 I welcome you all for module 3 lecture 8. In this lecture, we will be discussing about Taylor's principles of gauge design. And also, we will be discussing about the gauge tolerances, wear allowances provided on the gauges. And then, we will see some numerical problems. Now, we will start the Taylor's principle of gauging. Taylor has given some principles which are useful while designing the gauges. The first principle is a go gauge will have to check all the dimensions of the workpiece in the maximum metal condition, indicating the presence of the greatest amount of material permitted at a prescribed surface. It should check the size of the component, also the geometrical shape. Whereas, not go gauges will have to check only one dimension of the workpiece at a time, for the minimum metal conditions indicating the presence of the least amount of material permitted at a prescribed surface. In case of hole, the maximum metal condition is obtained when the hole is machined to the lower limit of the size. And minimum metal condition results when the hole is made to the high limit of the hole. In case of shock, the limits taken would be inverse of hole. Now, we know that in the case of manufacture, the machining of the components to the exact size will not be possible and it will be very difficult and it will be very expensive. So, to achieve the economy and to meet the functioning, some manufacturing tolerances are provided on the work parts. So, similarly in the gauges, some tolerances are provided. Gages like any other workpieces need manufacturing tolerances, like any other engineering components where in some manufacturing tolerance is provided to achieve the economical production. In the case of gauges also, some tolerance is provided, which is known as gauge makers tolerances. And it is always very expensive. We produce the gauges exactly to the maximum and minimum metal limit workpieces as suggested by the gauge designer. So, in order to achieve the economy, some modification is allowed for reasonable imperfection in the partnership of the gauge maker. So, this tolerance on the gauges provided is called gauge makers tolerance. Now, this is American gauge design standard. They specify different classes of tolerances. This is for plug and ring gauge only. So, different class of tolerance, sorry xx tolerance, x class, y class, z class and zz class. Zz class is applicable only for ground rings only, ring gauges only. And xx, they are very precise lapped gauges and they are used as masters. And these x and y, they are used as inspection gauges and z for the normal working gauges. Now, this table shows that for a particular size, that is 0.029 inch, all the values are in inches. For 0.029 inch to 0.825 inch, what is the tolerance that is allowed? If the gauge is xx class, then the tolerance that is allowed is 0.00002. And if it is the x class tolerance, then it is double of this value that is 0.00004. And for y class, it is 0.00007 inches. And for z class, 0.0001 inches. And for zz, it is 0.0002. So, similarly, for other range of sizes, the tolerance values are mentioned here. Now, we will take a simple example to show how the tolerance class can be selected. So, let us assume that we have a hole to be gauged with the basic size 1.25 inch plus or minus 0.006 inch. This is the tolerance that is provided on the hole. So, the work tolerance or the tolerance spread will be equal to double of this value that is 0.0012 inch. And in that case, the hole size varies from the maximum size will be 1.2506 inch and minimum size will be 1.25 minus 0.006 inch that is 1.2494 inch. Now, the gauge tolerance which is normally taken as 10 percent of the work tolerance. So, in this case, work tolerance is 0.0012 inch, 10 percent of this will be 0.000012 inch. So, if this is the case, from the table, we can see for this particular hole and for this gauge tolerance. So, the nominal size is 1.25. It falls in this range. And the gauge tolerance spread is 0.0012 inch. So, the Z class tolerance is selected. So, Z class tolerance zone is selected. Now, the go gauge size will be equal to, now the lower size of the hole go gauge is made to check the lower size of the hole that the lower size of the hole is 1.2494 inch plus this the gauge tolerance is to be added that is 0.00006 inch that is the 10 percent of this work tolerance. That is go gauge size will be 1.2494 plus or minus 0.00006 inch. For no go, the maximum size of the hole is 1.2506 plus or minus the gauge tolerance that is 0.00006 inch. So, like this we have to select the tolerance class and then we have to design the go side and no go side of the either plug gauge or ring gauge. Now, let us try to understand what is the meaning of we are allowance. Now, we in the previous classes we discussed about the use of gauges plug gauge ring gauge etcetera etcetera and we understood that the limit gauges they come in contact with the work piece. For example, this is the hole to be checked. So, we are using the double say double ended go no go gauge. So, no go size will be bigger. Now, this go end will enter into this and there will be contact between this surface gauge surface and the work surface. So, there will be always wear occurring on the gauging surfaces. Now, in order to prolong the service life of gauges wear allowance is added in the direction opposite to the wear. That means, when we use this gauge due to continuous usage of the gauge the diameter of the go plug gauge will be reducing. That means, the direction of wear will be in this direction which is shown here and if snap gauge is used it is used to check the diameters and there will be wear of this. So, wear direction will be in the opposite direction in this direction opposite to this particular direction. So, in order to increase the service life of the gauges we have to allow some wear allowance in the direction opposite to the wear direction. See the wear is occurring in this direction. So, we have to add wear allowance in the opposite direction. So, in case of snap gauges wear is occurring in this particular direction. So, wear allowance is given in the opposite direction like this. So, that is shown in this picture. This is the hole and this is the work tolerance for work tolerance for the hole and this is the upper limit of the hole and this is the lower limit of the hole. Now, go gauge is designed to the lower limit of the hole. Now, since the wear is occurring on the gauges we have to allow wear allowance in the opposite direction that you can see here wear allowance is provided. So, in this direction and then the gauge tolerance is provided. So, similarly for no-go gauge, no-go gauge is designed to this particular upper limit of hole and the tolerance is given outside the tolerance for hole. This is a general class of gauges. So, there are different types of classes of gauges, general type of gauges, workshop gauges, inspection gauges and in the case of general class of gauges, this is how the tolerance is provided. The gauge tolerance is provided inside the work tolerance and hence the wear allowance is also provided inside this consuming some portion of the work tolerance and the tolerance on no-go gauge is outside the work tolerance. Whereas, in the case of the inspection gauges, the allowance, I am sorry the tolerance, gauge tolerance is provided outside the work tolerance like this. Now, there is some problem with this method used. So, we are consuming some portion of the work tolerance. Now, let us assume that the work piece hole is somewhere here. Actually, it is within the work tolerance. So, it is acceptable, but since we are consuming some portion of the work tolerance, the go gauge is designed up to this size. So, when we try to insert this go gauge into the hole, it is obstructing. It will not enter because the hole is up to this. So, the operator will decide to reject that particular piece. So, that is the problem with this type of assigning the gauge tolerance and wear allowance. So, in the case of inspection, this problem is overcome. The tolerance is given outside the working tolerance. If some pieces are rejected by using the general gauges, such rejected pieces are sent to the inspector. He will use inspection type of gauges. Now, this go gauge will enter into the hole and it can be accepted. Now, similarly for shaft, this is the work tolerance, that is, shaft tolerance and this is the lower limit of the shaft and this is upper limit of the shaft. Now, we can see here to check the shaft, we use ring gauges or snap gauges. So, the wear will be in the reverse direction, in this direction. So, the tolerance and wear allowance is provided in the reverse direction as shown here. So, wear allowance is given in the opposite direction in which, opposite to the direction in which the wear is occurring. And similarly for no go gauge, the tolerance is outside this tolerance of the shaft. Now, we have taken an example of snap gauge here. Now, this is the go limit and this is no go limit and this is the tolerance for the shaft. So, this is shaft tolerance or work tolerance Now, we know that when we use snap gauges to check the work pieces, shafts, the wear is occurring in this direction and so the wear allowance is given in the opposite direction. So, wear, this is the tolerance, tolerance on the, this is gauge tolerance which is taken as 5 percent of the tolerance. This is total tolerance, 5 percent of this is taken as the gauge tolerance. In addition to that, wear allowance is given which is again taken as 5 percent of the tolerance. So, wear allowance then the gauge tolerance is provided. Due to this, the no go size will decrease because we are consuming this much of work tolerance, go size will reduce. So, this in the inspection type of the gauges, the tolerance is given outside the work tolerance. Similarly, for no go gauge, you can see from 5 percent of the work tolerance is taken and it is given outside the work tolerance. Now, we will take up problem on gauge design so that the concepts will be clear. Now, the problem is given here. We have to design general type go and no go gauge, no go gauges for a shaft hole assembly with a 25 h 7 f 8 fit. And we have to assume a wear allowance of 10 percent of gauge tolerance. Also, we have to determine the type of fit and allowance. Now, this 25 is the basic size and it falls in the diameter step of 18 to 30 millimeter. So, we can find the mean diameter using this relationship. So, mean diameter will be equal to 23.2 mm mm. Tolerance unit also we can find using this relationship. It will be 1.31 micrometer. For h 7 hole, the tolerance grade is I t 7, which is equal to 16 times I. So, 16 times 1.31 gives us tolerance for hole of 0.021 millimeter. So, once we know the tolerance value for hole, we can consider the value and find the limits for the hole. We know that fundamental deviation for h hole is equal to 0. So, minimum size of the hole will be equal to 25 millimeter and maximum size of the hole can be obtained by adding tolerance to the basic size. So, the maximum size of hole is equal to 25.021 millimeter. Now, moving to the shaft for f 8 shaft, tolerance grade is f 8 that is I t 8 is equal to 25 I. So, this will give us a tolerance for shaft of 0.033 millimeter and fundamental deviation for f shaft is equal to minus 5.5 times t to the power of 0.41. So, we get the fundamental deviation for f shaft that is nothing but upper deviation to be minus 0.020 mm. Now, once we find the tolerance value for the shaft and the upper deviation, we can get the limits for the shaft that is maximum size of the shaft is equal to basic size of the shaft minus 5.5. Fundamental deviation, you can see here we have this 0 line and the upper deviation for the shaft is negative value negative 0.020. So, we are showing the upper deviation 0.02 mm and then the tolerance value for the shaft is 0.033 mm. So, when we deduct this upper deviation from the basic size, we get upper limit for the shaft that is 24.98 millimeter. In order to find the minimum size of the shaft, we have to deduct this tolerance value for the shaft from maximum size of the shaft that is maximum size of the shaft minus tolerance will give us 24.947 millimeter. So, all these dimensions are shown in this picture h 7 hole with the tolerance 0.021 mm and this is the basic size and we have 0 line upper deviation f 8 shaft with tolerance of 0.033 millimeter. Now, once we get the tolerance limit for hole and shaft, we can proceed to design the plug gauge for checking the hole. The go gauge tolerance is taken as 10 percent of the work tolerance. So, work tolerance that is hole tolerance is 0.021 millimeter, 10 percent of that will give us 0.0021 millimeter and the whole tolerance is provided only for go gauge. The reason is only go gauge enters the hole and that is subjected to wear. So, wear allowance is provided only for gauge which is taken as 10 percent of the gauge tolerance. So, 10 percent of 0.0021 millimeter will give us 0.0021 millimeter. So, this is the amount of wear allowance provided on the go gauge. So, once we find the gauge tolerance and wear allowance, we can fix the limits for the go size. So, upper size of the go plug gauge will be basic size plus gauge tolerance plus wear allowance. So, basic size is equal to 25 millimeter and gauge tolerance is 0.0021 millimeter and then wear allowance will be 0.0021 millimeter. So, when we add these values, we get the upper size for the go plug gauge that is 25.0023 millimeter and then lower size of the plug gauge will be equal to basic size plus wear allowance that is 25.0021 millimeter and coming to the no go gauge. So, this is the go gauge, the work tolerance is 0.021 millimeter, 10 percent of this is 0.0021 millimeter, this is the gauge tolerance and 10 percent of gauge tolerance is taken as wear allowance. So, wear allowance amount is 0.0021 mm. So, now, the wear allowance is provided in this direction, the direction which is opposite to the direction in which the wear is occurring and then this is the wear allowance and this is gauge tolerance. So, the upper limit for go gauge will be this one and lower limit will be equal to this basic size plus wear allowance. That means, this much tolerance is provided for the go gauge. Now, coming to no go gauge, so we have the no go gauge here with the gauge tolerance of 0.0021 millimeter. So, this level will give us the upper limit for no go gauge. That means, in order to get this, we have to add basic size plus work tolerance plus gauge tolerance. So, this will give us the upper limit for the no go gauge, that is basic size plus work tolerance plus gauge tolerance. So, 25 plus 0.021 plus 0.0021 is equal to 25.0231 millimeter. So, this is the upper limit for the no go gauge and this is the lower limit for the no go gauge. So, in order to get this lower limit, we have to add 25 with the work tolerance, that is basic size plus work tolerance that is 25.021 millimeter will give us lower limit for the no go gauge. Now, coming to the ring gauge design, which is used to check the shaft for the lower limit, a go gauge, go ring gauge tolerance is again 10 percent of the work tolerance, that is shaft tolerance is 0.033 millimeter, 10 percent of this is 0.0033 millimeter and again for go no go ring gauge, where allowance is provided, so which is taken as 10 percent of gauge tolerance. So, gauge tolerance is 0.0033 millimeter, 10 percent of this will be 0.0033 millimeter. Now, once we calculate the gauge tolerance and wear allowance, now we can fix the limits for go ring gauge. The upper limit for go ring gauge will be equal to basic size. So, basic size minus fundamental deviation minus wear allowance, so this will give us 25 minus 0.02, this is the fundamental deviation and this is the wear allowance 0.0033 millimeter. So, the upper size will be equal to 24.979 millimeter and lower size for go ring gauge is upper size for go ring gauge is upper size minus gauge tolerance. So, that is 24.976 millimeter. So, coming to the no go ring gauge, so this is the no go ring gauge and this is the upper limit for the no go, this is the upper limit for the no go ring gauge. So, this gauge we can calculate by this relationship, upper limit is equal to basic size, so this is the basic size 25 millimeter minus fundamental deviation that is 0.02 millimeter minus work tolerance that is 0.033 millimeter. So, upper limit of no go ring gauge will be equal to 24.947 millimeter. So, this will be upper limit and is equal to 24.947 millimeter and this is the lower limit for no go ring gauge, this we can obtain subtracting the gauge tolerance from the upper limit. So, lower limit of no go ring gauge is equal to upper limit minus gauge tolerance that is 24.947 millimeter minus 0.0033 millimeter which is equal to 24.944 millimeter. So, now since the shaft size is smaller than the maximum size of the shaft is smaller than the minimum size of the hole, we have clearance fit here and then allowance is equal to difference between the maximum metal limits of the hole and shaft. So, maximum metal limit for hole is 25 millimeter and maximum metal limit for shaft is 24.98, so the upper limit is 0.020 millimeter. So, like this we can calculate, we can design the limits for go gauge as well as no go gauge. So, with this we will complete this lecture. In this lecture, we discussed about Taylor's principles of gauge design and we also learnt about gauge tolerances, wear allowances and also we saw a numerical problem to understand the gauge design. So, with this we will close this session. Thank you.