 module 4 lecture 2 on measurement of geometrical features. In the last class, we started discussion on measurement of straightness using spirit level and auto-calimator. We will continue with the discussion on straightness measurement. So in this session, we will be discussing about measurement of straightness using spirit level and auto-calimator and then we will move on to the measurement of straightness using coordinate measuring machines and we will see some of the tests like gap test and total indicator readout test and finger roll test and after that we will move to the measurement of perpendicularity. Now you can see some photographs of auto-calimator. We have the auto-calimator and this is the vertical stand to adjust the height of the kilometer tube depending upon the workpiece height. You can see the light source and then this is the power supply for the light source and we have to view the readings through this high piece and a micrometer is also attached to the high piece and you can see this is the surface plate whose straightness is to be tested. We have this reflector surface, the stand with the reflector surface, here there is a reflecting mirror. So light will fall on the mirror reflecting surface and then it gets reflected back. If there is some inclination, if the surface is like this some unevenness is there then because of this the mirror is at inclined position. Now light will reflect back in this path and then so inside we have a view field. So it looks like this. So when we observe through eyepiece the view field is like this, we have cross hairs. So when there is no error that means the workpiece is perfectly straight then this is the incident ray and this is the reflected ray they will get combined and we get this spot on this in this place. So if there is any inclination light will get, it will move in this path and this spot will move like this. So this distance we can read using the eyepiece. So like this at different locations, different positions we have to keep the reflector. So the total length whose total length of the surface is divided into some equal number of parts. This is 0 and you can see this is first position and this is second position, third position like this. We have to divide this into equal number of parts and then we have to keep on placing the reflector at different locations and then we should note down the readings. It is very essential that before we start the experiment the surface to be tested is thoroughly cleaned. If there are some dust particles then the inclination will change the inclination of this reflector stand will change that will give an error. So it is necessary that surface should be cleaned properly and then bottom of the reflecting surface also should be thoroughly cleaned. Now see there is arrangement say we have some surface which is inclined like this, inclined surface. So we can orient the autocalibrated tube with respect to this inclined surface. So for that this can be moved like rotated like this and height can be adjusted depending upon the workpiece height and also we can rotate the autocalibrated tube like this in this fashion. Now this shows the principle of working of autocalibrate. You can see we have the eyepiece here, this is eyepiece lens and then this is the micrometer and the light will fall on the reflector and then if there is some inclination theta then reflected light will move back and it will fall at this position. So this distance between R1 and R2 that is distance D can be measured using this can be read using the eyepiece and the light source is placed here. So light will fall like this and the semi-transmissive mirror is there. So light will change its path, it will fall on the reflector and then it will get reflected. If theta is equal to 0 then R2 will coincide with R1 and there will not be any error. Now whenever we want to take readings we should keep the autocalibrate at some distance about half meter to 0.75 meter from the surface to be tested and it is placed on a separate stand. It will not be placed on the surface which is to be tested and the parallel beam from the instrument is projected along the length of the surface to be tested. Now you can see here this is the guide surface whose straightness is to be checked and we have marked different positions here which would keep the reflector with the stand on the guide surface at different locations and then we have to take the readings through the eyepiece. Now inside the view field we have the cross hairs like this and a scale. So when the workpiece is perfectly straight then the incident ray and reflected ray will be on the same line and then there will not be any error, the spot will be at the center. If there is any error like this then this is the incident ray and reflected light will fall like this, there will be some angle theta. So light spot we get here and this reading we have to take. So at all locations we have to take this reading. Now you can see here initially this is the surface and this is the location A and this is location B. We have to keep the reflector here and then we should take the reading that is with the reflector set at AB this is the first reading, the eyepiece micrometer reading is noted and this line is treated as datum line. So with respect to this datum line all other readings are taken. Now you can see here this is the first location so this is A and this is B. So this line is taken as datum. With respect to this now this is the second position. So this is C. Now B, C, C, D, D like this the readings, autocalameter micrometer reading should be taken at different locations and all the readings should be added then we get cumulative height from the datum. And in the forward direction we should take reading and again in the reverse direction also we should take the readings and then average values we can take, mean values we can calculate. So this mean reading represents the angular position of the reflector in seconds relative to the optical axis of the autocalameter. This is the optical axis of the autocalameter or line of side. Now all the readings are tabulated as shown here. This is the first column shows the position of reflector. So starting point is A and then we have position AB, BC up to full length we have to take the readings. So mean reading of spirit level or see this is applicable both for spirit level as well as for autocalameter. Now mean readings in the forward direction we are taking the readings and also in the reverse direction we are taking the readings and then we have to find the mean values and those mean values in terms of seconds we have to record here. And then difference from the first reading. So that we have to take here if the say AB reading is 0 and at BC say it is 2. Then difference from first reading is 2. So like this we should mark. And then we should find whether there is rise or fall and then we have to see the cumulative, we have to add these values to get the cumulative rise or fall in terms of mm and then adjustment to bring both ends 0. It is like this distance along the surface in terms of mm and cumulative rise or fall. So we get the readings like this. This is cumulative rise or fall and then adjustment to bring both ends to 0. This is the last point and say this value is some plus 24. So we have to add minus 24 so that this will is brought back to 0 position. The second end is brought back to second. In that case we will be getting the line like this. So now it is brought back second both the ends are at 0 level and then we should find the error from the straight line. So this is the reference line and then this is the peak value and this is the bottom most point value and this distance will give us the error from the straight line. Also we can use least square method to find out the error. Now we will take a case study. We have taken some readings. So this is a position on the surface that is to be tested. 12 positions are there and then reading in minutes and seconds. This is the reading of spirit level or autocollimator reading. So in the first position the reading is 2 minutes 10 seconds. In the second position also 2 minutes 10 seconds. Like this up to 12 positions we have taken the readings and then difference from the first reading. So this is the first reading. Initially we mark it as 0 because there is no this is the starting point and difference. Now this is the second reading. The difference from this from the first reading is again 0 and third reading is 2 minutes 12 seconds. Difference from this first reading. This is plus 2 seconds. So like this we have to find difference from first reading for all the values and last reading you can see here this is 2 minutes 16 seconds whereas the first reading is 2 minutes 10 seconds. So difference is plus 6 seconds. Now we should find rise or fall in interval length in terms of 0.001 millimeter or directly in terms of micrometer. The first reading is 0 second reading is also 0. Now see 1 second of arc is equal to 0.0005 millimeter over the base length that is if the reflector is like this. So we will be having the 2 feet like this. So this is the base length L. So this is it can be some 100 millimeter or 120 millimeter like that. So one reading 1 second of arc is equal to 0.0005 millimeter in this case study. So the rise or fall interval is see difference in seconds is 2. So 2 x 0.0005 millimeter gives us 1 micrometer or 0.001 millimeter and then 0.0005 times 5. So this will give us plus 2.5 micrometer. So like this we have to find whether the rise or fall in the interval length and then we have to add these values to get the cumulative rise or fall again the values we get in terms of 0.001 mm or all these values are in terms of micrometer. So here this is added to 0 again we get 0 and then this is added to next reading. So we get 1. So this value is added to 2.5. So we get 3.5. So like this we have to get the cumulative values. Now you can see in the last position the reading is plus 24 micrometers. So we should bring this to 0. So now the cumulative value is like this. It is like this at the last point it is 24 micrometer. So in order to bring this down to 0 we have to add minus 24 to this adjustment to bring both ends to 0. So this end should be brought back to 0. So we have to add minus 24 then we get 0. So like this we have to add the adjustment values and finally we get errors from straight line in terms of 0.001 mm or directly in terms of micrometers. Now we can see here the maximum value is 3 micrometer from the straight line. So from the straight line that means so we have the reference line like this. So now the profile is like this. So this is the maximum from the reference line it is 3 micrometer. Now we can draw the graphs using those tabulated values. So on the x axis we have position on the surface we have 12 positions and then cumulative error in microns that is the column number 5 will give us cumulative rise or fall. So these values we have to take and then we have to plot here. So the cumulative error in terms of microns. Now we can see last reading is plus 24 micron. Now least square method we can apply to this and then we can find the error. And another graph we can write this can be brought down to 0 by adding the adjustment factor. So now this is the last position which is brought to 0 and again you can see the graph is plotted here different positions. Now error from horizontal line. So this place position number 7 we have the error like this it is approximately 3 microns. Now we can use coordinate measuring machines also to check the straightness of given surfaces or line or planes. In the recent years computer aided inspection procedures are used to find out the geometrical features. And the CMMs coordinate measuring machines it is possible to automate we can these CMMs can be used online or offline inspection. After the machining is over we can take out all the work pieces we can clean them properly deburr, deoid etc. And then we can load them onto the table of the CMM and we can give the appropriate program for checking the various geometrical features like the straightness or the roundness or parallelism perpendicularity all those things we can check using coordinate measuring machines. Also online inspection is also possible in the production line itself we can include CMMs and the features can be checked. If the errors exceed the specified values feedback given feedback can be given to the main computer and so that the changes are made in the programs and errors are brought back within the limits. And the number of points can be taken there are probes attached to the CMMs those probes can be contact probes or it can be non contact probes like laser spots. So, number of points we have to take for example we want to check the straightness of a surface. So, we have to take some depending upon the length we may have to take some 6 points or 12 or 18 and those data points are given to the software and software will calculate the straightness or whatever feature is required and then it will finally tell whether the component is ok or not. Now, these pictures show the commercially available coordinate measuring machine you can see the granite table and then two columns are there to support this bridge and then you can see the different axis. When the table moves in this fashion it is y axis and movement in this direction is x axis and vertical movement of the probe is z axis. So, we have granite surface plate which will act as primary datum surface and we can also have secondary or tertiary reference planes as and when needed. So, there is a dedicated computer for analyzing the various points and to find out the geometrical form errors and you can see a photograph of a contact type probe. So, these probes will make contact on the workpiece at the specified locations and data points are given to the computer for analysis for processing. Now, one reading is shown here. So, on a particular surface the probe reading readings given by the probes are given here in this table basically they give the coordinates with respect to some reference they give the coordinates of all these if this is say x and this is y and we have the surface like this. So, what is the coordinate of this particular point? So, x and y it will give like this different points it will give the x i values and y i values and now these values are given to the computer for the processing and finally, it will tell us what is the error. So, in this case you can see see this is point x values 0.39 approximately 0.4 and then 0.69 ok this is 0.8 and this is 1.2 and this is 1.6 millimeter. So, we have 0.39 it is somewhere here y value is negative that is 0.003. So, this is say 0.001, 0.002 and 0.003. So, the point will be somewhere here this is the first point and second point will be somewhere here and third point and fourth point is here. Now, we can join them to get the profile and also these data points are processed using algorithms for form evaluation based on computational geometric techniques. Also functional oriented devaluation can be performed and results can be presented may be for straightness, flatness, perpendicularity. So, all those geometric features can be measured using the coordinate measuring machines. Now, there are some tests as specified by ASTM. So, they are applicable for wires, rods and bars ok. So, one very common test is gap test ok this is applicable for wires, rods and bars for measurement of the straightness ok. So, this is applicable for wires less than 4.78 millimeter. It can also be used to check the straightness of rods within this range 4.78 to 6.35 and for bars with the diameter ranging from 6.35 to 101 millimeter. Now, in order to conduct this gap test a precision flat surface is needed we can use the surface plate as the reference plate. If the workpiece is very heavy then floor also very neat clean granite floor can be used for straightness measurement. And all the equipment surface plate or floor should be perfectly clean there should not be any cracks or no pits should be there. The surface should be in very good condition very good clean the condition. And we have to use a measurement device such as thickness gauge or gauge pins micrometers optical comparators can also be used to measure the gap. So, the procedure is like this we have to keep the specimen on the flat surface ok like this. This is the flat surface or surface plate and then we have to keep the wire or rod or bar horizontally like this. So, this is the specimen. Now, if there is any error there will be gap between the datum simulated datum that is surface plate surface and the specimen. So, now we can use thickness gauges now say the straightness that is specified is. So, straightness is specified as 0.01 millimeter that is 10 micrometer gap 10 micrometer error is allowed. So, what we have to do we have to take a thickness gauge of 10 micrometer 10 micrometer thickness gauge and we should try to insert here in the gap. So, that thickness gauge should be inserted here. So, we have to insert we have we should try to insert the thickness gauge throughout the length and then we should rotate at different rotation different orientations again we have to check the gap. If the thickness gauge does not enter then we say that wire or rod or bar is ok it is straight. If the gap enters if the gauge enters then there is an error the straightness error is exceeding the limits then the workpiece is rejected. Now there is another test specified by ASTM it is known as total indicator readout test. So, this is applicable for round rods with the diameter ranging from 4.78 to 6.35 millimeter 4.78 to 6.35 millimeter or round bars with the diameter 6.35 to 101 millimeter can be tested with this method. So, we require two or more V blocks in good condition and then a surface plate is required to conduct the test. Now we have to keep the specimen on two or more V blocks. So, this is the surface plate on which we have to keep the V blocks depending upon the length. If the length is length of the rod is 1 meter then we require only 2 if the length is say 2 meter 3 meter then we have to take 3 or more V blocks to support the rods. Now rod is kept on the V blocks we have to thoroughly clean the surface of the datum surface as well as the V blocks and the rod should be thoroughly clean and then it is placed on the V block. Now we have to take a indicator dial indicator and we have to keep the dial indicator approximately in the middle and then we have to note down the reading. So, we have to take initially you are just it to 0 and now you slowly rotate the rod through once one complete revolution and then again you take the reading at different orientation at different rotated positions we can take the reading. That means this will indicate if there is any bending it is indicated by the dial indicator. Now I can see some photographs how we can this will be these pictures will show how we can conduct the TIR test. Now we have supported the specimen specimen length is about 30 centimeter and with the diameter of about 12 millimeter and it is supported by 2 cleaned V blocks are kept on the surface plate and then the rod specimen is placed on the V blocks and we use the dial indicator or test dial indicator and then we have to rotate the specimen and then we have to take the readings and those readings are fed in the expression to get the error straightness error. So, these two are V block this is the specimen and the indicator. So, we have to rotate this and we have to take the reading. So, now we can see a minimum indicator reading that is IN and then maximum indicator reading IX. These values are fed in this expression TIR is equal to IX-IN. So, this and R plus the mod of both this reading IX reading and minus R minus mod of this reading IN reading. So, this will give us the total indicated reading where R is radius of the material that is being measured. Now there is another test finger roll test specified by ASTM this is a qualitative test method previous two methods that is TIR and gap test methods. They are quantitative test wherein we get what is the amount of error numerical value we get whereas, here this is qualitative test method this will not give any numerical value it will tell whether the wire or tube is straight or not. If the diameter is less than 0.25 millimeter then this finger roll test can be used. So, we should ensure that all the equipment surface plate and the wire is perfectly cleaned and then we should keep the specimen on the flat surface and the center of the test specimen should be pushed on to the flat surface with the finger that is we have this surface plate and then we have to keep the wire thin wire on the cleaned surface plate and we have to press where to push this specimen using the finger. So, using finger we should push this and we should move it we should roll it. If it does not roll we can always take the help of a pencil or pen or a plastic card. So, that the specimen rolls and it overcomes the friction and then starts to roll. Now when we roll the specimen in this fashion the remote ends this end and this end these remote ends should rotate smoothly on the flat surface without any wobbling. If there is any wobbling it indicates that the specimen is not straight. Now we can use a dial indicator or a test dial indicator to check the straightness of the generators on the cylinder. Now say this is the cylinder with some diameter and the straightness is specified to be say 0.01 millimeter. So, this is the specification tolerance, straightness tolerance. Now what we can do we can clean the workpiece or specimen to be tested for straightness and it is mounted between the two centers. And then we can use a dial indicator and we should mount it as shown in this figure. The magnetic stand is placed on the guide ways and the stylus or probe of indicator is placed on the top most generators so that it is perpendicular on it is touching the maximum top most generator. So, we should take the reading at this point or we can adjust it to 0 and slowly we can move this indicator to different positions. We can mark the positions like 0, 1, 2, 3 like this. So, total length is divided into some equal number of parts and then at these locations we can take the reading. And if you plot depending upon the values we get the profile like this and then we should take the peak value and we should take the peak and value. So, now we should calculate what is the gap between this peak and value. If this is smaller than the specified value that is 0.01, if this gap is smaller than the specified value then we say this particular generator is straight. So, similarly we can conduct this experiment on many generators we have to rotate the workpiece specimen and at different angles we should take the reading and in all the angular positions if the error is less than the specified value then we say the cylinder is straight. Now let me demonstrate how we can test the straightness of a generator on a cylindrical object. You can see we have a surface plate and on the surface plate we have kept two V blocks on which the cylindrical object is placed. So, we have to clean all the equipment like surface plate V block and specimen thoroughly and now at different positions we have to take the reading. Now we can see using the dial test indicator we are taking the readings. We have to move this stylus over the specimen and the maximum reading we should take. So, we have to see the maximum reading here and then we have to take that reading. Now we can see here it is 0. So, like this at different positions we have to take the readings and then we can find what is the straightness. So, now we will move to another geometric form that is perpendicularity. Now it is the condition when the surface or center plane or an axis is exactly at 90 degrees to the datum. That means we should have a datum and say we have some work piece like this and this surface if this surface is exactly at 90 degree then we say this particular surface A is perpendicular to the datum. It basically defines two parallel planes or cylindrical zone that must contain all the points of the phase. For example here we have this surface which is to be perpendicular to the datum. Now what we have to do is we have to consider two planes like this. This is one plane and this is another plane. If all the points on this particular surface or within these two planes then we say this surface is perpendicular to the datum surface. And if it is perpendicularity is applied to axis then we have to consider a cylindrical zone that is say this is the datum surface and then this is the work piece and we have this axis. So, if the perpendicularity condition is given to the axis and say the perpendicularity should be within 0.01 millimeter. Now we have to consider a cylinder here. The diameter being 0.01 that is specified value. Now the axis should be within this cylinder. It can be like this or it can be in the other direction. So, axis should be within this cylinder so that the work piece passes the test. Now these pictures show the perpendicularity tolerance on a flat surface. This is the work piece and this is the datum reference surface. And this is the surface which is to be perpendicular to the datum this surface and the tolerance that is allowed is 0.005 millimeter that is 5 microns. This surface should be perpendicular to this within this allowable deviation. So, the meaning of this is so I can see we have two tolerances. One is specified for the size of the object and another tolerance for the perpendicularity for deviation perpendicularity deviation. Now this particular work piece should satisfy both. Now we will consider the size tolerance. The maximum width should be below 2.03 okay. This is the maximum size and minimum size is 2 minus 0.03 that is 1.97 millimeter minimum size. So, now this is 2.03 to 1.97 this is the size tolerance and for this we say perfect form envelope. The object should be within this envelope. Now coming to the perpendicularity tolerance. Now we can see here this 1.97 is this line. So, this is 1.97 and this one is 2.03 2.03 that means the size tolerance the total zone is 0.06 0.06 millimeter that means 60 micrometer is allowed. And now coming to the perpendicularity tolerance it is only 5 microns. So, now let us assume that the work piece is like this. So, work piece is like this okay. Now it is within the limits. So, the total size is within the limits okay. Now we have to consider this surface to satisfy this perpendicularity tolerance. Now we have to so this is the one spot we have to draw a line here and this is another spot on the extreme end. So, all the points on the surface on this particular surface should be within 0.005 millimeter. So, in that case this work piece is accepted. That means this particular component should satisfy both size variation as well as form variation. And sometimes two datums are specified. So, in that case this particular surface should be perpendicular to this datum as well as this datum. So, with respect to these two we should conduct the test. Now perpendicularity applied to an axis. Now you can see here this is the work piece and this is the datum surface with reference to this the perpendicularity of the axis should be achieved. So, this is the symbol for perpendicularity and the diameter indicates that we have to consider the cylindrical zone. Since the tolerance perpendicularity tolerance is given to the axis we have to consider cylindrical zone and the variation allowed is 0.006 at the maximum material condition and the datum is here with respect to this the axis should be within this value. And the size of this portion cylinder is also mentioned it is 0.375 plus or minus 0.002 millimeter. Now you can see here the cylinder is considered here 0.006 cylindrical zone and you can also see. So, this is the 0.006 cylindrical tolerance and the axis should be within the specified tolerance. If that is the case then this work piece is accepted. Now this is the perpendicularity tolerance given for the hole internal feature that is hole. So, this is as specified this is the reference datum for which the axis should be perpendicular to this within this 0.008 tolerance at the maximum material condition. And since diameter is there and since it is specified perpendicularity tolerance is given to the axis we have to consider the cylindrical zone and again for the hole the size tolerance is given. You can see here we have considered a cylindrical zone with the diameter 0.008 millimeter as specified in the drawing and the axis should be within this cylindrical zone. In that case the work piece is accepted. So, with this we will conclude the session. In this session we discussed about the straightness measurement using spirit level and auto collimator. We also discussed about the different methods of studying the measuring the straightness that is TIR method gap test and finger roll test. Also we discussed about how we can check the straightness of a generator on the cylinder using dial indicator. Then we started discussion on the perpendicularity and what is the meaning of perpendicularity and how we specify the perpendicularity on surface and on the axis and what is the meaning of those perpendicularity errors tolerance that is specified. So, those things we discussed. In the next session we will continue the discussion on measurement of perpendicularity. Thank you.