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Chapter 6

Comparators

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All measurements require the unknown quantity to be compared with a known quantity, called a standard.

There are certain devices in which the standards are separated from the instrument. It compares the unknown length with the standard. Such measurement is known as comparison measurement and the instrument, which provides such comparison, is called a comparator.

Comparators are generally used for linear measurements, and various comparators available differ basically in the methods employed for amplifying and recording the variations measured.

Introduction

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Any instrument used to compare size of work piece to known standard

High degree of accuracy and precision

The scale should be linear and have a wide range

High amplification

Good resolution

Comparator should be versatile

Functional Requirements

3

Mechanical comparators

Mechanical‐optical comparator

Electrical and electronic comparators

Pneumatic comparators

Other types such as projection comparators, multi‐check comparators, etc.

Classification of Comparators

4

Mechanical Comparators

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Dial Indicators

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Dial Indicators

It is primarily used to compare work‐pieces against a master

It consists of a body with a circular graduated dial, a contact point connected to a gear train and an indicating hand, which directly indicates the linear displacement of the contact point.

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With the plunger set to approximately mid‐position, the face dial is set to read zero.

Dial Indicators

From this zero reference point, two rules apply:

• As the plunger moves out of the case, the needle travels counter‐clockwise...giving a NEGATIVE reading.

• As the plunger moves into the case, the needle travels clockwise...giving a POSITIVE reading.

Johansson Mikrokator

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A light pointer made of glass fixed to a thin twisted metal strip

While one end of the strip is fixed to an adjustable cantilever link, the other end is anchored to a bell crank lever

Any linear motion of the plunger will result in a movement of the bell crank lever, which exerts either a push or pull force on the metal strip.

Accordingly the glass pointer will rotate either clockwise or anti‐clockwise depending on the direction of plunger movement

A calibrated scale is employed with the pointer, so that any axial movement of the plunger can be conveniently recorded.

Johansson Mikrokator

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Mechanical Optical Comparators

13

As the name of the comparator itself suggests, this is a part mechanical and part optical comparator. Small displacements of a measuring plunger are initially amplified by a lever mechanism pivoted about a point as shown in figure.

Mechanical Optical Comparator

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Optical projector is a versatile comparator, which is widely used for inspection purpose.

It is especially used in tool room applications.

It projects a two‐dimensional magnified image of the work‐piece on to a viewing screen to facilitate measurement.

Optical Projector

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Profile optical projector comparator

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Electrical Comparators

They are in widespread use because of their instantaneous response and convenience to amplify the input.

Electronic comparator, in particular, can achieve exceptionally high magnification.

The mechanism carrying the pointer is very light and not sensitive to vibrations.

As the instrument is usually operated on A.C. supply, the cyclic vibration substantially reduces errors due to sliding friction.

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Disadvantages Heating of coils in the measuring unit may cause zero drift and alter

the calibration. This is usually more expensive than mechanical instrument.

The plunger is the sensing element, the movement of which displaces an armature inside a pair of coils. Movement of the armature causes change in inductance in the two coils, resulting in a net change in inductance.

This change causes imbalance in the bridge circuit, resulting in an output.

The output display device, whether it is analog or digital, is calibrated to show the readings in units of length, that is, linear displacement.

Elements of Electrical Comparator

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Electrical ComparatorsAURA MAKE ELECTRONIC COMPARATOR

COUNTER: A single line Display ‐Counter unit is provided which displays Signal from probe in digital form. Resolutionof this unit is Selectable ‐ 0.0001 m.m, 0.001 mm.

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Electrical Comparators

Electronic Gage

An electronic gage for measuring bore diameter. The measuring head is equipped with three carbide‐tipped steel pins for wear resistance. The LED display reads 29.158 mm. Source: Courtesy of TESA SA.

The movement at the probe tip actuates inductance transducer which is supplied with an a.c. source from the oscillator.

The transducer converts this movement into an electrical signal which is then amplified and fed via an oscillator to the demodulator.

The current in D.C. form, then passes to the meter and the probe tip movement is displayed as a linear measurement over a circular scale.

Sigma Electronic Comparator

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Sigma Electronic Comparator

Air Gauges or Pneumatic Comparators

Used to compare work piece dimensions with master gauge by means of air pressure or flow.

Pneumatic gauge provide gauging of several features at once, it has become essential part of production inspection in the industry.

It is possible to gauge length, diameter, parallelism, concentricity, etc using a simple set up.

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Two types:1. Flow ( Indicates air velocity)2. Pressure (indicates air pressure in system)

Compressed air with a pressure in the range 1.5 to 2 bars is passed through a tapered glass column, which contains a small metal float.

The air then passes through a rubber or plastic hose and exits to the atmosphere through the orifice in the gauging head.

Since the gauging head is inserted inside the work part, which is being inspected, there is a small clearance between the gauging head and the work part.

This restricts the flow of air, thereby changing the position of the float inside the tapered glass column.

Flow Air Gauge

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Rate of flow proportional to clearance Gage set to master Work piece larger than

hole size, float rises Smaller, float falls

Flow Air Gauge

Source: Mahr, S 1840 PE

This system uses a two orifice arrangement as shown in figure above. While the orifice O1 is called the control orifice, the orifice O2 is referred to as the measuring orifice.

The measuring head gets compressed air supply at a constant pressure ‘P’, which is called the source pressure

Depending upon the gap d, the back pressure Pb changes, thereby providing a means for measuring dimension ‘d’.

Back Pressure Gauge

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In the set up shown in figure above, the back pressure is let into a bourdon tube, which undergone deflection depending on the magnitude of air pressure. This deflection of the bourdon tube is amplified by lever and gear arrangement and indicated on a dial.

Back Pressure Gauge

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Back Pressure Gauge

Mahr Federal Micro‐Dimensionair

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• Holes may be checked for taper, out-of-roundness, concentricity, and irregularity

• Gage does not touch workpiece• Gaging heads last longer than fixed gages• More than one diameter may be checked at same time.

Advantages of Air Gauges

Pneumatic gauging is one of the widely used methods for inspection of holes.

The gauging elements can be adapted to measure nearly any feature of the hole including diameter, roundness, squareness and straightness.

Applications of Pneumatic Comparators

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Engineering Metrology

Prof. J. Ramkumar

Department of Mechanical EngineeringIIT Kanpur

October 24, 2017

Outline

Introduction and Types of Instruments

Engineering Tolerance

Common Metrology Instruments

Common Metrology Instruments

coordinate measuring machine (CMM)

Introduction to Metrology

I Metrology is the science of measurement

I Dimensional metrology is that branch of Metrology whichdeals with measurement of dimensions of a part or workpiece(lengths, angles, etc.)

I Dimensional measurements at the required level of accuracyare the essential link between the designer’s intent and adelivered product.

I The width, depth, angles and other dimensions all must beproduced and measured accurately for the machine tool tofunction as expected.

I Note: Metrology is a vast area. In this lecture, the mainfocus on Dimensional Metrology

Dimensional Metrology Needs

I Linear measurements

I Angular measurements

I Geometric form measurements(Roundness, Straightness,Cylindricity, Flatness etc.)

I Geometric relationships(Parallel, perpendicular,Concentric,runout etc.)

I Controlled surface texture

Types of Measurement and Instruments Used

Linear Measurement Devices

I Vernier Caliper: It is a visual aid that allows the user tomeasure more precisely than could be done unaided whenreading a uniformly divided straight or circular measurementscale.

Least count: The least count of a measuring instrument isthe smallest change in the measured quantity that can beresolved on the instrument’s scale


Least count of Vernier: It is the difference between the value ofone Main scale division and the value of one Vernier scale division.Let the smallest main scale reading, that is the distance betweentwo consecutive graduations (also called its pitch) be S and thedistance between two consecutive Vernier scale graduations be Vsuch that the length of (n-1) main scale divisions is equal to nVernier scale divisions.Then,the length of (n-1) main scale divisions = the length of n vernierscale divisionor, (n-1)S=nVor, nS-S=nVor, S/n = S − Vor (Pitch)/(Number of Vernier scale divisions) = (Length of onemain scale division − Length of one Vernier scale division)So, S/n and (S − V ) are both equal to the least count of vernierscale.


Example-1: Ten divisions on the vernier scale coincide with 9smallest divisions on the main scale (mm), Main scale Reading is2.6 cm and vernier scale coincides with 7 division of the main scale.a) Calculate the Least Count(L.C.) of the vernier scale.b) Calculate the observed reading.Solution: L.C. = Value of one main scale division - Value of onevernier scale divisionL.C. = 1 mm−9/10mm = 0.1mm = 0.01cmObserved Reading = Main scale reading + Vernier scale readingObserved Reading = 2.6 cm + 7 x L.C.Observed Reading = 2.6 cm + 7 x 0.01 cmObserved Reading = 2.67 cm


I Analog and Digital Micrometers:

(a) A vernier (analog) micrometer(Similar to Vernier caliper).(b) A digital micrometer with a range of 0 to 1 in. (0 to 25mm) and a resolution of 50 µin. (1.25 µm). It is generallyeasier to read dimensions on this instrument compared to theanalog micrometer

Angle Measuring Instruments

I Universal Bevel Protractor1) It is an angular measuring instrument capable of measuringangles to within 5 min2) The name universal refers to the capacity of the instrumentto be adaptable to a great variety of work configurations andangular interrelations.

Angle Measuring Instruments

I Sine Bar1) A sine bar is made up of a hardened steel beam having aflat upper surface.2) The bar is mounted on two cylindrical rollers and the axesof the two rollers are parallel to each other.3) The accuracy attainable with this instrument is quite high.

Angle Measuring InstrumentsUse of Sine Bar for Angle Measurement

sinθ =h

L(1)

For error in angle measurement, differentiating h with respect to θ,we have

dθ

dh=

secθ

L(2)

Therefore, the error in angle measurement dθ, due to an error dhin height h is proportional to secθ.

Measuring Roundness

Measuring Profiles

coordinate measuring machine (CMM)

I It is a device for measuring the physical geometricalcharacteristics of an object.

I Measurements are defined by a probe attached to the thirdmoving axis of this machine.

I Probes may be mechanical, optical, laser, or white light,among others.

Repeatability

I Repeatability is the consistency of a single appraiser tomeasure the same part multiple times with the samemeasurement system.

I it is related to the standard deviation of the measured values.

Reproducibility

Measurement Error

I Measurement Error is the statistical summing of the errorgenerated by Repeatibility (the variation within an appraiser)and Reproducibility (the variation between appraisers)

σerror =√σ2repeatability + σ2reproducibility (3)

where σrepeatability and σreproducibility are the standarddeviations of the measured values in repeatability andreproducibility.The formula for standard deviation is

σ =

√√√√√ N∑i=1

(xi − x̄)2

N − 1(4)

where xi is the measured value and x̄ is the mean value and Nis the number of observations in the sample

Example of Standard DeviationI Here, if we calculate the standard deviation of your marks

then xi is the individual’s marks and x̄ is the mean of classmarks and N is the number of students.

I This normal distribution includes your real marks(Mid-sem+Quiz+Lab exercise+lab Reports+Drawing)

Introduction to Engineering Tolerance

I Definition: The allowable deviation from a standard.

I Tolerance is the total amount a dimension may vary and is thedifference between the upper (maximum) and lower(minimum) limits.

I Types of Tolerance: Dimensional and Geometrical

I Allowance for a specific variation in the size of part is calledDimensional Tolerance.

I Allowance for a specific variation in the geometry of part iscalled Geometrical Tolerance.

I Tolerances are used to control the amount of variationinherent in all manufactured parts.

I One of the great advantages of using tolerances is that itallows for interchangeable parts, thus permitting thereplacement of individual parts.

Tolerance in relation to Cost

I Cost generally increases with smaller tolerance-Small tolerances cause an exponential increase in cost-Therefore your duty as an engineer have to consider : Doyou need φ1.0001cm or is 1.01cm good enough?

I Parts with small tolerances often require special methods ofmanufacturing.

I Parts with small tolerances often require greater inspectionand call for the rejection of parts → Greater QualityInspection → Greater cost.

I Do not specify a smaller tolerance than is necessary!

Dimensional Tolerance representation

Important Terms in Tolerancing

I Shaft: A term used by convention to designate all externalfeatures of a part, including those which are not cylindrical.

I Hole: A term used by convention to designate all internalfeatures of a part, including those which are not cylindrical.


I Basic Size: the nominal diameter of the shaft (or bolt) andthe hole. This is, in general, the same for both components.

I Actual Size: the measured size of the finished part aftermachining.

I Zero Line: It is a straight line corresponding to the basicsize. The deviations are measured from this line. The positiveand negative deviations are shown above and below the zeroline respectively.

I Limits of Size: The term limits of size referred to the twoextreme permissible sizes for a dimension of a part(hole orshaft), between which the actual size should lie.

I Maximum Limit of Size: The greater of the two limits ofsize of a part(Hole or shaft).


I Minimum Limit of Size: The smaller of the two limits ofsize of a part(Hole or shaft).

I Allowance: It is the difference between the basic dimensionsof the mating parts.When the shaft size is less than the hole size, then theallowance is positive and when the shaft size is greater thanthe hole size, then the allowance is negative.

I Tolerance: It is the difference between the upper limit andlower limit of a dimension.


I Tolerance Zone: It is the zone between the maximum andminimum limit size.

I Upper Deviation: It is the algebraic difference between themaximum size and the basic size.The upper deviation of a hole is represented by a symbol ES(Ecart Superior) and of a shaft, it is represented by es.

I Lower Deviation: It is the algebraic difference between theminimum size and the basic size.The lower deviation of a hole is represented by a symbol EI(Ecart Inferior) and of a shaft, it is represented by ei.

Tolerancing Example

Fit Types

I Clearance fit occurs when two toleranced mating parts willalways leave a space or clearance when assembled.

I Interference fit occurs when two toleranced mating parts willalways interfere when assembled.

I Transition fit occurs when two toleranced mating parts willsometimes be an interference fit and sometimes be a clearancefit when assembled.

Example of Fits

Clearance Fit

I In clearance fit, an air space or clearance exists between theshaft and hole

I Such fits give loose joint.

I A clearance fit has positive allowance, i.e. there is minimumpositive clearance between high limit of the shaft and lowlimit of the hole.

I Allows rotation or sliding between the mating parts.

Types of Clearance Fit

I Loose Fit: It is used between those mating parts where noprecision is required. It provides minimum allowance and isused on loose pulleys, agricultural machineries etc.

I Running Fit: For a running fit, the dimension of shaft shouldbe smaller enough to maintain a film of oil for lubrication. Itis used in bearing pair etc.

I Slide Fit or Medium Fit: It is used on those mating partswhere great precision is required. It provides mediumallowance and is used in tool slides, slide valve, automobileparts, etc.

Interference Fit

I A negative difference between diameter of the hole and theshaft is called interference.

I In such cases, the diameter of the shaft is always larger thanthe hole diameter.

I It used for components where motion, power has to betransmitted.

I Interference exists between the high limit of hole and low limitof the shaft.

Types of Interference Fit

I Shrink Fit or Heavy Force Fit: It refers to maximumnegative allowance. In assembly of the hole and the shaft, thehole is expanded by heating and then rapidly cooled in itsposition. It is used in fitting of rims etc.

I Medium Force Fit: These fits have medium negativeallowance.Considerable pressure is required to assemble thehole and the shaft. It is used in car wheels, armature ofdynamos etc.

I Tight Fit or Force Fit: One part can be assembled into theother with a hand hammer or by light pressure. A slightnegative allowance exists between two mating parts (morethan wringing fit). It gives a semipermanent fit and is used ona keyed pulley and shaft, rocker arm, etc.

Transition Fit

I It may result in either clearance fit or interference fitdepending on the actual value of the individual tolerances ofthe mating components.

I Transition fits are a compromise between clearance andinterference fits.

I They are used for applications where accurate location isimportant but either a small amount of clearance orinterference is permissible.

Types of Transition Fit

I Push Fit or Snug Fit: It refers to zero allowance and a lightpressure is required in assembling the hole and the shaft. Themoving parts show least vibration with this type of fit.

I Force Fit or Shrink Fit: A force fit is used when the twomating parts are to be rigidly fixed so that one cannot movewithout the other. It either requires high pressure to force theshaft into the hole or the hole to be expanded by heating. It isused in railway wheels, etc.

I Wringing Fit: A slight negative allowance exists between twomating parts in wringing fit. It requires pressure to force theshaft into the hole and gives a light assembly. It is used infixing keys, pins, etc.

Specifications of Tolerancing

where IT represents International tolerance

Standard Hole Basis Table

Hole Basis System; Fits

Shaft Basis System; Fits

Example

I Answer: Allowance: -0.1mmClearance: 0.05mmType of Fit: Transition FitSolve it!

...........

Thank You

Steam Condensers Steam condenser-its functions - Classifications – surface and jet condensers- Low level - High level Jet condenser and Ejector condenser - Shell and Tube Surface condenser - down flow - Central flow Surface - Evaporative condenser -Advantages and Disadvantages - Formulae for calculation cooling water required, Condenser efficiency - corrected vacuum, Absolute pressure and Vacuum efficiency - Simple problems on Steam condensers - Air Extraction, Types of Air Extraction systems, Dry-air Extraction and Wet-air Extraction systems, Air pump and Steam –Jet Air Ejector Steam condenser is a device in which the exhaust steam from steam turbine is condensed by means of cooling water. The main purpose of a steam condenser in turbine is to maintain a low back pressure on the exhaust side of the steam turbine Steam Condenser – Definition, Working, Types and Advantages Steam Condenser is a mechanical device which converts the low pressure exhaust steam from the turbine into water. Or in other words it is a device which is used to condense exhaust steam of the turbine into water. It does so with the help of cooling water circulated into it from the cooling tower. works to achieve two main objectives 1. To maintain low pressure (below atmospheric pressure) at the outlet of the steam turbine so as to obtain the maximum possible energy. 2. To supply pure feed water to the hot well and from hot well the water is again pumped to the boiler with the help of boiler feed pump. Requirements of Steam Condensing Plant The principle requirements of steam condensing plant are: Steam Condensing Plant

1. Condenser: It is a closed vessel used to condense the steam. The low pressure steam gives off its heat to the coolant (here water from cooling tower) and gets converted into water

during the process of condensation. 2. Condensate Extraction Pump: It is a pump which is installed in between the condenser and

hot well. It transfers the condensate from the condenser to the hot well. 3. Hot Well: It is a sump that lies in between the condenser and boiler. It receives the

condensate from the condenser by condensate pump. The feed water is transferred from the hot well to the boiler.

4. Broiler Feed Pump: It is a pump installed in between the hot well and boiler. It pumps the feed water from the hot well to the boiler. And this is done by increasing the pressure of condensate above boiler pressure.

5. Air Extraction Pump: It is a pump used to extracts or removes the air from the steam condenser.

6. Cooling Tower: It is a tower which contains the cold water and this water is made to circulate within the condenser for cooling of steam.

7. Cooling Water Pump: It is a pump lies in between the cooling tower and condenser. It circulates the cooling water through the condenser.

Working The steam condenser receives the exhaust steam from one end and comes in contact with the cooling water circulated within it form the cooling tower. As the low pressure steam comes in contact with the cooling water, it condenses and converts into water. It is connected to the air extraction pump and condensate extraction pump. After the condensation of steam, the condensate is pumped to the hot well with the help of condensate extraction pump. The air extraction pump extracts the air from the condenser and creates the vacuum inside it. The vacuum created helps in the circulation of cooling water and flow of condensate downward. Classification of Steam Condenser The steam condenser is classified as 1. Jet condensers or mixing type condenser 2. Surface condenser or non-mixing type condenser Jet Condenser Jet condenser is a condenser in which the condensate gets mixed with the cooling water. That’s why it is also called as mixing type condenser. This type of condenser is used sometime because it lost some of the condensate and requires high power for the pump during the process of condensation. In jet condenser, as the condensate is not free from the salt, so it cannot be used as feed water for the boiler. It can be used at the place where sufficient amount of good quality water is available. Types of Jet Condenser

(i) Parallel Flow Jet Condenser In parallel flow jet condenser, the steam and water enters into the condenser at the top and leaves at the bottom. The cooling water and steam enters at the top. As both steam and cooling water mix with each other, the steam gets condense. The condensate, cooling water and air moves downward and it is removed by two separate pumps known as air extraction pump and condensate extraction pump. The condensate pump transfers the condensate to the hot well and from there the extra water is

made to flow in cooling water tank or pond through overflow pipe ii) Counter Flow or Low Level Jet Condensers In counter Flow or low level jet condensers, the steam enters at the bottom and the cooling water at the top. The steam flows upward and meets the cooling water coming downward. In these types of steam Condensers, the air pump is located at the top. Air pump creates vacuum and this vacuum draws water from the cooling tower. The cooling water enter into the condenser and falls on the perforated conical plate. The perforated conical plates convert the cooling water into a large number of jets as shown in the figure. The falling jet of water caught in the trays and from there it escapes out in second series of jets and meets the exhaust steam entering at the bottom. As the steam mix with the water, it gets condense. The condensate and cooling water moves down through a vertical pipe to the condensate pump. And finally the pump delivers it to the hot well. iii) Barometric or High Level Jet Condenser

Barometric or high level jet condensers are provided at high level with a long vertical discharge tube or tailpipe. It does not have condensate extraction pump and the condensate and cooling water flows in the hot well because of the gravity. An injector pump is used to flow cooling water at the top of the condenser. These types of jet condensers are used at a high level with a vertical discharge pipe. In this condenser, the steam enters at the bottom and flows in upward direction and meets with the down coming cooling water. Its working is similar as the low level jet condenser. The vacuum is created at the top of the condenser shell. With the help of vacuum and injector pump, the cooling water is moved to the top of the condenser. The condensate and cooling water comes down in the hot well through a long vertical discharge pipe. And finally the extra hot water flows to the cooling tank or cooling pond by an overflow pipe (iv) Ejector Condenser

In ejector condensers, it has a non-return valve through which exhaust steam enters, hollow truncated cones, and diverging cone. In these condensers, the cooling water is injected at the top. The steam enters into the condenser through a non-return valve. The steam and water mixes with each other while passing through series of hollow truncated metal cones and steam changes into water. At the end of the metal cones a diverging cone is present. When the condensate passes through diverging cone, its kinetic energy is partly transformed into pressure energy.The condensate and cooling water is then discharged to the hot well.

Surface Condensor

Surface condenser is a type of steam condenser in which the steam and cooling water do not mix with each other. And because of this, the whole condensate can be used as boiler feed water. It is also called as non-mixing types condenser. The figure above shows the longitudinal section of a two pass surface condenser. It consists of a horizontal cylindrical vessel made of cast iron and packed with tubes. The cooling water flows through these tubes. The ends of the condensers are cut off by the perforated type plates. The tubes are fixed into these perforated type plates. It is fixed in such a manner that any leakage of water into the center of condensing space is prevented. The water tubes are passed horizontally through the main condensing space. The exhaust steam from the turbine or engine enters at the top and forced to move downward due to the suction of the air extraction pump. In this steam condenser, the cooling water enters into boiler through lower half of the tubes in one direction and returns in opposite direction through the upper half as shown in the figure above. This type of condenser is used in ships as it can carry only a limited quantity of water for the boiler. It is also widely used for the land installation where there is a scarcity of good quality of water Types of Surface Condensers The surface condenser on the basis of direction of flow of condensate, the arrangement of the tubing system and the position of the extraction pump are classified as 1. Down flow 2. Central flow 3. Regenerative 4. Evaporative The steam in down flow condenser flows perpendicular to the direction of flow of cooling water, so it is also called as cross-surface condenser In central flow condenser, the steam enters at the top of the condenser and flows in downward direction. In this the suction pipe of the air extraction pump is provided in the center of the tube nest as shown in the figure. Due to this placement of the suction pipe in the center of the tube nest, the exhaust steam flows radially inward over the tubes towards the suction pipe. The condensate is collected at the bottom of the condenser and pumped to the hot well.

In regenerative surface condensers, the condensate is heated by the use of regenerative method. In that the condensate is passed through the exhaust steam coming out from the turbine or engine. This raises its temperature and it is used as the feed water for the boiler.

In evaporative surface condensers, the steam enters at the top of the condenser in a series of pipes over which a film of cold water is falling. At the same time, current of air is made to circulate over the film of water. As the air circulates over the water film, it evaporates some of the cooling water. As a result of this rapid evaporation, the steam circulating inside the series of pipes gets condensed. Remaining cooling water that left is collected at an increased temperature and reused. It is brought to the original temperature by adding required quantity of cold water.

Advantages of Steam Condenser It increases the efficiency of the plant. It reduces the back pressure of the steam and as a result of this, more work can be done. It reduces the temperature of the exhaust steam and this allows to obtain more work.

It allows the reuse of condensate for the feed water and hence reduces the cost of power generation. The temperature of the condensate is more than the feed water. This reduces the supply of heat per kg of steam. Comparison of Jet and Surface Condenser in Tabular Form

S No

Jet Condenser Surface Condenser

1 Exhaustp steam and cooling water mixed with each other

Exhaust steam and cooling water are not mixed with each other.

2 It is less suitable for high capacity plants It is more suitable for high capacity plants

3 It is more suitable for high capacity plants

The condensing plant using surface condenser is costly and complicated.

4 Condensate is wasted and cannot be reused

The condensate is reused

5 Less quantity of circulating water is required

Large quantity of circulating water is required

6 It has low maintenance cost It has high maintenance cost

7 In jet condenser, more power is required for the air pump

In surface condenser, less power is required for the air pump

8 High power is required for water pumping

Less power is required for water pumping

Vacuumin Condenser: The vacuumin a condenser is defined as “The difference betweenbarometric pressure and absolute pressure in the condenser”. Vacuumcorrection to 760 mm of Hg: The vacuum gauge reading is corrected to standard reading I.e., 760 mm of Hg Corrected vacuum in mm of Hg = 760 – Absolute pressure in mm of Hg = 760 –Pabs The efficiency of the turbine depends on vacuum is maintained in the condenser Dalton’s law of partial pressures states that, “The pressure exerted by a mixture of air and vapour is equal to the sum of theindividual pressure of the each constituents of the mixture if it occupies the same space and temperature”. According to Dalton’slaw of partial pressure Pressure in the condenser, PC = Ps + Pa The absolute version is obtained from steam table’s, the pleasure of steam cards for 9 to temperature of mixture. Mass of air, maL………>Pa V = ma RT Vacuum Efficiency The vacuum efficiency may be defined as “the ratio of actual vacuum to the ideal vacuum I.e., maximum vacuum in the condenser”. Actual vacuum = Barometric reading – Actual pressure in the condenser Ideal vacuum = Barometric reading –Maximum absolute pressure in the condenser Vacuum efficiency, nv= Actual vacuum / Ideal vacuum = (Pb –Pab) / (Pb – Pc) Condenser Efficiency Condenser efficiency is defined as “the ratio of actual temperature rise of cooling water to the maximum permissible rise of temperature I.e., vacuum temperature – inlet cooling water”. Condenser efficiency,

nc= Actual temperature rise in cooling water / ( vacuum temp –inlet water cooling temperature) =(t2 – t1) / (that – t1) Mass of cooling water circulated in a condenser Heat lost by steam. = ms (h1 –h2) Heat gained by cooling water = mw Cpw (t2 – t1) Using energy balance in a condenser, Heat lost by the steam = Heat gained by the cooling water ms (h1 – h2) = mw Cpw (t2 – t1 Where, ms = mass of steam condensed , kg H1 = Enthalpy of condensate steam at inlet = hf1 + xhfg1 X = Dryness fraction of steam hf1 = Sensible heat of steam, kJ/kg ; hfg1 = Latent heat of steam kJ /kg h2 = Enthalpy of condensate at outlet = hf2 mw = mass of cooling water circulatedkgk Cpw = Specific heat of water = 4.187 kJ /kg K t2 = outlet temp of cooling water t1 = Inlet temp of cooling water Air pump is a machine which is used in the condenser to remove condensate air from the condenser. It is used in the condenser to remove both air and condensate from the condenser. There are two types of air pump available in the market. Dry air pump and wet Air pump The pump which extracts both condensate and air is called wet air pump and a pump which extracts only moist air is known as dry air pump. Sources of air in a condenser The following are the main sources for the air may enter into the condenser 1. The dissolved air in the feed water 2. Air leaks from atmosphere through various pipe joints which are internallyunder low pressure than atmosphere 3. In case of Jet condenser some air comes in cooling water in. which it is dissolved. Effects of air in a condenser Thea following are the important effects of the presence of air in a condenser 1. With increased amount of air condenser pressure increases this reduces the useful work done 2.presence of air Lowers the Pressure and saturation temperature of the steam due to this latent heat of steam increases and so more cooling water is required. 3. Air is a poor conductor of heat and hence reduces therate of heat transfer between cooling water and exhaust steam and hence efficiency of a condenser decreases 4. The presence of air reduces therate of condensation of exhaust steam 5. The air extraction pump is required to remove the air only but some quantity of air escapes with air this reduces the amount of condensate 6. Larger the amount of air present in the condenser, capacity of air pump increases and greater is the Corrosive action by the air. . Edward's Air Pump

Edward's air pump or reciprocating type air pump consists of a delivery valve or head valve. There is no suction and bucket valve present in the Edwards type air pump which is essential in ordinary reciprocating type air pump. This delivery valve or head valve is present on the top of the pump barrel level, see in the Edwards air pump sketch. A flat reciprocating piston of the pump is placed on its surface and conical at the bottom shown in the picture. The pump Lever has a ring of ports around its lower end for the whole circumference. This lever ring port communicates with condenser. edward's air pump In the Edward's air pump chamber, when the reciprocating piston is at the top position the condensate and air from the condenser enter into the pump in the conical portion of the lower part of the barrel through the ports.It stores at the lower portion of the pump's chamber and at this positon covers the ports.Now the piston starts to fall down from upward position and a vacuum is created at the top of the piston due to head valve is closed by water.Now ports are open.Again piston moves at downwards, mixture of condensate, vacuum, and air enters at the top of the piston. This mixture is compressed and its pressure will be slightly above the atmosphere pressure when piston starts to move in upward direction. At this position deliver valve is open, which allow the mixture to pass on the top of the cover. A relief valve is placed in the base of the cylinder to release the pressure.

Steam Jet Ejectors Type 555 Vacuum Ejector Steam jet Ejectors are based on the ejector-venturi principal and operate by passing motive steam through an expanding nozzle. The nozzle provides controlled expansion of the motive steam to convert pressure in to velocity which creates a vacuum with in the body chamber to draw in and entrain gases or vapours. The motive steam and suction gas are then completely mixed and then passed through the diffuser or tail, where the gases velocity is converted in to sufficient pressure to meet the predetermined discharge pressure. Vacuum Ejectors are used in a variety of applications in the process, food, steel and petrochemical industries. Typical duties involve filtration, distillation, absorption, mixing, vacuum packaging, freeze drying, dehysrating and degassing. Ejectors will handle both condensible and none condensible gas loads as well as small amounts of solids or liquids, however accidental entrainment of liquids can cause a momentary interruption in vacuum but this will not cause damage to the ejector. Primary advantages over other vacuum pumps can be seen below: No Moving Parts - Ejectors are exceedingly simple and reliable. There are no moving parts to wear or break in a basic ejector. Low Cost - Units are small in relation to the work they do and cost is correspondingly low. Versatile - Various piping arrangements permit adapting to environmental conditions. Self Priming - Ejectors are self-priming. They operate equally well in continuous or intermittent service. Easy to Install - Relatively light in weight, ejectors are easy to install, and require no foundations. Even multi stage units are readily adaptable to existing conditions. Corrosion and Erosion Resistant - Because they can be made of practically any workable material, or coated with corrosion-resistant materials, ejectors can be made highly resistant erosion and corrosion. High Vacuum Performance - Ejectors can handle air or other gases at suction pressures as low as 3 microns HgA. Ejectors range from Single upto Six Stage units, and can be either Condensing or Non-Condensing types. The number of Ejector stages required are usually determined by the economy of the ejectors and the level of vacuum required. The operating range for each stage of Vacuum Ejector can be seen below, also for reference 1 BarA = 760 mm HgA. 1st Stage : 810mm HgA - 30mm HgA 2nd Stage : 130mm HgA - 3 mm HgA 3rd Stage : 25mm HgA - 0.8mm HgA 4th Stage : 4mm HgA - 75 microns HgA 5th Stage : 0.4mm HgA - 10 microns HgA 6th Stage : 0.1mm HgA - 3 microns HgA Single Stage Ejectors Single stage Vacuum Ejectors generally cover vacuum ranges from 30mm HgA up to atmospheric pressure. To maximise performance eight different designs are available with each ejector being optimised to operate in a specific vacuum range. This allows the motive steam consumption to be kept at a minimum for the selected ejector, and also ensures that operation will be stable. All single stage ejectors are designed to discharge either at or slightly above atmospheric pressure. Sizes range from 1 Inch to 6 Inch, however large size are available if required. Standard materials of construction are carbon steel or stainless steel, both of which are fitted with a stainless steel nozzle.

Two Stage Ejectors Staging of Ejectors is required for more economical operation when the required absolute vacuum level is reduced. Two stage Vacuum Ejectors generally cover vacuum ranges between 3mm HgA to 130mm HgA, however depending up on actual operating conditions a Single Stage may be more economical if at the upper limit of the operational envelope, or a Three Stage Ejector System if conditions are at the lower end. In operation a two stage system consist of a primary High Vacuum (HV) Ejector and a secondary Low Vacuum (LV) Ejector. Initially the LV ejector is operated to pull vacuum down from the starting pressure to an intermediate pressure. Once this pressure is reached the HV ejector is then operated in conjunction with the LV ejector to finally pull vacuum to the required pressure. Two stage systems can also be either Condensing or Non-condensing types. Condensers can be used as pre-condensers, inter-condensers, and after-condensers, all of which help to reduce the gas load being passed on to the next ejector stage. This helps to reduce motive steam consumption and also allows smaller ejectors to be used with in the system. Depending up on the application Non-condensing systems can also be used, however this can be less efficient than Condensing Types as each ejector must entrain the full gas Three Stage Ejectors Three stage Vacuum Ejectors generally cover vacuum ranges between 0.8mm HgA to 25mm HgA, however depending up on actual operating conditions a Two Stage Ejector system may be more economical if at the upper limit of the operational envelope, or a Four Stage Ejector system if conditions are at the lower end. In operation a Three Stage system consist of a primary Booster, a secondary High Vacuum (HV) Ejector, and a tertiary Low Vacuum (LV) Ejector. As per the Two Stage System, initially the LV ejector is operated to pull vacuum down from the starting pressure to an intermediate pressure. Once this pressure is reached the HV ejector is then operated in conjunction with the LV ejector to pull vacuum to the lower intermediate pressure. Finally the Booster is operated (in conjunction with the HV & LV Ejectors) pull vacuum to the required pressure. Three stage systems are also usually of the Condensing type. Again as per the Two Stage system, condensers can be used as pre-condensers, inter-condensers, and after-condensers in order to reduce the gas load being passed on to the next ejector stage. Depending up on the application Non-condensing systems can also be used however this is less efficient than Condensing Types as each ejector must entrain the full gas load from the previous stage. Four, Five & Six Stage Ejectors These systems are similar to Three Stage Systems, however they include additional boosters which are equipped with Steam Jackets to prevent ice forming with in the ejectors. These systems are usually of the Condensing type to increase efficiency and reduce motive steam consumption.load from the previous stage. This can lead to ejectors becoming large and also increases motive steam consumption. Non-condensing types are usually used where it is not feasible to install condensers, or where service is intermittent, making operating costs a secondary consideration. Steam Jet Air Ejectors

Steam jet air ejectors have a low initial cost, so are an economical means and reliable equipment for producing a vacuum. The ejector design has basic advantages such as

absence of moving parts and simplicity of operation. The conventional steam jet ejector has four parts: the steam chest, the nozzle(s), the mixing chamber, and the diffuser; Figure

II/3.4-2 illustrates ejector operation. A high-pressure motivating fluid enters at the inlet of a converging–diverging nozzle and expands through it; the suction fluid enters at the steam chest and mixes with the motivating fluid in the mixing chamber; both are then recompressed through the diffuser.

It is one of the types of air ejector which is used in the steam like near the condenser to remove the non condensable gases and some vapour entering into main condenser by an air ejector and it is cooled by the main condensate and released in the ejector condenser.

The steam is used as the motive fluid to withdraw air and dissolved gases from the condenser by the ejector action. In each stage of the steam jet ejector, high pressure steam is expanded in a convergent /divergent nozzle. The steam leaves the nozzle at a very high velocity in the order of 1220 m/s and a proportion of the kinetic energy in the steam jet transferred by interchange of momentum to the body of air which entrained and passes along with the operating steam through a diffuser in which the kinetic energy of combined steam is re-converted to pressure energy.

The maximum pressure ratio that can be obtained with a single stage is roughly 5:1 and consequently it is necessary to use two or even three stages in series to establish a vacuum in the order of 724mm of Hg with reasonable steam consumption.

Chapter 8

Metrology of Surface Finish

If one takes a look at the topology of a surface, surface irregularities are superimposed on a widely spaced component of surface texture called waviness.

Surface Metrology Concepts

2

Surface irregularities arise primarily due to the following factors:

Feed marks of cutting tools Chatter marks on the work‐piece due to vibrations caused during the

manufacturing operation Irregularities on the surface due to rupture of work‐piece material

during metal cutting operation Surface variations caused due to deformation of work‐piece under

the action of cutting forces Irregularities in the machine tool itself such as lack of straightness of

guide ways

Surface Irregularities

3

Roughness

Waviness

Lay

Flaws

Surface texture

Error of Form

Terminology

4

5

Surface finish, also known a surface texture or surfacetopography, is the nature of a surface. It comprises the smalllocal deviations of a surface from the perfectly flat ideal (atrue plane).

Surface roughness, often shortened to roughness, is a component of surfacetexture. It is quantified by the deviations in the direction of the normal vector of areal surface from its ideal form. If these deviations are large, the surface is rough; ifthey are small, the surface is smooth.

Waviness is the measurement of the more widely spaced component of surface texture. It is a broader view of roughness because it is more strictly defined as "the irregularities whose spacing is greater than the roughness sampling length"

Lay is the direction of the surface pattern ordinarily determined by the production method used.

Terminology

Centre Line Average (Ra) Value

Analysis of Surface Traces

6

Roughness average Ra is the arithmetic average of theabsolute values of the roughness profile ordinates.

Ra is the universally recognized parameter of roughness.

Ten‐point height average (Rz) Value


7

Root Mean Square (R.M.S.) Value


8

Root mean square (RMS) roughness Rq is the root meansquare average of the roughness profile ordinates.

9


10

1. Root‐Means‐Square roughness (Ra or RMS)Closely related to the roughness average (Ra)Square the distances, average them, and determine the square root of the resultThe resulting value is the index for surface texture comparisonUsually 11% higher than the Ra value

2. Maximum Peak‐Valley Roughness (Rmax or Rt)Determine the distance between the lines that contact the extreme outer and inner

point of the profileSecond most popular method in industrySee figure A

3. Ten‐Point Height (Rz)Averages the distance between the five peaks and five deepest valleys within the

sampling lengthSee figure B

11


AFM Micrographs of surface structure of multilayers grown steel.

Symbols of Surface Texture

12

There are basically two approaches for the measurement of surface finish, namely, by comparison and direct measurement.

The former is the simpler of the two, but is more subjective in nature. The comparative method advocates assessment of surface texture by observation or feel of the surface.

Direct measurement enables a numerical value to be assigned to the surface finish.

Methods of Measuring Surface Finish

13

A skid or shoe drawn over the work‐piece surface such that it follows the general contours of the surface as accurately as possible. The skid also provides the datum for the stylus

A stylus which moves over the surface along with the skid, such that its motion vertically is relative to the skid. This factor enables the stylus to capture the contours of surface roughness independent of surface waviness.

An amplifying device for magnifying the stylus movements

A recording device to produce a trace or record of the surface profile

Stylus System of Measurement

14

This is a mechanical‐optical instrument designed by Dr Tomlinson of the National Physical laboratory of U.K.

Tomilson Surface Meter

15

The sensing element is the stylus, which moves up and down depending upon the irregularities of the work‐piece surface.

The stylus is constrained to move only in the vertical direction because of a leaf spring and a coil spring.

The tension in the coil spring P causes a similar tension in the leaf spring. These two combined forces hold a cross roller in position between the stylus and a pair of parallel fixed rollers.

A shoe is attached to the body of the instrument to provide the required datum for the measurement of surface roughness.

A diamond tip traces the profile of the work‐piece on a smoked glass sheet.

Tomilson Surface Meter

16

A stylus is attached to an armature, which pivots about the centre of piece of an ‘E’ shaped stamping. The outer legs of the E‐shaped stamping are wound with electrical coils. A pre‐determined value of alternating current (excitation current) is supplied to the coils.

The coils form part of a bridge circuit. A skid or shoe provides the datum to plot surface roughness. The measuring head can be traversed in a linear path by an electric motor.

Taylor Hobson Talysurf

17

As the stylus moves up and down due to surface irregularities, the armature is also displaced. This causes variation in the air gap and causes an imbalance in the bridge circuit.

The resulting bridge circuit output consists of modulation only. This is fed to an amplifier and caused to operate a pen recorder to produce a permanent record.

Taylor Hobson Talysurf

18

Skids simplify surface assessment while using stylus instruments. However, there is distortion because of phase relationship between the stylus and the skid.

In case A, the stylus and the skid are in phase. Therefore, roughness (the primary texture) will be relatively undistorted.

In case B, the two are out of phase. In this situation, waviness superimposes in the roughness reading and is misleading.

In case C also the stylus and skid are out of phase, resulting in unrealistic interpretation of roughness value

Wavelength, Frequency and Cutoff

19

Other methods for measuring Surface Roughness

Pneumatic Method

Light Interference Microscopes

The Mecrin Instrument

20

Mechanical Measurements and Metrology

Dr. K V S Rajeswara Rao, Dept. of IEM, RVCE, Bangalore-59. 1

Mechanical Measurements andMetrology – 10ME42B

UNIT - 3

Comparators and AngularMeasurement

Instructor

Dr. K V S Rajeswara RaoAssociate Professor,

Dept. of Industrial Engineering & Management,R V College of Engineering, Mysore Road

Bangalore – 59E-mail – [email protected]



Mechanical Measurements and Metrology – 10ME42B

UNIT – 3:Comparators and Angular measurement

Chapter Outline Comparators

– Introduction to comparators– Characteristics– Uses of Comparators– Classification of comparators– Mechanical comparators

• Dial indicator• Johnson Mikrokator• Sigma comparators

Optical comparators– Principles,– Zeiss ultra optimeter,

Electric and electronic comparators principles,– LVDT,

Pneumatic comparators,– Back pressure gauges,– Solex comparators.

Angular Measurements– Introduction,– Bevel protractor,– Sine principle– Uses of sine bars,– Sine centre,– Use of angle gauges– Numerical on building of angles,– Clinometers.

Comparators can give precision measurements, with consistent accuracy byeliminating human error. They are employed to find out, by how much the dimensions of thegiven component differ from that of a known datum. If the indicated difference is small, asuitable magnification device is selected to obtain the desired accuracy of measurements. It isan indirect type of instrument and used for linear measurement. If the dimension is less orgreater, than the standard, then the difference will be shown on the dial. It gives only thedifference between actual and standard dimension of the workpiece. To check the height ofthe job H2 ,with the standard job of height H1



Initially, the comparator is adjusted to zero on its dial with a standard job in positionas shown in Figure(a). The reading H1is taken with the help of a plunger. Then the standardjob is replaced by the work-piece to be checked and the reading H2 is taken. If H1and H2 aredifferent, then the change i~ the dimension will be shown on the dial of the comparator. Thusdifference is then magnified 1000 to 3000 X to get the clear variation in the standard andactual job.

In short, Comparator is a device which(1) Picks up small variations in dimensions.(2) Magnifies it.(3) Displays it by using indicating devices, by which comparison can be made with some

standard value.

Classification:1. Mechanical Comparator: It works on gears pinions, linkages, levers, springs etc.2. Pneumatic Comparator: Pneumatic comparator works by using high pressure air, valves,

back pressure etc.3. Optical Comparator: Optical comparator works by using lens, mirrors, light source etc.4. Electrical Comparator: Works by using step up, step down transformers.5. Electronic Comparator: It works by using amplifier, digital signal etc.6. Combined Comparator: The combination of any two of the above types can give the best

result.

Characteristics of Good Comparators:1. It should be compact.2. It should be easy to handle.3. It should give quick response or quick result.4. It should be reliable, while in use.5. There should be no effects of environment on the comparator.6. Its weight must be less.7. It must be cheaper.8. It must be easily available in the market.9. It should be sensitive as per the requirement.10. The design should be robust.11. It should be linear in scale so that it is easy to read and get uniform response.



12. It should have less maintenance.13. It should have hard contact point, with long life.14. It should be free from backlash and wear.

Mechanical Comparator:It is self controlled and no power or any other form of energy is required. It employs

mechanical means for magnifying the small movement of the measuring stylus. Themovement is due to the difference between the standard and the actual dimension beingchecked

The method for magnifying the small stylus movement in all the mechanicalcomparators is by means of levers, gear trains or combination of these. They are available ofdifferent make and each has it's own characteristic. The various types of mechanicalcomparators are dial indicator, rack and pinion, sigma comparator, Johansson mikrokator.

a. Dial Indicator:It operates on the principle, that a very slight upward pressure on the spindle at the

contact point is multiplied through a system of gears and levers. It is indicated on the face ofthe dial by a dial finger. Dial indicators basically consists of a body with a round graduateddial and a contact point connected with a spiral or gear train so that hand on the dial faceindicates the amount of movement of the contact point. They are designed for use on a widerange of standard measuring devices such as dial box gauges, portal dial, hand gauges, dialdepth gauges, diameter gauges and dial indicator snap gauge.

Corresponds to a spindle movement of 1 mm. The movement mechanism of theinstrument is housed in a metal case for it's protection. The large dial scale is graduated into100 divisions. The indicator is set to zero by the use of slip gauges representing the basic sizeof part.



Requirements of Good Dial Indicator:1. It should give trouble free and dependable readings over a long period.2. The pressure required on measuring head to obtain zero reading must remain constant

over the whole range.3. The pointer should indicate the direction of movement of the measuring plunger.4. The accuracy of the readings should be within close limits of the various sizes and ranges5. The movement of the measuring plunger should be in either direction without affecting

the accuracy.6. The pointer movement should be damped, so that it will not oscillate when the readings

are being taken.

Applications:1. Comparing two heights or distances between narrow limits.2. To determine the errors in geometrical form such as ovality, roundness and taper.3. For taking accurate measurement of deformation such as intension and compression.4. To determine positional errors of surfaces such as parallelism, squareness and alignment.5. To check the alignment of lathe centers by using suitable accurate bar between the

centers.6. To check trueness of milling machine arbours and to check the parallelism of shaper arm

with table surface or vice.

b) Johansson Mikrokator :This comparator was developed by C.F. Johansson.

Principle:It works on the principle of a Button spring, spinning on a loop of string like in the case ofChildren’s toys.

Construction:

The method of mechanical magnification is shown in Figure. It employs a twistedmetal strip. Any pull on the strip causes the centre of the strip to rotate. A very light pointermade of glass tube is attached to the centre of the twisted metal strip. The measuring plungeris on the slit washer and transmits its motion through the bell crank lever to the twisted metalstrip. The other end of the twisted metal strip is fastened to the cantilever strip. Theoverhanging length of the cantilever strip can be varied to adjust the magnification of theinstrument. The longer the length of the cantilever, the more it will deflect under the pull ofthe twisted metal strip and less rotation of the pointer is obtained.



When the plunger moves by a small distance in upward direction the bell crank leverturns to the right hand side. This exerts a force on the twisted strip and it causes a change inits length by making it further twist or untwist. Hence the pointer at the centre rotates bysome amount. Magnification up to 5000X can be obtained by this comparator

Advantages of Mechanical Comparator:1. They do not require any external source of energy.2. These are cheaper and portable.3. These are of robust construction and compact design.4. The simple linear scales are easy to read.5. These are unaffected by variations due to external source of energy such air, electricity

etc.

Disadvantages:1. Range is limited as the pointer moves over a fixed scale.2. Pointer scale system used can cause parallax error.3. There are number of moving parts which create problems due to friction, and ultimately

the accuracy is less.4. The instrument may become sensitive to vibration due to high inertia.

c) Mechanical - Optical Comparator:

Principle:In mechanical optical comparator, small variation in the plunger movement is

magnified: first by mechanical system and then by optical system.

Construction:The movement of the plunger is magnified by the mechanical system using a pivoted

lever. From the Figure the mechanical magnification = x2 / x1. High optical magnification is



possible with a small movement of the mirror. The important factor is that the mirror used isof front reflection type only.

The back reflection type mirror will give two reflected images as shown in Figure,hence the exact reflected image cannot be identified.

Advantages:1. These Comparators are almost weightless and have less number of moving parts, due to

this there is less wear and hence lessfriction.702. Higher range even at high magnification is possible as the scale moves past the index.3. The scale can be made to move past a datum line and without having any parallax errors.4. They are used to magnify parts of very small size and of complex configuration such as

intricate grooves, radii or steps.

Disadvantages:1. The accuracy of measurement is limited to 0.001 mm2. They have their own built in illuminating device which tends to heat the instrument.3. Electrical supply is required.4. Eyepiece type instrument may cause strain on the operator.5. Projection type instruments occupy large space and they are expensive.6. When the scale is projected on a screen, then it is essential to take the instrument to a dark

room in order to take the readings easily.

d) Sigma Comparator:The plunger is attached to a bar which is supported between the bending plates at the

top and bottom portion as shown in Figure (a)



The bar is restricted to move in the vertical direction. A knife edge is fixed to the bar.The knife edge is attached to the sapphire plate which is attached to the moving block. Theknife edge extorts a force on the moving block through sapphire plate. Moving block isattached to the fixed block with the help of crossed strips as shown in Figure (b). When theforce is applied on the moving block, it will give an angular deflection. A Y-arm which isattached to the moving block transmits the rotary motion to the driving drum of radius r. Thisdeflects the pointer and then the reading is noted.

If l = Distance from hinge pivot to the knife edgeL = Length of y-armR = Driving drum radiusD Length of the pointerThen the total magnification = (L/l) *(D/R)

Electrical Comparators:Electrical comparators give a wide range of advantages. As we know, components

like levers, gears, racks and pinions, activate mechanical devices. The accuracy and life of theinstruments are affected as they are subjected to wear and friction



Electrical comparators have no moving parts. Thus a high degree of reliability isexpected from these instruments. Generally there are two important applications of electricalcomparators:1. Used as measuring heads2. Used for electrical gauging heads, to provideusual indication to check the dimensions within the limits laid down. The first application isvery important when there is a requirement for precise measurement for e.g. Checking orcomparison of workshop slip gauges against inspection slip gauges. The second application isused to indicate with a green light if a dimension is within the limits. A red lamp indicates anundersize dimension; a yellow lamp indicates an oversize dimension. So the operator is notrequired to be aware of the actual tolerances on the dimension. After setting the instrumentcorrectly, all that needs to be done is to place the component under the plunger of the gauginghead. The signal lamps provide in standard positive indication of the acceptability of thedimension under test

Advantages:1. Measuring units can be remote from indicating units.2. Variable sensitivity which can be adjusted as per requirement.3. No moving parts, hence it can retain accuracy over long periods.4. Higher magnification is possible as compared to mechanical comparator.5. Compact sizes of probes arc available.

Disadvantages:1. The accuracy of working of these comparators is likely to be affect due to temperature

and humidity.2. It is not a self contained unit; it needs stabilized power supply for its operation.3. Heating of coils can cause zero drifts and it may alter calibration.4. It is more expensive than mechanical comparator



Pneumatic Comparators (Solex Gauge):

Principle:It works on the principle of pressure difference generated by the air flow. Air is

supplied at constant pressure through the orifice and the air escapes in the form of jetsthrough a restricted space which exerts a back pressure. The variation in the back pressure isthen used to find the dimensions of a component.

Working:As shown in Figure (a) the air is compressed in the compressor at high pressure which

is equal to Water head H. The excess air escapes in the form of bubbles. Then the metricamount of air is passed through the orifice at the constant pressure. Due to restricted area, atA1 position, the back pressure is generated by the head of water displaced in the manometertube. To determine the roundness of the job, the job is rotated along the jet axis, if novariation in the pressure reading is obtained then we can say that the job is perfectly circularat position A1.

Then the same procedure is repeated at various positions A2, A3, A4, position andvariation in the pressure reading is found out. Also the diameter is measured at position A1corresponding to the portion against two jets and diameter is also measured at variousposition along the length of the bore

Figure (b)

Any variation in the dimension changes the value of h, e.g. Change in dimension of0.002 mm changes the value of h from 3 to 20 mm. Moderate and constant supply pressure isrequired to have the high sensitivity of the instrument.



Advantages:1. It is cheaper, simple to operate and the cost is low.2. It is free from mechanical hysteresis and wear.3. The magnification can be obtained as high as 10,000 X.4. The gauging member is not in direct contact with the work.5. Indicating and measuring is done at two different places.6. Tapers and ovality can be easily detected.7. The method is self cleaning due to continuous flow of air through the jets and this

makes the method ideal to be used on shop floor for online controls.

Disadvantages:1. They are very sensitive to temperature and humidity changes.2. The accuracy may be influenced by the surface roughness of the component being

checked.3. Different gauging heads are needed for different jobs.4. Auxiliary equipments such as air filters, pressure gauges and regulators are needed.5. Non-uniformity of scale is a peculiar aspect of air gauging as the variation of back

pressure is linear, over only a small range of the orifice size variation.

Introduction to Angular Measurements:

For measuring the angle, no absolute standard is required. The measurement is donein degrees, minutes and seconds. The measurement of angular and circular divisions is animportant part of inspection. It is concerned with the measurement of individual angles,angular changes and deflections on components, gauges and tools. For precisionmeasurement of angles more skill is required. Like linear measurement, angularmeasurements have their own importance. The basic difference between the linear andangular measurement is that no absolute standard is required for angular measurement. Thereare several methods of measuring angles and tapers. The various instruments used are anglegauges, clinometers, bevel protractor, sine bar, sine centers, taper plug and ring gauges

Sine Bars:

It is used for measurement of an angle of a given job or for setting an angle. They arehardened and precision ground tools for accurate angle setting. It can be used in conjunctionwith slip gauge set and dial gauge for measurement of angles and tapers from horizontalsurface. As shown in Figure, two accurately lapped rollers are located at the extreme position.The center to center distance between the rollers or plugs is available for fixed distance i.e.l = 100, 200, 250, 300 mm. The diameter of the plugs or roller must be of the same size andthe center distance between them is accurate. The important condition for the sine bar is thatthe surface of sine bar must be parallel to the center lines of the plug



As shown in Fig. 2.47, the taper angle 8 of the job WX YZ is to be measured by thesine bar.

Principle of Working:

As shown in Figure the taper angle θ of the job WX YZ is to bemeasured by the sinebar. The job is placed over the surface plate. Thesine bar is placed over the job with plug orroller of one end of the bar touching the surface plate. One end of the sine bar is rested on thesurface plate and the other end is rested on the slip gauges

The angle of the job is then first measured by some non-precision instrument, such asbevel protector. That angle gives the idea of the approximate slip gauges required, at theother end of sine bar. And finally the exact number of slip gauges are added equal to height h,such that, the top most slip gauges touches the lower end of the roller. The height of the slipgauges required is then measured. Then the taper angle can be measured by making sine baras a hypotenuse of right angle triangle and slide gauge as the opposite side of the triangle asshown in Figure

h = Height in mmL = Center distance in mmSinθ = Opp / Hyp = (h/ L)



When the size of the job is large having taper then we use slip gauges for the both theside to find the taper angle of the job

For a small component, the component or work piece can be placed over a sine bar asshown in Figure. The job is held on the sine bar with some suitable accessories. The dialindicators are provided at the top position and the reading is taken at A position. The dialindicator is then moved to the right hand side and the reading is taken at position B. If there isa difference between reading at position A and B, then the height of the slip gauges isadjusted until the dial indicator shows the same reading at A and B. Then the angle iscalculated similar to previous method asSinθ = Opp / Hyp = (h/ L)

Use of Sine Bar.

(1) Measuring known angles or locating any work toa given angle.



For this purpose the surface plate is assumed to be having a perfectly flat surface, sothat its surface could be treated as horizontal. One of the cylinders or rollers of sine bar isplaced on the surface plate and other roller is placed on the slip gauges of height h. Let thesine bar be set at an angle θ. Then sin θ = h/l, where l is the distance between the centres ofthe rollers. Thus knowing θ, h can be found out and any work could be set at this angle as thetop face of sine bar is inclined at angle θ to the surface plate. The use of angle plates andclamps could also be made in case of heavy components. For better results, both the rollerscould also be placed on slip gauges, of height h1 and h2 respectively.

Then sin θ= (h2-h1)/l

(2) Checking of unknown angles.

Many a times, angle of a component to be checked is unknown. In such a case, it isnecessary to first find the angle approximately with the help of a bevel protractor. Let theangle be θ. Then the sine bar is set at an angle θ and clamped to an angle plate. Next, thework is placed on the sine bar and clamped to the angle plate as shown in Fig. and a dialindicator is set at one end of the work and moved to the other, and deviation is noted. Againslip gauges are so adjusted (according to this deviation) that dial indicator reads zero acrossthe work surface.

If deviation noted down by the dial indicator is δh over a length l‘ of work, thenheight of slip gauges by which it should be adjusted is equal to δh * (l/ l‘)



(3) Checking of unknown angles of heavy component.

In such cases where components are heavy and can’t be mounted on the sine bar, thensine bar is mounted on the component as shown in Fig. The height over the rollers can thenbe measured by a vernier height gauge ; using a dial test gauge mounted on the anvil ofheight gauge as the fiducial indicator to ensure constant measuring pressure. The anvil onheight gauge is adjusted with probe of dial test gauge showing same reading for the topmostposition of rollers of sine bar. Fig. 8.18 shows the use of height gauge for obtaining tworeadings for either of the roller of sine bar. The difference of the two readings of height gaugedivided by the centre distance of sine bar gives the sine of the angle of the component to bemeasured. Where greater accuracy is required, the position of dial test gauge probe can besensed by adjusting a pile of slip gauges till dial indicator indicates same- reading over rollerof sine bar and the slip gauges.

Advantages of sine bar:1. It is used for accurate and precise angular measurement.2. It is available easily.3. It is cheap.

Disadvantages:1. The application is limited for a fixed center distance between two plugs or rollers.2. It is difficult to handle and position the slip gauges.3. If the angle exceeds 45°, sine bars are impracticable and inaccurate.4. Large angular error may results due to slight error in sine bar.

Sine Centers:It is the extension of sine bars where two ends are provided on which centers can be

clamped, as shown in Figure. These are useful for testing of conical work centered at eachend, up to 60°. The centers ensure correct alignment of the work piece. The procedure ofsetting is the same as for sine bar. The dial indicator is moved on to the job till the reading issame at the extreme position. The necessary arrangement is made in the slip gauge height andthe angle is calculated as θ = Sin-1 (h/L)



Universal Bevel Protractor:It is used to measure angles accurately to 5 minutes. it is finely made tool with dial,

graduated in degrees, a base and a sliding blade. The blade can be locked against dial bytightening the blade clamp nut. The blade and dial can be rotated as one unit to any positionand locked by tightening the dial clamp nut for accurate measurement, a vernier or a fineadjustment device, is fitted on the dial. The dial is graduated into, I treads, , The vernier scaleis divided into twelve equal parts on each side of zero, every third division is numbered 0, 15,30, 45, 60 representing minutes.

Angle Gauges:In this method, the auto collimator used in conjunction with the angle gauges. It

compares the angle to be measured of the given component with the angle gauges. Anglesgauges are wedge shaped block and can be used as standard for angle measurement. Theyreduce the set uptime and minimize the error. These are 13 pieces, divided into three typessuch as degrees, minutes and seconds. The first series angle are 1°, 3°, 9°, 27° and 41 ° Andthe second series angle are 1', 3', 9' and27' And the third series angle are 3", 6", 18" and 30"These gauges can be used for large number of combinations by adding or subtracting thesegauges, from each other.



Nominal angles of combination angle gaugesDegrees 1 3 9 27 41Minutes 1 3 9 27 -Fraction of minute 0.05 0.1 0.3 0.5 -(or seconds) 3 6 18 30 -

Clinometer:A clinometer is a special case of the application of spirit level. In clinometer, the spirit

level is mounted on a rotary member carried in a housing. One face of the housing forms thebase of the instrument. On the housing, there is a circular scale. The angle of inclination ofthe rotary member carrying the level relative to its. base can be measured by this circularscale. The clinometer mainly used to determine the included angle of two adjacent faces ofworkpiece. Thus for this purpose, the instrument base is placed on one face and the rotarybody adjusted till zero reading of the bubble is obtained. The angle of rotation is then notedon the circular scale against the index. A second reading is then taken in the similar manneron the second face of workpiece. The included angle between the faces is then the differencebetween the two readings.

Clinometers are also used for checking angular faces, and relief angles on largecutting tools and milling cutter inserts.

These can also be used for setting inclinable table on jig boring; machines and angularwork on grinding machines etc.

The most commonly used clinometer is of the Hilger and Watts type. The circularglass scale is totally enclosed and is divided from 0° to 360° at 10′ intervals. Sub-division of10′ is possible by the use of an optical micrometer. A coarse scale figured every 10 degrees isprovided outside the body for coarse work and approximate angular reading. In someinstruments worm and quadrant arrangement is provided so that reading upto 1′ is possible.

In some clinometers, there is no bubble but a graduated circle is supported on accurateball bearings and it is so designed that when released, it always takes up the position relativeto the true vertical. The reading is taken against the circle to an accuracy of 1 second with theaid of vernier.

1. Precision Microptic Clinometer. These are used for measurement and checking of:angular faces, gauges, relief angles on large cutting tools, angle of milling cutter inserts, jigsand fixtures, levels of machine ways and bed plates, and for setting of inclinable tables on jigboring machines, and adjustable angle plates angular work on grinding and lapping machines.With the appropriate accessories these can be used for measuring angular displacements ofsmall parts, and setting out angles.



The special features of precision microptic clinometer are direct reading over therange 0°—360°, optical reading system ;totally enclosed glass circles and easy-to-read scales;main scale and micrometer scale visible simultaneously in the eyepiece external scale forrapid coarse setting, slow motion screw for fine setting, eyepiece rotatable to most convenientviewing position, and hardened ground steel base

Fig (a)

.

Fig (b) Fig (c)

Precision Microptic Clinometer utilises bubble unit with a prismatic coincidencereader which presents both ends of the bubble as adjacent images in a split field of view. Asthe vial is levelled, the two half-mages move into coincidence, making it very easy to seewhen the bubble is exactly centered, without reference to any graduations. [Refer Fig(b)].



To determine the inclination of the clinometer, the bubb is levelled and the scalesread. On looking through the eyepiece, three apertures can be seen. The upper aperturecontains two pairs of double lines and two single lines ; to set the micrometer, the knob isturned until the single lines are brought exactly central B between the double lines. The scalescan then be read, the required angle being the sum of the readings of the main scale and themicrometer scale. [Refer Fig(c)].

The double lines are imaged from one side of the circle and the single ones from apoint diametrically opposite ; by using the double lines as an index for the single line, anyresidual centring error of the circle is cancelled out.

The scales are illuminated by an integral low voltage lamp. The bubble unit isdaylight illuminated, but is also provided with a lamp for alternative illumination.

A locating face on the back allows the instrument to be used horizontally with theaccessory worktable or reflector unit.

The reference for inclination is the bubble vial. In order to measure the inclination ofa surface, the vial—to which the circle is attached is turned—until it is approximately level ;then the slow motion screw is used for a final adjustment to centre the bubble.

To measure the angle between two surfaces, the clinometer is placed on each surfacein turn and the difference in angle can be calculated.

The clinometer can be used as a precision setting tool to set a tool head or table at aspecific angle. First the micrometer scale is set and then the glass scale is rotated to bring therelevant graduation to the index, using the slow motion screw for final adjustment. This setsthe clinometer for the required angle. Then the work surface it tilted until the bubble isexactly centred. The work surface is thus set to the specified angle relative to a level plane.

75

Angular Measuring

Devices UNIT 6 ANGULAR MEASURING DEVICES

Structure

6.1 Introduction

Objectives

6.2 Line Standard Angular Measuring Devices

6.2.1 Protractors

6.2.2 Universal Bevel Protractors

6.3 Face Standard Angular Measuring Devices

6.4 Measurement of Inclines

6.4.1 Spirit Level

6.4.2 Clinometer

6.5 Angle Comparators

6.6 Summary

6.7 Key Words

6.8 Answers to SAQs

6.1 INTRODUCTION

There are a wide variety of geometric features that are measured in angular units. These

varieties include angular separation of bounding planes, angular spacing conditions

related to circle, digression from a basic direction etc. Because of these diverse

geometrical forms, different types of methods and equipment are available to measure

angles in common angular units of degree, minute and second. Several factors come into

picture in selection of suitable angular measuring instruments. These factors may be the

size and general shape of the part, the location and angular accessibilities of the feature

to be measured, expected range of angle variations, the required sensitivity and accuracy

of measurement etc. Because of the different systems and techniques in angular

measuring instruments, it is difficult to categorize them completely. As in linear

measurement, they can be categorized in two groups. The first one is line standard

instrument. It includes divided scales like protractors, bevel gauges. The second

category of angular measuring instruments is called face standard instruments. Sine bars

and angle gauges falls in this category. In this unit, we will discuss both types of angular

measuring devices and the techniques used in determining the angle. In addition to that,

we will have an overview of angle comparators (autocollimators).

Objectives

After studying this unit, you should be able to

familiarise yourself with various types of angular measuring devices, and

choose a suitable angular measuring device according to the precision

required.

6.2 LINE STANDARD ANGULAR MEASURING DEVICES

Line standard gives direct angular measurement from the engraved scales in the

instruments. They are not very precise. Hence they are not used when high precision is

required. However, they can be used in initial estimation of the angles in measurement.

We will discuss some of the line standard angular measuring devices in the following

sub-sections.

76

Metrology and

Instrumentation 6.2.1 Protractors

It is the simplest instrument for measuring angles between two faces. It consists of two

arms and an engraved circular scale. The two arms can be set along the faces between

which the angle is to be measured. The body of the instrument is extended to form one of

the arms, and this is known as the stock. It is the fixed part of the protractor and should

be perfectly straight. The other arm is in the form of a blade that rotates in a turret

mounted on the body. One of the bodies of the turret carries the divided scale and the

other member carries a vernier or index. The ordinary protractor measures angles only in

degrees and used for non-precision works. By using angular vernier scale along with it,

precision up to 5 can be achieved. Figure 6.1 shows the diagram of a protractor.

Figure 6.1 : Protractor

6.2.2 Universal Bevel Protractors

It is an angular measuring instrument capable of measuring angles to within 5 min. The

name universal refers to the capacity of the instrument to be adaptable to a great variety

of work configurations and angular interrelations. It consists of a base to which a vernier

scale is attached. A protractor dial is mounted on the circular section of the base. The

protractor dial is graduated in degrees with every tenth degree numbered. The sliding

blade is fitted into this dial; it may be extended to either direction and set at any angle to

the base. The blade and the dial are rotated as a unit. Fine adjustment are obtained with a

small knurled headed pinion that, when turned, engages with a gear attached to the blade

mount. The protractor dial may be locked in any position by means of the dial clamp nut.

Measurement in a universal bevel protractor is made either by embracing the two

bounding elements of the angle or by extraneous referencing, for example, the part and

the instrument resting on a surface plate.

The vernier protractor is used to measure an obtuse angle, or an angle greater than 90

but less than 180. An acute angle attachment is fastened to the vernier protractor to

measure angles of less than 90. The main scale is divided into two arcs of 180. Each

arc is divided into two quadrants of 90 and has graduation from 0 to 90 to the left and

right of the zero line, with every tenth degree numbered.

The vernier scale is divided into 12 spaces on each side of its zero (total 24). The

spacing in the vernier scale is made in such a way that least count of it corresponds to 1/12

th of a degree, which is equal to 5.

If the zero on the vernier scale coincides with a line on the main scale, the number of

vernier graduations beyond the zero should be multiplied by 5 and added to the number

of full degrees indicated on the protractor dial. Figure 6.2 shows a diagram of a bevel

protractor.

77

Angular Measuring

Devices

Figure 6.2 : Universal Bevel Protractor

SAQ 1

(a) What are the various line standard angular measuring devices?

(b) Name the parts of a universal bevel protractor and state the functions of

each.

6.3 FACE STANDARD ANGULAR MEASURING

DEVICES

Face standard angular measuring devices include angle gauges and sine bars. The

measurements are done with respect to two faces of the measuring instruments. Precision

obtained in such instruments is more than the precision obtained in line standard angular

measuring devices. Some commonly used face standard angular measuring devices are

discussed in the following sub-sections.

6.3.1 Sine Bar

A sine bar is made up of a hardened steel beam having a flat upper surface. The bar is

mounted on two cylindrical rollers. These rollers are located in cylindrical grooves

specially provided for the purpose. The axes of the two rollers are parallel to each other.

They are also parallel to the upper flat surface at an equal distance from it.

Unlike bevel protractors sine bars make indirect measurements. The operation of a sine

bar is based on known trigonometric relationship between the sides and the angle of a

right angle triangle. Here, dimension of two sides determine the size of the third side and

of the two acute angles. The accuracy attainable with this instrument is quite high and

the errors in angular measurement are less than 2 seconds for angle up to 45. Generally,

right-angled triangle is obtained by using a horizontal and precise flat plate on which

gage blocks are stacked in the direction normal to the plane of the plate.

Sine block itself is not a measuring instrument. It acts as an important link in the angle

measuring process. The actual measurement consists in comparing the plane of the part’s

top element to the plane of supporting surface plate. Mechanical or electronic height

gauges are essentially used in the process.

78

Metrology and

Instrumentation

Figure 6.3 : Sine Bar

Figure 6.3 shows the schematic diagram of a sine bar. It is specified by the distance

between the two centres of two rollers. The high degree of accuracy and precision

available for length measurement in the form of slip and block gauges may be utilized

for measurement of angle using the relationship as shown in Figure 6.4, where we have,

sinh

L .

Figure 6.4 : Use of Sine Bar for Angle Measurement

Apparently, the accuracy of angle measurement depends upon the accuracy with which

length L, of the sine bar and height h under the roller is known. Since the gage blocks

incorporate a very high degree of accuracy, the reliability of angle measurement by

means of sine bar depends essentially on the accuracy of the sine bar itself.

Now, differentiating h with respect to , we have

1

cos .dh

L d

1 sec

cos

d

dh L L

Therefore, the error in angle measurement d, due to an error, dh in height h is

proportional to sec . Now sec increases very rapidly for angle greater than 45.

Therefore, sine bars should not be used for measurement of angles greater than 45 and

if at all they have to be used, sine bars should measure the complement of the angle

rather than the angle itself.

SAQ 2

(a) Why is sine bar not preferred for measuring angle more than 45?

(b) Calculate the gauge block buildup required to set a 10 cm sine bar to an

angle of 30.

79

Angular Measuring

Devices 6.4 MEASUREMENT OF INCLINES

Inclination of a surface generally represents its deviation from the horizontal or vertical

planes. Gravitational principle can be used in construction of measurements of such

inclinations. Spirit levels and clinometer are the instruments of this category. We will

discuss these instruments in brief in the following sub-sections.

6.4.1 Spirit Level

Spirit level is one of the most commonly used instruments for inspecting the horizontal

position of surfaces and for evaluating the direction and magnitude of minor deviation

from that nominal condition. It essentially consists of a close glass tube of accurate form.

It is called as the vial. It is filled almost entirely with a liquid, leaving a small space for

the formation of an air or gas bubble. Generally, low viscosity fluids, such as ether,

alcohol or benzol, are preferred for filling the vial. The liquid due to its greater specific

weight tends to fill the lower portion of the closed space. Upper side of the vial is

graduated in linear units. Inclination of a surface can be known from the deviation of the

bubble from its position when the spirit level is kept in a horizontal plane. Temperature

variations in the ambient condition cause both liquid and vial to expand or contract.

Therefore, selection of proper liquid and material for the spirit level is very important for

accurate result. To reduce the effect of heat transfer in handling spirit levels are made of

a relatively stable casting and are equipped with thermally insulated handles. Figure 6.5

shows a schematic diagram of a spirit level.

Figure 6.5 : Spirit Level

Sensitivity of the vial used in spirit level is commonly expressed in the following two

ways.

Each graduation line representing a specific slope is defined by a tangent relationship,

e.g. 0.01 cm per meter.

An angular value is assigned to the vial length covered by the distance of two adjacent

graduation lines, i.e. the distance moved by the bubble from the zero will correspond the

angle directly.

6.4.2 Clinometer

A clinometer is a special case of application of spirit level for measuring, in the vertical

plane, the incline of a surface in relation to the basic horizontal plane, over an extended

range. The main functional element of a clinometer is the sensitive vial mounted on a

rotatable disc, which carries a graduated ring with its horizontal axis supported in the

housing of the instrument. The bubble of the vial is in its centre position, when the

clinometer is placed on a horizontal surface and the scale of the rotatable disc is at zero

position. If the clinometer is placed on an incline surface, the bubble deviates from the

centre. It can be brought to the centre by rotating the disc. The rotation of the disc can be

read on the scale. It represents the deviation of the surface over which the clinometer is

placed from the horizontal plane. Figure 6.6 shows a diagram of a clinometer.

A number of commercially available clinometers with various designs are available.

They differ in their sensitivity and measuring accuracy. Sensitivity and measuring

accuracy of modern clinometers can be compared with any other high precision

measuring instruments. For shop uses, clinometers with 10 graduations are available.

80

Metrology and

Instrumentation

Figure 6.6 : Clinometer

Applications

Two categories of measurement are possible with clinometer. Care must be taken

to keep the axis of the rotatable disc parallel to the hinge line of the incline. The

two categories of measurement are :

(i) Measurement of an incline place with respect to a horizontal plane. As

discussed earlier, this is done by placing the instrument on the surface to be

measured and rotating graduated disc to produce zero inclination on the

bubble. The scale value of the disc position will be equal to the angle of

incline.

(ii) Measurement of the relative position of two mutually inclined surfaces.

This is done by placing the clinometer on each of the surface in turn, and

taking the readings with respect to the horizontal. The difference of both the

readings will indicate the angular value of the relative incline.

SAQ 3

(a) How the inclination is estimated with the help of a spirit level?

(b) Describe the principle, working and uses of a clinometer.

6.5 ANGLE COMPARATORS

Angle comparators are the metrological instruments used for finding the difference

between two nearly equal angles. The principle used in angle comparators is same as that

of linear comparators. In practice, they are frequently used in calculating the difference

between the angle of working standard gauges or instruments. It is also used in

measuring angle of a number of angle gauges wrung together, or the angle between two

faces of a standard polygon.

The most widely used angle comparators are Autocollimators. They are designed to

measure small angles by comparison. They are quite accurate and can read up to

0.1 seconds, and may be used for distance up to 30 meters. We will discuss the principle

and the working of an autocollimator in the following section.

81

Angular Measuring

Devices 6.5.1 Autocollimators

Principle

The two main principles used in an autocollimator are

(a) the projection and the refraction of a parallel beam of light by a lens,

and

(b) the change in direction of a reflected angle on a plane reflecting

surface with change in angle of incidence.

To understand this, let us imagine a converging lens with a point source of light O at its

principle focus, as shown in Figure 6.7(a). When a beam of light strikes a flat reflecting

surface, a part of the beam is absorbed and the other part is reflected back. If the angle of

incidence is zero, i.e. incident rays fall perpendicular to the reflecting surface, the

reflected rays retrace original path. When the reflecting plane is tilted at certain angle,

the total angle through which the light is deflected is twice the angle through which the

mirror is tilted. Thus, alternately, if the incident rays are not at right angle to the

reflecting surface they can be brought to the focal plane of the light sources by tilting the

reflecting plane at an angle half the angle of reflection as shown in Figure 6.7(b).

(a) Reflector is at 90 with the Direction of Rays

Figure 6.7(b) : Reflector is not at Right Angles to the Direction of the Rays

Now, from the diagram, OO = 2 f = x, where f is the focal length of the lens.

Thus, by measuring the linear distance x, the inclination of the reflecting surface

can be determined. The position of the final image does not depend upon the

distance of the reflector from the lens. If, however, the reflector is moved too long,

the reflected ray will then completely miss the lens and no image will be formed.

Working

In actual practice, the work surface whose inclination is to be obtained forms the

reflecting surface and the displacement x is measured by a precision microscope

which is calibrated directly to the values of inclination .

The optical system of an autocollimator is shown in Figure 6.8. The target wires

are illuminated by the electric bulb and act as a source of light since it is not

convenient to visualize the reflected image of a point and then to measure the

displacement x precisely. The image of the illuminated wire after being reflected

from the surface being measured is formed in the same plane as the wire itself.

The eyepiece system containing the micrometer microscope mechanism has a pair

of setting lines which may be used to measure the displacement of the image by

setting to the original cross lines and then moving over to those of the image.

82

Metrology and

Instrumentation Generally, a calibration is supplied with the instrument. Thus, the angle of

inclination of the reflecting surface per division of the micrometer scale can be

directly read.

Autocollimators are quite accurate and can read up to 0.1 seconds, and may be

used for distance up to 30 meters.

Figure 6.8 : Optical System of an Autocollimator

SAQ 4

Describe the principle and working of an autocollimator.

6.6 SUMMARY

In this unit, principles and techniques of angular measuring devices have been discussed.

The unit begins with description of line standard angular measuring devices like

protractor and bevel protractor. Next, face standards angular measuring devices, viz. slip

gauges and sine bars are discussed. Instruments used for measurement of inclinations,

viz. spirit level inclinometers are discussed in the next section. The unit finishes with the

discussion of the principle and working of angle comparator, viz. autocollimators.

6.7 KEY WORDS

Protractor : It is the simplest angle-measuring device and can

give reading up to 5.

Clinometer : It is a device for measuring angle between two

faces. It uses the principle of spirit level.

Sine Bar : It is an indirect angle-measuring instrument which

gives measurement up to 2.

Angle Gauges : It is a precision angular measuring device that can

give accuracy up to 3.

Vial : The closed glass tube of accurate size in a spirit

level, which is used for storing the liquid, is called

the vial. It is graduated in linear scale and the

bubble moves inside it.

Autocollimator : It is an angle comparator based on the principle of

reflection of light. Least measurement given by

autocollimator is up to 1.

83

Angular Measuring

Devices 6.8 ANSWERS TO SAQs

SAQ 1

(a) See preceding text for answer.

(b) See preceding text for answer.

SAQ 2


(b) Buildup = 10 sin 30

= 10 0.5

= 5 cm

SAQ 3


(b) See preceding text for answer.

SAQ 4

See preceding text for answer.

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