Chapter (2) : Linear Measurements Dr Jehad Yamin Linear Measurements 1. Introduction : When man first sought a unit of length, he adopted parts of his body, mainly his hands, arms and feet. For example, ancient Egyptians used the “Cubit” for their measurements. It is equal to the distance between the tip of the forefinger to the elbow. Today, the entire industrial world has adapted the “International Meter” as a standard for linear measurement. It was defined in 1960 officially as being 1650763.73 wavelengths of the orange-red radiation given off by electrically excited Krypton 86 gas under vacuum. Accordingly, the English Inches has been officially defined as 2.54 cm, thus, the inch is 41929.399 wavelengths of the orange-red radiation given off by electrically excited Krypton 86 gas under vacuum. Classification : There are several ways of classification of linear measurement instruments. One such classification is: (1) Line Measurement (i.e. measuring distance between two lines) & (2) End Measurement (i.e. measuring distance between two faces or ends). Another method is based on the resolution as follows: (1) Low Resolution (e.g. scale alone or in conjunction with other devices like calipers) (2) Medium Resolution (e.g. micrometer, vernier instruments) (3) High Resolution, and, (4) Super Resolution. (e.g. interferometers) 2.1 Low Resolution Line Measurement Instruments These are devices that incorporate graduation spacing representing known distances. Accuracy is affected by: (1) Accuracy of graduation, (2) Resolution of graduation lines, (3) Quality of graduation lines, (4) Instrument design, (5) Geometric deficiencies, and, (6) Workman’s experience. Observational errors are mainly due to: (1) Parallax and (2) Misalignment. Sensitivity of these instruments depend on the instrument’s basic design (i.e. least count). Chapter (2) : Linear Measurements Dr Jehad Yamin 2.1.1 Steel Rule Type: This is a low-resolution line-measuring instrument. Operating principle: comparing an unknown length to a previously calibrated one. Construction: It consists of a strip of hardened steel having line graduations etched or engraved at intervals of fraction of standard unit of length. These graduations may not be uniform all throughout its length. This allows for multiple use for particular range as per accuracy required. How to use: As shown in figure below. Chapter (2) : Linear Measurements Dr Jehad Yamin Basic desirable qualities: (1) Clearly engraved lines, (2) Minimum thickness, (3) Good quality spring steel, (4) Graduations on both sides, (5) Low coefficient of thermal expansion. Degree of accuracy affected by: (1) Quality of rule, (2) Skill of user in estimation the parts of mm. Reliability of measurement when using scale for direct measurement depends on the proper positioning of the scale in relation to workplace. Graduate rule accessories: For good reliability, several accessories are available to help improve accuracy of positioning. These include: Hooks (This is used for (1) Good alignment of the “zero” point of the scale with border line of an object surface, (2) Keep the rule in position normal to the edge of the surface), Clamping shafts, decimal rules (these are short rules used for measurement of lengths below 1/64” it has least count of 0.01”), Foot rests, square head and center finders (used to allow for location of centerline on the face of round objects), Parallel clamps (used for proper alignment of rule with axis of cylinder). 2.1.2. Calipers These are accessories to scales and help measuring directly those parts that cannot be measured directly by the scale. Construction & Use: They consist of two legs hinged at the top with the ends of the legs span the parts to be inspected. Classification: Calipers may be broadly classified as : 1. Spring Type calipers (where the spring tension holds the legs of the calipers firmly against the adjusting nuts. Chapter (2) : Linear Measurements Dr Jehad Yamin 2. Firm-Joint calipers (where the friction created at the junction of the legs tension holds the legs of the calipers firmly. They can also be further classified as : Inside, Outside, Transferable, and Hermophrodite calipers. 2.1.3. Firm Joint Calipers Operating principle: They are devices for comparing measurements against known dimensions. Construction: The legs are made from carbon & alloy steel containing not more than 0.05% Sulphur, and 0.05% Phosphorous with working ends suitably hardened and tempered to hardness of 400-500 HV and faces up to 650 + 50 HV. They are joined together by a rivet. They have rectangular cross section. Qualities: They should be free from cracks, seams, dirt, flaws and must have smooth bright finish. Nominal Size is the distance between the center of the rolling end and the extreme working end of a leg. Caliper’s Capacity is the maximum dimension that can be measured by the caliper. It should not be lesser than the nominal size. The accuracy depends on the sense and feel of the operator. Therefore, caliper should be held gently and square to the work with slight gauging pressure applied. 2.1.4. Spring Calipers One end of the adjusting screw is hinged to one leg and a steel ball is positively fixed to the free end of the adjusting screw for the purpose of retaining the adjusting nut. Chapter (2) : Linear Measurements Dr Jehad Yamin 2.1.4. Outside Calipers Used to measure the outside dimensions. 2.1.5 Inside Calipers Used to measure the inside dimensions and to transfer reading to a scale with hooks. 2.1.6 : Dial Calipers: Provide typical direct reading capability of 0.02mm. Self reading: transfer calipers, Hermophrodite calipers, surface plates, V-blocks, combination set. 2.2. Precision (medium resolution) linear measurement Since modern production is more concerned with interchangeability of products, great precision dimensional control became a must. This necessitates the use of more precise measuring instruments. 2.2.1. Characteristics of precise measuring instruments (1) High degree of sensitivity, (2) High degree of accuracy, (3) Minimum inertia in moving parts, and (4) Freedom from variance. In order to achieve the above characteristics, the following principles must be observed : Principle of alignment, Principle of kinematics, Principle of measuring contacts, Selection of measuring instrument, and Inspection must guarantee that this same measurement technique will yield comparable results if repeated. 2.2.2. The Vernier Instruments Operating principle: when two scales or divisions slightly different in sizes are used, the difference between them can be utilized to enhance the accuracy of measurement. Chapter (2) : Linear Measurements Dr Jehad Yamin Construction: Explain with reference to figure below. Reading the Vernier Scale : (1) The last numbered division on the main scale to the left of the “Zero” of vernier scale is noted. If the scale is graduated in cm, then multiply by 10 mm, as this is the official engineering dimensional unit. (2) Note how many graduations are showing between this numbered division and the “Zero” of the vernier scale. If the scale is graduated in Cm, then multiply this number with 1 mm. (3) Find the line on the vernier scale, which coincides with a line on the main scale. Multiply this number with the least count of the vernier scale. Chapter (2) : Linear Measurements Dr Jehad Yamin Design of the vernier scale : A relation can be derived between the size of the size of divisions on the main scale and the size of divisions on the vernire scale. Let, Cm = size of divisions on main scale (mm) Cv= size of divisions on vernier scale (mm) N = number of the total divisions on vernier scale. Now, when the zeros on the two scales coincide, we have (n-1) * Cm = n * Cv Hence, the size of the division on the vernier scale “Cv” is found as : [(n-1)/n] * Cm = Cv And the accuracy of the scale is found by subtracting the size of the vernier scale from that f the main scale. Hence; Accuracy = Cm – Cv = Cm /n Example on how to read the vernier scale : Let us take the first example as shown in the fisgure below : Hence; Cv = [24/25] * 0.5 = 0.48mm Accuracy = 0.5/25 = 0.02mm This represents the accuracy to which the reading can be taken. The dimension on the vernier caliper is taken as follows : Step (1) : Calculate the accuracy of the vernier caliper. Step (2) :Take the value on the main scale against the zero division of the vernier scale. Step (3) : Count the number of the division on the vernier scale that totally coincides with anyone on the main scale. Total reading = main scale reading of step (2) + Accuracy * number of division of step (3). Chapter (2) : Linear Measurements Dr Jehad Yamin For figure (a) above : Accuracy = 0.5/25 = 0.02mm Main scale reading opposite to zero division of VS = 22mm Division number 16 totally coincides with one division on M.S. Total reading = 22 + 0.02 * 16 = 22.32mm Graduation characteristics: they should be clearly engraved so that they are clearly visible. Sources of Errors with Vernier Caliper : Caliper not properly set to zero, Manipulation of the vernier scale reading, Wear in measuring tips, non-perpendicular plane between bar and jaws, or between jaws and workpiece. Care to be taken in using the Vernier Scale : (1) Not to be treated as a wrench or hammer since they are not rugged, (2) Should not be dropped or tossed aside rather, handled with care, (3) Should be cleaned from dirt. Precautions : (1) Use the fixed jaw as the reference jaw, (2) Do not play with the sliding jaw on the scale in order not to lose accuracy, (3) Regularly check the tips of the jaws for possible wear. Other types of vernier scales are : Vernier Height Scale; Vernier Depth Scale; Master Dial Indicator V.C. : 2.2.3. The Micrometer Operating principle: a circular movement of a threaded spindle produces an axial movement. The distance moved by the spindle (axial or linear movement) per revolution (circular movement of the thimble) depends on the pitch of the threaded spindle. Chapter (2) : Linear Measurements Dr Jehad Yamin Advantages of micrometer over V.C. : Easier and clearer readability, Lesser observational errors due to parallax, Portable, Easy to handle, Easy operation, Reasonable cost. Construction & Operation: Explain with reference to figure below. Chapter (2) : Linear Measurements Dr Jehad Yamin The micrometer is used as follows : 1) Check the zero reading, (2) Place the part to be measured in between the measuring faces, (3) Advance the spindle by rotating the ratchet until it begins to slip and a sound of click is heard. This indicates that there is no further ovement of the spindle, finally (4) Take the reading as explained below. Reading the micrometer Scale: (1) The last numbered division showing above the index line to the left of the thimble is noted (this is usually in mm). (2) Note if there is any half-mm line showing below the index line between the last numbered division and the thimble and add 0.5mm to the first reading.. (3) Add the number of lines on the thimble that coincides with the index lie. Reading on micrometer = Reading uncovered on the barrel + Accuracy * number of divisions on the thimble scale that coincides with horizontal line on barrel From figure above : Accuracy = 0.5/50 = 0.01mm Barrel reading = 11.5mm Division number 47 (zero line is not counted) matches. Total reading = 11.5 + 0.01 * 47 = 11.97mm. The measurement to a third degree of decimal can be made with micrometer by employing vernier scale alongwith the thimble and barrel divisions. This vernier scale is employed on the barrel or sleeve as shown below. This system is called Vernier Micrometer. Chapter (2) : Linear Measurements Dr Jehad Yamin Reading the Vernier micrometer Scale: Reading on micrometer = Reading uncovered on the barrel + Accuracy of sleeve * number of divisions on the thimble scale that is just below that on the horizontal line on barrel + Accuracy of vernier * number of divisions on the vernier scale that coincides with horizontal line on thimble Total reading = 10.5 (reading on barrel) + 0.01 * 16 (on sleeve) + 0.001 * 6 (on vernier scale) = 10.666mm Errors in reading: Lack of flatness of anvil, Inaccurate setting to “Zero” reading before use, Lack of parallelism between anvil and spindle or anvil and workpiece. Cleaning of micrometer : Clean after every time of use, should never be dunked in solvent or kerosene as a whole, should always remain free from oil, dust, grit or dirt. Precautions : (1) Apply workpiece gently between spindle and anvil, (2) Use proper size for proper dimensions, (3) Follow proper method of handling, (4) Regularly inspect parts and make sure that spindle moves freely. Accuracy with micrometer measurements depends on : (1) Degree of calibration of spindle movement. (2) Linearity of spindle movement. Other types of micrometers are : Inside Micrometer : pp. 145; Depth Gauge Micrometer : pp. 149; Threaded Gauge Micrometer : pp. 150; Outside Gauge Micrometer : Digital Micrometer : pp. 154 2.2.4. The Slip Gauges (Gauge Blocks) Basic Principle: End type linear measurement device. Construction & Operation: Explain with reference to figures below. Chapter (2) : Linear Measurements Dr Jehad Yamin Classification : based on their guaranteed accuracy, they are classified as : AA Master Slip Gauge. Has accuracy of + 2 microns per meter. A Reference Slip Gauge. Has accuracy of + 4 microns per meter. B Working Slip Gauge. Has accuracy of + 8 microns per meter. Grades of slip gauges : based on their guaranteed accuracy, they are classified as : O Grade. Used for inspection. OO Grade. Used as a standard in the standard room only. Calibration Grade. Has actual size for calibration. 2 Grade. Workshop grade for machine tools …etc. 1 Grade. For more precise work such as with sine bars. Sets of gauge blocks :They are available in different sets for different units Metric and English: Metric (56 pieces) Metric (103 pieces) English (81 pieces) 9 Pieces 1.001-1.009 49 pieces 1.01-1.49 9 pieces 0.1001-0.1009” ++0.001 mm ++0.01mm ++0.0001” 9 Pieces 1.01-1.09 49 pieces 0.50-24.5 49 pieces 0.1010-0.1490” ++0.010 mm ++0.5 mm ++0.001” 9 Pieces 1.0-1.9 4 pieces 25, 50, 75, 19 pieces 0.0500-0.9500” ++0.100 mm 1000 mm ++0.050” 25 Pieces 1-25 1 piece 1.005mm 4 pieces 1.0,2.0,3.0,4.0” ++1.000 mm ++1.0” 3 Pieces 25-75 ++ 25 mm 1 Piece 1.0005 Chapter (2) : Linear Measurements Dr Jehad Yamin Protecting Gauge Blocks: Another two gauges are added which are made extra wear resistant to reduce wear during inspection. They are called “Protector Gauge Blocks”. Usually have dimensions of 1mm, 1.5mm, 2mm or 2.5mm. They are marked with letter “P” on its measuring faces. Selecting and building up of blocks: To build up the blocks to the required length follow these steps : (1) Note down the required dimension, (2) Deduct from it the size of two protecting blocks, (3) Add blocks that eliminates the least digit of the number, (4) Continue till you reach zero. Accuracy is affected by : (1) Dimensional instability of material, (2) Wear during operation or use, (3) Damage during storage and handling, (4) Change in parallelism. To reduce errors and improve accuracy : (1) Repeated and periodical inspection and calibration, (2) Select the least number of gauge blocks for a given or required size (this helps reducing accumulative errors). Calibration : because of the repeated use of gauges, the may develop wear or damage of certain type. Repeated and regular inspection is needed to care for any error that may arise. There are several methods of calibration. One such method is by the use of interferometers (read by yourself). Example: List the slips to be wrung together to produce an overall dimension of 92.357mm using two protective gauge blocks of 2.5mm size. Chapter (2) : Linear Measurements Dr Jehad Yamin Answer: (1) Original size = 92.357 (2) Deduct two protective slip gauges = 05.000 Remainder = 87.357 (3) Add block to eliminate least digit = 01.007 Remainder = 86.350 (4) Repeat step No. (3) = 01.050 Remainder = 85.300 (5) Repeat step No. (3) = 01.300 Remainder = 84.000 (6) Reduce to nearest big number = 09.000 Remainder = 75.000 (7) Add one block of 75.000mm = 75.000 Remainder = 00.000 How to wring Blocks together When wringing blocks together, take care not to damage them. The correct sequence of movement to wring blocks together, illustrated as follows : 1. Clean the blocks with a clean, soft cloth. 2. Wipe each of the contacting surfaces on the clean palm of the hand or on the wrist. This procedure removes any dust particles left by the cloth and also applies a light film of oil. 3. Place the end of one block over the end of another block as shown in Figure. 4. While applying pressure on the two blocks, slide one block over the other. NOTE: If the blocks do not adhere to each other, it is generally because the blocks have not been thoroughly cleaned. Care of Gage Blocks 1. Gage blocks should always be protected from dust and dirt by being kept in a closed case when not in use. Chapter (2) : Linear Measurements Dr Jehad Yamin 2. Gages should not be handled unnecessarily since they absorb heat from the hand. Should this occur, the gage blocks must be permitted to return to room temperature before use. 3. Fingering of lapped surfaces should be avoided to prevent tarnishing and rusting. 4. Care should be taken not to drop gage blocks or scratch their lapped surfaces. 5. Immediately after use, each block should be cleaned, oiled, and replaced in the storage case. 6. Before gage blocks are wrung together, their faces must be free from oil and dust. 7. Gage blocks should never be left wrung together for any length of time. The slight moisture between the blocks can cause rusting, which will permanently damage the blocks. Effect of Temperature While the effect of temperature on ordinary measuring instruments is negligible, changes in temperature are important when precision gage blocks are handled. Gage blocks have been calibrated at 68°F (20°C), but human body temperature is about 98°F (37°C). A 1°F (0.5°C) rise in temperature will cause a 4-in. (100-mm) stack of gage blocks to expand approximately 0.000025 in. (0.0006 mm); therefore, these blocks should be handled as little as possible. The following suggestions are offered to eliminate as much temperature-change error as possible : 1. Handle gage blocks only when they must be moved. 2. Hold them by hand for as little time as possible. 3. Hold them between the tips of the fingers so that the area of contact is small, or use insulated tweezers. 4. Have the work and gage blocks at the same temperature. 5. If a temperature-controlled room is not available, both the work and gage blocks may be placed in kerosene until both are at the same temperature. 6. Where extreme accuracy is necessary, use insulating gloves and tweezers to prevent temperature change during handling.