Mechanical measurement and metrology notes pdf

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1 Mechanical Measurement & Metrology Course Contents 1.1 Introduction 1.2 Need Of Inspection 1.3 Objectives of Metrology 1.4 Precision And Accuracy 1.5 Errors in Measurement 1.6 General Care Of Metrological Instrument 1.7 Standardization and Standardizing Organization Department of Mechanical Engineering Darshan Institute of Engineering & Technology, Rajkot Page 1.1 1. Introduction Mechanical Measurement & Metrology (2141901) 1.1 Introduction  Metrology is a science of measurement. Metrology may be divided depending upon the quantity under consideration into: metrology of length, metrology of time etc. Depending upon the field of application it is divided into industrial metrology, medical metrology etc.  Engineering metrology is restricted to the measurement of length, angles and other quantities which are expressed in linear or angular terms.  For every kind of quantity measured, there must be a unit to measure it. This will enable the quantity to be measured in number of that unit. Further, in order that this unit is followed by all; there must be a universal standard and the various units for various parameters of importance must be standardized.  It is also necessary to see whether the result is given with sufficient correctness and accuracy for a particular need or not. This will depend on the method of measurement, measuring devices used etc.  Thus, in a broader sense metrology is not limited to length and angle measurement but also concerned with numerous problems theoretical as well as practical related with measurement such as: 1. Units of measurement and their standards, which is concerned with the establishment, reproduction, conservation and transfer of units of measurement and their standards. 2. Methods of measurement based on agreed units and standards. 3. Errors of measurement. 4. Measuring instruments and devices. 5. Accuracy of measuring instruments and their care. 6. Industrial inspection and its various techniques. 7. Design, manufacturing and testing of gauges of all kinds. 1.2 Need of Inspection  Inspection means checking of all materials, products or component parts at various stages during manufacturing. It is the act of comparing materials, products or components with some established standard. Department of Mechanical Engineering Page 1.2 Darshan Institute of Engineering & Technology, Rajkot Mechanical Measurement & Metrology (2141901) 1. Introduction  In old days the production was on a small scale, different component parts were made and assembled by the same craftsman. If the parts did not fit properly at the time of assembly, he used to make the necessary adjustments in either of the mating parts so that each assembly functioned properly.  Therefore, it was not necessary to make similar parts exactly alike or with same accuracy as there was no need of inspection.  Due to technological development new production techniques have been developed. The products are being manufactured on a large scale due to low cost methods of mass production. So, hand fit method cannot serve the purpose any more. The modern industrial mass production system is based on interchangeable manufacture, when the articles are to be produced on a large scale.  In mass production the production of complete article is broken up into various component parts. Thus the production of each component part becomes an independent process. The different component parts are made in large quantities in different shops. Some parts are purchased from other factories also and then assembled together at one place. Therefore, it becomes essential that any part chosen at random should fit properly with any other mating parts that too selected at random. This is possible only when the dimensions of the component parts are made with close dimensional tolerances. This is only possible when the parts are inspected at various stages during manufacturing.  When large number of identical parts are manufactured on the basis of interchangeability if their dimensions are actually measured every time lot of time will be required. Hence, to save the time gauges are used, which can tell whether the part manufactured is within the prescribed limits or not. Thus, the need of inspection can be summarized as: 1. To ensure that the part, material or a component conforms to the established standard. 2. To meet the interchangeability of manufacture. 3. To maintain customer relation by ensuring that no faulty product reaches the customers. Department of Mechanical Engineering Darshan Institute of Engineering & Technology, Rajkot Page 1.3 1. Introduction Mechanical Measurement & Metrology (2141901) 4. Provide the means of finding out shortcomings in manufacture. The results of inspection are not only recorded but forwarded to the manufacturing department for taking necessary steps, so as to produce acceptable parts and reduce scrap. 5. It also helps to purchase good quality of raw materials, tools, equipment which governs the quality of the finished products. 6. It also helps to co-ordinate the functions of quality control, production, purchasing and other departments of the organization. To take decision on the defective parts i.e., to judge the possibility of making some of these parts acceptable after minor repairs. 1.3 Objectives of Metrology While the basic objective of a measurement is to provide the required accuracy at minimum cost, metrology would have further objective in a modern engineering plant with different shops like Tool Room, Machine Shop, Press Shop, Plastic Shop, Pressure Die Casting Shop, Electroplating and Painting Shop, and Assembly Shop; as also Research, Development and Engineering Department. In such an engineering organization, the further objectives would be as follows: 1. Thorough evaluation of newly developed products, to ensure that components designed is within the process and measuring instrument capabilities available in the plant. 2. To determine the process capabilities and ensure that these are better than the relevant component tolerance. 3. To determine the measuring instrument capabilities and ensure that these are adequate for their respective measurements. 4. To minimize the cost of inspection by effective and efficient use of available facilities and to reduce the cost of rejects and rework through application of Statistical Quality Control Techniques 5. Standardization of measuring methods. This is achieved by laying down inspection methods for any product right at the time when production technology is prepared. 6. Maintenance of the accuracies of measurement. This is achieved by periodical calibration of the metrological instruments used in the plant. 7. Arbitration and solution of problems arising on the shop floor regarding methods of measurement. Department of Mechanical Engineering Page 1.4 Darshan Institute of Engineering & Technology, Rajkot Mechanical Measurement & Metrology (2141901) 1. Introduction 8. Preparation of designs for all gauges and special inspection fixtures. Development of Material Standard  The need for establishing standard of length was raised primarily for determining agricultural land areas and for the erection of buildings and monuments. The earliest standard of length was established in terms of parts of human body. The Egyptian unit was called a cubit. It was equal to the length of the forearm (from the elbow to the tip of the middle figure).  Rapid advancement made in engineering during nineteenth century was due to improved materials available and more accurate measuring techniques developed. It was not until 1855 that first accurate standard was made in England. It was known as imperial standard yard. This was followed by International Prototype meter made in France in the year 1872. These two standards of lengths were made of material (metal alloys) and hence they are called as material standards in contrast to wavelength standard adopted as length standard later on. Imperial Standard Yard  The imperial standard yard is made of 1 inch square cross-section bronze bar (82% copper, 13% tin, 5% zinc) 38 inches long. The bar has two 1/2 inch diameter X 1/2 inch deep holes. Each hole is fitted with 1/10th inch diameter gold plug. The top surface of these plugs lie on the neutral axis of the bronze bar. The purpose of keeping the gold plug lines at neutral axis has the following advantages. - Due to bending of beam the neutral axis remains unaffected - The plug remains protected from accidental damage. The top surface of the gold plugs is highly polished and contains three lines engraved transversely and two lines longitudinally. The yard is defined as the distance between two central transverse lines on the plugs when, 1. The temperature of the bar is constant at 62°F and, 2. The bar is supported on rollers in a specified manner to prevent flexure. Department of Mechanical Engineering Darshan Institute of Engineering & Technology, Rajkot Page 1.5 1. Introduction Mechanical Measurement & Metrology (2141901) Figure 1.1 Imperial Standard Yards International Standard Meter (Prototype)  This standard was established originally by International Bureau of Weights and Measures in the year 1875. The prototype meter is made of platinum-iridium alloy (90% platinum and 10% iridium) having a cross-section as shown in Fig. 1.2.  The upper surface of the web is highly polished and has two fine lines engraved over it. It is in-oxidisable and can have a good finish required for ruling good quality of lines. The bar is kept at 0°C and under normal atmospheric pressure. It is supported by two rollers of at least one cm diameter symmetrically situated in the same horizontal plane. The distance between the rollers is kept 589 mm so as to give minimum deflection. The web section chosen gives maximum rigidity and economy of costly material. The distance between the centers portions of two lines engraved on the polished surface of this bar of platinum-iridium alloy is taken as one meter.  According to this standard, the length of the meter is defined as the straight line distance, at 0°C between the centre portions of pure platinum-iridium alloy (90% platinum, 10% iridium) of 102 cm total length and having a web cross-section as shown in Fig. 1.2. Department of Mechanical Engineering Page 1.6 Darshan Institute of Engineering & Technology, Rajkot Mechanical Measurement & Metrology (2141901) 1. Introduction Figure 1.2 International Prototype Meter Cross-sections  The metric standard when in use is supported at two points which are 58.9 cm apart as calculated from Airy's formula, according to which the best distance between the supporting points is given by √ Where, L = total length of bar (assumed uniform), b = distance between points, n = number is supports  For prototype meter, √  This reference was designated as International Prototype Meter M in 1899. It is preserved by (BIPM) at Sevres in France. The BIPM is controlled by the International Committee of Weights and Measure.  The imperial standard yard was found to be decreasing in length at the rate of one- millionth of an inch for the past 50 years when compared with internal standard meter. The prototype meter is quite stable. There-fore, yard relationship had to be defined in terms of meter as 1 yard = 0.9144 meter, or inch = 25.4 mm. Disadvantages of Material Standard 1. The material standards are influenced by effects of variation of environmental conditions like temperature, pressure, humidity and ageing etc., and it thus changes in length. 2. These standards are required to be preserved or stored under security to prevent their damage or destruction. 3. The replica of these standards was not available for use somewhere else. Department of Mechanical Engineering Darshan Institute of Engineering & Technology, Rajkot Page 1.7 1. Introduction Mechanical Measurement & Metrology (2141901) 4. These are not easily reproducible. 5. Conversion factor was to be used for changing over to metric working. 6. Considerable difficulty is experienced while comparing and verifying the sizes of gauges. Wavelength Standard  The major drawback with the metallic standards meter and yard is that their length changes slightly with time. Secondly, considerable difficulty is experienced while comparing and verifying the sizes of gauges by using material standards. This may lead to errors of unacceptable order of magnitude. It therefore became necessary to have a standard of length which will be accurate and invariable. Jacques Babinet a French philosopher suggested that wavelength of monochromatic light can be used as natural and invariable unit of length.  In 1907 the International Angstrom (A) unit was defined in terms of wavelength of red cadmium in dry air at 15°C (6438.4696 A = 1 wavelength of red cadmium). Seventh General Conference of Weights and Measures approved in 1927, the definition of standard of length relative to the meter in terms of wavelength of the red cadmium as an alternative to International Prototype meter.  Orange radiation of isotope krypton-86 was chosen for new definition of length in 1960, by the Eleventh General Conference of Weights and Measures. The committee decided to recommend that Krypton-86 was the most suitable element and that it should be used in a hot-cathode discharge lamp maintained at a temperature of 63° Kelvin. According to this standard meter was defined as equal to 1650763.73 wavelengths of the red orange radiation of Krypton isotope 86 gases. 9  The standard as now defined can be reproduced to an accuracy of about 1 part in 10 . The meter and yard were redefined in terms of wave length of orange Kr-86 radiation as, 1 meter = 1650763.73 wavelengths, and 1 yard = 0.9144 meter = 0.9144 x 1650763.73 wavelengths = 1509458.3 wavelengths. Department of Mechanical Engineering Page 1.8 Darshan Institute of Engineering & Technology, Rajkot Mechanical Measurement & Metrology (2141901) 1. Introduction Meter as of Today  Although Krypton-86 standard served well, technologically increasing demands more accurate standards. It was through that a definition based on the speed of light would be technically feasible and practically advantageous. Seventeenth General Conference of Weights and Measure. Agreed to a fundamental change in the definition of the meter on 20th October 1983.  Accordingly, meter is defined as the length of the path travelled by light in vacuum in 1/299792458 seconds. This can be realized in practice through the use of an iodine- stabilized helium-neon laser.  The reproducibility is 3 parts in 1011, which may be compared to measuring the earth's mean circumference to an accuracy of about 1 mm. With this new definition of meter, one standard yard will be the length of the path travelled by light travelled in 0.9144 x -9 1/299792458 sec. I. e., in 3 x 10 sec. The advantages of wavelength standard are: 1. It is not a material standard and hence it is not influenced by effects of variation of environmental conditions like temperature, pressure, humidity and ageing. 2. It need not be preserved or stored under security and thus there is no fear of being destroyed as in case of meter and yard. 3. It is not subjected to destruction by wear and tear. 4. It gives a unit of length which can be produced consistently at all the times in all the circumstances, at all the places. In other words it is easily reproducible and thus identical standards are available with all. 5. This standard is easily available to all standardizing laboratories and industries. 6. There is no problem of transferring this standard to other standards meter and yard. 7. It can be used for making comparative measurements of very high accuracy. The error of 11 reproduction is only of the order of 3 parts in 10 Subdivision of standards The international standard yard and the international prototype meter cannot be used for general purposes. For practical measurement there is a hierarchy of working standards. Thus depending upon their importance of accuracy required, for the work the standards are subdivided into four grades; 1. Primary standards 2. Secondary standards Department of Mechanical Engineering Darshan Institute of Engineering & Technology, Rajkot Page 1.9 1. Introduction Mechanical Measurement & Metrology (2141901) 3. Territory standards 4. Working standards. 1. Primary Standards For precise definition of the unit, there shall be one, and only one material standard, which is to be preserved under most careful conditions. It is called as primary standard. International yard and International meter are the examples of primary standards. Primary standard is used only at rare intervals (say after 10 to 20 years) solely for comparison with secondary standards. It has no direct application to a measuring problem encountered in engineering. 2. Secondary Standards Secondary standards are made as nearly as possible exactly similar to primary standards as regards design, material and length. They are compared with primary standards after long intervals and the records of deviation are noted. These standards are kept at number of places for safe custody. They are used for occasional comparison with tertiary standards whenever required. 3. Tertiary Standards The primary and secondary standards are applicable only as ultimate control. Tertiary standards are the first standard to be used for reference purposes in laboratories and workshops. They are made as true copy of the secondary standards. They are used for comparison at intervals with working standards. 4. Working Standards Working standards are used more frequently in laboratories and workshops. They are usually made of low grade of material as compared to primary, secondary and tertiary standards, for the sake of economy. They are derived from fundamental standards. Both line and end working standards are used. Line standards are made from H-cross-sectional form. Figure 1.3 Working Line Standards Most of the precision measurement involves the distance between two surfaces and not with the length between two lines. End standards are suitable for this purpose. For shorter Department of Mechanical Engineering Page 1.10 Darshan Institute of Engineering & Technology, Rajkot Mechanical Measurement & Metrology (2141901) 1. Introduction lengths up to 125 mm slip gauges are used and for longer lengths end bars of circular cross- section are used. The distance between the end faces of slip gauges or end bars is controlled to ensure a high degree of accuracy. Sometimes the standards are also classified as: 1. Reference standards- Used for reference purposes. 2. Calibration standards - Used for calibration of inspection and working standards. 3. Inspection standards - Used by inspectors. 4. Working standards - Used by operators, during working. Line and End Measurements A length may be measured as the distance between two lines or as the distance between two parallel faces. So, the instruments for direct measurement of linear dimensions fall into two categories. 1. Line standards. 2. End standards. Line Standards When the length is measured as the distance between centers of two engraved lines, it is called line standard. Both material standards yard and meter are line standards. The most common example of line measurements is the rule with divisions shown as lines marked on it. Characteristics of Line Standards 1. Scales can be accurately engraved but the engraved lines themselves possess thickness and it is not possible to take measurements with high accuracy. 2. A scale is a quick and easy to use over a wide range. 3. The scale markings are not subjected to wear. However, the leading ends are subjected to wear and this may lead to undersize measurements. 4. A scale does not possess a "built in" datum. Therefore it is not possible to align the scale with the axis of measurement. 5. Scales are subjected to parallax error. 6. Also, the assistance of magnifying glass or microscope is required if sufficient accuracy is to be achieved. End standards When length is expressed as the distance between two flat parallel faces, it is known as end standard. Examples: Measurement by slip gauges, end bars, ends of micrometer anvils, Department of Mechanical Engineering Darshan Institute of Engineering & Technology, Rajkot Page 1.11 1. Introduction Mechanical Measurement & Metrology (2141901) vernier calipers etc. The end faces are hardened, lapped flat and parallel to a very high degree of accuracy. Characteristics of End Standards 1. These standards are highly accurate and used for measurement of close tolerances in precision engineering as well as in standard laboratories, tool rooms, inspection departments etc. 2. They require more time for measurements and measure only one dimension at a time. 3. They are subjected to wear on their measuring faces. 4. Group of slips can be "wrung" together to build up a given size; faulty wringing and careless use may lead to inaccurate results. 5. End standards have built in datum since their measuring faces are f l at and parallel and can be positively locked on datum surface. 6. They are not subjected to parallax effect as their use depends on feel. Comparison between Line Standards and End Standards: Sr. Characteristic Line Standard End Standard No. 1. Principle Length is expressed as the Length is expressed as distance between two lines the distance between two flat parallel faces 2. Accuracy Limited to ± 0.2 mm for high Highly accurate for accuracy, scales have to be used measurement of close in conjunction with magnifying tolerances up to ± 0.001 glass or microscope mm. 3. Ease and time Measurement is quick and easy Use of end standard & requires skill and is time measurement consuming. 4. Effect of wear Scale markings are not subject to These are subjected to wear. However, significant wear wear on their measuring may occur on leading ends. Thus surfaces. it may be difficult to assume zero of scale as datum. 5. Alignment Cannot be easily aligned with the Can be easily aligned Department of Mechanical Engineering Page 1.12 Darshan Institute of Engineering & Technology, Rajkot Mechanical Measurement & Metrology (2141901) 1. Introduction axis of measurement. with the axis of measurement. 6. Manufacture Simple to manufacture at low Manufacturing process is and cost cost. complex and cost is high. 7. Parallax effect They ate subjected to parallax They ate not subjected error to parallax error 8. Examples Scale (yard, meter etc.) Slip gauges, end bars, V- caliper, micrometers etc. The accuracy of both these standards is affected by temperature change and both are originally calibrated at 20 ± 0.5°C. It is also necessary to take utmost case in their manufacture to ensure that the change of shape with time, secular change is reduced to negligible. Classification of Standards and Traceability  In order to maintain accuracy and interchangeability in the items manufactured by various industries in the country, it is essential that the standards of units and measurements followed by them must be traceable to a single source, i.e., the National Standards of the country. Further, the National Standards must also be linked with International Standard to maintain accuracy and interchangeability in the items manufactured by the various countries.  The national laboratories of well-developed countries maintain close tolerance with International Bureau of Weights and Measures, there is assurance that the items manufactured to identical dimensions in different countries will be compatible. Application of precise measurement has increased to such an extent that it is not practicable for a single national laboratory to perform directly all the calibrations and standardizations required by a large country. It has therefore become necessary that the process of traceability technique needs to be followed in stages, that is, National laboratories, standardizing laboratories, etc. need to be established for country, states, and industries but all must be traceable to a single source as shown in Fig. 1.4 below. Department of Mechanical Engineering Darshan Institute of Engineering & Technology, Rajkot Page 1.13 1. Introduction Mechanical Measurement & Metrology (2141901) Figure 1.4 Classifications of Standards in Order Clearly, there is degradation of accuracy in passing from the defining standards to the standard in use. The accuracy of a particular standard depends on a combination of the number of times it has been compared with a standard of higher order, the recentness of such comparisons, the care with which it was done, and the stability of the particular standard itself Measuring system element A measuring system is made of five basic elements. These are: 1. Standard 2. Work piece 3. Instrument 4. Person 5. Environment. The most basic element of measurement is a standard without which no measurement is possible. Once the standard is chosen a measuring instrument incorporations this standard is should be obtained. This instrument is then used to measure the job parameters, in terms of units of standard contained in it. The measurement should be performed under standard environment. And, lastly, there must be some person or mechanism (if automatic) to carry out the measurement. Methods of Measurement Department of Mechanical Engineering Page 1.14 Darshan Institute of Engineering & Technology, Rajkot Mechanical Measurement & Metrology (2141901) 1. Introduction These are the methods of comparison used in measurement process. In precision measurement various methods of measurement are adopted depending upon the accuracy required and the amount of permissible error. The methods of measurement can be classified as: 1. Direct method 6. Coincidence method 2. Indirect method 7. Deflection method 3. Absolute/Fundamental method 8. Complementary method 4. Comparative method 9. Contact method 5. Transposition method 10. Contactless method etc. 1. Direct method of measurement. This is a simple method of measurement, in which the value of the quantity to be measured is obtained directly without any calculations. For example, measurements by using scales, vernier calipers, micrometers, bevel protector etc. This method is most widely used in production. This method is not very accurate because it depends on human insensitiveness in making judgment. 2. Indirect method of measurement. In indirect method the value of quantity to be measured is obtained by measuring other quantities which are functionally related to the required value. E.g. angle measurement by sine bar, measurement of screw pitch diameter by three wire method etc. 3. Absolute or Fundamental method. It is based on the measurement of the base quantities used to define the quantity. For example, measuring a quantity directly in accordance with the definition of that quantity, or measuring a quantity indirectly by direct measurement of the quantities linked with the definition of the quantity to be measured. 4. Comparative method. In this method the value of the quantity to be measured is compared with known value of the same quantity or other quantity practically related to it. So, in this method only the deviations from a master gauge are determined, e.g., dial indicators, or other comparators. 5. Transposition method. It is a method of measurement by direct comparison in which the value of the quantity measured is first balanced by an initial known value A of the same quantity, and then the value of the quantity measured is put in place of this known value and is balanced again by another known value B. If the position of the element indicating equilibrium is the same in Department of Mechanical Engineering Darshan Institute of Engineering & Technology, Rajkot Page 1.15 1. Introduction Mechanical Measurement & Metrology (2141901) both cases, the value of the quantity to be measured is√ . For example, determination of a mass by means of a balance and known weights, using the Gauss double weighing method. 6. Coincidence method. It is a differential method of measurement, in which a very small difference between the value of the quantity to be measured and the reference is determined by the observation of the coincidence of certain lines or signals. For example, measurement by vernier caliper micrometer. 7. Deflection method. In this method the value of the quantity to be measured is directly indicated by a deflection of a pointer on a calibrated scale. 8. Complementary method. In this method the value of the quantity to be measured is combined with a known value of the same quantity. The combination is so adjusted that the sum of these two values is equal to predetermined comparison value. For example, determination of the volume of a solid by liquid displacement. 9. Method of measurement by substitution. It is a method of direct comparison in which the value of a quantity to be measured is replaced by a known value of the same quantity, so selected that the effects produced in the indicating device by these two values are the same. 10. Method of null measurement. It is a method of differential measurement. In this method the difference between the value of the quantity to be measured and the known value of the same quantity with which it is compared is brought to zero. 11. Contact method. In this method the sensor or measuring tip of the instrument actually touches the surface to be measured. e.g., measurements by micrometer, vernier caliper, dial indicators etc. In such cases arrangement for constant contact pressure should be provided to prevent errors due to excessive contact pressure. Department of Mechanical Engineering Page 1.16 Darshan Institute of Engineering & Technology, Rajkot Mechanical Measurement & Metrology (2141901) 1. Introduction 12. Contactless method. In contactless method of measurement, the there is no direct contact with the surface to be measured. e.g., measurement by optical instruments, such as tool makers microscope, projection comparator etc. 1.4 Precision and Accuracy Precision  The terms precision and accuracy are used in connection with the performance of the instrument. Precision is the repeatability of the measuring process.  It refers to the group of measurements for the same characteristics taken under identical conditions. It indicates to what extent the identically performed measurements agree with each other. If the instrument is not precise it will give different (widely varying) results for the same dimension when measured again and again. The set of observations will scatter about the mean. The scatter of these measurements is designated as 0, the standard deviation. It is used as an index of precision. The less the scattering more precise is the instrument. Thus, lower, the value of 0, the more precise is the instrument. Accuracy  Accuracy is the degree to which the measured value of the quality characteristic agrees with the true value. The difference between the true value and the measured value is known as error of measurement.  It is practically difficult to measure exactly the true value and therefore a set of observations is made whose mean value is taken as the true value of the quality measured. Distinction between Precision and Accuracy  Accuracy is very often confused with precision though much different. The distinction between the precision and accuracy will become clear by the following example. Several measurements are made on a component by different types of instruments (A, B and C respectively) and the results are plotted.  In any set of measurements, the individual measurements are scattered about the mean, and the precision signifies how well the various measurements performed by same instrument on the same quality characteristic agree with each other. Department of Mechanical Engineering Darshan Institute of Engineering & Technology, Rajkot Page 1.17 1. Introduction Mechanical Measurement & Metrology (2141901) Figure 1.5 Precision And Accuracy  The difference between the mean of set of readings on the same quality characteristic and the true value is called as error. Less the error more accurate is the instrument. Figure 1.5 shows that the instrument A is precise since the results of number of measurements are close to the average value. However, there is a large difference (error) between the true value and the average value hence it is not accurate.  The readings taken by the instruments are scattered much from the average value and hence it is not precise but accurate as there is a small difference between the average value and true value. Fig. 1.5 (c) shows that the instrument is accurate as well as precise. 1.5 Errors in Measurement  It is never possible to measure the true value of a dimension, there is always some error. The error in measurement is the difference between the measured value and the true value of the measured dimension. Department of Mechanical Engineering Page 1.18 Darshan Institute of Engineering & Technology, Rajkot Mechanical Measurement & Metrology (2141901) 1. Introduction  Error in measurement =Measured value - True value. The error in measurement may be expressed or evaluated either as an absolute error or as a relative error. Absolute Error  True absolute error. It is the algebraic difference between the result of measurement and the conventional true value of the quantity measured.  Apparent absolute error. If the series of measurement are made then the algebraic difference between one of the results of measurement and the arithmetical mean is known as apparent absolute error. Relative Error  It is the quotient of the absolute error and the value of comparison used for calculation of that absolute error. This value of comparison may be the true value, the conventional true value or the arithmetic mean for series of measurement. The accuracy of measurement, and hence the error depends upon so many factors, such as: - Calibration standard - Work piece - Instrument - Person - Environment etc. as already described. No matter, how modern is the measuring instrument, how skillful is the operator, how accurate the measurement process, there would always be some error. It is therefore attempted to minimize the error. To minimize the error, usually a number of observations are made and their average is taken as the value of that measurement.  If these observations are made under identical conditions i.e., same observer, same instrument and similar working conditions excepting for time, then, it is called as Single Sample Test'.  If however, repeated measurements of a given property using alternate test conditions, such as different observer and/or different instrument are made, the procedure is called as `Multi-Sample Test'. The multi-sample test avoids many controllable errors e.g., personal error, instrument zero error etc. The multi-sample test is costlier than the single sample test and hence the later is in wide use. Department of Mechanical Engineering Darshan Institute of Engineering & Technology, Rajkot Page 1.19 1. Introduction Mechanical Measurement & Metrology (2141901)  In practice good numbers of observations are made under single sample test and statistical techniques are applied to get results which could be approximate to those obtainable from multi-sample test. Types of Error During measurement several types of error may arise, these are 1. Static errors which includes - Reading errors - Characteristic errors - Environmental errors. 2. Instrument loading errors. 3. Dynamic errors. Static errors These errors result from the physical nature of the various components of measuring system. There are three basic sources of static errors. The static error divided by the measurement range (difference between the upper and lower limits of measurement) gives the measurement precision. Reading errors Reading errors apply exclusively to the read-out device. These do not have any direct relationship with other types of errors within the measuring system. Reading errors include: Parallax error, Interpolation error. Attempts have been made to reduce or eliminate reading errors by relatively simple techniques. For example, the use of mirror behind the readout pointer or indicator virtually eliminates occurrence of parallax error. Interpolation error. It is the reading error resulting from the inexact evaluation of the position of index with regards to two adjacent graduation marks between which the index is located. How accurately can a scale be readthis depends upon the thickness of the graduation marks, the spacing of the scale division and the thickness of the pointer used to give the reading Interpolation error can be tackled by increasing; using magnifier over the scale in the viscinity of pointer or by using a digital read out system. Department of Mechanical Engineering Page 1.20 Darshan Institute of Engineering & Technology, Rajkot

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