Errors, Com Para Tors, And Angular Measurements

8/6/2019 Errors, Com Para Tors, And Angular Measurements

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EXPERIMENT-03 ERRORS, COMPARATORS, AND ANGULAR MEASUREMENTS

Aim: To study about errors, comparators and the angular measurements.

Comparators

Comparators are being used in all types of mass production works as their employment reducesthe inspection time and makes the production line move faster. A comparator is a device, whichis not a measuring device, but it is a comparing device. In general the comparators comparesthe objects with reference to a standard master piece. Comparators finds their application is alltype of production works as these require very less skill and reduces the time of inspection as itrequires just a comparison of the values or the dimensions of the product produced.Comparators are in general are classified in to many categories based on the type of principleapplied for obtaining the readings.

Mechanical comparator

Mechanical-optical comparator

Electrical and electronic comparator

Pneumatic comparator

Fluid displacement comparator

Projection comparators

Multi check comparators

Automatic gauging comparators

Irrespective of the type to which the comparators belongs it should fulfill some of the basiccharacteristics

Characteristics of Comparators1) A comparator should posses a robust design and construction so as it should give anaccurate value even at the worst possible conditions at available at the level of ordinary usage.2) When a magnification system is used for obtaining deadbeat readings care should be taken

to eliminate the backlash, wear resistance in the mechanical components and make the inertiagets reduced to the minimum possible extent.3) A large range of temperature should be taken in to condition. The comparators should sustainall the temperatures, which are possible in the global context.4) A scale with linear and having a straight line characteristic should be employed5) The indicator should be constant when it retains its position back to zero6) Irrespective of its sensitiveness a comparator should with stand a reasonable ill usage orwrong handling when the user does not cause a permanent harm.


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7) The comparator should be prepared in such a way that it can be employed for a wide rangeof applications8) The measuring pressure should be always constant and should be low.

Uses of comparatorsComparators find their usage in many areas of production irrespective of the job being

produced.1) They find usage in mass production where the components are required to be checked at afaster rate.2) These are also used as laboratory standards and are used for making the working orinspection gauges correlated and set3) Comparators are used for inspecting newly purchased gauges4) These can also used as some special attachments to the production machines such that thework being done can be regularly checked so as to reduce the wastage of the work due toerrors5) These finds usage in assembly sections where more than three parts are to be assembled

Mechanical comparators

The Johansson Mikrokator used a twisted strip witha pointer attached. as the plunger is depressed, itcauses the strip to stretch. As the twisted strip isstretched, it changes the angle of the pointer, andthus the indicated deflection

Advantages1) Cheaper than all the other type of comparators


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2) Does not require any external source of power or air supply3) These comparators use a linear scale that can be easily understood.4) Usually these comparators are robust and compact but are very easy to handle5) These are small in size and can are portable from one place to other very easily withoutmuch difficulty

Disadvantages1) Contains more number of moving parts so there develops friction which in turn reduces theaccuracy2) Slackness in the moving parts reduces accuracy very drastically3) These have more inertia so the instrument is prone to vibrational effects4) Limited range of the instrument is another drawback as the pointer moves over a fixed scale5) Parallax error may also arise when proper scale is used

Optical comparators

An optical comparator is a device that applies the principles of optics to the inspection ofmanufactured parts. In a comparator, the magnified silhouette of a part is projected upon the

screen, and the dimensions and geometry of the part are measured against prescribed limits.

Advantages1) Less number of moving parts hence more accuracy2) High range and no parallax error3) High magnification possible4) Weight less optical lever

Disadvantages1) Due to high magnification the heat produced from the lamp may cause drift2) Electrical supply is necessary3) Large in size and expensive4) Dark room is required to take the readings

5) These cannot be used continuously as the scale is viewed through a microscope

Electrical comparators

Advantages1) Small number of moving parts2) High range of usage3) Not sensitive to vibrations4) As a A.C source is used for the working of comparator the cyclic vibration generated by A.Csource reduces the sliding friction5) Measuring unit can be made very small

Disadvantages1) Requires external power supply2) Calibration may be altered due to heating elements used3) Expensive
http://en.wikipedia.org/wiki/Opticshttp://en.wikipedia.org/wiki/Inspectionhttp://en.wikipedia.org/wiki/Engineering_tolerancehttp://en.wikipedia.org/wiki/Engineering_tolerancehttp://en.wikipedia.org/wiki/Engineering_tolerancehttp://en.wikipedia.org/wiki/Inspectionhttp://en.wikipedia.org/wiki/Optics


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electrical comparator

Pneumatic comparators

Systems of Pneumatic Gauges

Based on the physical phenomena on which the operation of pneumatic gauges is based, thesemay be classified as(i) Flow or velocity type, (ii) Back pressure type.Flow or velocity type pneumatic gauges operate by sensing and indicating the momentary rateof air flow. Flow could be sensed by a glass tube with tapered bore, mounted over a graduatedscale. Inside the bore a float is lifted by the air flow.Velocity of air in velocity type pneumatic gauges can also be sensed by sensing the velocity

differential i.e., differential pressure across a venturi chamber. Such systems have quickresponse. These permit use of large clearance between nozzle and object surface, resulting inreduced wear of the gauging members. There is less air consumption. Magnification of the orderof 500 to 5000 times is possible

Advantages1) No wear2) High accuracy3) Less friction and less inertia4) Indicating instrument can be remote from the measuring instrument5) High magnification is possible6) Very small diameter holes can be easily measured even when the length is very large

7) Best instrument for determining the ovality and taperness of the circular bores

Disadvantages1) many instruments are used in addition to the normal set up2) scale is not uniform3) when the indicating device is kept in a glass tube a high level of magnification is required so


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as to minimize meniscus errors

4) machine is not easily portable as it has large equipment5) different gauging heads are required

ANGULAR MEASUREMENTS

Introduction:

The angle is defined as the opening between two lines which meet at a point. (Vertex of the

angle)

The basic unit in angular measurement is the right angle, which is defined as the anglebetween two lines which intersect so as to make the adjacent angle equal.

If the circle is divided into 360 equal parts each part is called as degree ( ).

Each degree is divided in 60 minutes () and each minutes into 60 seconds ().

This method of defining angular units is called as sexagesimal system, which is usedengineering purpose. Sexagesimal is a numeral system with sixty as its base.

Length of the arc s

Radius of the circle r

Scaling constant k(which depends on the units of measurement

that are chosen):
http://en.wikipedia.org/wiki/File:Angle_measure.svg


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An alternative method of defining angle is based on the relationship between the radius and arcof a circle. It called radian.

Radian is defined as the angle subtended at the centre by an arc of a circle of length equal to itsradius. Widely used in mathematical investigation.

Instruments for Angular Measurements:

Many instruments which are available used for angular measurement.

Selection of instrument depends upon the component and the accuracy of measurement.

As concerned metrological work high precision work may be measured in few seconds to obtainhigh accuracy.

Following instruments are generally used for angular measurement:

Vernier Bevel Protractor

Combination Protractor

Universal bevel Protractor

Sine bar

Sine centre

Angle gauge block

Auto collimator

Angle dekkor

Roller and cylindrical method

Optical prism method.

One radian is equal to 180/ degrees = 57.2958:

Degrees 0 30 45 60 90 180 2

Radians 0
http://en.wikipedia.org/wiki/File:Radian_cropped_color.svg


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Vernier Bevel Protractor:

It is the simplest angle measuring instrument. It consist of

Main body

Base plate stock

Adjustable blade

Circular plate containing vernier scale

Acute angle attachment

Vernier Bevel Protractor

The base plate is attached to the main body and adjustable blade is attached to the circularplate containing vernier scale. A circle can be divided into 360 equal angles. Each angle iscalled degree. So a circle is 360 degrees (360o). An acute angle attachment is provided at thetop for measuring acute angle. The blade can be moved along throughout its length and canalso be reversed. The acute acute angle attachment can be readily fitted into the body andclamped in any position. As shown in fig the main scale is graduated in degree of arc.

The vernier scale has 12 divisions each side of centre zero. These are marked 0-60 minutes ofarc. So that each division equals 1/12 or 60, that is 5minuts of arc.

Reading of Vernier Bevel Protractor:

Zero on the vernier scale has moved 28 whole degrees to the right of the 0 on the main scaleand the 3th line on the vernier scale coincides with a line upon the main scale as indicated.Multiplying 3 by 5, the product, 15, is the number of minutes to be added to the whole number ofdegrees, thus indicating a setting of 28 degrees and 15 minutes.


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Uses of vernier bevel Protractor


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Inside beveled face of a ground surface

For checking v blocks

For measuring acute angle etc.

Universal Bevel Protractor:

The universal bevel Protractor is used for measuring and laying out of angles accurately andprecisely within 5 minutes.

The Protractor dial is slotted to hold a blade which can be rotated with the dial to the requiredangle.

It can also be adjusted independently to any desired length.

The blade can be locked in any position.

Sine bar:

Sine bar is precision instrument used along with slip gauges for the measurement of angles.

It is used for

To measure the angles very accurately

To locate the work to a given angle within very close limit.

It consists of a steel bar and two rollers.


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The sine bar is made of high carbon, high chromium corrosion resistance steel, suitablehardened, precision ground and stabilized.

The rollers are of accurate and equal diameters. They are attached at the both end of bar.

The normal distance between the axes of the roller is exactly 100mm, 200mm or 300mm etc.

Types of Sine bar: the sine bar are available in several designs for different applications.

From in which the rollers are so arranged that their outer surfaces on one side are level with theplane top surface of the sine bar.

A sine bar which is hollow rollers which outside diameter is equal to the width of sine bar. It isuseful in instance where the width of the bar enters into calculation of work height.

A sine bar with pin on both sides. This is used where the ordinary sine bar cannot be used onthe top surface due to interruption.

A sine bar which is generally preferred as the distance between rollers can be adjusted exactly.It is used with slip gauges.

IS-5359-1969, Nomenclature of sine bar and Types:


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Principle of Sine bar:

The principle of operation of sine bar is based on the law of trigonometry.

One roller of the bar is placed on the surface plate.

Combination of slip gauges placed on second roller.

If h is the height of the combination of slip gauges.

L the distance between the roller centers.

Then

Use of sine bar for measuring unknown angles:

When the component is of small size:

When the component is of large size.

When the component is of small size:


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First find the angle approximate with bevel protractor.

Then setup at the nominal angle on a surface plate by suitablecombination of slip gauges.

The component to be checked is placed over the surface of thesine bar. (if necessary it may be clamped with angle plate)

Then the dial gauge set one end of the work and moved alongthe upper surface of the component.

If there is a variation in parallelism adjust the combination of slipgauges so that the upper surface of the component is trulyparallel with the surface plate.

The angle of component is then calculated by the relation

When the component is of large size.

In such case sine bar is placed over the component.

The height over the rollers can then be measured by a vernier height gauge using dial indicator.

The height gauge is thus used to obtain two readings, if h is the difference in the height and L

distance between the roller centers of the sine bar, then


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SINE CENTRE:

When difficult of mounting of conical work piece on conventional sine bar, sine centre are used.

Two blocks are mounted on the surface of sine bar. These blocks accommodate with centersand can be clamped at any position on the sine bar.

The centre can also the adjusted as per length of work piece.

The work piece is held between these centers.

The procedure of the measuring angle assame of conventional sine bar.


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Angle Gauges:

Angle gauges were developed by Dr. Thomlison in 1941.

These are very precise and easy to use for measurement of angle between two surfaces.

These are hardened and stabilized steel.

The measuring faces are lapped and polished to high degree of accuracy and flatness.

They are 75mm long and 16mm wide and are available in two sets.

One set consist of 12 and another 13 and square blocks.

Set on 12 pieces

1 , 3 , 9 , 27 & 41

1, 3, 9, & 27

6, 18 & 30

Another set having 3 addition one gauge.

Every gauge is accurate to within one second.

Every gauge marked with V which indicates direction of inclined.

Limitation: when the combination of angle gauges may be produce error.

< addition

> Subtraction

Example: An angle of 33 -9-15 is to be measured with the help of the above standard anglegauge

27 +9 -3 +9+18-3 = 33 -9-15


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Auto- collimator:

An autocollimator is an optical instrument that is used to measure small angles with very highsensitivity.

The autocollimator has a wide variety of applications including precision alignment, detection ofangular movement, verification of angle standards, and angular monitoring.

Principle of Working:

If a light source is placed in the focus of a collimating lens, it is projected as a parallel beam oflight.

If this beam is made to strike a plane reflector, kept normal to the optical axis.

It is reflected back along its own path and is brought to same focus.

If the reflector is tilted through a small angle , the parallel beam is deflected twice that angleand is brought to a focus in the same plane as the light source, but to one side at a distance x=

2f

f= focal length of lens

=angle of inclination of reflecting mirror.

Construction Details and Application refer the notes.


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Angle Dekkor:

It consist of microscope, collimating lens and two scale engraved on a glass screen which isplace in the focal plane of the objective lens.One of the scales called datum scale is horizontaland fixed. It is engraved across the centre of the screen and always visible in the microscopeeye piece.Another scale is an illuminated vertical scale fixed across the centre of the screen and

the reflected image of the illuminated scale is received at right angles of the fixed scale, and thetwo scales, in the position intersect each other.

Thus the reading on illuminated scale measures angular deviations from one axis at 90 to theoptical axis, and the reading on the fixed datum scale measures the deviations about an axismutually perpendicular to the other two.Thus the change in angular position of the reflector intwo planes is indicated by change in the point of intersection of two scales.


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ERRORS

Errors are broadly classified in three categories :

Systematic error

Random error

Gross error

A systematic error impacts accuracy of the measurement. Accuracy means how close is themeasurement with respect to true value. A true value of a quantity is a measurement, whenerrors on all accounts are minimized. We should distinguish accuracy of measurement withprecision of measurement, which is related to the ability of an instrument to measure valueswith greater details (divisions).

The measurement of a weight on a scale with marking in kg is 79 kg, whereas measurement ofthe same weight on a different scale having further divisions in hectogram is 79.3 kg. The laterweighing scale is more precise. The precision of measurement of an instrument, therefore, is afunction of the ability of an instrument to read smaller divisions of a quantity.

True value of a quantity is an unknown. We can not know the true value of a quantity, even ifwe have measured it by chance as we do not know the exact value of error in measurement.We can only approximate true value with greater accuracy and precision.

An accepted true measurement of a quantity is a measurement, when errors on all accountsare minimized.

Accuracy means how close is the measurement with respect to true measurement. It isassociated with systematic error.

Precision of measurement is related to the ability of an instrument to measure values ingreater details. It is associated with random error.

1. Systematicerror

A systematic error results due to faulty measurement practices. The error of this category ischaracterized by deviation in one direction from the true value. What it means that the error is

introduced, which is either less than or greater than the true value. Systematic error impacts theaccuracy of measurement not the precision of the measurement.

Systematic error results from :

faulty instrument

faulty measuring process


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personal bias

Clearly, this type of error cannot be minimized or reduced by repeated measurements. A faultymachine, for example, will not improve accuracy of measurement by repeating measurements.

1.1 Instrument error

A zero error, for example, is an instrument error, which is introduced in the measurementconsistently in one direction. A zero error results when the zero mark of the scale does notmatch with pointer. We can realize this with the weighing instrument we use at our home. Often,the pointer is off the zero mark of the scale. Moreover, the scale may in itself be not uniformlymarked or may not be properly calibrated. In vernier calipers, the nine divisions of main scaleshould be exactly equal to ten divisions of vernier scale. In a nutshell, we can say that theinstrument error occurs due to faulty design of the instrument. We can minimize this error byreplacing the instrument or by making a change in the design of the instrument.

1.2 Procedural error

A faulty measuring process may include inappropriate physical environment, proceduralmistakes and lack of understanding of the process of measurement. For example, if we arestudying magnetic effect of current, then it would be erroneous to conduct the experiment in aplace where strong currents are flowing nearby. Similarly, while taking temperature of humanbody, it is important to know which of the human parts is more representative of bodytemperature.

This error type can be minimized by periodic assessment of measurement process andimprovising the system in consultation with subject expert or simply conducting an audit of themeasuring process in the light of new facts and advancements.

1.3 Personal bias

A personal bias is introduced by human habits, which are not conducive for accuratemeasurement. Consider for example, the reading habit of a person. He or she may have thehabit of reading scales from an inappropriate distance and from an oblique direction. Themeasurement, therefore, includes error on account of parallax.

We can appreciate the importance of parallax by just holding a finger (pencil) in the hand, whichis stretched horizontally. We keep the finger in front of our eyes against some reference marking


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in the back ground. Now, we look at the finger by closing one eye at a time and note the relativedisplacement of the finger with respect to the mark in the static background. We can do thisexperiment any time as shown in the figure above. The parallax results due to the angle atwhich we look at the object.

It is important that we read position of a pointer or a needle on a scale normally to avoid error on

account of parallax.

2. Random errors

Random error unlike systematic error is not unidirectional. Some of the measured values aregreater than true value; some are less than true value. The errors introduced are sometimespositive and sometimes negative with respect to true value. It is possible to minimize this type oferror by repeating measurements and applying statistical technique to get closer value to thetrue value.

Another distinguishing aspect of random error is that it is not biased. It is there because of the

limitation of the instrument in hand and the limitation on the part of human ability. No humanbeing can repeat an action in exactly the same manner. Hence, it is likely that same personreports different values with the same instrument, which measures the quantity correctly.

2.1 Least count error

Least count error results due to the inadequacy of resolution of the instrument. We canunderstand this in the context of least count of a measuring device. The least count of a deviceis equal to the smallest division on the scale. Consider the meter scale that we use. What is itsleast count? Its smallest division is in millimeter (mm). Hence, its least count is 1 mm i.e. 103 mi.e. 0.001 m. Clearly, this meter scale can be used to measure length from 103 m to 1 m. It isworth to know that least count of a vernier scale is 104 m and that of screw gauge and

spherometer 105 m.

Returning to the meter scale, we have the dilemma of limiting ourselves to the exactmeasurement up to the precision of marking or should be limited to a step before. For example,let us read the measurement of a piece of a given rod. One end of the rod exactly matches withthe zero of scale. Other end lies at the smallest markings at 0.477 m (= 47.7 cm = 477 mm). Wemay argue that measurement should be limited to the marking which can be definitely relied. Ifso, then we would report the length as 0.47 m, because we may not be definite about millimeterreading.

This is, however, unacceptable as we are sure that length consists of some additional length only thing that we may err as the reading might be 0.476 m or 0.478 m instead of 0.477 m.

There is a definite chance of error due to limitation in reading such small divisions. We would,however, be more precise and accurate by reporting measurement as 0.477 some agreedlevel of anticipated error. Generally, the accepted level of error in reading the smallest division isconsidered half the least count. :


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2.2 Mean value of measurements

It has been pointed out that random error, including that of least count error, can be minimizedby repeating measurements. It is so because errors are not unidirectional. If we take average ofthe measurements from the repeated measurements, it is likely that we minimize error bycanceling out errors in opposite directions.

Here, we are implicitly assuming that measurement is free of systematic errors. The ave ragingof the repeated measurements, therefore, gives the best estimate of true value. As such,average or mean value ( am ) of the measurements (excluding "off beat" measurements) is thenotional true value of the quantity being measured. As a matterof fact, it is reported as truevalue, being our best estimate.

am=(a 1+ a2+ a3+ a4...+an)/n

3. Gross Errors : -

The class of error mainly covers human mistake in reading instruments recording andcalculating result.The responsibility of the mistake normal lies with the experimental. The experimental maygrossly misreal the scale. For example, he may, due to oversight, read 31.5 degree C implaceof 35.1 degree C (actually reading ). Error in recording but as long as human being involvead,some gross errors will definility being committee. Although complete elimination of gross error isimpossible, one should try to anticipate & correct them.These can be avoided by two means :-> Great care should be taken with reading & recording the data.> 2, 3 or more reading should be taker for the quantity under measurement.

Reducing Measurement Error

So, how can we reduce measurement errors, random or systematic? One thing you can do is topilot test your instruments, getting feedback from your respondents regarding how easy or hardthe measure was and information about how the testing environment affected theirperformance. Second, if you are gathering measures using people to collect the data (asinterviewers or observers) you should make sure you train them thoroughly so that they aren'tinadvertently introducing error. Third, when you collect the data for your study you shoulddouble-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 yourdata 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 rathersimple formulas you can apply directly to your data to very complex modeling procedures for

modeling the error and its effects. Finally, one of the best things you can do to deal withmeasurement errors, especially systematic errors, is to use multiple measures of the sameconstruct. Especially if the different measures don't share the same systematic errors, you willbe able to triangulate across the multiple measures and get a more accurate sense of what'sgoing on.

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Errors, Com Para Tors, And Angular Measurements

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