Abstract:
An apparatus and a method for aligning a vertical shaft or multiple axially coupled vertical shafts in a hydroelectric turbine generator or a similar vertical-shaft system, and for providing precise plumb inclination alignment of a vertical rotating shaft. Precision inclinometers attached to the vertical shaft measure plumb inclination. Proximity probe displacement devices mounted externally of the vertical shaft measure radial movement, throw, or run out at various shaft elevations as the shaft is rotated relative to a fixed point. Data acquisition devices and communication devices accumulate and transmit alignment data to a micro-computer which receives and processes such data. Methods of defining shaft plumb inclination in a static single rotational position and defining plumb inclination of the virtual centerline of a shaft&#39;s rotational throw position. A method of swinging, tilting, or adjusting a vertical shaft to a corrected or different plumb position relative to the earth&#39;s gravity.

Description:
FIELD OF INVENTION 
   The present invention relates generally to the alignment of vertical shafts and, more particularly, to aligning a vertical shaft to the plumb position, and to measurement of the built in throw (run out) of a shaft as the shaft is rotated. The present invention also relates to a method and an apparatus for aligning a vertical shaft, or a plurality of axially coupled vertical shafts, of a hydroelectric turbine generator or of a similar vertical-shaft system. 
   Vertical shafts (particularly hydroelectric generator/turbine shafts) have been aligned using various methods for over 100 years. The most common method (industry standard) is called the 4 plumb wire method. To check the plumb or verticality of a shaft, 4 music wires (or piano wires) are connected to a bracket at an upper elevation and at 4 equally spaced locations, 90 degrees apart, around the shaft. These wires are connected at the bottom to large plumb bobs (usually fifty pound weights) which are immersed in a bath of high viscosity oil or other fluid for damping. Readings are taken of distances from the wires to the shaft at multiple elevations with electric micrometers. The micrometers give an audible click in the earphones of an operator when the micrometer makes contact between the wire and shaft. The electric micrometer basically acts as a switch to allow current to flow through the operator&#39;s earphones when the circuit is completed through the wire and shaft which are electrically connected. By measuring these distances from the wires to the shaft at a top and bottom elevations on the shaft, the amount of deviation from plumb can be determined for the shaft. By measuring these distances from the wires at elevations on each side of a shaft system coupling, kink (deviation from parallel centerlines; also called “dogleg”) and offset (non-concentric centerlines) can be determined. By measuring the plumb of the shaft at various rotational positions (i.e. 0 deg, 90 deg, 180 deg, and 270 deg), the shaft throw (run out) can be determined. 
   The alignment of vertical shafts in hydroelectric generating units and similar rotating shafts in other machinery, such as vertical pumps, usually requires equalizing the thrust bearing shoe or thrust member loads; plumbing the shafts (plumb to gravity); and plumbing the centerline of shaft throw circles (run out). Many of the tools and methods used to accomplish such alignments date back as long as 100 years. These dated methods and tools tend to be slow and awkward to use. The conventional 4 plumb wire method is a workable method; however, it is very time-consuming, both in setup and in the execution of data gathering. It also requires a lot of user training because of its abstract methods and calculations. 
   The recognition of these deficiencies, along with the advent of more modern sensor technologies, led to the conception of this invention. 
   SUMMARY OF THE INVENTION 
   A purpose of this invention is to align a vertical shaft&#39;s axis or center of rotation with the earth&#39;s gravitational pull (i.e., to plumb the shaft) and to measure the shaft&#39;s throw (shaft run out) as the shaft is rotated. The invention was designed primarily to align the vertical generator/turbine shafts in hydroelectric units; however, it is fully capable of aligning vertical shafts in pumps and similar equipment. It is important to align a vertical shaft with the direction of to the earth&#39;s gravity in order to reduce and/or equalize the bearing load and thus, to reduce the wear on the equipment&#39;s bearings. Very close tolerances are strived for based on industry standards. A condition of excessive throw (shaft run out) can lead to reduced bearing life; therefore, it is advantageous to know this condition prior to returning the equipment to service so that corrective action can be taken. 
   The present vertical shaft alignment tool invention is the result of a determination to invent a quicker and more user-friendly method and tool for aligning vertical shafts. For any vertical shaft alignment tool and method to successfully take the place of the standard 4 plumb wire method, these would have to be performed: 
   1. Initially measure plumb at one position without rotating the shaft. 
   2. Measure the plumb of the center of rotation of the shaft as it is rotated. 
   3. Measure throw (run out) of the shaft as it is turned. 
   4. Measure the shaft kink and coupling offset. 
   5. Provide a method of adjusting the thrust bearing shoes to tilt the shaft toward the plumb position without changing the thrust loading on the shoes. 
   6. Provide easier and faster use. 
   The vertical shaft alignment tool meets all of these requirements, using supportive technologies that have only recently become available, such as electronic digital inclinometers, proximity sensors and micro computers. An inclinometer is a device that measures inclination or deviation from plumb; whereas, a proximity sensor is a device which measures distances from itself to an object, such as a shaft. Digital inclinometers, such as the Wyler AG Zerotronic inclinometer, used in the vertical shaft alignment tool invention, provide more accurate plumb measurements than the 4 plumb wire method and are less subject to vibration and error. These advanced inclinometers have been available for only the past couple of years. Therefore, the vertical shaft alignment tool is based on the very latest technology. 
   Plumbing of vertical shafts was made possible through the vertical shaft alignment tool due to this tool&#39;s unique design of mounting the inclinometers on the shaft, and the methodology of performing the calculations in determining deviation from plumb. Shaft rotational throw (run out) is obtained through the proximity sensor measurements from a stationary point relative to the shaft movement. The vertical shaft alignment tool&#39;s unique methodology performs these calculations while factoring out any horizontal movement or skate which can occur due to movement of the shaft in the clearances of the radial guide bearings as the shaft is rotated. The vertical shaft alignment tool is able to use any type of proximity sensor, such as, eddy current (currently used), capacitive, inductive, laser, or mechanical (like common mechanical dial indicators). 
   The advantages of this vertical shaft alignment tool are: 
   The system allows for faster alignments, setup and execution; 
   There are no plumb wires to install, which is time consuming and the wires are prone to kinking, leading to errors; 
   Removes potential for oil spills and environmental problems since the required wires and oil dampers are not used; 
   Allows for instantaneous viewing of alignment changes from the inclinometers and proximity sensors, unlike the 4 plumb wire method which requires the wire distances to be measured again; and 
   Measurements are taken as the shaft is rotated, directly giving the plumb of the center of rotation, unlike the 4 plumb wire method which requires graphing of the results. 
   It is therefore an object of this invention to provide an alignment system that provides precise plumb inclination alignment of a vertical shaft. 
   It is another object of the invention to plumb a shaft in a static single position by taking readings from inclinometers, attached to the shaft surfaces, without rotating the shaft. 
   It is another object of the invention to plumb the virtual centerline of a shaft&#39;s rotational throw circle (run out), with inclinometers attached to the shaft surface, by rotating the shaft. 
   It is another object of the invention to measure the diameter of the shaft&#39;s throw circle (run out) by use of proximity probes or other displacement measuring devices, as the shaft is rotated. 
   It is another object of the invention to measure a shaft&#39;s straightness or kink and centerline deviations or coupling offset by use of proximity probes or other displacement measuring devices, during rotation of the shaft. 
   It is another object of the invention to measure a shaft&#39;s straightness or kink by use of inclinometers attached to the shaft surface, without rotating the shaft. 
   It is another object of this invention is to provide an alignment system that is simple to use, is portable, and provides an accurate vertical shaft alignment according to accepted industry standards. 
   In general, the invention provides an apparatus and a method for aligning a vertical shaft or multiple axially coupled vertical shafts in a hydroelectric turbine generator or similar vertical shafting system. It also provides a precise plumb inclination alignment of a vertical rotating shaft, as defined in a static single position, and plumb of the virtual centerline of the shaft&#39;s rotational throw position. 
   More particularly, the present invention provides an improved apparatus and method for aligning vertical shafts to the plumb position, relative to the prior art, such as the 4 plumb wire apparatus and method. The improved apparatus comprises precision inclinometers attached to the vertical shaft to measure the plumb inclination; proximity probe devices mounted externally of the vertical shaft to measure radial movement or throw (run out) at various shaft elevations as the shaft is rotated; data acquisition devices and communication devices used to accumulate and transmit alignment data; and a micro-computer used to receive and process such data. The improved alignment methods consist of a method of placing the inclinometers on the vertical shaft to measure plumb inclination at one static position; a method of placing inclinometers on vertical shaft and rotating the shaft to measure the plumb inclination of the shaft&#39;s centerline of throw circle (run out); a method of measuring the diameter of the shaft&#39;s throw circle (run out) as the shaft is turned; a method of measuring the shaft coupling kink or straightness with inclinometers; a method of measuring shaft coupling kink (straightness) and coupling offset with proximity probes; and a method of correcting a shaft&#39;s deviation from plumb by adjusting the thrust bearing shoe elevations or thrust bearing support structure. 
   Other objects, advantages and features of the present invention will be apparent to those skilled in the art from the following detailed description when read in conjunction with the drawings and appended claims. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     A complete understanding of the present invention may be obtained by reference to the accompanying drawings, when considered in conjunction with the subsequent, detailed description, in which: 
       FIGS. 1(   a ) and ( b ) are perspective views of the vertical shaft alignment equipment. 
       FIG. 2  is a perspective view of an upper alignment equipment assembly on a shaft. 
       FIG. 3  is a perspective view of a lower alignment equipment assembly on a shaft. 
       FIG. 4(   a ) is an assembled view of an inclinometer assembly 
       FIG. 4(   b ) is an exploded view of an inclinometer assembly. 
       FIG. 5  is a cross sectional view of inclinometers attached to a shaft. 
       FIGS. 6(   a ),  6 ( b ) and  6 ( c ) are perspective views of an inclinometer arrangement. 
       FIG. 7(   a ) is an assembled view of a proximity probe assembly. 
       FIG. 7(   b ) is an exploded view of a proximity probe assembly. 
       FIG. 8  is a cross sectional view of a proximity probe assembly relative to a shaft. 
       FIG. 9  is a perspective view of an inclinometer method of determining initial (static) plumb. 
       FIG. 10  is a perspective view of an inclinometer method of determining rotational plumb. 
       FIG. 11  is a perspective view of a shaft centerline throw circle. 
       FIG. 12(   a ) is a perspective view of a shaft coupling kink. 
       FIG. 12(   b ) is a perspective view of a shaft coupling offset. 
       FIG. 13  is a perspective view of a thrust bearing shoe segment assembly. 
       FIG. 14  is a perspective view of a thrust bearing shoe and elevation adjustment screw assembly. 
   

   For purposes of clarity and brevity, like elements and components will bear the same designations and numbering throughout the FIGURES. 
   DESCRIPTION OF THE PREFERRED EMBODIMENT 
     FIGS. 1(   a ) and  1 ( b ) are overall perspective views of the vertical shaft alignment tool  10  as assembled on a vertical rotating shaft of a shaft  20 , which is comprised of two shaft sections (lower and upper)  40 ,  50  coupled together. A turbine runner  15  ( FIG. 1(   a )) is attached at the end of the lower portion of the shaft  20 . Although a turbine shafting system is shown, the vertical shaft alignment tool  10  will function with any vertical shaft system, such as, vertical pumps and others.  FIG. 1(   b ) shows the vertical shaft  20  in two expanded sections, the lower shaft section  40  and the upper shaft section  50 , with the vertical shaft alignment tool  10  components attached. The normal shaft centerline  60  is shown passing through the center of the shaft  20 . The shaft&#39;s vertical thrust load is supported on the thrust bearing assembly  90  and is transmitted to the stationary surrounding structure (not shown) by way of the thrust adjustment screw assembly  100 . 
   The sensors which measure the plumb inclination of the shaft  20  are shown in  FIG. 1(   b ). The two inclinometer assemblies  499  ( FIGS. 6(   a ),  6 ( b ), and  6 ( c )), attached to the lower portion of the shaft  20  and positioned at 90 degrees apart are referred to as the lower x-axis inclinometer  110  and the lower y-axis inclinometer  120 . The two inclinometer assemblies  499  sensing the plumb inclination of the upper portion of the shaft are referred to as the upper x-axis inclinometer  130  and the upper y-axis inclinometer  140 . Plumb inclination is defined as the deviation of the shaft&#39;s vertical rotational axis from the virtual perpendicular line passing through the earth&#39;s surface to its center as defined by the earth&#39;s gravitational field. 
   The sensors which measure the radial position of the shaft, relative to the stationary support structure, are shown in  FIG. 1(   a ) at four different vertical elevations which will be referred to, from top to bottom, as elevation  1  (at level  212 ), elevation  2  (at level  192 ), elevation  3  (at level  172 ), and elevation  4  (at level  152 ). At each elevation two proximity probe assemblies are positioned 90 degrees apart and measure the gap between the end of the probe sensor and the surface of the shaft. The proximity probe assemblies  531  ( FIGS. 7(   a ) and  7 ( b )) at elevation  1  are referred to as elevation  1  x-axis proximity probe  210  and elevation  1  y-axis proximity probe  220 . The proximity probe assemblies  531  at elevation  2  are referred to as elevation  2  x-axis proximity probe  190  and elevation  2  y-axis proximity probe  200 . The proximity probe assemblies  531  at elevation  3  are referred to as elevation  3  x-axis proximity probe  170  and elevation  3  y-axis proximity probe  180 . The proximity probe assemblies  531  at elevation  4  are referred to as elevation  4  x-axis proximity probe  150  and elevation  4  y-axis proximity probe  160 . 
   The measurement readings from the proximity probe assemblies  531  from elevation  1  ( 212 ) and elevation  2  ( 192 ) are read by analog-to-digital data acquisition equipment shown as the upper data acquisition box  320  (see  FIGS. 1(   a ) and ( 2 )). This data acquisition box  320  includes a power supply for powering the proximity probes and an analog-to-digital converter for converting the analog signals to digital signals that may serve as inputs to the micro computer  350 . The analog-to-digital converter is similar to that made by Advantech Corporation ADAM Module series or equal. Proximity probe cable  290  and proximity probe cable  300  provide power and transfer signals between the proximity probe assemblies at elevation  1  and the upper data acquisition box  320 . Proximity probe cable  270  and proximity probe cable  280  provide power and transfer signals between the proximity probe assemblies, at elevation  2  ( 192 ), and the upper data acquisition box  320 . The analog-to-digital converter transmits its data to the micro computer  350  by way of a standard addressable RS-485 network; however, any multi-node networking technology, such as Ethernet or others, can be used. 
   The measurement readings from the proximity probe assemblies from elevation  3  ( 172 ) and elevation  4  ( 152 ) are read by analog-to-digital data acquisition equipment shown as the lower data acquisition box  340  in  FIGS. 1(   b ) and  3 . This data acquisition box  340  includes a power supply for powering the proximity probes and an analog-to-digital converter for converting the analog signals to digital signals that may serve as inputs to the micro computer  350 . The analog-to-digital converter is similar to that made by Advantech Corporation Adam Module series or equal. Proximity probe cable  250  and proximity probe cable  260  provide power and transfer signals between the proximity probe assemblies  531  at elevation  3  ( 172 ) and the lower data acquisition box  340 . Proximity probe cable  230  and proximity probe cable  240  provide power and transfer signals between the proximity probe assemblies  531  at elevation  4  ( 152 ) and lower data acquisition box  340 . The analog-to-digital converter transmits its data to the micro computer  350  by way of a standard addressable RS-485 network; however, any multi-node networking technology, such as Ethernet or others, can be used. 
   Measurement of the plumb inclination of the upper portion  50  of the shaft  20  is read from the upper x-axis inclinometer  130  and upper y-axis inclinometer  140 , and is transmitted by way of upper radio box y-cable  390  to the upper radio transmitter  370  ( FIG. 2 ), such as a Radio Box manufactured by Wyler AG Corporation. The upper radio transmitter  370  transmits the plumb inclination data wirelessly to the upper inclinometer receiver and display  330 , such as a Levelmeter 2000 manufactured by Wyler AG Corporation. The upper inclinometer receiver and display  330 , displays the inclinometer data locally and transmits the data via communications cable  410  using the RS-232 standard to the upper data acquisition box  320 . The upper data acquisition box  320  contains a converter, such as that manufactured by Advantech Corporation ADAM module series or equal, which converts the RS-232 signal to an addressable RS-485 signal that can be transmitted on the RS-485 network to the micro computer  350 . 
   Measurement of the plumb inclination of the lower portion  40  of the shaft  20  is read from the lower x-axis inclinometer  110  and lower y-axis inclinometer  120  and transmitted by way of lower radio box y cable  380  to the lower radio transmitter  360  ( FIG. 3 ), such as a Radio Box manufactured by Wyler AG Corporation. The lower radio transmitter  360  transmits the plumb inclination data wirelessly to the lower inclinometer receiver and display  331 , such as a Levelmeter 2000 as manufactured by Wyler AG Corporation. The lower inclinometer receiver and display  331  displays the inclinometer data locally and transmits the data via communications cable  411  using the RS-232 standard to the lower data acquisition box  340 . The lower data acquisition box  340  contains a converter, such as that manufactured by Advantech Corporation ADAM module series or equal, which converts the RS-232 signal to an addressable RS-485 signal that can be transmitted on the RS-485 network to the micro computer  350 . 
   The wireless transmission of inclinometer data to the micro computer is advantageous to avoid any problems associated with handling cabling as the shaft is rotated. 
   The upper data acquisition box  320  is connected to the lower data acquisition box  340  and the micro computer  350  via network cable  310  and data acquisition transmit cable  430  on the RS-485 network. These cables can be replaced with wireless technologies, such as those manufactured by Advantech Corporation, ADAM module series, wireless Ethernet, or equal. 
     FIG. 2  is an enlarged perspective view showing the upper equipment assembly  80  taken from a portion of the overall assembly of the vertical shaft alignment tool  10  shown in  FIG. 1(   b ). This enlarged view shows the upper x-axis inclinometer  130  and upper y-axis inclinometer  140  attached to the shaft  20  with their outputs connected to upper radio box y cable  390  which is connected to the upper radio transmitter  370 . The upper radio transmitter  370  communicates with the upper inclinometer receiver and display  330  via the radio communications signal  440 . The upper inclinometer receiver and display  330  displays the inclinometer data locally and transmits the data via communications cable  410  using the RS-232 standard to the upper data acquisition box  320 . The upper data acquisition box  320  contains a converter, such as that manufactured by Advantech Corporation ADAM module series or equal, which converts the RS-232 signal to an addressable RS-485 signal that can be transmitted on the RS-485 network to the micro computer  350 .  FIG. 2  shows elevation  2  x-axis proximity probe  190  and elevation  2  y-axis proximity probe  200 . These proximity probes are connected to the upper data acquisition box  320  via proximity probe cable  270  and proximity probe cable  280 . The elevation  1  x-axis proximity probe  210  and the elevation  1  y-axis proximity probe  220  (shown in  FIG. 1(   b )) are connected to the upper data acquisition box  320  via proximity probe cable  290  and proximity cable  300 . The upper data acquisition box  320  is connected to the RS-485 network via network cable  310 . 
     FIG. 3  is a perspective view showing the lower equipment assembly  70  taken from a portion of the overall assembly of the vertical shaft alignment tool  10  shown in  FIG. 1(   b ). This enlarged view shows the lower x-axis inclinometer  110  and lower y-axis inclinometer  120  attached to the lower section  40  of the shaft  20  with their outputs connected to lower radio box y cable  380  which is connected to the lower radio transmitter  360 . The lower radio transmitter  360  communicates with the lower inclinometer receiver and display  341  via the radio communications signal  440 . The lower inclinometer receiver and display  341  displays the inclinometer data locally and transmits the data via communications cable  411  using the RS-232 standard to the lower data acquisition box  340 . The lower data acquisition box  340  contains a converter, such as that manufactured by Advantech Corporation ADAM module series or equal, which converts the RS-232 signal to an addressable RS-485 signal that can be transmitted on the RS-485 network to the micro computer  350 . 
     FIG. 3  also shows elevation  4  x-axis proximity probe  150  and elevation  4  y-axis proximity probe  160 . These proximity probes are connected to the lower data acquisition box  340  via proximity probe cable  230  and proximity probe cable  240 . The elevation  3  x-axis proximity probe  170  and the elevation  3  y-axis proximity probe 180 (shown in  FIG. 1(   b )) are connected to the lower data acquisition box via proximity probe cable  250  and proximity cable  260 . The lower data acquisition box  340  is connected to the RS-485 network via network cable  310  and connected to the micro computer  350  via communications cable  430 . 
     FIG. 4(   a ) shows an assembled view of an inclinometer assembly  499 .  FIG. 4(   b ) shows an exploded view of an inclinometer assembly  499 . This inclinometer assembly  499  is typical of the upper x-axis inclinometer  130 , upper y-axis inclinometer  140 , lower x-axis inclinometer  110 , and lower y-axis inclinometer  120  shown in  FIG. 1(   b ). The assembly consists of the inclinometer module  460 , such as model Zerotronic type  3  as manufactured by Wyler AG Corporation, mounted on the inclinometer base  450 , with the inclinometer module screws  468 . The inclinometer module  460  is the sensor that measures the plumb inclination of the assembly attached to the shaft  20 . The inclinometer module  460  transmits a digital signal encoded with the inclination measurement to the data acquisition system and micro computer  350 . 
   The inclinometer assembly  499  is attached to a magnetic shaft  20  by way of the inclinometer mount magnet  452  which is engaged with, and disengaged from, the shaft  20  by way of a threaded knob  458  which engages into a mating threaded hole in the inclinometer mount magnet  452 . The spring  470  supplies tension to the knob  458  and provides stability. The magnet dowel  490  on the side of the inclinometer mount magnet  452  and mating slot  491  in the inclinometer base  450  prevents rotation of the inclinometer mount magnet  452  as it is actuated. The knob  458  on the inclinometer mount magnet  452  assembly is supported by the base extension  454 , attached to the inclinometer base  450  by the base extension screws  466 , and the knob plate  456  which is attached to the base extension  454  by the knob plate screws  464 . 
   Handles  462  are attached to the top and bottom of the inclinometer base  450  in order to handle the inclinometer assembly  499  and to protect the inclinometer module  460 . The handles are attached to the inclinometer base  450  by the handle screws  478 . A bubble level  474  is attached to the bottom of the base extension  454  by way of level screws  476 . The bubble level  474  is used to level the inclinometer assembly  499  about the center axis passing through the inclinometer module  460  and perpendicular to the inclinometer base  450 . Spring plungers  472  are screwed into equally spaced threaded holes in the inclinometer base  450  and are used to stabilize the inclinometer assembly  499  when attached to the shaft  20  by preventing side to side rocking motion. 
     FIG. 5  shows a cross-sectional view of shaft  20  with an inclinometer assembly  499  mounted on each of two axes, 90 degrees apart, to allow for plumb inclination measurements on both axes at the same time. From this rectangular (x,y) measurement the overall polar or vector notation can be calculated by accepted mathematical methods to describe the plumb inclination of the shaft by a magnitude and angle relative to a fixed position. 
     FIGS. 6(   a ),  6 ( b ) and  6 ( c ) show perspective views of the arrangement of the inclinometer assembly  499  connection to the shaft  20  as viewed from above looking down and from the side relative to plumb. The inclinometer module  460  is attached to the inclinometer base  450  which is attached to the shaft  20  as shown in  FIG. 5 . The surfaces of the inclinometer base  450  are flat and parallel, thereby allowing the inclinometer module  460  to assume a perpendicular attachment to the shaft  20  as it is mounted. The flat contact surface on the inclinometer base  450  provides a single line contact  494  with the curved surface of the shaft  20 . This single line contact  494  automatically squares the inclinometer base  450 , and therefore the inclinometer module  460 , perpendicular to the shaft  20  surface. This arrangement is superior to vee block arrangements because the single line contact  494  allows for only one possible alignment of the inclinometer assembly  499  to the shaft  20  and thereby the most accurate contact. Vee blocks have a two line contact arrangement that can skew the squaring of the component to the shaft as the vee block is rotated about its center axis during attachment to the shaft  20 , and multiple contact surfaces provide for multiple contact errors. Therefore, a single line contact  494  provides for the least number of contact errors and the greatest accuracy. Spring plungers  472  in the inclinometer base  450  on either side of the single line contact  494  prevent side-to-side rocking motion of the inclinometer assembly  499  on the shaft  20  surface. As earlier explained, the mounting of the inclinometer mount magnet  452  with its dowel  490 , shown in  FIGS. 4(   a ) and  4 ( b ), also helps to provide stability and resist the side-to-side rocking motion. The angle  492  of inclination of the shaft surface relative to the plumb can thereby be measured by the inclinometer module  460 . 
     FIGS. 7(   a ) and  7 ( b ) illustrate a proximity probe assembly  531 . This assembly allows for multiple degrees of freedom of movement to facilitate the setup of the proximity sensor  500  relative to the shaft  20  when the assembly is attached to a stationary surface near the shaft. The proximity probe assembly  531  is attached to a stationary surface near the shaft  20  by the proximity probe magnet  508  which is attached to the proximity probe magnet base  506  by the magnet screw  528 . The proximity probe magnet base  506  is attached to one end of the extension bracket  504  which can swivel about the base screw  526  and is locked by the magnet base knob  514 . The extension bracket  504  can be moved about its longitudinal axis relative to the proximity probe magnet base  506  by way of a slot that accommodates the base screw  526 . A slot is shown in the top portion of the extension bracket  504  but, another slot (not shown) also exists in the other leg of the bracket. Either of the two slots may be used to facilitate setup. 
   The tilting bracket  516  is attached to the other end of the extension bracket  504  and can be swiveled about the threaded tilting angle knob  510 . The tilting angle knob  510  can be threaded and locked into a threaded hole in the extension bracket  504 . The micrometer slide  502  is attached to the tilting bracket  516  by the micrometer slide screws  530 . The micrometer slide  502  is a precision micrometer type micrometer slide that is capable of incrementing by 0.001 inch, such as the model 450 micrometer slide as manufactured by the Del-tron Corporation. This allows for precise movements of the proximity sensor  500  and facilitates its setup. 
   The proximity sensor  500 , such as model PA222 as manufactured by the Electro Corporation, is mounted in the proximity probe mount  512  by sensor nuts  520 , and the mount is connected to the micrometer slide  502  by the proximity probe mount screws  522 . The setup of the proximity probe assembly  531  is accomplished by magnetically mounting the assembly near the shaft  20  and adjusting the multiple adjustment points such that the sensing end of the proximity sensor  500  is close to the shaft  20 . Fine adjustment of the gap between the end of the proximity sensor  500  and the shaft  20  is accomplished by adjusting of the micrometer slide  502 . 
     FIG. 8  shows a cross-sectional view of shaft  20  with a proximity probe assembly  531  mounted on each of two axes, 90 degrees apart, to allow for the displacement measurement on each axis at the same time. From this rectangular (x,y) measurement the overall polar or vector notation can be calculated by accepted mathematical methods to describe the radial movement of the center of the shaft  20  by a magnitude and angle relative to a fixed position. The proximity sensors  500  sense the position of the shaft  20  through an air gap  550  that is normally adjusted to the middle range position as specified by the manufacturer. The vertical shaft alignment tool  10  is able to use any type of displacement sensor, such as eddy current, capacitive, inductive, laser, or mechanical indicators and equivalents. 
     FIG. 9  illustrates an inclinometer method of measuring plumb inclination of a static shaft  20 , single position. This inclinometer method allows for an initial measurement of the plumb inclination of the shaft  20 , at a single position, without rotating the shaft  20  and is referred to as the static plumb method.  FIG. 9  shows the lower x-axis inclinometer  110  and the lower y-axis inclinometer  120  which are attached to the shaft  20 , 90 degrees apart, and which are referenced, respectively, as inclinometers B and A. Referencing a standard fixed Cartesian coordinate system, looking down, the x-axis is 0–180 degrees, and the y-axis is 90–270 degrees. This setup is also typical of the upper x-axis inclinometer  130  and upper y-axis inclinometer  140  on the upper portion of the shaft  20  above the shaft coupling  400  shown in  FIGS. 1(   a ) and  1 ( b ). 
   In the initial plumb method, inclinometer A is mounted at the 270 degree position on the shaft  20 , and inclinometer B is mounted at the 180 degree position on the shaft  20 . Measurement of the plumb inclination is read from both inclinometers and recorded respectively as A 270  and B 180 . This is shown as the first static plumb reading  610  in  FIG. 9 . The inclinometer A is then moved to the 90 degree position on the shaft, and inclinometer B is moved to the 0 degree position of the shaft  20 . This is shown as the second static plumb reading  620  in  FIG. 9 . Measurement of plumb inclination is read from both inclinometers and recorded, respectively, as A 90  and B 0 . 
   Initial plumb is calculated by the following equation for the two axes, x and y: x equation, (B 0 −B 180 )/2=out of plumb inclination P 1 ; y equation, (A 90 −A 270 )/2=out of plumb inclination P 2 . From this rectangular (x,y) measurement the overall polar or vector notation can be calculated by accepted mathematical methods to describe the plumb inclination of the shaft  20  by a magnitude and angle relative to a fixed position. Measurement of the plumb inclination is typically read in inches per foot of slope; however, other angular measurement units can be used. When using a Wyler AG Zerotronic inclinometer, a positive inclination indicates the bottom of the shaft is toward the 0 or 90 degree positions, as defined by the second static plumb reading  620  in  FIG. 9 . Other inclinometers may be different. 
   As long as the inclinometers are not disturbed from their last position as defined in the second static plumb reading  620  in  FIG. 9 , any deviations of the shaft&#39;s plumb inclination can be thereafter monitored and calculated, without moving the inclinometers. This method is performed by calculating what the x and y axis inclinometers should read in order to yield a perfectly plumb inclination (i.e., zero inclination). Thereby, when the shaft  20  is perfectly plumb, the inclinometers would indicate the calculated reading for perfectly plumb inclination. For the x-axis, or B inclinometer, the perfectly plumb value is calculated by the equation (B 0 −P 1 )=plumb inclination reading PP 1 . For the y-axis, or A inclinometer, the perfectly plumb value is calculated by the equation (A 90 −P 2 )=plumb inclination reading PP 2 . PP 1  and PP 2  are the plumb inclination readings that the inclinometers B and A, respectively, will read when the shaft  20  is perfectly plumb. Any deviations in the shaft&#39;s plumb inclination can be measured by comparing the current inclinometer readings with PP 1  and PP 2 . The current out-of-plumb inclination can be calculated for the x-axis, or B inclinometer, by the equation (B 0 −PP 1 )=x-axis plumb inclination. The current out-of-plumb inclination can be calculated for the y-axis, or A inclinometer, by the equation (A 90 −PP 2 )=y-axis plumb inclination. 
     FIG. 10  illustrates an inclinometer method of measuring plumb inclination of a shaft&#39;s center of rotation by rotating the shaft  20 , and is referred to as the rotational plumb method. As the shaft  20  is rotated, it will revolve around a virtual normal shaft centerline  60 , as shown in  FIG. 11 , and this is referred to as the center of rotation. Plumbing the center of rotation is desired since the loads on the guide and thrust bearings will be distributed equally on the bearing surfaces for each revolution of the shaft. This minimizes temperature problems and increases bearing reliability. 
   The rotational plumb method is the more accurate of the two inclinometer methods of measuring plumb inclination since the inclinometers remain fixed at one position of the shaft  20  (not moved relative to shaft) and the plumb inclination is measured relative to the center of rotation of the shaft  20 , as it would normally operate. The rotational plumb method consists of setting inclinometer assemblies  499  B and A, 90 degrees apart on the shaft  20 , at one elevation on the shaft  20  and reading the inclinometer&#39;s inclination at 4 equally spaced shaft positions by rotating the shaft  20 . The shaft  20  is rotated in 90 degree increments, stopped at each increment, and the inclinometer assemblies  499  B and A are read. 
     FIG. 10  shows the lower x-axis inclinometer  110  and the lower y-axis inclinometer  120  which are attached to the shaft  20 , 90 degrees apart, and which are referenced, respectively, as inclinometers B and A. Referencing standard fixed Cartesian coordinate system, looking down, the x-axis is 0–180 degrees, and the y-axis is 90–270 degrees. This setup is also typical of the upper x-axis inclinometer  130  and the upper y-axis inclinometer  140  on the upper portion of the shaft  20  above the shaft coupling  400 . 
   The start position is referred to as the rotational plumb reading 0 degree position  630 , with inclinometer B attached to the 0 degree position and inclinometer A attached to the 90 degree position. Measurement of the plumb inclination, such as in inches per foot, is recorded as B 0  and A 90  for the B and A inclinometers, respectively. Without moving or disturbing the inclinometers, the shaft  20  is rotated 90 degrees to the next position referred to as the rotational plumb reading 90 degree position  640 . Measurement of the plumb inclination is recorded as B 90  and A 180  for the B and A inclinometers respectively. Without moving or disturbing the inclinometers, the shaft is rotated 90 degrees to the next position, referred to as the rotational plumb reading 180 degree position  650 . Measurement of the plumb inclination is recorded as B 180  and A 270  for the B and A inclinometers respectively. Without moving or disturbing the inclinometers, the shaft  20  is rotated 90 degrees to the next position, referred to as the rotational plumb reading 270 degree position  660 . Measurement of the plumb inclination is recorded as B 270  and A 0  for the B and A inclinometers, respectively. Without moving or disturbing the inclinometers, the shaft is rotated 90 degrees to the next position referred to as the rotational plumb reading 0 degree position  630 , or the original starting point. Measurement of the plumb inclination is recorded as B 360  and A 450  for the B and A inclinometers, respectively. 
     FIG. 10  shows the shaft  20  being turned counterclockwise as the measurements are taken; however, it is possible to turn the shaft in the opposite direction as long as the inclinometers are read correctly, that is, identified in the correct location. 
   By using two inclinometers spaced at 90 degrees and taking readings at four equally spaced rotational positions, the plumb inclination of the shaft&#39;s center of rotation can be calculated twice; once from the 0 to 180 degree rotation and again from the 90 to 270 degree rotation. Plumb inclination of a shaft&#39;s center of rotation can be calculated for the x-axis by the equation (B 0 −B 180 )/2=out of plumb P 1 , and for the y-axis by the equation (A 90 −A 270 )/2=out of plumb P 2 , by using the 0 to 180 degree rotational readings. Plumb inclination can be calculated again for the x-axis by the equation (A 0 −A 180 )/2=out of plumb P 1 , and for the y-axis by the equation (B 90 −B 270 )/2=out of plumb P 2 , by using the 90 to 270 degree rotational readings. 
   In both cases above, P 1  (from 0–180 degrees) should equal P 1  (from 90–270 degrees), and P 2  (from 0–180 degrees) should equal P 2  (from 90–270 degrees). If they do not match, the turbine runner, shaft  20 , or other rotating part could have contacted a stationary point as the shaft  20  was rotated. This method acts as a check to detect problems in the rotation of shaft  20 . From this rectangular (x,y) measurement the overall polar or vector notation can be calculated by accepted mathematical methods to describe the plumb inclination of the shaft  20  by a magnitude and angle relative to a fixed position. 
   As long as the inclinometers are not disturbed from their last position, as defined in the rotational plumb reading 0 degree position  630  in  FIG. 10 , any deviations of the shaft&#39;s plumb inclination can be thereafter monitored and calculated without moving the inclinometers and without rotating the shaft again. This method is performed by calculating what the x and y axis inclinometers should read in order to yield a perfectly plumb inclination (i.e., zero inclination). Thus, when the shaft  20  is perfectly plumb, the inclinometers would indicate the calculated reading for perfectly plumb inclination. For the x-axis, or B inclinometer, the perfectly plumb value is calculated by the equation (B 0 −P 1 )=plumb inclination reading PPR 1 . For the y-axis, or A inclinometer, the perfectly plumb value is calculated by the equation (A 90 −P 2 )=plumb inclination reading PPR 2 . PPR 1  and PPR 2  are the plumb inclination readings that the inclinometers B and A, respectively, will read when the shaft  20  is perfectly plumb. Any deviations in the shaft&#39;s plumb inclination can be measured by comparing the current inclinometer readings with PPR 1  and PPR 2 . The current out-of-plumb inclination can be calculated for the x-axis, or B inclinometer, by the equation (B 0 −PPR 1 )=x-axis plumb inclination. The current out of plumb inclination can be calculated for the y-axis, or A inclinometer, by the equation (A 90 −PPR 2 )=y-axis plumb inclination. From this rectangular (x,y) measurement the overall polar or vector notation can be calculated by accepted mathematical methods to describe the plumb inclination of the shaft by a magnitude and angle relative to a fixed position. 
     FIG. 11  is a perspective view of a shaft centerline throw circle  66 . The shaft centerline throw circle  66  is caused by the shaft&#39;s thrust collar or thrust bearing runner/journal not being machined perfectly square to the shaft&#39;s rotational axis or normal shaft centerline  60 . This results in an angle different from the preferred 90 degrees shown as the thrust collar angle  406  in  FIG. 12(   a ). The thrust collar angle  406  of 90 degrees would result in a non-existent throw circle. The vertical shaft alignment tool  10  can measure the shaft centerline throw circle  66  magnitude by two methods referred to as the inclinometer method and proximity probe method. The more accurate of the two methods is the proximity probe method. The inclinometer method is considered an approximate measurement method since the shaft contact surface condition between the inclinometer base  450  and the shaft  20  can skew the results. 
   In the inclinometer method, unitized (i.e., inches per foot of slope) shaft throw (run out), can be calculated by comparing the plumb inclination of the normal shaft centerline  60  to the plumb inclination at one position on the shaft centerline throw circle  66 . As an example, comparing the plumb inclination of the normal shaft centerline  60  to the shaft centerline 0 degree position  62 , as shown in  FIG. 11 , yields the radius of the shaft centerline throw circle  66 . This can also be done with the shaft centerline 90 degree position  63 , shaft centerline 180 degree position  64 , and the shaft centerline 270 degree position  65  to yield similar results. Assuming the inclinometers have not been disturbed since the plumb inclination of a shaft&#39;s center of rotation was calculated, the shaft centerline throw circle  66  radius magnitude can be calculated by subtracting the perfectly plumb results for plumb inclination found in the rotational plumb method, PPR 1  and PPR 2 , from the perfectly plumb indications for plumb inclination found in the static plumb method, PP 1  and PP 2 , respectively. The results of this calculation yield x and y coordinates that can be converted to polar or vector notation which will yield the magnitude of the shaft centerline throw circle  66  as a vector (unitized: i.e., inches per foot). Actual throw (i.e., inches), run out, at a given elevation can be calculated by multiplying the vector&#39;s magnitude by the distance from the thrust bearing assembly  90 . Since the vector is actually the radius of the shaft centerline throw circle  66 , it is multiplied by 2 to yield the diameter. The vector&#39;s angle component is the direction that the bottom of the shaft  20  is pointing toward. 
   In the proximity probe method, proximity sensors are used to measure shaft  20  movements relative to a fixed point as the shaft is rotated. The shaft centerline throw circle  66  magnitude is measured by mounting multiple sets of two proximity sensors  500  at different elevations relative to the shaft  20  but sharing the same vertical planes. Proximity sensors  500  are mounted on the x-axis at the 0 degree position and on the y-axis at the 90 degree position, as shown in  FIG. 8 . With these x and y proximity sensors  500 , 90 degrees apart, the displacement of the center of the shaft  20  can be measured.  FIGS. 1(   a ) and  1 ( b ) show four pairs of proximity sensors  500 , with one pair mounted at each of elevation  1  ( 212 ), elevation  2  ( 192 ), elevation  3  ( 172 ), and elevation  4  ( 152 ). The shaft is rotated in 90 degree increments, referred to as 0, 90, 180, and 270 degree rotational positions, and stopped at each position, and the displacement readings are read for each proximity sensor. The initial proximity sensor  500  displacement readings from the 0 rotational position are subtracted from all other rotational position readings in order to zero the proximity sensor  500  displacement readings. Therefore, the 0 rotational position readings will all be zero, and all the other rotational position readings, taken as the shaft  20  is rotated, will be relative to the 0 rotational position readings. 
   The top set of x and y proximity sensor  500  displacement readings at elevation  1  ( 212 ) are subtracted from the corresponding x and y readings at elevation  2  ( 192 ), elevation  3  ( 172 ), and elevation  4  ( 152 ) in order to subtract out any skate or radial movement that might occur as the shaft  20  is rotated and possibly moved in the radial guide bearing clearance. This yields the net radial shaft  20  displacement (run out) at each elevation and is shown in  FIG. 11  at the shaft centerline 0 degree position  62 , shaft centerline 90 degree position  63 , shaft centerline 180 degree position  64 , and the shaft centerline 270 degree position  65 . 
   The actual shaft centerline throw circle diameter  66  at each elevation is calculated from the four rotational position readings (rotational positions 0, 90, 180, and 270 degrees) by choosing three of the four points to pass a circle through. Commonly available mathematical methods are used to calculate the diameter of a circle passing through these three points, yielding the shaft centerline throw circle  66  magnitude, or the same can be accomplished by standard graphical or plotting methods. By subtracting the center x and y coordinates of this calculated circle from the proximity sensor  500  displacement readings at the last rotational position and converting results to polar or vector notation, the magnitude of the shaft centerline throw circle  66  vector, and the directional angle the bottom of the shaft  20  is pointing to can be found at each of the four elevations. The shaft centerline throw circle  66  calculated for the each of the different elevations allows for the calculation of shaft  20  straightness, shaft kink  402 , and shaft coupling offset  404  as shown in  FIGS. 12(   a ) and  12 ( b ). 
     FIGS. 12(   a ) and  12 ( b ) are perspective views of the shaft kink  402  and the coupling offset  404  conditions. Shaft kink  402  (dogleg) is a condition in which a shaft  20  is bent or in which two coupled shafts do not share axes on parallel planes. The vertical shaft alignment tool can measure shaft kink  402  by two different methods. 
   The first method of measuring kink is to measure the plumb deviation of the shaft  20  at different elevations by using the static plumb method as shown in  FIG. 9 . A straight (non-kinked) shaft  20  would exhibit the same plumb measurement, magnitude and direction at each elevation. With coupled shafts (typical for hydroelectric shafts) the plumb inclination is measured on each side of the coupling  400 . The difference between the plumb inclinations of two elevations is the amount of kink in the shaft  20  between those elevations. Accuracy of this method is limited to the condition of the shaft  20  surface to which the inclinometer base  450  is mounted. 
   The second method of measuring kink is by using the shaft centerline throw circle  66  vectors as calculated above regarding the proximity probe method of measuring the shaft centerline throw circle  66  at different elevations. Shaft kink  402  is calculated by comparing the difference in the shaft centerline throw circle  66  vectors from elevation  1  ( 212 ) to elevation  2  ( 192 ) with the difference from elevation  3  ( 172 ) to elevation  4  ( 152 ). Differences are divided by distances (i.e., feet) from elevation  1  ( 212 ) to elevation  2  ( 192 ) and elevation  3  ( 172 ) to elevation  4  ( 152 ), respectively, yielding unitized (i.e., inches per foot of distance) shaft centerline throw circle  66  vector deviations for each section of shaft  20  (the section above the shaft coupling  400  versus the section below the shaft coupling  400 ). A straight (non-kinked) shaft  20  would exhibit the same unitized shaft centerline throw circle  66  vector magnitude, in the same direction (in phase), for each section of shaft  20 . The difference between the unitized shaft centerline throw circle  66  vector magnitudes is the amount of kink  403  existing between those shaft sections. The direction of the kink  403  can be found be analyzing the shaft centerline throw circle  66  vector angles. 
   Shaft coupling offset  404  is a condition in which two coupled shaft&#39;s axes do not share the same normal shaft centerline  60  or are not concentric as shown in  FIG. 12(   b ). The vertical shaft alignment tool invention measures shaft coupling offset  404  by using the shaft centerline throw circle  66  vectors as calculated in the discussion above regarding the proximity probe method of measuring the shaft centerline throw circle  66  at different elevations. As in the shaft kink method above, the shaft coupling offset  404  is calculated by comparing the difference in the shaft centerline throw circle  66  vectors from elevation  1  ( 212 ) to elevation  2  ( 192 ) with the difference from elevation  3  ( 172 ) to elevation  4  ( 152 ). The differences are divided by the distances (i.e., feet) from elevation  1  ( 212 ) to elevation  2  ( 192 ) and elevation  3  ( 172 ) to elevation  4  ( 152 ), respectively, yielding unitized (i.e., inches per foot of distance) shaft centerline throw circle  66  vector deviations for each section of shaft  20  (the section above the shaft coupling  400  versus the section below the shaft coupling  400 ). These unitized shaft centerline throw circle  66  vectors are extrapolated (inches per foot times distance) to the shaft coupling  400  split. If these extrapolated shaft centerline throw circle  66  vectors are equal then the shaft offset  404  is zero. The difference between the extrapolated shaft centerline throw circle  66  vectors is the amount of offset  405  in the shaft&#39;s centerlines. The direction of the offset can be found by analyzing the shaft centerline throw circle  66  vector angles. 
     FIG. 13  is a perspective plan view of a thrust bearing shoe assembly  90 , with  8  shoes, that is also shown in  FIG. 1(   b ).  FIG. 14  is a perspective side view of the thrust bearing shoe assembly  90  and of an elevation adjustment screw assembly  100  that also is shown in  FIG. 1(   b ). Vertical hydroelectric shafts typically use multi-segment thrust bearings like those manufactured by Kingsbury Corporation. The number of shoes usually vary from 6 to 16 shoes, with 8 shoes being common for hydroelectric turbine generators. These types of bearings have a jack screw (adjustment screw) under each thrust bearing shoe for adjusting its elevation and load. The vertical shaft alignment tool  10  includes a method of correcting deviations of a shaft&#39;s plumb inclination to the perfectly plumb position or another plumb inclination position by adjusting the thrust bearing assembly shoe elevations shown in  FIGS. 13 and 14 . This method allows for changes in the plumb inclination without changing the thrust load on the thrust bearing assembly  90  or the individual load on each thrust bearing shoe. 
   The vertical shaft alignment tool  10  uses a vector analysis method to calculate the individual thrust bearing shoe elevational changes to move or swing the shaft  20  to the corrected plumb inclination position. In this method the x and y components of plumb inclination, as calculated above relative to  FIGS. 9 and 10 , are converted from their rectangular form to polar or vector form. As in all of the above methods, the standard Cartesian coordinate system is used, as shown in  FIG. 13 . The magnitude of the plumb inclination vector (typically in inches per foot) is referred to as variable RV and is calculated by the equation
 
 RV=SQRT ( x^ 2 +y ^2).  (1)
 
The angle of the plumb inclination vector (degrees) is referred to as variable ANG and is calculated by the equation
 
 ANG =tan −1 ( x/y ) (in degrees).  (2)
 
   In  FIG. 13 , the variable R is the thrust adjustment screw pin circle radius  101  (typically in inches); the variable SA 99 is the individual thrust bearing shoe offset angle from 0 degrees (in degrees) that will vary according to each thrust bearing shoe position. The elevational change movement of an individual thrust bearing shoe is referred to as variable SM (thrust bearing shoe movement typically in inches). The thrust bearing shoe movement SM is calculated by the equation
 
 SM=− 1( RV *( R/ 12))*(COS(( SA−ANG )).  (3)
 
   A positive result would move the thrust bearing shoe up, and a negative result would move the thrust bearing shoe down. 
   As an example, for a 8 shoe thrust bearing, suppose the shaft  20  inclination was measured to be 0.001 inch per foot out of plumb toward the 67.6 degrees position. Using the standard Cartesian coordinate system, as shown in  FIG. 13 , the turbine runner  15  would be bending toward the center of the second thrust shoe  92 . Using the equation SM=−1(RV*(R/12))*(COS(SA−ANG)) to calculate each shoe movement (SM) to plumb the shaft for the eight shoe example, shown in  FIGS. 13 &amp; 14 , for the first thrust shoe  91 , then RV equals 0.001 inch, SA equals 22.5 degrees, ANG equals 67.5 degrees, and we assume R in this example is 30 inches, and calculate as follows: 
   SM (shoe 91)=−1(0.001*(30/12))*(COS(22.5−67.5))=−0.0018 INCH 
   For the other seven shoes, the SM values are calculated by inputting their respective angular positions, SA, as follows: 
   SM (shoe 92)=−1(0.001*(30/12))*(COS(67.5−67.5))=−0.0025 INCH 
   SM (shoe 93)=−1(0.001*(30/12))*(COS(112.5−67.5))=−0.0018 INCH 
   SM (shoe 94)=−1(0.001*(30/12))*(COS(157.5−67.5))=0.0000 INCH 
   SM (shoe 95)=−1(0.001*(30/12))*(COS(202.5−67.5))=+0.0018 INCH 
   SM (shoe 96)=−1(0.001*(30/12))*(COS(247.5−67.5))=+0.0025 INCH 
   SM (shoe 97)=−1(0.001*(30/12))*(COS(292.5−67.5))=+0.0018 INCH 
   SM (shoe 98)=−1(0.001*(30/12))*(COS(337.5−67.5))=0.0000 INCH 
   Assuming all thrust shoes are loaded equally, then, the shoe movements (SM) are implemented, the shaft  20  will move or swing to the plumb position. Shaft plumbing corrections, and corresponding shoe movements SM, for a thrust bearing with shoe numbers different from 8 shoes, can be calculated using the same method and equation but with appropriate shoe offset angle SA. 
   The same method can be applied to shafting systems which have fixed, non-adjustable thrust bearing assemblies  90  (such as spring-loaded thrust bearings) by calculating elevational changes (shim changes would equal shoe movements SM) applied to the thrust supports under the stationary surrounding structure supporting the thrust bearing assembly. 
   While specific embodiments of the invention have been illustrated and described herein, it is realized that numerous modifications and changes will occur to those skilled in the art. It is therefore to be understood that the appended claims are intended to cover all such modifications and changes as fall within the true spirit and scope of the invention.