 I welcome you all for module 8 lecture 2, a series of lecture on metrology. In the last lecture 1, we discussed about different kinds of instruments used for measurement of taper. We discussed about bevel protractors, sine bar, sine center and sine table. In this lecture number 2, we will continue with the discussion on the other instruments used for measurement of taper, angle and tilt. In this lecture, we will be covering the following topics. Internal taper measurement by using two balls of same diameter, then we will discuss about internal taper measurement by using two balls of different diameters and then we will learn about the clinometer, profile projector and auto collimator. Now, let us start the discussion on external taper measurement by using two rollers of same diameter. In this sketch, in this photograph, you can see the tapered component. This is the tapered component, tapered plug gauge. The taper angle of this is to be determined. The arrangement you can see here, we have kept two slip gauges of same height. Over that, we have kept two rollers of same diameter and then these rollers are in contact with the surface of the tapered plug gauge. Then over the rollers, we have to take the measurement. Using the appropriate instrument, for example, varnier caliper. So, the schematic arrangement, schematic diagram will be like this. We have the surface plate on which we have to keep the tapered component and then we have to keep slip gauge of equal height. Say this is a height h1 over which we have to keep the rollers, two rollers of same diameter. The rollers should contact the tapered component and then we have to take the measurement over roller. So, this is say m1 and then we have to change the height and again we have to keep two slip gauges of different height h2 and then over these slip gauges again, we have to keep the rollers. These two rollers should be in contact with the tapered component and over roller, we have to take the width m2 using varnier caliper or any other appropriate instrument. Then using the relationships, we can find the angle theta. Now, we will conduct an experiment on the taper measurement, external taper measurement by rollers, by using rollers of same diameter. Now, we can see the tapered component. The taper angle of this component is to be determined. Now, we have to take two rollers of same diameter. We should note down what is the diameter of the roller. So, in this case, you can see the diameter of roller is 10 millimetre. So, we have two rollers of same diameter. Now, we have a slip gauge of 30 millimetre height. We are taking two slip gauges of 20 millimetre and 10 millimetre thickness. We have to bring them together to build a height of 30 millimetre and then we have to keep the two slip gauges. Over the slip gauges, we have to place the two rollers such that they contact the tapered surface of the plug gauge. Now, we have to take the measurement over rollers. So, this is m1. I can see the reading is 62 millimetres. Reading is 62 millimetres. Now, we have to take another set of slip gauges. Now, we are ringing two slip gauges of 30 millimetre and 20 millimetre thickness. So, total height is 50 millimetre. So, another slip gauge of 50 millimetre height. Now, we have to keep the two rollers on the slip gauges of height 50 millimetre and over the rollers, we have to take the measurement over rollers. Now, the reading is 65, 66, 67, 67 and then we have to see the coinciding division. So, the one-year reading is 67.8 millimetre. Now, we have recorded the observations. The roller diameter is 10 millimetre and difference in height of slip gauges is equal to 50 minus 30 is equal to 20 millimetre and width over rollers at a height of 55 millimetre. So, 50 millimetre is the height of slip gauge plus 5 millimetre is the roller dia. So, total height is 55 millimetre. So, at a height of 55 millimetre, the measurement over roller is 67.8 millimetre. Similarly, width over rollers at a height of 30 millimetre, 30 plus 5 millimetre, 35 millimetre height is 62 millimetres. So, the taper angle is 16.5 degrees that is 16 degree and 30 minutes is the taper angle of the component. Now, we will learn internal taper measurement by two balls of different diameters and by using a depth micrometer. You can see the photograph here. This is the tapered component having internal taper and then we are using a depth micrometer and then we have to use the two balls of different diameters. Now, the schematically we can show like this. This is the surface plate and this is the tapered component. Now, we have to keep a ball of some diameter. We have to note down what is the diameter of the ball and then using the depth micrometer, we have to measure what is the depth. So, we have to note down what is the reading. The spindle of the depth micrometer should just touch the top point on the ball and then we have to note down the reading. So, we have to note down this reading say H1 and then we have to remove this ball and then we have to insert another ball of bigger diameter and then again we have to take the measurement say this is H2 from this top surface reference surface. So, this will be H2 and then by knowing the diameters of two balls and these values H1 and H2, we can calculate the taper of taper angle of this component. Now, we will conduct an experiment to learn the measurement of internal taper of a component. Now, you can see the arrangement measurement arrangement. We have two balls of different diameters and we have a tapered component, internal tapered component and then we have a depth micrometer with different spindles of different size and then we have a veneer caliper for measurement of diameter of balls. Now, I am measuring the diameter of balls. You can see the diameter is 25 millimeter and then we have to see the coinciding division. The diameter of second ball you can see the tapered component. We have the internal taper I am measuring the total height of the component. So, it is 79 millimeter on the main scale and then we have to see the coinciding division 10 15 25 25th division is coinciding. So, 25 into 0.02 that is 0.5 that is diameter the total height of the component is 79.5 millimeter. Now, we have to keep the ball in the internal tapered component and then we have to measure the height of the topmost point from this reference surface and then we have to record what is the reading. You can see the spindle is just touching the top point on the ball. Then we have to note down the reading it is. Now, we have removed the bigger ball and now I am keeping the smaller ball into the hole tapered hole and then again we have to measure the depth. I am changing the spindle and I am putting the spindle of longer length. Now, we can see I have inserted the spindle of longer length into the micrometer. Now, I am measuring measuring the depth we have to note down what is the reading. Now, these are the observations after conducting the experiment the diameter of smaller ball is 25.4 millimeter. So, the radius of the smaller ball smaller is 12.7 millimeter diameter the bigger ball is 31.7 millimeter. So, the radius of the bigger ball is 15.85 millimeter depth with the bigger ball is equal to 9.05 millimeter depth with smaller ball is equal to 51 millimeter. So, height of the component is 79.3 millimeter. So, now we can calculate the taper angle using this relationship. So, we get a taper angle of 4.65 degrees. Now, let us move to another instrument known as a clinometer it is also called inclinometer which measures the surface tilt. The arrangement of the instrument is like this we have a base precisely finished base and then we have a micrometer. So, when we operate this micrometer a screw inside there is a screw when we operate this micrometer this spirit level the round part containing this spirit level will rotate. And then this circular scale which is housed inside the body will directly give what is the tilt of the surface. Initially we have to keep this instrument on a leveled surface that is surface plate and we have to keep the inclinometer like this and then we should check the whether spirit level is reading 0 or not whether the scale is reading 0 or not and then we have to keep this instrument on the surface which is inclined like this and then we have to operate the micrometer till the spirit level again reads 0. So, this circular scale will directly give what is the tilt of the surface. Now, we can see the commercially available single axis electronic inclinometer this is the base this base should be placed on the surface whose tilt is to be measured. So, this electronic inclinometer will directly give what is the tilt angle this is another instrument with a better accuracy. These electronic inclinometers accuracy can typically range from 0.01 degree to plus r minus 2 degrees depending upon the sensor that is used. Two axis inclinometers that are built with MEMS tilt sensors provides simultaneous two dimensional tilt angle readings of the surface. So, these two axis inclinometers they eliminate TDS trial and error experienced when using single axis levels to adjust machine footings to attain a precise leveling position. Two axis inclinometers can be digitally compensated and precisely calibrated for non-linearity for operating temperature variation resulting in higher angular accuracy over wider angular measurement range. These two axis inclinometer with built in accelerometer sensors generates numerical data tabulated in the form of vibration profiles. It enables machine installer to track and assess alignment quality in real time and verify structure positional stability by comparing machines leveling profiles before and after setting up. Now, what are the specific functions of these inclinometers? They measure the slope angle during distance measurement and measuring the height of a building tree or other feature using a vertical angle and a distance determined by taping or pacing using trigonometry. They alert an equipment operator that it may tip over. So, this photograph shows a two axis inclinometer. Now, let us move to another very important instrument used for measurement of angles that is profile projector. This profile projector optical profile projector it is a versatile instrument widely used in the many phases of quality control. It has made possible the effective measurement of great numbers of components which because of size or dimensional characteristic pose serious difficulties to other measurement methods. For example, if the workpiece is very fragile, it is very thin and other instruments are it is not possible to use other types of instruments for measurement of such a fragile or thin component. In such cases, this profile projector will be very, very useful. So, these are also known as contour projectors, optical comparators, shadow graphs, micro projectors etc. They display magnified images on a viewing screen. This is very important. They display magnified images on a viewing screen. That means we can always select what is the magnification that is desired whether it is 10x or 20x or 50x or 100x. So, depending upon the magnification that is needed, we can amplify the image and then we can make the measurement and then we can find the dimensions, form and physical characteristic of the parts that also can be checked. They possess a special capability of displaying 2D projection. See other instruments like micrometer or vernier, they measure only one dimension at a time. These profile projector at a time they can display 2D projection rather than a single dimension as with most other gauging devices. Now, what are the essential features of these profile projectors? You can see a schematic diagram of a profile projector. You can see the various optical elements like lenses, light sources, mirrors for deflecting the light, collimating lenses to have a parallel beam of light. The light sources normally they are made out of tungsten filament and we have the collimating lens system to get a parallel beam of light. So, work piece table, this is very important. Work piece that can be placed on the table. You can see the work table here. Normally, these work stages or work tables they have glass plate on which we have to keep the work piece. So, light will pass through the glass plate and they will pass through the work piece and then we get the projected image, amplified image. You can see we have lens system and then we have mirror and then we have another mirror and finally, we get the magnified view of the shadow of the component on the screen. Now, these tables in some cases they are stationary. In some models they are movable. We can move in the x direction or y direction. That is we can move the table parallel to the column or perpendicular to the column. Sometimes they can be rotated. So, this rotatable table is very useful when we use the optical projector for measurement of angles. For example, screw thread measurement and sometimes the work pieces, the tables can be moved up and down for proper focusing and then we have projection optical system and then we have a weaving screen which is made out of glass on which we get the amplified image and different magnifications are possible. So, commercially 10x, 20x, 50x, 100x magnifying lenses are available and with special request even 500x and 1000x magnifying lenses are also available and screen sensor to load data points. So, we can always mount a screen sensor on the screen. So, a sensor can be mounted here. So, which will sense the data points and then it could be fed to the microprocessor unit for processing of the data and then we have light beam system, horizontal lighting system, vertical lighting system and surface elimination. So, the surface elimination will be very useful to study the surface characteristic of the work pieces and then we have a fixture called elix angle rotation for thread measurement. So, we have we can rotate the thread so that the thread becomes parallel to the light beam and then we can take the measurement and then there are measuring devices incorporated into the profile projector like rotary scale with vernier and x y micrometers for measurement of movement of the table and then digital indicators to indicate what is the movement of the table and then data process also incorporated to process the data. Now, you can see here elix angle rotation facility. So, this is the light ray. So, and this is the elix angle. So, now because this is elix angle projection normal to this screw thread axis projection is normal to this screw thread axis. In this case there will be interference and we do not get a proper clear image. So, what we have to do is we have to rotate the screw thread by elix angle so that light rays will move parallel to the elix threads so that we get a very clear picture. Now, you can see the photograph of a profile projector. This is the viewing screen. You can also see the rotary scales protractor rings are provided on the viewing screen and then there is a vernier attached to the screen and then we have magnifying lens. There is a turret here. On this turret we can mount three magnifying lenses at a time that is 10x, 20x, 50x like that we can the magnifiers can be fixed. Manually we can rotate this turret and we can select the appropriate magnifying lens and this is the work stage or work table. You can see two micrometers are attached. So, this is one micrometer, this is another micrometer. By operating these wheels the table can be moved perpendicular to the column or parallel to the column and we can see there is a helix angle rotation fixture is there and two centers are there. Using these two centers we can mount the thread screw thread and then we can rotate through helix angle to get a clear image on the screen and then we have this is the main switch and we have two types of eliminations. One is surface elimination and one other one is throw elimination. The surface elimination by using this surface elimination we can study the surface characteristic of the work piece and by using throw elimination the light rays will pass through the work piece and we get the contour image on the screen viewing screen and then by using the reference cross lines by moving the cross lines on the screen we can make the measurements and this is the data processor unit. You can see the enlarged view various functional keys are there by selecting appropriate key we can make the measurement. For example, if you want to measure the diameter of a round part we have to keep the round part on the glass plate and then we should get the contour on the screen and then we have to move the cross lines, reference lines and then we can take the measurement. So, when we want to measure the diameter of a work piece, so we have to select three points on the contour. So, this image will be there on this screen the shadow will be there on the screen we have to select one point we have to select another point and then we have to select third point. So, like that we have to select where we should input three points and then after loading all the three points the data processor will process and finally, it will give what is the diameter of the work piece. So, there are different techniques by which we can make the measurement using the profile projectors that is measurement by movement that is using cross lines on the screen we can move the cross lines and then for example say we want to measure the diameter of a work piece and this contour is obtained on the viewing screen. Now, we have this cross line, so we should move the cross line, so that it just touches one point on the periphery say this is reading is 0 and then we should move it and then we should make it to touch the other point and then we should note down what is the reading say 10. So, the diameter is 10 millimeter, so like this by moving the cross lines we can make the measurement also by rotating the cross lines we can make the measurement say we have a thread profile on the screen like this and we want to measure what is the thread angle. So, one cross lines we should make it to align with this particular flank say the reading is 0 degree and then we should rotate the cross lines, so that it aligns with another flank say this is reading is 60 degree, so this thread angle is 60 degree. So, like this by movement we can make the measurement similarly we can measure the depth say we have a step here we want to know we want to measure what is the depth. So, the cross line should be aligned with this say the reading is 0 and then you should move down and then we should make it to align with this particular surface say the reading is 10 this is not degree this is 0 mm and this is the 10 mm. So, the depth is 10 millimeter like this by movement by movement we can make the measurement. So, another technique is measurement by comparison that means on the screen we have we have to paste a chart which is known as chart gauge say for example, we want to measure the screw thread. So, we have to mount the chart gauge of appropriate magnification with two contour lines. So, one for the maximum size and another for this is the tolerance band and then we have to get the shadow of the thread which is to be inspected now it falls if it falls like this between the two contour lines then the workpiece is accepted. If the image falls outside then it is not accepted like this by comparison we can make the measurement and other technique is measurement by translation using tracer, follower and pantograph. That means, there will be a pantograph mechanism and then we have to keep the workpiece with the profile on the table and there will be a tracer a ball tracer which will trace the surface of the workpiece and on the other side of the pantograph there is a follower. So, follower will be moving now this follower is projected onto the viewing screen. So, the projected image of the follower will be like this and again there will be a chart with two contour lines one maximum size and one minimum size like that. So, when we move the tracer onto the workpiece the follower will also be moving if the image of the follower moves within these two limits then the workpiece is accepted. So, this is measurement by translation. Now, we will see a profile projector I can see a profile projector this is the viewing screen with protractor ring. Now, this is the magnifying lens 20x and then we can see another magnifying lens of 10x and you can see the light source for surface elimination purpose we have to keep the workpiece on this glass table glass plate this is the table work table and this is the glass plate on which we have to keep the workpiece we have to we want to study the surface characteristic and then we should use surface elimination that means light will move like this and here it will be tilted and then again it gets reflected and then the image we get on the viewing screen this is the turret in this turret we can mount three magnifying lens. So, this turret can be manually rotated to bring a magnifying lens of appropriate magnification in line with the workpiece. Now, we can see a fixture this is a fixture to mount the screw thread we have the two centers these centers can be moved in and out the clamps are provided to fix the centers at the desired location and then you can see there is a pivot here this is the pivot we can tilt this screw thread by helix angle so that we get clear image and that angle also we can see here what is the helix angle rotation we can see by using this scale. Now, we can see the helix angle rotation facility this is the reference on one side we have up to 10 degrees and on the other side we have another 10 degrees. Now, you can see the projected image of the screw thread and you can also see the protractor ring here this is the 0 and in the anticlockwise direction it is 5 degree 10 degree 15 20 30 40 it goes up to 350 355 360 complete 360 degree rotation it can measure and then we have a vernier so each degree is divided into 60 parts. So, the least count of this arrangement is 1 minute so 1 degree is divided into 60 parts so least count is 1 minute. Now, you can see this is the main switch and this is the switch to activate the surface elimination and then this by operating this switch we can have the vertical elimination system to get the shadow of the workpiece and again we can select high intensity light or low intensity light depending upon the requirement. Now, this is the pivot of the helix angle rotation arrangement and this is the workpiece you can see the light it is passing through the workpiece you can clearly see the screw thread and this is the glass plate 20 x magnifier. Now, you can see the data processor microprocessor attachment we have to load the data points into this microprocessor and then by selecting appropriate keys we can get the radius diameter angle measure diameter minor diameter etcetera etcetera. You can see the various function keys here to find the included angle we can select this k and to get the diameter of a component we have to select o and to find the radius we have to select l like this and then what is the if you want to find the distance between a point from a line which is passing through 2.23 then we have to select this key j now if you select this l so 5 measurement points are required. Now, you can see the display unit. So, this is x micrometer and y micrometer now they are set to 0. So, by operating the micrometers so when we want to measure the pitch so we should move the vertical cross line and then we can measure the pitch. So, we have to make the vertical cross line to pass through this point and then we should note down what is the reading and then we should move the vertical cross line to this particular point and then again we should note down what is the reading the distance gives the pitch. So, like this we can make the measurement and finally, the data processor will process and it will give what is the now we can see the we have measured the thread angle it is 56 degree 54 minutes. Now, we can see thread angle measurement using data processor we should select appropriate processing function keys. Thread angle measurement it is like this say we have a profile like this. So, we should make we should load totally 4 points 4 points are needed we have to select the key and then we have to input the 4 points. So, first point, second point, third point, 4 points we have to select on the flanks and then we have to input these 4 points and the data processor will process these 4 data points and finally, it will print what is the intersection angle. So, similarly in order to find the diameter of a component we have to feed 3 data points. So, first data point, second data point and third data point like this we should give 3 points. So, in that case we should select the key O. Similarly, we can find the distance of point 1 from a straight line passing through 2 points say this is 2 and say this is 3. So, now what is the distance between point and this straight line passing through these 2 points that we can find by selecting appropriate key. Now, you can see here thread angle measurement using circular scale and vernier. So, we have circular scale here this is circular scale or say protractor ring and this is the vernier scale. Now, one cross line should align with one flank and then what is the reading we should take and then we should rotate the cross line. We should make it parallel to the other flank and then again we should take the reading the difference will give the thread angle. So, now we will conduct an experiment to show how to use profile projector to measure thread angle. I can see the protractor ring it is showing 30 degree, 40 degree, 50 degree etcetera and then this is the vernier. So, the least count is 1 minute. Now, the reading is when the cross line is parallel to one flank the reading is 31, 32, 33 degrees and coinciding division is 25, 33 degrees, 25 minutes. Now, we can see I am rotating the screen. So, that the cross line becomes parallel to another flank now it is parallel to the other flank and then again we have to note down what is the reading. Now, you can see the reading is 331, 332 degrees and 21 degrees. So, this is the reading is the difference we should take to get the thread angle. Now, you can see the observations first reading is 33 degree, 25 minutes and second reading is that 332 degrees 20 minutes. So, this we have to deduct from 360 degrees. So, 360 degrees minus 332 degrees 20 minutes is equal to 27 degrees 40 minutes. So, the thread angle is we have to add this 27 degree 40 minute with 33 degree 25 minutes. So, the thread angle is 61 degrees 5 minutes. So, like this we can use profile projector for measurement of thread angle. Let us see what are the cost advantages of using profile projector. See, if the components are very fragile, very thin then other measuring instruments cannot be used. So, this is the only option and if the complex workpiece geometry is very complex then multiple settings are required if we use the other types of instruments like micrometer or vernier caliper. Whereas, in this profile projector in a single setting we can measure the multiple dimensions 2D measurement is also possible and in conventional instruments and gauges there is a problem of wear frequently we have to check the gauges and we have to replace the gauges. Whereas, in the case of optical gauging there is no wear of light beam. So, the optical gauges can be used when the gauge is not subjected to wear. So, the frequent checking and frequent replacement problem will not be there. When the design of the workpiece changes, fixed gauges should be change new set of gauges should be purchased. In the case of optical gaze we need not have to purchase new profile projector can be used even when the design of the workpiece changes. Only thing is chart gauges may have to change like this the profile projector offers many cost advantages. So, with this let us conclude this mod 8 module 8 lecture 2. In this lecture we discussed about the various instruments used for measurement of angle like clinometer and then we also discussed about profile projector what are the various measurement techniques of profile projector and what are the cost advantages of profile projector those things we discussed. We will conclude this lecture in the next class we will continue the discussion. Thank you.