Published on May 9, 2014
Lecture notes by Meet Bakotia Unit 4: Linear Measurements, Dial indicators and Comparators Metrology: Metrology means science of measurement. Engineering metrology is the measurement of dimensions: length, thickness, diameter etc. Terms used in measurement: 1. Accuracy:- “Accuracy is the degree to which measured value agrees with the true value of quantity of interest.” Accuracy denotes the closeness of measured value with the true value. For example if an instrument like micrometer measures dimension of part as 25mm and if stated accuracy is +0.01mm then the true dimension could lie between 24.99mm and 25.01mm. 2. Precision. “Precision means the degree of repeatability of measuring process.” Precision has no meaning for only one measurement but it exists when set of measurements is carried out. Suppose 10 measurements are performed. Then, precision means how well these 10 measured values agree with each other i.e. how nearer the readings of these 10 measurements are and how less is the variation between each value. Distinction between Precision and Accuracy: Accuracy is very often confused with precision, but both are different. Consider gun shots on a dart In figure (a), since the gunshots have hit the target region and all the gunshots are nearer to each other, they are precise and accurate. In figure (b), gunshots are far away from the target region, so the gunshots are inaccurate but they are nearer to each other, so they are precise. In fig (c), the gunshots are much apart from each other and nor is their average position within the target region, so the gunshots are neither accurate nor precise. 3. Calibration. Calibration is the procedure in which the measuring instrument is checked against a known standard.” For e.g. Calibrating a Thermometer involves checking its reading in ice (of pure water). Instruments must be calibrated often since they lose accuracy on frequent uses.
Lecture notes by Meet Bakotia 4. Sensitivity Sensitivity is the ability of measuring device to detect small differences in quantity being measured. The indication of this characteristic is the smallest variation of the quantity that can be detected by the instrument. Sensitivity is also called Resolution. The greater the resolution of device, the smaller will be the things it can resolve and greater will be magnification required to expand these measurements upto the point where they can be observed by naked eye. Sensitivity is also related to measuring instrument/device. 5. Readability. Readability is the susceptibility of a measuring device to have its indications converted to a meaningful number.” It refers to ease with which the readings of a measuring instrument can be read. 6. Magnification: Magnification means increasing the magnitude of output signal of measuring instrument many times to make it more readable. The magnification obtained in measuring instrument may be mechanical, electrical, electronic, optical, and pneumatic or combination of these. It is obtained by means of levers or gear trains in mechanical comparators. Errors in Measurement All measurements are inaccurate to some extent. Measurement error is the difference between the measured values and true values. Errors are broadly classified as- (A) Systematic errors. (B) Random errors. (A) Systematic errors (controllable errors) Systematic error occurs due to experimental mistakes. They are controllable in both magnitude and sense. These can be determined and reduced, if attempts are made to analyse them. 1) Calibration errors. These are caused due to the variation in the calibrated scale from its nominal value. The actual length of standards such as slip gauges and engraved scale will vary from the nominal value by small amount. This will cause an error in measurement of constant magnitude. Sometimes the instrument inertia and hysteresis effects do not allow the instruments to transfer the measurement accurately. For eg. Drop in voltage along the wires between the transducer and the electric meter occurs. This may induce an error called signal transmission error in measurement. 2) Avoidable errors:- These errors are of large magnitude having two main causes- a) Misreading an instrument.- eg a Vernier is read faulty as 20.5 or 19.5 mm instead of correct reading 20.1mm. b) Arithmetic errors: Usually, they are mistakes made in addition.
Lecture notes by Meet Bakotia 3) Alignment errors:- If while measuring the length of workpiece the measuring scale is inclined to the true line of the dimension being measured there will be an error in measurement. Fig. below shows that the dimension ‘L’ that is being measured with scale (foot ruler) which is held at an angle θ to the line of measurement. The above error is also called as Cosine Error. 4) Environmental errors. Variation in atmospheric condition (i.e. temperature, pressure and moisture content) at the place of measurement from internationally agreed standard values (temperature- 20o C and pressure-760 mm of Hg) can give rise to error in the measured size of a component. Temperature is the most significant factor which causes error in the measurement due to expansion or contraction of component being measured or of instrument used for the measurement. 5) Stylus pressure (contact pressure). Variations in the force applied by the anvils of micrometer on the work to be measured result in the difference in its readings. The error is caused by the distortion of both micrometer frame and workpiece. To avoid this effect of contact pressure micrometer is fitted with a ratchet mechanism with an operating thimble. The ratchet slips when the applied pressure exceeds the minimum required operating pressure. (B)Random errors Random errors occur randomly and are accidental in nature. Their specific causes cannot be determined. These vary in unpredictable manner when certain dimension is measured several times under same conditions. Their magnitudes and sense cannot be determined from the knowledge of measuring system or conditions of measurement. Possible sources of such errors are- a) Small variations in the position of setting standard and workpiece. b) Slight displacement of lever joints in the measuring joints in measuring instrument c) Fluctuations in the friction in measuring instrument. d) Operator error in scale reading. Non precision measuring instruments: 1) Steel rule:
Lecture notes by Meet Bakotia Steel rule is a line measuring device. It has series of equally spaced lines engraved on it. Steel rule are available in 150, 300, 600, 1000mm lengths. Steel rules have accuracy of 0.5mm or 1mm according to different types of scale. 2) Callipers:- A calliper is used to transfer the distance between the faces of component to a scale or a micrometer. It converts an end measurement situation to the line system or the rule. Outside callipers have two legs which are bent inwards while the inside calliper is made with straight legs bend outwards at the ends. 3) Surface plate. Surface plate forms the basis of measurement. They are used in workshops and metrological laboratories where inspection is carried out. They are used as a reference or datum surface for testing flatness of surfaces or reference surfaces for measuring instruments having flat bases like V- Blocks, angle plates, sine bars, height gauges, etc. Generally Cast Iron is preferred over the other two materials such as Granite and Glass surface plates. 4) Angle plate.
Lecture notes by Meet Bakotia An angle plate is used for supporting or setting up work vertically, and is provided with holes and slots through which securing bolts can be located. It is made of cast iron and ground to a high degree of accuracy. They have two working surfaces truly perpendicular to each other. They are used for checking vertical faces, perpendicularity of adjacent faces and for mounting work on beds of machines. 5)V- Block V- Blocks are made of Cast iron. They are mainly used for following purposes (1) Hold cylindrical workpieces. (2) Checking out roundness of cylindrical workpieces. (3) To support rectangular components at 450 to datum. (4) They are manufactured in pairs for holding and supporting long cylindrical components. Precision measuring instruments: (a) Vernier calliper (b) Outside and inside micrometer (c) Vernier height gauge (a) Vernier calliper Principle of Vernier calliper: “The difference between the two scales i.e. Vernier scale and main scale which are nearly alike but not same, due to the small difference in their divisions, enables to measure the precise dimensions of parts”. V.C. are Available in ranges from 0-125mm, 0-200mm, 0-300mm, 0- 500mm, 0-750mm, 0-1000mm etc. Vernier callipers are accurate upto 0.02mm.
Lecture notes by Meet Bakotia Least count of Vernier calliper:- The value of division on Vernier scale is slightly smaller than the value of division on main scale. This difference is the least count. Smallest division on main scale is 1mm and there are 50 divisions of Vernier scale. Zero error in Vernier calliper:- Before taking reading, zero of main scale should coincide with zero of Vernier scale, when two jaws are in touch with each other, and if it this condition is not satisfied then the error is zero error. If zero of Vernier scale is on the left of zero of main scale then the error is negative error. If the zero of Vernier scale is on the right of the zero of main scale then the error is positive error. Hence positive error should be subtracted from the total reading and negative error should be added. (b) Outside micrometer: Micrometer works on the principle of screw and nut. When screw is turned through nut through one revolution, screw advances by one pitch distance. Micrometer has a screw of 0.5 mm pitch, i.e. when screw moves by 0.5 mm, it completes one revolution. Thus, screw and nut arrangement permits the opening and closing of thimble on barrel. Barrel has main scale readings engraved on it, while thimble has circular/Vernier scale readings engraved on it. Ratchet screw at the end of the thimble prevents too much pressure being applied on micrometer. Least count of outside micrometer Micrometer has a screw of 0.5mm pitch, with a thimble graduated in 50 Vernier divisions.
Lecture notes by Meet Bakotia Zero error in Micrometer. When the zero mark of circular scale and main scale do not coincide, instrument has zero error. If the circular scale may be in advance or behind zero of main scale by certain number of divisions on circular scale. If the zero of circular scale is below the main scale, then the error is negative error. If the zero of circular scale is above the main scale , then the error is positive error. Hence positive error should be subtracted from the total reading and negative error should be added. Possible errors in Vernier calliper and Micrometer: Errors in taking reading by use of Vernier calliper are mainly due to manipulation or mishandling of instrument. Various causes of errors are :- 1. Parallax error. 2. Zero error. 3. Backlash error. 4. Error caused by incorrect reading as scales are difficult to read. Precautions in use of Vernier calliper and Micrometer: 1. Line of measurement must coincide with line of scale i.e. following Abbe’s principle correctly. 2. While measuring outside diameters with Vernier calliper or micrometer, instrument should not be tilted or twisted. 3. Do not apply unnecessary extra pressure while taking measurements. 4. Handle and grip the instrument near or opposite to the jaws while taking the measurement.
Lecture notes by Meet Bakotia 5. Accuracy of measurement primarily depends on two senses – sense of sight (eyes) and sense of touch (feel). Imperfect vision and improper eyesight can cause error so use of proper magnifying glass should be done. (c) Vernier height gauge Vernier height gauge is similar to Vernier calliper but only difference is that here there is a graduated bar which is held in vertical position and is used with a surface plate. The function of fine adjustment arrangement is that- Once the workpiece whose height is to be measured is placed on the surface plate and when the lower gauging surface of measuring jaw comes in contact with top surface of jaw, then upon the sense of correct feel, the final adjustment is made by final (fine) adjustment clamp screw. Slip gauges Slip gauges are end standards used in linear measurements. They are rectangular blocks, made of high grade steel, having cross section about 30mm X10mm. These blocks are made into required sizes and hardened to resist wear and allowed to stabilize so as to relieve internal stresses. After hardening the blocks, measuring faces are carefully finished to fine degree of surface finish, flatness and accuracy. This high grade surface finish is obtained by super finishing process known as lapping. Wringing of slip gauges
Lecture notes by Meet Bakotia The measuring face of the gauges is flat and it possesses high surface finish. If two slip gauges are forced against each other on measuring faces, because of contact pressure, gauges stick together and considerable force is required to separate these blocks. This is known as wringing of slip gauges. Slip gauges are wrung to build desired dimension. Figure shows 1) Parallel wringing of slip gauges 2) Cross wringing of slip gauges. Care of slip gauges and precautions to be taken while using slip gauges. 1. Protection from dust, dirt and moisture. 2. Always keep unused gauges in their case. 3. Gauges should not become magnetized; otherwise they will attract ferrous dust. 4. Fingering of lapped faces should be avoided. 5. Damage to gauges is likely to occur on the edges if the gauge is dropped. M45 is a normal set of slip gauges. Range (mm) Steps Pieces 1.001 to 1.009 0.001 9 1.01 to 1.09 0.01 9 1.1 to 1.9 0.1 9 1 to 9 1 9 10 to 90 10 9 Total 45 Slip gauge accessories. The various slip gauge accessories are- 1. Measuring jaws 2. Scribing and centre point 3. Holders
Lecture notes by Meet Bakotia 4. Base. 1. Measuring jaws. Measuring jaws are always supplied in pairs. These are of 2 types : Type A and Type B . Type A jaws are used for both internal and external measurement only. Type B jaws are used for external measurement only. 2. Scribing and center points. These are used in conjunction with holder and slip gauges for very accurate marking out purposes. 3. Holders. Holders are shown with measuring jaws. Holders are made of suitable design for holding rigidly combination of slip gauges within their range. 4. Base. Base is made with robust construction. It is designed in such a manner that holder can be attached to it. Standards of measurement The various standards for linear measurements are- 1. Line Standards. 2. End Standards. 3. Wavelength standards.
Lecture notes by Meet Bakotia 1. Line Standards. Line standard is the length between two lines. International prototype metre or yard is line standard. (A prototype is an original type, form, or instance of something serving as a typical example, basis, or standard for other things of the same category) International Prototype Metre or yard is defined as the distance between scribed lines on a bar of metal under certain conditions of temperature and support. Line standards are quick and easy to use, but they are not so accurate. The accuracy of measurement by these standards depends upon the skill of the user. 2. End standards End standard is the distance between two flat parallel faces. Length is expressed as the distance between two flat parallel faces. Example slip gauges, length bars, ends of micrometer anvil, gap gauges, etc. 3. Wavelength Standard. Line standards and end standards are physical i.e. they are material standards and are subjected to destruction and their dimensions change slightly with time. It therefore became necessary to have a standard of length, which will be accurate and invariable. A French philosopher suggested that wavelength of monochromatic light can be used as natural and invariable units of length. In 1960, orange radiation of isotope Krypton-86 was chosen for new definition of length; standard metre or yard were defined in terms of wavelengths of Kr-86. Wavelength standard is not subjected to destruction by wear and tear. Dimensions of wavelength standard do not change with time. 1metre= 165076373wavelengths and 1yard = 0.9144 metre. Comparators Comparator is an indirect type of measuring instrument. It does not measure actual dimension but indicates how much it differs from basic dimension. Classification of comparators: 1. Mechanical comparators 2. Electrical comparators 3. Pneumatic comparators 4. Optical comparators 5. Electronic comparators etc. Dial Indicators/Mechanical Comparators. Dial indicator is a mechanical comparator. There are small indicating devices in dial indicator which are used as mechanical means such as gears and pinions for magnification system.
Lecture notes by Meet Bakotia Principle of operation of dial indicator: Dial indicators measures the displacement of its plunger or stylus on circular dial by means of rotating pointer. Hence it converts linear displacement of plunger into radial displacement of pointer by mechanical means such as gears and pinions. However a dial indicator by itself is not a much use unless it is properly mounted and set before using for inspection as shown in figure below. Least count/Sensitivity of Dial indicator. Scale on dial is calibrated in 10 bigger divisions i.e. 10, 20, …….90,100 which clearly indicates that there are total 100 divisions on dial. Each bigger division is divided into 10 smaller divisions, thus one small division corresponds to 0.01mm. 1 complete revolution of pointer corresponds to 10 big divisions =1mm. Small dial pointer moved by 1 division indicates the one complete revolution of pointer on large dial. Sensitivity is the appropriate term used for dial indicator, instead of using the term least count. Sensitivity of dial indicator is 0.01mm. The meaning of sensitivity is the smallest variation of the quantity that can be detected by the instrument. Working principle of Dial indicator. Dial indicator consists of a plunger which slides in bearing and carries a rack at its inner end. Rack meshes with pinion (P1) which drives another gear and pinion. Rack guide prevents rotation of plunger about its own axis. Plunger is kept in its normal extended position by means of light coil spring. The line arm movement of a plunger is magnified by gear train consisting of several gears and pinions and transmitted to the pointer on dial scale. When the plunger is in contact with workpiece, little movement causes rack to turn the pinion (P1) which is attached to gear (G1). Gear (G1) further meshes with pinion (P2). Another gear (G2) is attached to (P2) which further meshes to (P3). Gear (G3) meshes with Pinion (P3). Overall magnification of final pinion P3 is
Lecture notes by Meet Bakotia Where Tg1, Tg2, Tp2, Tp3 are no. of teeth of gears g1 and g2 and pinions p2 and p3. Pneumatic comparator: Pressurized air is used a working medium and means of magnification in pneumatic comparators. Air at low but constant pressure (p) is allowed to flow through a control orifice (Oc) into an intermediate chamber and then to the measuring orifice (Om) from where it is allowed to escape in to atmosphere. The pressure Pi in the intermediate chamber can be changed by varying the restriction applied to the measuring jet. This pressure pi is a function of difference in two diameters of two orifices Oc and Om. Orifice size Oc is fixed and effective size of Om can be varied by varying the distance d between the gauge and the work restriction. As the distance d changes, Pi changes.
Lecture notes by Meet Bakotia Solex air gauge (Pneumatic comparator): A calibrated manometer tube is connected between the cylinder and control orifice as shown in the fig above. If the pressure of the air supplied is higher than the desired pressure, some air will bubble out from the bottom of the dip tube and air moving to the control volume will be at the desired constant pressure. The constant pressure air then passes through the control orifice and escapes from the measuring jets. When there is no restriction to the escape of air, the level of water in the manometer tube will coincide with that in the cylinder. But, if there is a restriction to the escape of air through the jets, a back pressure will be induced in the circuit and level of water in the manometer tube will fall. The restriction to the escape of air depends upon the variations in the dimensions to be measured. Thus the variation in the dimensions to be measured is converted into corresponding pressure variations, which can be read from the calibrated scale provided with the manometer.
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