You have to imagine that you are now looking at your drive system from above. When you are looking at the drive system from the side view with the motor to your left and the pump to your right, which way are you looking (north, south, east, or west)? Getting this direction correct is very important because there is nothing worse than moving your machinery the right amount in the wrong direction. In our motor and pump drive system we are working on here, let us say that we are looking toward the east as we view the machinery as shown in Figure 8.8 and Figure 8.9. Now that we are going to be viewing our machines from above when modeling the top view, we want to zero the indicator on the side that is pointing toward the top of the graph paper and plot the reading that is on the side that is pointing toward the bottom of the graph paper. In this case, the direction pointing toward the top of the graph paper in the top view is going to be east. Therefore we want to zero the indicator on the east side of each shaft and plot the reading we will obtain on the west side of each shaft. There are two ways that we can do this. One way is to physically rotate the bracket and indicator over to the east side of each shaft, zero the indicator there, and then rotate the bracket and dial indicator 1808 over to the west side and record the dial indicator readings we get there. The other way is to mathematically manipulate the east and west reading we obtained from the complete set of dial indicator readings to zero the east sides. Figure 8.10 shows how to perform this math on the east and west readings. Original sag compensated readings Motor 0 0 +30 −10 +20 −40 0+50 = +50 −50+50 = 0 +10+50 = +60 −40+50 = +10 0–30 = –30 +30−30 = 0 −10−30 = −40 +20−30 = −10 T T EW B E T T EW B EW B T T E W B E E E W W W B W B +10−50 Pump Motor Motor Motor Pump Pump Pump Sag compensated readings Sag compensated readings Sag compensated readings Mathematcially zero the east readings Original sag compensated readings with the east reading zeroed −10 0 0 +60 −40 0 +60 −50 +10 0 −40 +30 East to west readings to be plotted in the top view FIGURE 8.10 Zeroing the east readings. Piotrowski / Shaft Alignment Handbook, Third Edition DK4322_C008 Final Proof page 330 6.10.2006 12:13am 330 Shaft Alignment Handbook, Third Edition The original readings with the indicator zeroed on the top and the new readings with the indicator zeroed on the east are telling us the same thing about the misalignment condition between the two shafts. All we did was zero the indicator in a different position and notice that the validity rule still applies whether we zero on top or on the east. Now that we are going to be plotting the shafts in the top view, the top and bottom readings are meaningless, only the east and west readings are important. Figure 8.11 and Figure 8.12 show how to plot the east and west readings onto the top view alignment model. Notice that the scale factor in the top view is not the same as the scale factor in the side view. They do not have to be the same scale factor in both views but remember what the scale factors are in each view. Without being too repetitive here, remember that you only plot half of the dial indicator reading onto the graph. Also remember that whatever shaft the dial indicator is taking readings on is the shaft that you want to draw on the graph paper. Two of the major graphing mistakes people make are to forget to only plot half of the rim reading and drawing the wrong shaft onto the graph. The alignment models shown in Figure 8.9 through Figure 8.12 were generated using the reverse indicator method, which is covered in more detail in Chapter 10. The other four alignment Motor Motor Top view East Pump Pump 20 mils Scale: 5 in. 540 mils Notice the scale factor here. Plot half (20 mils) of this measurement here. 0 E W −40 Pump FIGURE 8.11 (See color insert following page 322.) Plotting the pump shaft in the top view. Piotrowski / Shaft Alignment Handbook, Third Edition DK4322_C008 Final Proof page 331 6.10.2006 12:13am Alignment Modeling Basics 331 methods (face–rim, double radial, shaft to coupling spool, and face–face) and their associated graphing and modeling techniques will be discussed in Chapter 11 through Chapter 15. 8.4.6 DETERMINING CORRECTIVE MOVES TO MAKE ON ONE MACHINE FROM THE ALIGNMENT MODEL Let us look at another example. Figure 8.13 shows a motor and a fan shaft misalignment condition in the side view. As you can see, the shafts are not in alignment with each other. Now what do we do? The next logical step is to determine the movement restrictions imposed on the machine cases at the control or adjustment points (i.e., where the foot bolts are). Movement restrictions define the boundary condition that help you to make an intelligent decision on what alignment correction would be easy and trouble free to accomplish. Trouble-free movement solutions? I fully understand that any corrective moves you make on rotating machinery are not going to be trouble free and easy to make. But there are some moves that will be far more difficult to make than others. You really need to have a wide Motor Motor Pump Pump Top view East Plot half (30 mils) of this measurement here. Motor 0 E W +60 Scale: 5 in. 20 mils 30 mils FIGURE 8.12 (See color insert following page 322.) Plotting the motor shaft in the top view. Piotrowski / Shaft Alignment Handbook, Third Edition DK4322_C008 Final Proof page 332 6.10.2006 12:13am 332 Shaft Alignment Handbook, Third Edition variety of options to make the most effective and intelligent alignment correction. Therefore, keep an open, objective mindset when you attempt to fix your alignment problem. In Figure 8.13, notice that if you wanted to keep the fan in its current position, you would have to move the motor downward at both the inboard and outboard ends. As shown in Figure 8.13, the amount of movement at the outboard bolts is obtained by counting the number of squares (at 3 mils per square with this scale factor) from where the actual motor shaft centerline is at the outboard bolting plane to the extended centerline of rotation of the fan. In this particular case, this is, 166 mils (0.166 in.). The amount of movement at the inboard bolts is obtained by counting the number of squares from where the actual motor shaft centerline is at the inboard bolting plane to the extended centerline of rotation of the fan. In this case, that is, 66 mils (0.066 in.). If there is 166 mils under both outboard bolts and 66 mils under both inboard bolts (that are not soft foot shims) then a good alignment solution would be to remove that amount of shim stock from under the appropriate feet. But what if there are not that many shims under the inboard and outboard feet? As bizarre as this may sound, I have seen people in a situation like this, remove the motor from the baseplate and grind the baseplate away. Unbelievable, but true. And it is still done somewhere today. 8.4.7 OVERLAY LINE OR FINAL DESIRED ALIGNMENT LINE The final desired alignment line (a.k.a. the overlay line) is a straight line drawn on top of the graph, showing the desired position both shafts should be in to achieve colinearity of centerlines. It should be apparent that if one machine case is stationary, in this case the fan shaft, that machine’s centerline of rotation is the final desired alignment line as shown in Figure 8.13. There is another way to correct the misalignment problem on this motor and fan that will be far less troublesome. Since adjustments are made at the inboard and outboard feet of the machinery, some logical alternative solutions would be to consider using one or more of these feet as pivot points. Both outboard feet or both inboard feet, or the outboard foot of one machine case and the inboard foot of the other machine case could be used as pivot points. By Up Motor Side view Fan Motor shaft centerline 66 mils down 166 mils down Scale: 5 in. 30 mils Fan shaft centerline FIGURE 8.13 Movement solutions for the motor only. Piotrowski / Shaft Alignment Handbook, Third Edition DK4322_C008 Final Proof page 333 6.10.2006 12:13am Alignment Modeling Basics 333 drawing the overlay line through these foot points, shaft alignment can usually be achieved with smaller moves. In real life situations, you will typically have greater success aligning two machine cases a little bit rather than moving one machine case a lot. Figure 8.14 shows using the overlay line to connect the outboard bolting plane of the motor with the outboard bolting plane of the fan. The inboard bolting planes are then moved the amount shown in Figure 8.14 to correct the misalignment condition in the up and down direction. No shims had to be removed and better yet, no baseplates had to be ground away. 8.4.8 SUPERIMPOSE YOUR BOUNDARY CONDITIONS,MOVEMENT RESTRICTIONS, AND ALLOWABLE MOVEMENT ENVELOPE When viewing the machinery in the up and down direction (side view), the movement restrictions are defined by the amount of movement the machinery can be adjusted in the up and down directions. How far can machinery casings be moved upward? There is virtually an unlimited amount of movement in the up direction, within reason, that is. Machine cases are typically moved upward by installing shims (i.e., sheet metal of various thicknesses) between the undersides of the machinery feet and the baseplate. How far can the machinery casings be moved downward? Well, it depends on the amount of shim stock currently under the machinery feet that are not soft foot corrections. How far can you move a machine down? I don’t know. You are going to have to look under the machine to see how much shim stock could be removed from under the machinery feet on every machine in the drive system. Maybe there are 10, 20, or 50 mils of shim stock under the machinery feet that can be removed that are not soft foot corrections that could be taken out. You will have to see what is there. These shims define the ‘‘downward movement envelope,’’ or as some people call it, the ‘‘basement floor,’’ or as other people call it, the ‘‘baseplate restriction point.’’ Shim stock typically refers to sheet metal thicknesses ranging from 1 mils (0.001 in.) to 125 mils (0.125 in.). There are several companies that manufacture precut, U-shaped shim stock in Up Side view Raise 48 mils up Overlay line Motor Pivot here Motor shaft centerline Scale: 5 in. 30 mils Raise 138 mils up Fan Pivot here Fan shaft centerline FIGURE 8.14 (See color insert following page 322.) Movement solutions for the inboard feet of both the motor and the pump by pivoting at the outboard feet of both machines. Piotrowski / Shaft Alignment Handbook, Third Edition DK4322_C008 Final Proof page 334 6.10.2006 12:13am 334 Shaft Alignment Handbook, Third Edition 4 standard sizes and 17 standard thicknesses. Once shim thicknesses get over 125 mils, they are typically referred to as spacers or plates and are custom made from plate steel. So if you want to move a machine downward and there are no shims under the machinery feet, you are already on the basement floor and that is defined as a downward vertical movement restriction or a baseplate restriction point. Figure 8.15 shows the same motor and fan but now we have observed that there are 75 mils of shim stock under the outboard feet and 25 mils of shims under the inboard feet that are not soft foot corrections that could be removed if we wanted to. By counting down 75 mils from the centerline of the motor shaft and the outboard bolting plane and drawing a baseplate restriction point there, we can now see how far that end can come down without removing metal from the baseplate or machine casing. Similarly, by counting down 25 mils from the centerline of the motor shaft and the inboard bolting plane and drawing a baseplate restriction point there, we can now see how far that end can come down without removing metal. In this particular case, there were no shims under any of the feet of the fan so its baseplate restriction points are positioned directly on the fan centerline at the inboard and outboard ends as shown in Figure 8.15. Now that we know what the lowest points of downward movement could be without removing metal, one possible solution would be to use the outboard feet of the fan and the inboard feet of the motor as pivot points removing 72 mils of shims from under the outboard feet of the motor and installing 42 mils of shims under the inboard feet of the fan as shown in Figure 8.15. 8.4.8.1 Lateral Movement Restrictions In addition to aligning machinery in the up and down direction, it is also imperative that the machinery be aligned properly side to side. Machinery is aligned side to side by translating the machine case laterally. This sideways movement is typically monitored by setting up dial indicators along the side of the machine case at the inboard and outboard hold down bolts, anchoring the indicators to the frame or baseplate, zeroing the indicators, and then moving the inboard and outboard ends the prescribed amounts. Here is where realignment typically becomes extremely frustrating since there is a limited amount of room between the shanks of the hold down bolts and the holes drilled in the machine case feet. Up Side view Overlay line Motor Pivot here Lower 72 mils down 75 mils of shims available to remove 25 mils of shims available to remove Scale: 5 in. 30 mils Baseplate restriction points Raise 42 mils up Fan pivot here No shims available to remove Fan shaft centerline No shims available to remove FIGURE 8.15 (See color insert following page 322.) Movement solutions using the outboard feet of the fan and the inboard feet of the motor as pivot points. Piotrowski / Shaft Alignment Handbook, Third Edition DK4322_C008 Final Proof page 335 6.10.2006 12:13am Alignment Modeling Basics 335 If, for example, you wanted to move the outboard end of a machine 120 mils to the south, began moving the outboard end monitoring the move with a dial indicator, and the machine case stopped moving after 50 mils of translation, this would be considered a movement restriction commonly referred to as a ‘‘bolt bound’’ condition. The problem in moving machinery laterally is that there is a limited amount of allowable movement in either direction. The total amount of side-to-side movement at each end of the machine case is referred to as the ‘‘lateral movement envelope.’’ To find the allowable lateral movement envelope, remove a bolt from each end of the machine case, look down the hole, and see how much room exists between the shank of the bolt and the hole drilled in the machine case at that foot. If necessary, thread the bolt into the hole a couple of turns, and measure the gaps between the bolt shank and the sides of the hole with feeler or wire gauges. It is very important for one to recognize that trouble free alignment corrections can only be achieved when the allowable movement envelope is known. Perhaps one of the most import- ant statements that will be made in this chapter is When you consider that both machine cases are movable, there are an infinite number of possible ways to align the shafts, some of which fall within the allowable movement envelope. It seems ridiculous, but many people have ground baseplates or the undersides of machin- ery feet away because they felt that a machine had to be lowered. When machinery becomes bolt bound when trying to move it sideways, people frequently cut down the shanks of the bolts or grind a hole open more. There is typically an easier solution. Disappointingly, many of the alignment measurement systems shown in this book force the user to name one machine case stationary and the other one movable which will invariably cause repositioning problems when the machine case has to be moved outside its allowable movement envelope. This may not happen the first time you align a drive system, or the second or third time, but if you align enough machinery, eventually you will not be able to move the movable machine the amount prescribed. Once the centerlines of rotation have been determined and the allowable movement envelope illustrated on the graph, it becomes very apparent what repositioning moves will work easily and which ones will not. Figure 8.16 shows the top view alignment model of a motor and pump. Not knowing any better, it appears that all you would have to do is move the outboard end of the motor 14 mils to the east and the inboard end of the motor 4 mils to the west. Easy enough. But what if the outboard end of the motor is bolt bound to the east already? By removing one bolt from the inboard and outboard ends of both the motor and pump, the lateral movement restrictions can be observed. In this case the following restrictions were observed: 1. Outboard end of motor—bolt bound to east and 40 mils of possible movement to the west 2. Inboard end of motor—bolt bound to east and 40 mils of possible movement to the west 3. Inboard end of pump—32 mils of possible movement to the east and 8 mils of possible movement to the west 4. Outboard end of pump—36 mils of possible movement to the east and 4 mils of possible movement to the west By plotting the eastbound and westbound restriction onto the alignment model, you can now see the easy corridor of movement. One possible solution (out of many) is shown in Figure 8.16. Piotrowski / Shaft Alignment Handbook, Third Edition DK4322_C008 Final Proof page 336 6.10.2006 12:13am 336 Shaft Alignment Handbook, Third Edition Please, for your own sake, follow these four basic steps to prevent you from wasting hours or days of your time correcting a misalignment condition: 1. Find the positions of every shaft in the drive train by the graphing and modeling techniques shown in this and later chapters. 2. Determine the total allowable movement envelope of all the machine cases in both directions. 3. Plot the restrictions on the graph or model. 4. Select a final desired alignment line or overlay line that fits within the allowable movement envelope (hopefully) and move the machinery to that line. If you are involved with aligning machinery, by following the four steps above, it is guaranteed that you will save countless hours of wasted time trying to move one machine where it does not really want to go. 8.4.8.2 Where Did the Stationary–Movable Alignment Concept Come From? I don’t know. Every piece of rotating machinery in existence has, at one time or another, been placed there. Mother Earth never gave birth to a machine. They are neither part of the Earth’s mantle nor firmly imbedded in bedrock. Every machine is movable, it is just a matter of effort (pain) to reposition it. So why have the vast majority of people who align machinery called one machine stationary and the other machine movable? The only viable reason that I can come up with is this—in virtually every industry there is an electric motor driving a pump. When you first approach a motor pump arrangement, you immediately notice that the pump has piping attached to it and the only appendage attached to the motor is conduit (usually flexible conduit). From your limited vantage point at this time it would appear to be easier to move the motor because there is no piping attached to it like the pump. You would prefer to just move the motor because it looks easier to move than the pump (and so would I). The assumption is made that the pump will not be moved, no matter what position you find the motor shaft in with respect to the pump shaft. Motor Top view 32 mils of possible movements to the east here Pivot here Pump 36 mils of possible movement to the east here Move 14 mils east here 4 mils of possible movement to the west here 8 mils of possible movement to the west here Lateral movement restriction points 40 mils of possible movement to the west here 20 mils 5 in. Scale: Move 20 mils west here East boundary line West boundary line Move 22 mils west here Bolt bound to east here East FIGURE 8.16 (See color insert following page 322.) Applying lateral movement restrictions to arrive at an easy sideways move within the east and west corridors. Piotrowski / Shaft Alignment Handbook, Third Edition DK4322_C008 Final Proof page 337 6.10.2006 12:13am Alignment Modeling Basics 337 But what do you do when you have to align a steam turbine driving a pump? They are both piped; which machine do you call the stationary machine—the pump or the turbine? No matter what your answer is, you are going to have to move one of them and they both have piping attached to their casings. Piping is no excuse not to move a piece of machinery, particularly in light of what most of us know about how piping is really attached to machinery. For some people, they are afraid to loosen the bolts holding a machinery with piping attached to it because the piping strain is so severe that they fear the machine will shift so far that it will never get back into alignment. So is the problem with the alignment process or the piping fit-up? Refer to Chapter 3 for information on this subject. If you align enough machinery and insist that one machine will be stationary, eventually you will get exactly what you deserve for your shallow range of thinking. 8.4.8.3 Solving Piping Fit-Up Problems with the Overlay Line Although we have been showing that the overlay line (a.k.a. final desired alignment line) is drawn through foot bolt points, it is important to see that the overlay line could be drawn anywhere and the machinery shafts moved to that line. This can be particularly beneficial if there are other considerations that have to be taken into account such as piping fit-up problems. Figure 8.17 shows a motor and pump where the suction pipe is 1=4 in. higher than the suction flange on the pump and there is a 1=4 in. excessive gap at the discharge flanges. Rather than align both shafts, then install an additional 0.250Љ Motor Pump 15Љ Motor Pump Side view 15Љ 5.5Љ Bracket clamping positions Scale: Suction flange location 7Љ 14.5Љ10Љ 5.5Љ 7Љ 14.5Љ 5Љ 10.25Љ 1Љ 1Љ 0.250Љ 5 in. FIGURE 8.17 (See color insert following page 322.) Scaling off the dimensions for a motor and pump including the location of the suction flange on the pump. Piotrowski / Shaft Alignment Handbook, Third Edition DK4322_C008 Final Proof page 338 6.10.2006 12:13am 338 Shaft Alignment Handbook, Third Edition 250 mils (1=4 in.) under all the feet, another easier solution exists. Scale off where the suction flange of the pump is onto the alignment model. Extend the centerline of the pump to go out to the suction flange point. Place a mark 250 mils above the pump shaft centerline where the suction flange is located. Construct an overlay line to go from that point to the outboard bolts of the motor as illustrated in Figure 8.18. Then solve for the moves at each bolting plane not only to eliminate the piping fit-up problem but also to align the shafts. We have reviewed many of the basic concepts behind alignment modeling in this chapter. Determining your maximum misalignment deviation and whether you are within acceptable alignment tolerances will be covered in the next chapter. Specific instruction on how to perform all five-alignment measurement methods and their associated modeling techniques will be covered in Chapter 10 through Chapter 15. BIBLIOGRAPHY Dodd, V.R., Total Alignment, Petroleum Publishing Company, Tulsa, OK, 1975. Dreymala, J., Factors Affecting and Procedures of Shaft Alignment, Technical and Vocational Depart- ment, Lee College, Baytown, TX, 1970. Piotrowski, J., Basic Shaft Alignment Workbook, Turvac Inc., Cincinnati, OH, 1991. Suction flange moves up 250 mils at this point Pivot here Raise 47 mils up Scale: 5 mils Motor 0 T B E W T B E W −60 +10 +90 +80 0 − 10 Sag compensated readin g s −70 Pump Up Side view Raise 170 mils up Raise 235 mils up 5 in. FIGURE 8.18 (See color insert following page 322.) Overlay line positioned to correct the piping fit-up problem and align the shafts with one move. Piotrowski / Shaft Alignment Handbook, Third Edition DK4322_C008 Final Proof page 339 6.10.2006 12:13am Alignment Modeling Basics 339 [...]... / Shaft Alignment Handbook, Third Edition DK4 32 2 _C008 Final Proof page 34 0 6.10 .20 06 12: 13am Piotrowski / Shaft Alignment Handbook, Third Edition DK4 32 2 _C009 Final Proof page 34 1 9 26 .9 .20 06 8:42pm Defining Misalignment: Alignment and Coupling Tolerances 9.1 WHAT EXACTLY IS SHAFT ALIGNMENT? In very broad terms, shaft misalignment occurs when the centerlines of rotation of two (or more) machinery shafts... Turbine 1 .20 0 Generator 1 .20 0 Exciter Side view looking east LPC Turbine Piotrowski / Shaft Alignment Handbook, Third Edition DK4 32 2 _C009 Final Proof page 3 52 26.9 .20 06 8:42pm Shaft Alignment Handbook, Third Edition Piotrowski / Shaft Alignment Handbook, Third Edition DK4 32 2 _C010 Final Proof page 35 3 6.10 .20 06 12: 14am 10 Reverse Indicator Method The reverse indicator method is also often called the indicator... further divided into 60 parts called seconds of arc Therefore there are 21 ,600 min of arc and 1 ,29 6,000 s of arc in a circle Piotrowski / Shaft Alignment Handbook, Third Edition DK4 32 2 _C009 Final Proof page 34 3 Defining Misalignment: Alignment and Coupling Tolerances 26 .9 .20 06 8:42pm 34 3 Parallel misalignment Angular misalignment “Real world” misalignment usually exhibits a combination of both parallel and... view Piotrowski / Shaft Alignment Handbook, Third Edition DK4 32 2 _C009 Final Proof page 34 9 26 .9 .20 06 8:42pm 34 9 Defining Misalignment: Alignment and Coupling Tolerances If you rotate this shaft only, you will align the centerline of rotation with the centerline of the improperly bored coupling hub, not the other shaft centerline of rotation 10 _ 0 + 10 20 20 30 30 40 50 40 Centerline of rotation To align... Handbook, Third Edition DK4 32 2 _C010 Final Proof page 35 4 6.10 .20 06 12: 14am 35 4 Shaft Alignment Handbook, Third Edition 10 _0 + 10 20 20 30 30 40 50 40 Driver Driven 40 50 40 30 30 20 20 10 _0 + 10 Indicator readings log Driver • Procedure • 1 Attach the alignment bracket(s) firmly to one (both) shaft( s) and position the indicator(s) on the perimeter of the other shaft (or coupling hub) 2 Zero the indicator(s)... = − (Y ) of Driver C Outboard feet = (C + D + E ) (X + Y ) − (X ) of Driven C FIGURE 10.6 Reverse indicator mathematics for correcting moves on either machine case Piotrowski / Shaft Alignment Handbook, Third Edition DK4 32 2 _C010 Final Proof page 35 8 6.10 .20 06 12: 14am 35 8 Shaft Alignment Handbook, Third Edition View looking east Motor Pump 10 _ 0 + 10 20 20 30 30 40 50 40 30 30 40 50 40 10 20 15 in... Piotrowski / Shaft Alignment Handbook, Third Edition DK4 32 2 _C009 Final Proof page 34 5 34 5 Defining Misalignment: Alignment and Coupling Tolerances Driver shaft Maximum alignment deviation occurs here Driver offset (in mils) 26 .9 .20 06 8:42pm Driven shaft Driven offset (in mils) Misalignment is the deviation of relative shaft position from a colinear axis of rotation measured at the points of power transmission... taken on the shaft where the bracket was initially clamped 40 50 40 30 30 20 20 10 _ 0 + 10 10 _ 0 + 10 _ 0 + 10 20 20 30 30 40 50 40 10 20 20 30 30 40 50 40 Then here “Target” plate 40 Indicator attached to this shaft 50 40 30 30 20 20 10 _ 0 + 10 An alternative method is to clamp a bracket onto a shaft that supports a rod extending over to the other shaft An indicator is then attached to the shaft that... However, as the misalignment is expressed in mils per inch, whether the deviations are measured where the readings were taken, or at the ends of the shafts, or at the flexing points Piotrowski / Shaft Alignment Handbook, Third Edition DK4 32 2 _C009 Final Proof page 34 8 34 8 26 .9 .20 06 8:42pm Shaft Alignment Handbook, Third Edition Motor Side view Up Fan 30 mils Motor shaft centerline 15 mils Fan shaft centerline... definition, let us dissect each part of this statement to clearly illustrate what is involved Piotrowski / Shaft Alignment Handbook, Third Edition DK4 32 2 _C009 Final Proof page 34 4 34 4 26 .9 .20 06 8:42pm Shaft Alignment Handbook, Third Edition Collinear means in the same line or in the same axis If two shafts are collinear, then they are aligned The deviation of relative shaft position accounts for the . following page 32 2 .) Plotting the pump shaft in the top view. Piotrowski / Shaft Alignment Handbook, Third Edition DK4 32 2 _C008 Final Proof page 33 1 6.10 .20 06 12: 13am Alignment Modeling Basics 33 1 methods. top view. Piotrowski / Shaft Alignment Handbook, Third Edition DK4 32 2 _C008 Final Proof page 3 32 6.10 .20 06 12: 13am 3 32 Shaft Alignment Handbook, Third Edition variety of options to make the most. 33 9 6.10 .20 06 12: 13am Alignment Modeling Basics 33 9 Piotrowski / Shaft Alignment Handbook, Third Edition DK4 32 2 _C008 Final Proof page 34 0 6.10 .20 06 12: 13am 9 Defining Misalignment: Alignment