GRADE.

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The tolerance of a size is defined as the difference between the upper and lower limit

dimensions of the part. In order to meet the requirements of various production branches for

accuracy of the product, the system ISO implements 20 grades of accuracy. Each of the

tolerances of this system is marked "IT" with attached grade of accuracy (IT01, IT0, IT1 ...

IT18).

Field of use of individual tolerances of the system ISO:

IT01 to

IT6For production of gauges and measuring instruments

IT5 to

IT12For fits in precision and general engineering

IT11 to

IT16For production of semi-products

IT16 to

IT18For structures

IT11 to

IT18

For specification of limit deviations of non-tolerated

dimensionsNote: When choosing a suitable dimension it is necessary to also take into account the used

method of machining of the part in the production process. The dependency

between the tolerance and modification of the surface can be found in the table in

paragraph [5].

TOLERANCE ZONES

The tolerance zone is defined as a spherical zone limited by the upper and lower limit

dimensions of the part. The tolerance zone is therefore determined by the amount of the

tolerance and its position related to the basic size. The position of the tolerance zone, related

to the basic size (zero line), is determined in the ISO system by a so-called basic deviation.

The system ISO defines 28 classes of basic deviations for holes. These classes are marked by

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capital letters (A, B, C, ... ZC). The tolerance zone for the specified dimensions is prescribed

in the drawing by a tolerance mark, which consists of a letter marking of the basic deviation

and a numerical marking of the tolerance grade (e.g. H7, H8, D5, etc.). This paragraph

includes graphic illustrations of all tolerance zones of a hole which are applicable for the

specified basic size [1.1] and the tolerance grade IT chosen from the pop-up list.

Though the general sets of basic deviations (A ... ZC) and tolerance grades (IT1 ...

IT18) can be used for prescriptions of hole tolerance zones by their mutual combinations, in

practice only a limited range of tolerance zones is used. An overview of tolerance zones for

general use can be found in the following table. The tolerance zones not included in this table

are considered special zones and their use is recommended only in technically well-grounded

cases.

Prescribed hole tolerance zones for routine use (for basic sizes up to 3150 mm):

B8

C8

A9

B9

C9

A10

B10

C10

A11

B11

C11

A12

B12

C12

A13

B13

C13

E5

CD6

D6

E6

CD7

D7

E7

CD8

D8

E8

CD9

D9

E9

CD10

D10

E10

D11

D12

D13

EF3

F3

EF4

F4

EF5

F5

EF6

F6

EF7

F7

EF8

F8

EF9

F9

EF10

F10

FG3

G3

FG4

G4

FG5

G5

FG6

G6

FG7

G7

FG8

G8

FG9

G9

FG10

G10

H1 H2 H3 H4 H5 H6 H7 H8 H9 H10 H11 H12 H13 H14 H15 H16 H17JS1 JS2 JS3 JS4 JS5 JS6 JS7 JS8 JS9 JS10 JS11 JS12 JS13 JS14 JS15 JS16 JS17

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K3

K4

K5

J6

K6

J7

K7

J8

K8

M3

N3

M4

N4

M5

N5

M6

N6

M7

N7

M8

N8

M9

N9

M10

N10

N11

P3 P4 P5 P6 P7 P8 P9 P10 R3 R4 R5 R6 R7 R8 R9 R10 S3 S4 S5 S6 S7 S8 S9 S10

T5

U5

T6

U6

T7

U7

T8

U8

U9

U10

V5

X5

V6

X6

Y6

V7

X7

Y7

V8

X8

Y8

X9

Y9

X10

Y10

Z6

ZA6

Z7

ZA7

Z8

ZA8

Z9

ZA9

Z10

ZA10

Z11

ZA11

ZB7

ZC7

ZB8

ZC8

ZB9

ZC9

ZB10

ZC10

ZB11

ZC11

Note: Tolerance zones with thin print are specified only for basic sizes up to 500 mm.

Hint: For hole tolerances, tolerance zones H7, H8, H9 and H11 are used preferably.

SHAFT TOLERANCE ZONES

The tolerance zone is defined as a spherical zone limited by the upper and lower limit

dimensions of the part. The tolerance zone is therefore determined by the amount of the

tolerance and its position related to the basic size. The position of the tolerance zone, related

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to the basic size (zero line), is determined in the ISO system by a so-called basic deviation.

The system ISO defines 28 classes of basic deviations for shafts. These classes are marked by

lower case letters (a, b, c, ... zc). The tolerance zone for the specified dimensions is prescribed

in the drawing by a tolerance mark, which consists of a letter marking of the basic deviation

and a numerical marking of the tolerance grade (e.g. h7, h6, g5, etc.). This paragraph includes

graphic illustrations of all tolerance zones of a shaft which are applicable for the specified

basic size [1.1] and the tolerance grade IT chosen from the pop-up list.

Though the general sets of basic deviations (a ... zc) and tolerance grades (IT1 ...

IT18) can be used for prescriptions of shaft tolerance zones by their mutual combinations, in

practice only a limited range of tolerance zones is used. An overview of tolerance zones for

general use can be found in the following table. The tolerance zones not included in this table

are considered special zones and their use is recommended only in technically well-grounded

cases.

Prescribed shaft tolerance zones for routine use (for basic sizes up to 3150 mm):

c8

a9

b9

c9

a10

b10

c10

a11

b11

c11

a12

b12

c12

a13

b13

cd5

d5

cd6

d6

cd7

d7

cd8

d8

cd9

d9

cd10

d10

d11

d12

d13

ef3

ef4

e5

ef5

e6

ef6

e7

ef7

e8

ef8

e9

ef9

e10

ef10

f3

fg3

f4

fg4

f5

fg5

f6

fg6

f7

fg7

f8

fg8

f9

fg9

f10

fg10

g3 g4 g5 g6 g7 g8 g9 g10

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h1 h2 h3 h4 h5 h6 h7 h8 h9 h10 h11 h12 h13 h14 h15 h16 h17 h18js1 js2 js3 js4 js5 js6 js7 js8 js9 js10 js11 js12 js13 js14 js15 js16 js17 js18

k3

k4

j5

k5

j6

k6

j7

k7

k8

k9

k10

k11

k12

k13

m3

n3

m4

n4

m5

n5

m6

n6

m7

n7

m8

n8

m9

n9

p3 p4 p5 p6 p7 p8 p9 p10 r3 r4 r5 r6 r7 r8 r9 r10 s3 s4 s5 s6 s7 s8 s9 s10

t5

u5

t6

u6

t7

u7

t8

u8

u9

v5

x5

v6

x6

y6

v7

x7

y7

v8

x8

y8

x9

y9

x10

y10

z6

za6

z7

za7

z8

za8

z9

za9

z10

za10

z11

za11

zb7

zc7

zb8

zc8

zb9

zc9

zb10

zc10

zb11

zc11

Note: Tolerance zones with thin print are specified only for basic sizes up to 500 mm.

Hint: For shaft tolerances, tolerance zones h6, h7, h9 and h11 are used preferably.

SELECTION OF FIT

This paragraph can be used to choose a recommended fit. If you wish to use another fit than

the recommended one, define hole and shaft tolerance zones directly in the paragraphs. When

designing the fit itself, it is recommended to follow several principles:

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• Design a fit in a hole basis system in a shaft basis system.

• Use hole tolerances greater or equal to the shaft tolerance.

• Tolerances of the hole and shaft should not differ by more than two grades.

Hint: In case you wish to find a suitable standardized fit with regard to its specific properties

(a fixed amount of clearance or fit interference is required), use the function of

automatic fit design in paragraph [4].

SYSTEM OF FIT

Although there can be generally coupled parts without any tolerance zones, only two methods

of coupling of holes and shafts are recommended due to constructional, technological and

economic reasons.

A. Hole basis system

The desired clearances and interferences in the fit are achieved by combinations of various

shaft tolerance zones with the hole tolerance zone "H". In this system of tolerances and

fits, the lower deviation of the hole is always equal to zero.

B. Shaft basis system

The desired clearances and interferences in the fit are achieved by combinations of various

hole tolerance zones with the shaft tolerance zone "h". In this system of tolerances and

fits, the upper deviation of the hole is always equal to zero.

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where:

d=D ... basic size

//// ... hole tolerance zone

\\\\ ... shaft tolerance zone

The option of the system for the specified type of product or production is always influenced

by the following factors:

• Constructional design of the product and the method of assembly.

• Production procedure and costs for machining the part.

• Type of semi-product and consumption of material.

• Costs for purchase, maintenance and storage of gauges and production tools.

• Machine holding of the plant.

• Options in use of standardized parts.

Hint: Although both systems are equivalent in the view of functional properties, the hole

basis system is used preferably.

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TYPE OF FIT

Depending on the mutual position of tolerance zones of the coupled parts, 3 types of fit can be

distinguished:

A. Clearance fit

It is a fit that always enables a clearance between the hole and shaft in the coupling. The

lower limit size of the hole is greater or at least equal to the upper limit size of the shaft.

B. Transition fit

It is a fit where (depending on the actual sizes of the hole and shaft) both clearance and

interference may occur in the coupling. Tolerance zones of the hole and shaft partly or

completely interfere.

C. Interference fit

It is a fit always ensuring some interference between the hole and shaft in the coupling.

The upper limit size of the hole is smaller or at least equal to the lower limit size of the

shaft.

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RECOMMENDED FITS.

A sufficient fit can be selected in the pop-up list.

The list of recommended fits given here is for information only and cannot be taken as

a fixed listing. The enumeration of actually used fits may differ depending on the type and

field of production, local standards and national usage and last but not least, depending on the

plant practices. Properties and field of use of some selected fits are described in the following

overview. When selecting a fit it is often necessary to take into account not only

constructional and technological views, but also economic aspects. Selection of a suitable fit

is important particularly in view of those measuring instruments, gauges and tools which are

implemented in the production. Therefore, follow proven plant practices when selecting a fit.

FIELDS OF USE OF SELECTED FITS (PREFERRED FITS ARE IN

BOLD):

Clearance fits:

H11/a11, H11/c11, H11/c9, H11/d11, A11/h11, C11/h11, D11/h11

Fits with great clearances with parts having great tolerances.

Use: Pivots, latches, fits of parts exposed to corrosive effects, contamination with dust and

thermal or mechanical deformations.

H9/C9, H9/d10, H9/d9, H8/d9, H8/d8, D10/h9, D9/h9, D9/h8

METROLOGY AND INSTRUMENTATION (M602) -MODULE 1

Running fits with greater clearances without any special requirements for accuracy of guiding

shafts.

Use: Multiple fits of shafts of production and piston machines, parts rotating very rarely or

only swinging.

H9/e9, H8/e8, H7/e7, E9/h9, E8/h8, E8/h7

Running fits with greater clearances without any special requirements for fit accuracy.

Use: Fits of long shafts, e.g. in agricultural machines, bearings of pumps, fans and piston

machines.

H9/f8, H8/f8, H8/f7, H7/f7, F8/h7, F8/h6

Running fits with smaller clearances with general requirements for fit accuracy.

Use: Main fits of machine tools. General fits of shafts, regulator bearings, machine tool

spindles, sliding rods.

H8/g7, H7/g6, G7/h6

Running fits with very small clearances for accurate guiding of shafts. Without any noticeable

clearance after assembly.

Use: Parts of machine tools, sliding gears and clutch disks, crankshaft journals, pistons of

hydraulic machines, rods sliding in bearings, grinding machine spindles.

H11/h11, H11/h9

METROLOGY AND INSTRUMENTATION (M602) -MODULE 1

Slipping fits of parts with great tolerances. The parts can easily be slid one into the other and

turn.

Use: Easily demountable parts, distance rings, parts of machines fixed to shafts using pins,

bolts, rivets or welds.

H8/h9, H8/h8, H8/h7, H7/h6

Sliding fits with very small clearances for precise guiding and centring of parts. Mounting by

sliding on without use of any great force, after lubrication the parts can be turned and slid by

hand.

Use: Precise guiding of machines and preparations, exchangeable wheels, roller guides.

Transition fits:

H8/j7, H7/js6, H7/j6, J7/h6

Tight fits with small clearances or negligible interference. The parts can be assembled or

disassembled manually.

Use: Easily dismountable fits of hubs of gears, pulleys and bushings, retaining rings,

frequently removed bearing bushings.

H8/k7, H7/k6, K8/h7, K7/h6

Similar fits with small clearances or small interferences. The parts can be assembled or

disassembled without great force using a rubber mallet.

Use: Demountable fits of hubs of gears and pulleys, manual wheels, clutches, brake disks.

H8/p7, H8/m7, H8/n7, H7/m6, H7/n6, M8/h6, N8/h7, N7/h6

METROLOGY AND INSTRUMENTATION (M602) -MODULE 1

Fixed fits with negligible clearances or small interferences. Mounting of fits using pressing

and light force.

Use: Fixed plugs, driven bushings, armatures of electric motors on shafts, gear rims, flushed

bolts.

Interference fits:

H8/r7, H7/p6, H7/r6, P7/h6, R7/h6

Pressed fits with guaranteed interference. Assembly of the parts can be carried out using cold

pressing.

Use: Hubs of clutch disks, bearing bushings.

H8/s7, H8/t7, H7/s6, H7/t6, S7/h6, T7/h6

Pressed fits with medium interference. Assembly of parts using hot pressing. Assembly using

cold pressing only with use of large forces.

Use: Permanent coupling of gears with shafts, bearing bushings.

H8/u8, H8/u7, H8/x8, H7/u6, U8/h7, U7/h6

Pressed fits with big interferences. Assembly using pressing and great forces under different

temperatures of the parts.

Use: permanent couplings of gears with shafts, flanges.

Hint: If not in contradiction with constructional and technological requirements, preferably

use some of the preferred fits. Preferred fits are marked by asterisk "*" in the list.

METROLOGY AND INSTRUMENTATION (M602) -MODULE 1

Note: Preferred fits designed for preferred use in the USA are defined in ANSI B4.2. This

standard prescribes the following groups of preferred fits:

- Clearance fits: H11/c11, H9/d9, H8/f7, H7/g6, H7/h6, C11/h11, D9/h9, F8/h7,

G7/h6

- Transition fits: H7/k6, H7/n6, K7/h6, N7/h6

- Interference fits: H7/p6, H7/s6, H7/u6, P7/h6, S7/h6, U7/h6

HOLE TOLERANCE ZONE.

Limit deviations of the hole tolerance zone are calculated in this paragraph for the

specified basic size [1.1] and selected hole tolerance zone.

The respective hole tolerance zone is automatically set up in the listing during

selection of any of the recommended fits from the list in row [1.8]. If you wish to use another

tolerance zone for the hole, select the corresponding combination of a basic deviation (A ...

ZC) and a tolerance zone (1 ... 18) in pop-up lists in this row.

Though the general sets of basic deviations (A ... ZC) and tolerance grades (IT1 ...

IT18) can be used for prescriptions of hole tolerance zones by their mutual combinations, in

practice only a limited range of tolerance zones is used. An overview of tolerance zones

specified for general use can be found in the table in paragraph [1.3]. The tolerance zones

which are not included in the selection are considered special zones and their use is

recommended only in technically well-grounded cases.

Attention: In case you select a hole tolerance zone which is not defined in the ISO system for

the specified basic size, limit deviations will be equal to zero and the tolerance

mark will be displayed in red.

METROLOGY AND INSTRUMENTATION (M602) -MODULE 1

Hint: For hole tolerances, tolerance zones H7, H8, H9 and H11 are used preferably.

SHAFT TOLERANCE ZONES.

Limit deviations of the hole tolerance zone are calculated in this paragraph for the

specified basic size [1.1] and selected shaft tolerance zone.

The respective shaft tolerance zone is automatically set up in the listing during

selection of any of the recommended fits from the list in row [1.8]. If you wish to use another

tolerance zone for the shaft, select the corresponding combination of a basic deviation (a ...

zc) and a tolerance zone (1 ... 18) in pop-up lists in this row.

Though the general sets of basic deviations (a ... zc) and tolerance grades (IT1 ...

IT18) can be used for prescriptions of shaft tolerance zones by their mutual combinations, in

practice only a limited range of tolerance zones is used. An overview of tolerance zones

specified for general use can be found in the table in paragraph [1.3]. The tolerance zones

which are not included in the selection are considered special zones and their use is

recommended only in technically well-grounded cases.

Attention: In case you select a shaft tolerance zone which is not defined in the ISO system

for the specified basic size, limit deviations will be equal to zero and the tolerance

mark will be displayed in red.

Hint: For shaft tolerances, tolerance zones h6, h7, h9 and h11 are used preferably.

PARAMETERS OF THE SELECTED FIT.

Parameters of the selected fit are calculated and mutual positions of tolerance zones of the

hole and shaft are displayed in this paragraph.

METROLOGY AND INSTRUMENTATION (M602) -MODULE 1

Note: Dimensional data on this picture are given in mm.

ANSI B4.1: Preferred limits and fits for cylindrical parts. [2]

This paragraph can be used for selection of a preferred fit of cylindrical parts according to

ANSI B4.1. This standard defines a system of dimensional tolerances and prescribes a series

of those preferred fits of cylindrical part, which are specified for preferred use.

Note: All numerical values of tolerances and deviations given in this paragraph are related to

those parts, whose dimensions are determined at 68 °F.

Basic size.

It is the size whose limit dimensions are specified using the upper and lower deviations. In

case of a fit, the basic size of both connected elements must be the same.

Note: Standard ANSI B4.1 defines a system of preferred fits only for basic sizes up

to 16.69 in.

Tolerance of a basic size for specific tolerance grade.

The tolerance of a size is defined as the difference between the upper and lower limit

dimensions of the part. The standard ANSI B4.1 implements 10 tolerance grades to meet the

requirements of various production branches for accuracy of products. The system of

tolerances is prescribed by the standard for basic sizes up to 200 in.

Note: When choosing a suitable dimension it is necessary to also take into account the used

method of machining of the part in the production process. The dependency

between the TOLERANCE AND MODIFICATION OF THE SURFACE CAN

BE FOUND IN THE TABLE IN PARAGRAPH [5].

METROLOGY AND INSTRUMENTATION (M602) -MODULE 1

SYSTEM OF FITS.

The standard ANSI B4.1 defines two basic methods of coupling of holes and shafts for the

selected series of preferred fits.

A. Hole basis system

In this system of tolerances and fits, the lower deviation of the hole is always equal to

zero.

B. Shaft basis system

In this system of tolerances and fits, the upper deviation of the hole is always equal to

zero.

where:

d=D ... basic size

//// ... hole tolerance zone

\\\\ ... shaft tolerance zone

METROLOGY AND INSTRUMENTATION (M602) -MODULE 1

The option of the system for the specified type of product or production is always influenced

by the following factors:

• Constructional design of the product and the method of assembly.

• Production procedure and costs for machining the part.

• Type of semi-product and consumption of material.

• Costs for purchase, maintenance and storage of gauges and production tools.

• Machine holding of the plant.

• Options in use of standardized parts.

Hint: Although both systems are equivalent in the view of functional properties, the hole

basis system is used preferably.

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