WO2002003028A1

WO2002003028A1 - Method and system for calculating and compensating for shaft misalignment

Info

Publication number: WO2002003028A1
Application number: PCT/US2000/018066
Authority: WO
Inventors: John M. Zatezalo
Original assignee: ALIGNMENT SOLUTIONS LLC
Current assignee: ALIGNMENT SOLUTIONS LLC
Priority date: 2000-06-30
Filing date: 2000-06-30
Publication date: 2002-01-10
Anticipated expiration: 2002-12-30
Also published as: AU2000260614A1

Abstract

The present invention is a method and associated apparatus for calculating relativealignment of machines coupled by rotatable shafts on the basis of alignment measurementdata. The present invention provides a user-friendly and highly accurate alignment system. The method computes relative positions of pertinent machine parts, such as adjustment points(1081-1092), on the basis of alignment descriptions or measurement data. The methodrepresents the relative positions of pertinent machine parts graphically, preferably using acomputer with a graphical user interface. The method of the present invention defines (1210) a reference line (1120, 1130) to serve as the basis for relative alignment. Using a referenceline, the method of the present invention can calculate a set of machine movement values (1220), which when applied to the machines at the pertinent positions, would bring themachines into relative alignment.

Description

METHOD AND SYSTEM FOR CA LCULATING AND COMPENSATING FOR SHAFT MISALIGNMENT

Technical Field

The invention is a method and an apparatus for aligning rotating machinery. In particular, the invention is a method for performing alignment checks, including hot alignment checks on rotating, coupled machines.

Background Art

When two or more rotating machine shafts are coupled, the shafts should be aligned to within predetermined tolerances in order to ensure optimum performance of the machines, and to reduce vibration and possible damage to the machines. For many machinery arrangements, the optimum alignment exists when the axes or rotation of all the shafts coincide along a straight line that extends through each such axis of rotation. A number of shaft alignment methods are available to perform shaft alignments. These methods generally involve placement of jigs, measuring devices and other components on or near the shafts in order to take measurements that can then be used to compute shaftmisaligmnent. The measuring devices may be direct reading instruments such as dial indicators. Other measuring devices employ lasers to measure misalignment. Most current alignment systems are complicated arrangements that require significant time to install, require experience and expertise to operate, and are susceptible to erroneous results due to a combination of operator error and environmental factors. These environmental factors include overhung rotor effect, journal movements, effect of gravity on the measurement apparatus, and atmospheric interference with laser and other optical systems, for example. Current systems require training and practice to use effectively and do not provide a graphical user interface that simplifies use and application of the systems. Moreover, these systems are only capable of cold alignment checks and cannot empirically account for environmental effects such as thermal growth, for example. Summary of the Invention The present invention is a method and associated apparatus for calculating relative alignment of machines coupled by rotatable shafts on the basis of alignment measurement data. The present invention provides a user-friendly and highly accurate alignment system. The method computes relative positions of pertinent machine parts, such as adjustment points, on the basis of alignment measurement data. The method represents the relative positions of pertinent machine parts graphically, preferably using a computer with a graphical user interface. The method of the present invention defines a reference line to serve as the basis for relative alignment. Using a reference line, the method of the present invention can calculate a set of machine movement values, which when applied to the machines at the pertinent positions, would bring the machines into relative alignment. Out of many possible sets of machine movement values that would accomplish this result, the method of the present invention can eliminate unacceptable answer sets and choose an answer set that best solves the misalignment problem.

The present invention also is a method and associated apparatus for measuring relative alignment of machines coupled by rotatable shafts and describing that relative alignment. The present invention provides a user-friendly and highly accurate alignment system. The method measures employs a reference device from which distances to machine surfaces, perpendicular to an axis of shaft rotation are measure. On the basis of these measured distances, the present invention computes relative positions of pertinent machine parts, such as adjustment points. The relative positions of pertinent machine parts can be utilized with the aid of a graphical user interface to calculate a set of machine movement values, which when applied to the machines at the pertinent positions, would bring the machines into relative alignment.

The method of the present invention is capable of achieving many advantages, some of which may include the following: The method of the present invention can be utilized to perform a "hot check" of machine alignment before the machines have cooled and thermal growth has disappeared. The method of the present invention can be accomplished on theis basis of a minimal amount of measurement data that can be obtained in the field quickly and easily. The method of the present invention can accommodate for factors related to thermal growth and dynamic forces. The method of the present invention can calculate multiple alignment solutions. The method of the present invention can account for physical machine constraints. The method of the present invention can calculate optimal alignment solutions. These and other advantages offered by some or all embodiments of the present invention will be apparent from the following drawings and detailed description. Description of Drawings

Figure I depicts a machine train and corresponding coordinate points vertically. Figure 2 depicts a machine train and corresponding coordinate points horizontally.

Figure 3 is diagram of points in a vertical plane and a horizontal plane. Figure 4 is a flowchart of a method according to the present invention. Figure 5 is block diagram of a computer according to the present invention. Figure 6 illustrates an alignment measurement device according to the present invention.

Figure 7 illustrates alignment measurements about a shaft end or coupling face. Figure 8 is a geometric interpretation of the alignment measurements illustrated in Figure 7.

Figure 9 illustrates alignment measurements concerning two machines. Figure 10 is a geometric interpretation of the alignment measurements illustrated in Figure 9.

Figure 11 is another geometric interpretation of the alignment measurements illustrated in Figure 9.

Figure 12 illustrates an alignment measurement device according to the present invention.

Figures 13 and 14 illustrate graphical user interfaces according to the present invention. Disclosure of Invention

The method and system of the present invention ultimately calculates movement values needed to bring a train of machines into alignment. The method can be implemented on a variety of systems or hardware platforms. Preferably, a graphical user interface is used. The method may begin with various forms of input data. In one form, the input data are direct field results obtained with alignment measurement devices, such as commercially available, "alignment computers," which may be based on laser or indicator measurements. Such results may be expressed in terms of angularity and offset, as described below. In another form, the input data are direct field measurements taken using the EZ-LLNE(TM) or ICAD (TM) (integrated coupling and alignment device) devices available from the assignee of the present invention. Typically, these devices measure distances from which physical locations of machine parts in relation to another machine with respect to relative alignment or misalignment can be quantitatively determined. Also, direct field measurements taken using the

"reversed" method may constitute the input data. Alternatively, the input data may be the physical locations of machine parts just described. The input data may be accessed from a database of machinery data. The input data may include, for example, the effects of thermal growth and dynamic factors, such as journal movement, static tilt, and/or gear clearance. If not already included, these effects may be factored into the data before beginning. The data relating to these effects may be empirical or analytically estimated.

In the case where the input data are direct field measurements obtained with alignment measuring devices, the field measurements are used to derive relative physical locations of machine parts. Techniques for deriving relative physical locations of machine parts from field measurements obtained with alignment measuring devices are described in detail later in this document. The pertinent machine parts are adjustment points on the machines. For example, the bottom feet of a machine may be vertical adjustment points, where adjustments may be made by shimming under the feet. Similarly, machine parts that serve as horizontal adjustment points exist.

The outputs of the method of the present invention are movement values that, when applied to the adjustment points, would bring the train of machines into a desired alignment configuration. Typically, the desired alignment configuration is approximately perfect relative alignment.

In conceptual terms, the processing of the present invention begins by noting the relative physical locations of pertinent macliine parts as points in a three dimensional coordinate system. If the machines are perfectly aligned, the points would coincide on a straight line. If the machines are misaligned, the points will be non-collinear. The present invention contemplates teclmiques for displacing the points so as to cause them to be collinear. A preferred technique for accomplishing this goal is to first define a straight reference line in the coordinate system. Given a reference line, a set of displacement vectors is calculated so as to move each point onto the reference line.

When the corresponding machine parts are moved in accordance with the displacement vectors, the machines are brought into alignment.

In a preferred embodiment of the method, the three dimensional, alignment problem is decomposed into two independent two-dimensional alignment problems. In other words, the alignment problem is solved in two planes, one at a time. First, the relative physical locations of pertinent machine parts are resolved into orthogonal components. Preferably, the orthogonal components are along a vertical plane and a horizontal plane. One axis of each plane is generally directed along the same direction as the drive shafts of the machine train, and adjustments to the points are made perpendicular to this axis. Because the planes are orthogonal, adjustments can be made in one plane without effect in the other.

Figure I illustrates what has just been described in conceptual terms. Figure I (a) is a side perspective of a machine train of five rotating machines 1001-1005. Four couplings 1011-1014 couple rotating machines 1001 - 1005 piecewise. Each machine is illustrated with several bottom feet 1021-1032, which serve as vertical adjustment points. For example, the first machine 1001 has a front foot 1021 and a rear foot 1022; the second machine 1002 has a front foot 1023, a rear foot 1026, and two intermediate feet 1024 and 1025. Each machine contains a rotating shaft that terminates at one or two coupling faces. For example, a coupling face 1041 of the first machine 1001 is directed in the general direction of a coupling face 1042 of the second machine and linked to the coupling face 1042 of the second machine by the coupling 1011. Though the invention is illustrated and described with reference to "coupling faces," the invention works equally as well with any surface of the machine that is perpendicular to the axis of rotation. For example, a shaft end of a machine may be used rather than a coupling face.

Gross vertical misalignment of the machines 1001-1005 is depicted in Figure I to better illustrate the operation of the present invention. In reality, the degree of misalignment, even if severe, may be undetectable to the human eye. The first machine 1001 and the second machine 1002, as illustrated in Figure 1 (a), are vertically offset but have parallel internal shafts. On the other hand, the coupling face 1043 of the second machine 1002 and the coupling face 1044 of the third machine 1003 are not vertically offset with respect to each other but have internal shafts that are not parallel. The first machine 1001 and the second machine 1002 have relative offset misalignment but not angularity misalignment. The second machine 1002 and the third machine 1003 have relative angularity misalignment but no offset misalignment. As can be seen from the figure, the other coupled machine pairs have both offset and angularity misalignment to varying degrees. Figure 1(b) is a representation of Figure 1(a) in a vertical plane. In Figure 1(b) the ordinate axis 1051 is directed in the same general direction as the shaft train in Figure 1(a). The abscissa axis 1052 is directed in the same general direction in which the machines 1001-1005 are adjustable at adjustable feet 1021-1032. Points 1061- 1072 represent the "locations" of the adjustable feet 1021-1032 in the sense of relative alignment. In particular, the first coordinates of the points 1061-1072 correspond to the locations of adjustable feet 1021-1032 along the same general direction as the shaft train. The second coordinates of the points 1061-1072 correspond to the vertical orientation of the machine shafts sampled at the positions of the adjustable feet 1021- 1032. This relationship is illustrated in Figure I for the fifth macliine 1005.

Figure 2 is analogous to Figure I but depicts horizontal alignment rather than vertical alignment. Figure 2(a) is a top perspective of the 1001-1005. The machines 1001 1005 are horizontally adjustable at horizontal adjustment points 1081-1092. Figure 2(b) is a representation of the horizontal alignment of the shafts of machines 1001-1005. The points 1101-1112 represent the horizontal adjustment points 1081-

1092 in relative alignment "locations" with respect to each other.

Figure 3 graphically illustrates reference lines and movement values. Figure 3(a) is the same vertical plane diagram as Figure 1(b). Figure 3(b) is the same horizontal plane diagram as Figure 2(b) with a different scale. In the vertical plane of Figure 3(a), a vertical plane reference line 1120 is shown as being the same as the ordinate axis 1051. An equation for the vertical plane reference line 1120 is y_v = 0. In the horizontal plane of Figure 3(b), a horizontal plane reference line 1130 is illustrated. The horizontal plane reference line 1130 may be generally characterized by the standard linear equation y_h(x_h)=m_hx_h+b_h where m_h, is the slope of the line and b_h is the y-intercept. Note that the vertical plane reference line 1120 may be said to have parameters ^ = b_v= 0. Various teclmiques for choosing m_h,x_h and b_v are described later. For now, given parameters of the vertical plane reference line 1120, vertical movement values are calculated as differences in abscissa values from points 1061- 1072 and the vertical plane reference fine 1120. Because the vertical plane reference line 1120 is everywhere zero in this instance, the vertical movement values in this case are simply the additive inverses (i.e., multiplied by -1) of the second coordinates of the points 1061-1072. For example, if the point 1064 has coordinates, (x^y^) =

(11.32, 3.20), then the corresponding vertical movement value is vm₄= -3.2,'meaning that the corresponding adjustable foot needs to be lowered by 3.2 units (typically thousandths of an inch) as part of the alignment operation.

The more general case of movement value calculations is illustrated in the horizontal plane of Figure 3(b). Again, the movement value is the distance from the reference line 1120 to the (adjustment) points 1061-1072. As. an example, consider the point I 110 and assume itscoordinates are given by (x_hlo,y_hιo)- Then, because the reference line is defined, by y_h(x_h)=m_hx_h+ b_h, the horizontal movement value is calculated according to well understood plane geometry equations as hm_hlo=y_hlo-y_h(x_hl0)=y_hlo-

^mh^Xhl0^'Dh-

Next will be described various techniques for defining a reference line. In general, a line may be defined by two points. Thus, it is possible to define a reference line by choosing two points, such as the two (adjustment) points 1061 and 1062 shown in Figure 3(a). When a particular point is chosen to define the reference line, then, because the reference line will pass through that point, the resulting movement value for the adjustment point corresponding to that particular point will be zero. Thus, according to the present invention, points where adjustment is impossible or least desirable can be isolated and not adjusted while still accomplishing alignment. Possible reasons for not being capable or desirable to adjust a point include "bolt bound" conditions and pipe strain. A bolt bound condition is one in which further horizontal adjustment is constrained because bolts fastening the machine to the floor permit only a limited range of movement. Pipe strain refers to a condition in which further adjustment to a machine would strain a physical interface to the machine.

When two points of the same machine are chosen to define the reference line, then that machine need not be adjusted. This has the effect of using that machine as the reference to which all other machines are aligned. This is the case in Figure 3(a), where the first machine 1001 is held still while the other machines 1002-1005 are moved into relative alignment with the first macliine 1001.

Another possibility for defining a reference line is to calculate its parameters using linear regression or linear curve fitting, which are generally well known. One such curve fitting technique is linear least squares, which produces a straight line that

"best" fits the points in the sense that it minimizes a metric defined as the sum of the squared second coordinate differences from the points to the resulting line. Other "best" fits can be obtained by minimizing other metrics, such as the maximum second coordinate difference (i.e., "mini-max"), as is also well known. It is possible to perform linear regression or curve fitting on the basis of less than all of the points, by ignoring some points that are less sensitive to extreme movement ranges.

Those skilled in the art will also readily appreciate that linear regression or linear curve fitting techniques can be utilized with constraints. For example, if one or more points are bolt bound and cannot be adjusted further in one direction, then a best fit that minimizes the chosen metric without violating the constraints can be found, utilizing well known techniques of constrained optimization.

An overall method of the present invention is illustrated in the flow chart of Figure 4. The method begins by calculating point coordinates, such as points 1061- 1072 or 1101-1112, as depicted in the calculating step 1200. Next, a reference line is defined according, for example, to one of the aforementioned teclmiques, as depicted in the defining step 1210. Then, a set of movement values are calculated as described previously, as depicted in determining step 1220. The points and reference line and possibly other information such as calculated movement values may be displayed, as shown in the displaying step 1230. A human user might examine the results and determine if the results are acceptable, as shown in the decision step 1240. Alternatively or additionally, an automatic check of possibly unacceptable conditions, such as bolt bound or pipe strain conditions, may be performed as part of the processing illustrated in the decision step 1240. In a more sophisticated embodiment, expert systems and/or artificial intelligence techniques may be employed in the decision step 1240 to adaptively continue if unacceptable. If the results are unacceptable, anew reference line is determined and the steps 1210-1240 are repeated. If the results are acceptable, the adjustments to the machines may be made, as shown in the adjusting step 1250. One skilled in the art will appreciate that many variations are possible for the processing depicted in the flowchart of Figure 4. For example, not all steps need be performed. In particular, the calculating step 1200 may be bypassed if the method begins with a given set of points. The adjusting step 1250 also need not be performed. Also, variation in the order of the steps is possible. In particular, the order of the determining step 1220 and the displaying step 1230 is arbitrary. Steps may be performed simultaneously rather than the sequential approach illustrated in the flowchart. Finally, additional unillustrated steps, such as recording the final movement values, may be performed. Other variations to the processing illustrated in Figure 4 are possible, as one skilled in the art would appreciate.

A block diagram of computer hardware of the present invention is illustrated in Figure 5. Input data in the form of machine data from a database, measurement data from the field, and/or point coordinates directly are received by a data input device 1300. The input device 1300 may be a keyboard, point and click device (e.g., mouse), touch screen, modern, data port, light beam port, or something similar. The data received by the data input device 1300 is stored in a data memory 1310, where it is accessed by a processor 1320. The processor 1320 is preferably a general purpose microprocessor that executes program instructions stored in the program memory 1330. The program memory 1330 may be physically packaged together or separately from the processor 1320. The program memory 1330 may be a computer readable storage device, such as a disk, tape or memory chip. The program instructions direct the processor 1320 to define a reference line and calculate movement values. Final results, intermediate results, and other information generated by the processor 1320 may be displayed on the display 1340. The computer hardware may also include a user input device 1350, by which a user may interact with the program. The user input device 1350 and the data input device 1300 may be the same device or separate devices. The input device 1300 and the data memory 1310 together perform the function of accessing data. The processor 1320 and the program memory 1330 together (i.e., block 1350) perform the function of determining a reference and movement values. Therefore block 1350 is a means for determining a reference and movement values. However, other equivalent structures are possible for the block 1350. For example, the same function may be performed by a hardwired circuit such as an ASIC (application specific integrated circuit), or a firmware programmable device such as a gate array or programmable logic array.

In one embodiment of the present invention, the input data includes historical information about past movements applied to the particular machine train under consideration. The present invention may then analyze the historical data to detemiine trends or otherwise try to predict future misalignment. With such information, the method of the present invention may perturb the final movement values to compensate for predicted drift. For example, the present method may predict the points 1061-1072 and/or 1101-1112 at the time of the next scheduled alignment check, say three months in the future, compute a set of movement values to align that predicted future configuration, and then average the presently needed movement values with the predicted future configuration values so as to minimize the time averaged misalignment over the next three months. Various other methods for analyzing the historical data, including intelligence-based, rule-based, neural network, artificial intelligence and expert systems, are possible.

Next will be described methods and devices for measuring alignment data and deriving physical locations or positions of pertinent machine parts. These methods and devices relate specifically to the processing illustrated in block 1200 of Figure 4 and the program instructions, or equivalent functionality of calculating step 1350 in Figure 5.

Figure 6 depicts an alignment measurement device 1400 situated between a first shaft end 1041 and a second shaft end 1042. The alignment measurement device 1400 depicted in Figure 6 is similar to the EZ-LINE (TM) device available from the assignee of the present invention and described in greater detail in the parent U.S. patent application serial no. 08/949,187. The alignment measurement device 1400 comprises a main shaft 1401 that is extended to fit between the two shaft ends 1041 and 1042. Extending perpendicularly from the main shaft 1401 are two2 rigid arms 1404 and 1405. Along each rigid arm is a measurement device such as dial indicators

1408 and 1409, both of which measure a distance to the respective shaft ends. Other electronic or manual distance measuring devices may be used in place of the dial indicators 1408 and/or 1409. The main shaft 1401 is placed between the two shaft ends 1041 and 1042 by means of one6 or more telescopically extending ends. When compressed, the telescopically extending ends7 permit the main shaft 1401 to be inserted between the two shaft ends 1041 and 1042. When the8 telescopically extendable end(s) fully extends, the alignment measuring device 1400 fits snugly between the two shaft ends 1041 and 1042. Each end of the main shaft 1401 may be tapered to fit in the center of the respective shaft end. Alternatively, each end of the mam shaft 1401 mayl be or -terminated with a ball, which may be a swivelling ball joint. Preferably, the alignment measuring device 1400 can be rotated easily about the axis of the main shaft 1401 to permit taking distance measurements from the arms 1404 and 1405 to the shaft ends 1041 and 1042,respectively, at any point along the rim of the shaft ends.

Many variations of the alignment measurement device 1400 are possible. Both rigid arms 1404 and 1405 need not be attached to the main shaft 1401 simultaneously. A single rigid arm that can be attached to and detached from each end of the main shaft 1401 may be utilized. Alternatively, a single rigid arm. attached anywhere to the main shaft 1401 may be utilized to measure distances to each shaft end or coupling face by providing two oppositely directed distance measuring devices or one reversible distance measuring device, provided accurate distance measurements are possible across the span contemplated. When two rigid arms are present, they need not point in the same direction. In fact, the measurement distances to the first shaft end or coupling face 1041 is independent of the measurement of distances to the second shaft end or coupling face 1042, provided that the planes of measurement (e.g., the planes in which rigid arms 1404 and 1405 rotate) are parallel and separated by a fixed distance.

The alignment measuring device 1400 as depicted in Figure 6 may be utilized to measure alignment or misalignment data in the following mamier. First, the alignment of the shaft ends or coupling faces 1041 and 1042 in a first plane, such as the vertical plane, is measured. Second, the alignment of the shaft ends or coupling faces 1041 and 1042 in a second plane, such as the horizontal plane is measured. The same set of measurements may be utilized to determine alignment in both planes. To measure alignment in the vertical plane, for example, the device 1400 is first configured as illustrated in Figure 6, viewed as a side perspective, where the rigid arms 1404 and 1405 point in the generally upward direction. In this position, dial indicator measurements are recorded. Then the entire device 1400 is rotated about the axis of the main shaft 1401 so that the rigid arms 1404 and 1405 point generally downward, at which position dial indicator measurements are taken again. With respect to the first coupling face 1041, the dial indicator measurement taken in the top position may be denoted x_lτ and the dial indicator measurement read from the bottom position may be denoted x_lb. Likewise with respect to second shaft end or second coupling face 1042, the top and bottom dial- indicator measurements are denoted as x_2T and x_2B respectively. Also, the exact or nearly exact angular direction of the rigid arms 1404 and 1405 is recorded at the points when the top and bottom distance measurements are taken. These angular measurements from the vertical plane are denoted with respect to the first shaft end or first coupling face 1041 as β_lτ and β_1B respectively, with similar notation used with respect to the second shaft end or second coupling face 1042. Finally, note is taken of the radial distance from the center of device 1400 to the point on the rigid arms 1404 and 1405 at which the distance measurements were taken. With respect to the first shaft end or first coupling face 1041, these radial distances are denoted r_1T and r_1B at the top and bottom positions respectively, with similar notation used with respect to the second shaft end or second coupling face 1042. The measurements just described are illustrated in Figures 7(a) and 7(b). Figure 7(a) shows a side perspective of a first machine 1001 with a first shaft end or first coupling face 1041. From this side perspective, the first surface distance measurements x_1T and x_1B are as illustrated, and the vertical separation between the dial indicator positions is indicated as dl. Figure 7(b) illustrates the dial indicator measurements as viewed facing directly towards the first shaft end or first coupling face 1041. From this perspective, the angular offsets from the vertical plane are readily apparent as denoted by β_lτ and β_1B. Also, the radial distance from the center of the ridged main shaft 1401 to the dial indicator position is denoted at the point of top measurement as r_1T and at the point of bottom measurement as r_1B Figure 7(b) illustrates how d_x, the vertical separation between the dial indicator positions, is derived. In particular, by using well known trigonometric relationships, the vertical separation between the dial indicator positions is derived as d_!=r_1T | cos(β_lτ) | + r_1B |cos(β_1B)| . When β_lτ~β_1B»0, this expression simplifies to d^^ + r_1B. When r_π~r_1B = r, such as when the same rigid arm is rotated around to make both measurements, then this expression simplifies further to d_x= 2r.

The relative vertical orientation of the first shaft end or first coupling face 1041 is illustrated graphically in Figure 8 as a triangle 1420. The hypotenuse of the triangle 1420 represents the first shaft end or first coupling face 1041, which is shown to be offset in the vertical plane by an angle «. The other two sides of the triangle 1420 are d_! and x_1T-x_1B, as shown in the figure. Figure 9 illustrates two machines 1001 and 1002 with two shaft ends or coupling faces 1041 and 1042 in relative misalignment. The measurements d_l5 x_1T, and x_1B are illustrated withl3 respect to the first shaft end or first coupling face 1041 of a first machine 1001 and are as described above in relation to Figures 7 and 8. Likewise, analogous quantities - α^, x_2T and x_2B — are illustrated with respect to the second shaft end or second coupling face 1042 of a second machine 1002. Also illustrated in Figure 9 are horizontal distances between various points of interest, including the center points of each shaft end or coupling face and adjustment feet locations, as denoted by the symbols c, 1_1R, 1_1F, 1_2R and 1_2F.

Next will be described a method for bringing the second shaft end or second coupling face 1042 into alignment with the first shaft end or first coupling face 1041 while holding the first machine 1001 still. The geometry of this movement and this calculation is illustrated in Figure 11. In Figure 11, the triangle 1420 represents the angularity of the first shaft end or first coupling face 1041. Likewise the triangle 1450 represents the angularity of the second shaft end24 or second coupling face 1042. The triangle 1440 represents the offset between the first shaft end or first coupling face 1041 and the second shaft end or second coupling face 1042. According to Figure 11, bringing the second shaft end or second coupling face 1042 into alignment with the first shaft end or first coupling face 1041 can be accomplished by making three adjustment that are added together to result in a total adjustment. First, an adjustment to compensate for the angle <* representing the offset of the second shaft end or second coupling face 1042 from the first shaft end or first coupling face 1041 is made.

This first adjustment may be denoted s₀ and can be derived, for example, by using simple triangular proportions as s₀ = _c(x_π-x_lB)/d_x. The adjustment is applied to all adjustable feet locations of the second machine 1002. Next, an adjustment to compensate for the angles and γ representing the angularity of the first and second shaft ends or coupling faces 1041 and 1042, respectively, is made. This second adjustment is different for the different adjustable feet of the second machine 1002. This second adjustment applied to the front adjustable foot 1023 of the second machine 1002 is given by l2F(^XlT"^XlB)' dι+l_2F X_2τ-X_2B)/ ₂, where the first term of this expression corrects for the angularity and the second term accounts for the angularity γ. Similar consideration to the rear adjustable foot 1024 yields an adjustment value given by

(¹2F+l₂r)(XlT-Xl_B)/d2 + (l2F⁺l₂R)(^X2T-^X2B)/d2- Thus, the overall correction needed to the front adjustable foot 1023 is s_2F=_c (x_ι x_1B)/d₁+ι_2F[(x_lτ-x_1B)/d₁ +(χ₂τ- _2By<y and to the rear adjustable foot 1024 is

^S2R^{— S}2F *2RL(^X1T"^X1B)' °-ι Η^X2T""^X2B) '^2- •

As an alternative to the preceding calculations, next will be described a method for adjusting each machine 1001 and 1002 at its respective adjustable feet locations so as to bring them into relative alignment. In this technique, each machine is adjusted independently to bring it into alignment with the reference line which runs through the axis of the main shaft 1401 of the device 1400. The geometry of this calculation is illustrated in Figure.10, where two triangles are illustrated. The top or right triangle 1420 is the same triangle as illustrated in Figure 8. The bottom triangles 1430 and

1435 are similar triangles to the triangle 1420, as the angles α are the same as indicated. Adjustable feet positions 1_1F and 1_1R are indicated on the bottom triangles. Because of the similarity of the triangles, the vertical adjustment or movement values s_1F and s_1R can be described from the measured values d_x, x_1T, x_1B and 1_1F and 1_1R. In particular, the expressions for s_1F and s_1R are as follows: s_1F=l_1F(X_1T-x_1B)/d, and

Thus, by shimming under the front adjustable foot 1022 an amount s_1F and by shimming under the rear adjustable foot 1021 an amount s_1R, the first shaft end or first coupling face 1041 of the first machine 100 1 is brought into vertical orientation. Similarly for the second machine 1002, the following expressions for adjustment movement values can be derived:

Thus, by shimming under the adjustable 1023 and 1024, by amounts s_2F and s_2R respectively, the second shaft end or second coupling face 1042 of the second machine 1002 can be brought into vertical orientation. Overall, the first shaft end or first coupling face 1041 of the first machine 1001 and the shaft end or second coupling face 1042 of the second machine 1002 are brought into relative vertical alignment.

The foregoing methods have been described as aligning one shaft end or coupling face with another shaft end or coupling face. However, this is equivalent to aligning the two shaftsattached to each respective shaft end or coupling face, if each shaft end or coupling face is perpendicular to the axis of rotation of the attached shaft. If there is a known deviation from exact perpendicularity, then this known deviation can be easily accounted for in the calculations of the present method.

What has just been described is a method for correcting vertical misalignment between two machines. The foregoing method is equally applicable to correction of misalignment in any plane, not just the vertical plane, as one skilled in the art will realize. Typically, the foregoing method should be applied in two perpendicular planes to bring the pair of machines into total alignment. Due to orthogonality, alignment in a first plane is independent of alignment in a second plane perpendicular to the first. Therefore, the preceding method, as described with regard to the vertical plane, can also be utilized to correct for misalignment in the horizontal plane by simply thinking of top as being left and bottom as being right, or vice versa. Graphically, this can be accomplished by viewing Figure 6 as a top perspective rather than a side perspective. Although it is generally only necessary to apply the foregoing method in two planes, it may be applied in additional plane(s), the results in the additional plane(s), perhaps, being used to verify the other results.

In a preferred embodiment for dual plane alignment, four distances are measured to a machine surface perpendicular to the axis of shaft rotation. When viewed as facing directly towards the first shaft end or first coupling face 1041, as shown in Figure 7(b), the dial indicator measurements are preferably taken at β=0, β =

L/2, β=TI and β=θH/2 (i.e., at the twelve o-clock, three o-clock, six o-clock, and nine o-clock positions). The β=0 and β = II measurements are used for vertical alignment, and the β= IT/2 and β=3iI/2 measurements are used for horizontal alignment.

The four distance measurements taken at β=0, β=H/2, β = LT and β = 3/2 can be utilized to detect aberrations, holes, or warping in the first shaft end or first coupling face 1041. If the distance measurements at these points are denoted d,2, d3, d6, and dg, then there is a warp, hole, bump, or other surface aberration if dl2 + d6 o d3 + dg. Alternatively, only three distances measurements may be utilized to calculate misalignment in both planes simultaneously, because three points determine a plane.

With reference to Figure 7(a), it is apparent that the horizontal separation between the dial indicator positions is given by d, = rlT I sin(PIT) I + rlB I sin(OIB) I. Just as the cosine function projects the radial vectors into the vertical plane, the sine function projects the radial vectors into the horizontal plane. Therefore, given any two points of measurement about.a coupling face or shaft end, those two measurements can be utilized to calculate misalignment in either the horizontal or vertical plane.

The foregoing method can be utilized in conjunction with the alignment measurement device 1800 depicted in Figure 12(a). The alignment device 1800 is an example of the ICAD (TM) (integrated coupling and alignment device) device available from the assignee and described in greater detail in the parent U.S. patent application serial no. 08/949,187. In this case, shaft ends or coupling face distances measurements can be taken with dial indicators, such as the dial indicator 1805, at fixed locations where holes or notches are provided, such as hole 1810. The alignment measurement device 1800 provides a fixed reference device, just as the alignment measurement device 1400 (Figure 6) provides a fixed reference device, for enabling alignment data to be measured. Many variations of the alignment measurement device 1800 are possible to fit various coupling faces. The alignment measurement device 1800 depicted in Figure 12 is just one example appropriate for one type of coupling face. The measurement data may be input into a computer in various forms and using various data collection teclmiques.

Figure 12(b) shows a end perspective of the alignment measurement device 1800. Figure 12(b) illustrates a configuration with the three holes 1810-1812, where distances measurements can be taken with dial indicators. The centers of the three holes are equidistant from the center of the device 1800 (all a.distance r) and are equally spaced by 120 degrees. Therefore, the vertical separation between hole 1812 and hole 1811 is d_v= r+|r cos(120°)|=3r/2 ; and the horizontal separation between holes 1810 and 1811 is d_H= jr sin(120°)l+lr sin(120°)|=rv 3. Figure 12(a) also illustrates that the various measurement holes or notches, such as hole 1810, may be keyed differently or drilled to different depths to differentiate among each other. For instance, by drilling the wider base part of the three holes 1810-1812 to three different depths that are much more different than expected differences in measured distance, the holes can be automatically identified on the basis of the measurements. As an example, if the expected range of measured distance differences is on the order often thousandths of an inch, then by drilling the base of the left hole 1811 one-hundred thousandths of an inch deeper than the base of the top hole 1812, and by drilling the base of the right hole one-hundred thousandths of an inch deeper than the base of the left hole, then measurement results of 22, 84, and 231 (all in thousandths of an inch) respectively correspond to the top hole 1812, the left hole 1811, and the right hole 1810. Various other ways of minimizing the possibility of human error are possible by varying the physical attributes of the measurement locations. To this point, the method of the present invention has been described for relative lignment of two machines capable of being coupled. The foregoing methods can be applied pairwise to adjacent machines in a multi-machine train of arbitrary length. The result of each pairwise analysis is a set of movement values that would align one of the shaft ends or coupling faces of one machine with a generally oppositely directed shaft end or coupling face of the other macliine in the pair. The results of these pairwise alignment analyses can be combined togenerate compound alignment data. For example, the movement values calculated to align the shaft end or second coupling face 1042 of the second machine 1002 to the shaft end or first coupling face 1041 of the first machine 1001 will result in a movement of the opposite shaft end or coupling face 1043 of the second macliine. By adding this amount to the calculated movement values required to align the shaft end or coupling face 1044 of the third machine 1003 to the shaft end or coupling face 1043 of the second machine 1002, the resulting movement values for the third machine will bring into alignment the first, second, and third machines. One skilled in the art will appreciate that this process can be continued arbitrarily in either direction as far as necessary to achieve global relative alignment along the entire machine train.

Although the preferred technique for obtaining alignment/misalignment data for a train of machines is to do pairwise measurements as just described, it is also possible to takemeasurements of all machines jointly. For example, one fixed reference can be used with respect to all machines in a train to take relative measurements, such as positions, shaft offset, shaft angularity, etc. Regardless of how the measurements are taken or alignment/misalignment data is otherwise obtained, the methods for computing the movements needed to bring the machines into relative alignment can be performed jointly or pairwise, as described above.

Given a movement value or adjustment value that represents the amount of movement or adjustment needed at a pertinent point on a machine so as to bring the machine into some form of relative alignment, it is a simple matter to reverse the sign of this movement value (i.e., multiply by -1) to describe the present position or location of the machine, relative to an aligned position, such as illustrated in Figures

1-3.

Figures 13 and 14 depict graphical user interfaces according to the present invention, as might be shown on the display 1340. The graphical user interface provides a visual representation of the positions of pertinent machine parts with respect to relative alignment. The points 1901-1906 are depictions of adjustable feet locations. Line segments 1911-1913 connect the points that correspond to tile same machine. Typically, the pertinent machine adjustment points are collinear or can be treated as collinear, though that need not be the case. The graphical user interface also provides a visual representation of a reference line 1920. In Figure 13, the reference line 1920 is the same as the second coordinate axis and passes through both feet of the leftmost machine. In Figure 14, the reference line 1920 is sloping downward with respect to the second coordinate axis and passes through points 1902 and 1906. The graphical user

interface displays numerical movement values 1931-1936 required to bring each point into relative alignment along the reference line 1920.

A user of the graphical user interface can alter the reference line 1920. One way of altering the reference line 1920 is illustrated in Figures 13-14 as input boxes 1941 - 1942 and input increment/decrement buttons 1943 - 1946. The value entered in input box 1941, which can be incremented or decremented by buttons 1943 and 1944, respectively, set. the second coordinate or Y axis value of the reference line 1920 at the first point 1901. Likewise, the value entered in input box 1942, which can be incremented or decremented by buttons 1945 and 1946, respectively, sets the second coordinate or Y axis value of the reference line 1920 at the sixthpoint 1906. Other ways of controlling the reference line 1920 would be apparent to those skilled in the art.

The terms and descriptions used herein are set forth by way of illustration only and are not meant as limitations. Those skilled in the art will recognize that numerous variations are possible within the spirit and scope of the invention as defined in the following claims.

Claims

CLAIMS 1. A method for aligning a plurality of machines coupled by one or more rotatable shafts, the method comprising: representing the relative alignment of the plurality of machines as points in a first plane, wherein one coordinate of each point is based on a respective first adjustment location on a respective machine and the other coordinate of each point is based on a respective relative alignment of the respective machine; defining a reference line in the plane; and determining displacements in the plane from each point to the reference line.

2. The method of claim I further comprising: adjusting each of the plurality of machines in accordance with the determined movement values.

3. The method of claim 1 further comprising: accessing alignment measurement data for the plurality of machines; and converting the alignment measurement data into the points in the first plane.

4. The method of claim I wherein the alignment measurement data is EZ- LLNE alignment measurement data.

5. The method of claim 1 wherein the alignment measurement data is ICAD alignment measurement data.

6. The method of claim 1 wherein the alignment measurement data is rim and face measurement data.

7. The method of claim 1 wherein the alignment measurement data is reverse method alignment measurement data.

8. The method of claim 1 wherein the alignment measurements are laser measurement data.

9. The method of claim I wherein the first adjustment locations are feet locations.

10. The method of claim I further comprising: graphically displaying the points in the first plane.

11. The method of claim 10 farther comprising: graphically displaying a plurality of line segments in the first plane, wherein each line segment intercepts at least 13 wo points in the first plane corresponding to adjustment locations on a respective machine.

12. The method of claim I further comprising: graphically displaying the reference line in the first plane.

13. The method of claim 1 wherein the reference line intercepts at least two of the points.

14. The method of claim 13 wherein the at least two intercepted points correspond to the same machine.

15. The method of claim I wherein defining the reference line comprises: fitting the reference line to the points so as to minimize a metric.

16. The method of claim 15 wherein the metric is a sum of squared distances between at least some of the points and the reference line.

17. The method of claim 1 further comprising: moving the reference line; and determining a movement value for each point, wherein each movement value is based on a displacement in the first plane from the corresponding point to the moved reference line.

18. The method of claim 1 further comprising: representing the relative alignment of the plurality of machines as points in a second plane, wherein one coordinate of each point is based on a respective second adjustment location on a respective machine and the other coordinate of each point is based on a respective relative alignment of the respective machine; defining a second reference line in the second plane; determining a second movement value for each point, wherein each second movement value is based on a displacement in the second plane from the corresponding point to the second reference line; and

19. The method of claim 18 further comprising: adjusting each of the plurality of machines in accordance with the determined second movement values .

20. The method of claim 18 further comprising: accessing alignment measurement data for the plurality of machines; and converting the alignment measurement data into the points in the second plane.

21. The method of claim 18 wherein the second plane is approximately perpendicular to the first plane.

22. The method of claim I wherein the plurality of machines coupled by one or more rotatable shafts is two machines coupled by one rotatable shaft.

23. The method of claim 1 wherein the plurality of machines coupled by one or more rotatable shafts comprises a turbine.

24. The method of claiml wherein the plurality of machines coupled by one or more rotatable shafts comprises a motor.

25. The method of claim 1 wherein the plurality of machines coupled by one or more rotatable shafts comprises a pump.

26. The method of claim 1 wherein the plurality of machines coupled by one or more rotatable shafts comprises a gearbox.

27. The method of claim 1 further comprising: determining whether a movement value is outside of an acceptable range.

28. The method of claim 27 further comprising: accessing a database to determine the acceptable range.

29. The method of claim 27 further comprising: indicating that the movement value is outside of the acceptable range, if the movement value is outside of an acceptable range.

30. The method of claim 27 further comprising: defining a new reference line and determining new movement values, if the movement value is outside of an acceptable range.

31. The method of claim 1 wherein the step of determimng a movement value for each point comprises accounting for thermal growth.

32. The method of claim I wherein the step of determining a movement value for each point comprises accounting for dynamic factors.

33. The method of claim 32 wherein the dynamic factors comprise journal movement.

34. The method of claim 32 wherein the dynamic factors comprise static tilt.

35. The method of claim 32 wherein the dynamic factors comprise gear clearance.

36. The method of claim 1 further comprising: recording the determined movement values.

37. The method of claim 36 further comprising: accessing a history of movement values; predicting a predicted movement values on the basis of the history; comparing the predicted movement values to the determined movement values; and modifying the determined movement values on the basis of the comparing step.

38. A computer readable storage device comprising executable program instructions that, implement the method of any 11 of claims 1-37.

39. An apparatus comprising: a first memory for storing alignment data for a plurality of machines coupled by one or more rotatable shafts; second memory for storing executable program instructions; and processor, connected to the first memory and the second memory, that operates in accordance with the executable program instructions to determine a reference and machine movement values based on the alignment data.

40. The apparatus of claim 39 further comprising: a display, connected to the processor, that displays the reference as a line and the movement values as points displaced from the line in accordance with the sign and magnitude of the movement values.

41. The apparatus of claim 39 further comprising: an input device, connected to the first memory, capable of receiving the alignment data.

42. The apparatus of claim 41 wherein the input device is a data port.

43. The apparatus of claim 41 wherein the input device is a keyboard.

44. The apparatus of claim 41 wherein the input device is a touch screen.

45. The apparatus of claim 41 wherein the input device is a modem.

46. The apparatus of claim 41 wherein the input device is a point and click device.

47. The apparatus of claim 41 wherein the executable program instructions comprise an expert systems program.

48. An apparatus comprising: means for accessing alignment data for a plurality of machines coupled by rotatable shafts; and means for determining a reference and machine movement values based on the alignment data.

49. The apparatus of claim 48 further comprising: means for converting the reference and machine movement values to a new reference and new machine movement values.

50. The apparatus of claim 48 further comprising: means for displaying the reference as a line and the movement values as points displaced from the line in accordance with, the sign and magnitude of the movement values.

51. The apparatus of claim 48 further comprising: means for inputting the alignment data.

52. A graphical user interface system comprising: a display, wherein the display comprises: a reference line; and a set of points corresponding to parts of plurality of machines coupled by one or more rotatable shafts

53. The graphical user interface system of claim 52 wherein the display further comprises: a plurality of movement value indications, each movement- value indication representing a distance from a respective point to the reference line.

54. The graphical user interface system of claim 53 wherein the plurality of movement value indications are numeric values.

55. The graphical user interface system of claim 53 wherein the plurality of movement value indications are bars.

56. The graphical user interface system of claim 52 further comprising: a user input device.

57. The graphical user interface system of claim 57 wherein the reference line can be moved in accordance with input by the user input device.

58. The graphical user interface system of claim 52 wherein the display further comprises: planar coordinate axes.

59. A method for aligning a plurality of machines, each machine having a rotatable shaft, the method comprising: inserting a reference device between a pair of connectable machines; measuring distances from the reference device to a first surface of a first machine of the pair, the first surface being perpendicular to an axis of rotation of the shaft of the first machine; measuring distances from the reference device to a second surface of a second machine of the pair, the second surface being perpendicular to an axis of rotation of a shaft of the second machine; and determining relative alignment of the pair of machines on the basis of the measured distances.

60. The method of claim 59 wherein the step of measuring distances from the reference device to a first surface of a first machine comprises: measuring a plurality of first surface distances from a first reference plane fixed by the reference device to the first surface, each surface distance being measured at a respective first radial distance from the center of the shaft of the first macliine; and wherein the step of measuring distances from the reference device to a second surface of a second machine comprises: measuring a plurality of second surface distances from a reference plane fixed by the reference device to the second surface, each surface distance being measured at a respective second radial distance from the center of the shaft of the second macliine.

61. The method of claim 60 wherein the step of determining relative alignment of the plurality of the machines comprises: computing a position of the shaft of the second machine with respect to the shaft of the first machine on the basis the plurality of first surface distances, the respective first radial distances, the plurality of second surface distances and the respective second radial distances.

62. The method of claim 61 wherein the step of computing a position comprises: computing an offset of the shaft of the second machine with respect to the shaft of the first machine; and computing an angularity of the shaft of the second machine with respect to the shaft of the first machine.

63. The method of claim 61 wherein the step of computing a position comprises: computing a position of the shaft of the second macliine with respect to the shaft of the first machine in a first plane; and computing a position of the shaft of the second machine with respect to the shaft of the first machine in a second plane.

64. The method of claim, 61 wherein the first plane is the vertical plane and the second plane is the horizontal plane.

65. The method of claim 61 wherein the step of computing a position comprises: accounting for thermal growth.

66. The method of claim 61 wherein the step of computing a position

comprises: accounting for dynamic factors.

67. The method of claim 61 wherein the dynamic factors comprises journal movement.

68. The method of claim 61 wherein the dynamic factors comprises static tilt.

69. The method of claim 61 wherein the dynamic factors comprises gear clearance.

70. The method of claim 60 wherein the step of determimng relative alignment of the plurality of the machines comprises: computing a set of movement values for the second machine on the basis the plurality of first surface distances, the respective first radial distances, the plurality of second surface distances and the respective second radial distances, the set of movement values being such that the shaft of the second machine, when moved in accordance with the set of movement values, would be in relative alignment with the shaft of the first machine.

71. The method of claim 70 wherein the step of computing a set of movement values comprises: computing a set of movement values in a first plane; and computing a set of movement values in a second plane.

72. The method of claim 71 wherein the first plane is the vertical plane and the second plane is the horizontal plane.

73. The method of claim 70 further comprising: adjusting the second machines in accordance with the set of movement values.

74. The method of claim 70 wherein the step of computing a set of movement values for the second machine is based on the equations s_2F=c(x_1T-x_1B)/d₁+l_2FL(x_1T-x_1B)]/d₁+(x_2T-x_2B)/d₂ and

^S2 ^=S2F^"^l2R[(^XlT~^XlB)'^Cn^"K^X2f^X2B)'^C where s_2F a movement value corresponding to a front adjustment point of the second machine,s_2R is a movement value corresponding to a rear adjustment point of the second macliine, c is a distance between the first surface and the second surface, x_1T and x_1B distances measured from the reference device to the first surface, x_2T and x_2B distances measured from the reference device to the second surface, d, is a distance between surface measurements on thefirst surface, d₂ is a distance between surface measurements on the second surface, 1_2F is a distance from the second surface to the front adjustment point, and 1_2R a distance from the front adjustment point to the rear adjustment point.

75. The method of claim 74 wherein each of the plurality of first surface distances is measured at a respective radial angle in the reference plane, and wherein d₁=[r_lτcos(β_lτ)+r_1Bcos(β_1B)] where r_1T and r_1B are respective radial distances, and β_lτ and β_1B are respective radial angles in the reference plane.

76. The method of claim 75 further comprising: approximating β_lτ and β_1B as Zero.

77. The method of claim 75 further comprising: approximating β_lτ and β_1B to be equal.

78. The method of claim 70 wherein the step of computing a set of movement values comprises: accounting for thermal growth.

79. The method of claim 70 wherein the step of computing a position comprises: accounting for dynamic factors.

80. The method of claim 79 wherein the dynamic factors comprises journal movement.

81. The method of claim 79 wherein the dynamic factors comprises static tilt.

82. The method of claim 79 wherein the dynamic factors comprises gear clearance.

83. The method of claim 59 wherein the reference device is an EZ-LLNE device.

84. The method of claim 59 wherein the reference device is an ICAD device.

85. The method of claim 59 further comprising: determining relative alignment of a third machine with respect to the second machine, the third macliine being connectable to the second machine;

86. The method of claim 85 further comprising: computing a set of movement values for the second machine, the set of movement values being such that the shaft of the second machine, when moved in accordance with the set of movement values, would be in relative alignment with the shaft of the first machine; computing a set of intermediate movement values for the third macliine, the set of movement values being such that the shaft of the third machine, when moved in accordance with the set of intermediate movement values, would be in relative alignment with the shaft of the second machine; and summing the set of intermediate movement values for the third machine with values related to the set of movement values for the second machine to obtain final movement values corresponding to the third machine.

87. The method of claim 86 further comprising:

adjusting the third machine in accordance with the final set of movement values.

88. A method for checking a surface of a machine, the method comprising: measuring distances from a reference device to the surface of the machine, the distances being measured at four positions equidistant from a common center point and spaced 90 degrees apart; calculating two sums of the measured distances, the first sum being of distances measured at two positions 180 degrees apart, the second sum being of the distances measured at the other two positions; comparing the first sum to the second sum; and determining that the surface is flawed if the first sum is not approximately equal to thesecond sum.

89. A computer readable storage device comprising executable program instructions that implement the method of claim 88.

90. An apparatus comprising: a first memory for storing measurement data for a plurality of machines coupled by one or more rotatable shafts; a second memory for storing executable program instructions; and a processor, connected to the first memory and the second memory, that operates in accordance with the executable program instructions to determine relative alignment of the plurality of machines on the basis of the measurement data.

91. The apparatus of claim 90 further comprising: a display, connected to the processor, that displays the relative alignment of the plurality of machines.

92. The apparatus of claim 90 further comprising: an input device, connected to the first memory, capable of receiving the measurement data.

93. The apparatus of claim 92 wherein the input device is a data port.

94. The apparatus of claim 92 wherein the input device is a keyboard.

95. The apparatus of claim 92 wherein the input device is a touch screen.

96. The apparatus of claim 92 wherein the input device is a modem.

97. The apparatus of claim 92 wherein the input device is a point and click device.

98. An apparatus comprising: means for measuring alignment data for a plurality of machines coupled by rotatable shafts; and means for determining relative alignment of the plurality of machines on the basis of the measurement distances.

99. The apparatus of claim 98 further comprising: means for displaying the relative alignment of the plurality of machines.